searching for radio pulses from the redback pulsar

Searching for Radio Pulses from theRedback Pulsar Candidate

3FGL J0212.1+5320

A dissertation submitted to the University of Manchesterfor the degree of Master of Science by Research

in the

Faculty of Science and Engineering

2020

ByEoin T. O’Kelly

Department of Physics and Astronomyin the School of Natural Sciences

http://www.se.manchester.ac.uk/

2

Contents

Contents 2

List of Figures 6

List of Tables 7

Abbreviations 8

Physical Constants 9

Abstract 10

Declaration of Authorship 11

Copyright Statement 12

Acknowledgements 13

1 Introduction 141.1 Introduction to Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.1.1 P− P Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.1.2 Types of Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.1.3 Spider Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.2 Properties of Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.2.1 Mass and Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.2.2 Pulsar Structure and Moment of Inertia . . . . . . . . . . . . . . . . 231.2.3 Magnetic Field Strength . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.3 Pulsar Timing and Observational Properties . . . . . . . . . . . . . . . . . . 241.3.1 Spin Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.3.2 Age and Braking Index . . . . . . . . . . . . . . . . . . . . . . . . . 251.3.3 The Radio Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.3.4 Dispersion Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.3.5 Spectral Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.4 Background of 3FGL J0212.1+5320 . . . . . . . . . . . . . . . . . . . . . . . 321.5 Aim of the Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3

2 Pulsar Search Techniques 362.1 Observation and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2 Standard Pulsar Search Procedure . . . . . . . . . . . . . . . . . . . . . . . 39

2.2.1 Radio Frequency Interference . . . . . . . . . . . . . . . . . . . . . . 392.2.2 Dedispersion Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.2.3 Searching for period pulses using Fourier Transforms . . . . . . . . 422.2.4 Binary Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.2.5 Pulsar Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.3 Time Domain Searching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.3.1 Fast Folding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.3.2 Single Pulse Searches . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.4 Adopted Search Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462.4.1 Sky Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462.4.2 J0212+5320 Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.5 PRESTO Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472.6 Dedispersion Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482.7 Filterbank Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.8 Radio Frequency Interference Masking . . . . . . . . . . . . . . . . . . . . . 512.9 Incoherent Dedispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.10 Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.11 Acceleration Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.12 Harmonic Summing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562.13 Signal-to-Noise Ratio and Chi-Square . . . . . . . . . . . . . . . . . . . . . 572.14 Candidate Optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.15 Prepfold Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

2.15.1 Subintegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.15.2 Pulse Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.15.3 Subbands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602.15.4 Dispersion Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . 602.15.5 Period and Period Derivative . . . . . . . . . . . . . . . . . . . . . . 60

2.16 Candidate Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602.17 Candidate Sifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3 Results and Discussion 623.1 Prepfold Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.1.1 Prepfold - RFI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.1.2 Pulsar Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Candidate 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Candidate 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Candidate 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Candidate 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4

3.2.1 Non-detection of a Pulsar . . . . . . . . . . . . . . . . . . . . . . . . 793.2.2 Radio Search Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . 853.2.3 Flux Comparison with Millisecond Pulsars . . . . . . . . . . . . . . 85

3.3 Significance of Pulsar Detection . . . . . . . . . . . . . . . . . . . . . . . . . 86

4 Conclusion 884.1 Conclusion and Future Study . . . . . . . . . . . . . . . . . . . . . . . . . . 88

A Prepfold Plots 90

Word count: 22432

5

List of Figures

1.1 P-P Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.2 Pulsar Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.3 Intrabinary Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.4 Neutron Star / Pulsar Mass Distribution . . . . . . . . . . . . . . . . . . . . 231.5 Pulsar’s Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271.6 Pulsar Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.7 YMW16 Galactic Electron Density Model . . . . . . . . . . . . . . . . . . . 301.8 Pulsar Sample Flux Density Spectra . . . . . . . . . . . . . . . . . . . . . . 311.9 Pulsar Sample Spectral Index . . . . . . . . . . . . . . . . . . . . . . . . . . 321.10 Fermi-LAT r’ Band Image of Target System . . . . . . . . . . . . . . . . . . 331.11 Spectral Energy Distribution of Target System . . . . . . . . . . . . . . . . 331.12 Light Curves of Target System . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.1 Sample DDPlan Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.2 Pulsar Binary Orbit Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 442.3 Dedispersion Plan Plot 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.4 RFI Mask for Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.5 Prepfold Plot Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.1 Candidate Plot 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.2 Candidate Plot 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.3 Prepfold Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.4 Prepfold Plot of RFI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.5 Prepfold Pulsar Candidate 1 - Plot #1 . . . . . . . . . . . . . . . . . . . . . . 673.6 Prepfold Pulsar Candidate 1 - Plot #2 . . . . . . . . . . . . . . . . . . . . . . 683.7 Prepfold Pulsar Candidate 2 - Plot #1 . . . . . . . . . . . . . . . . . . . . . . 693.8 Prepfold Pulsar Candidate 2 - Plot #2 . . . . . . . . . . . . . . . . . . . . . . 703.9 Prepfold Pulsar Candidate 2 - Plot #3 . . . . . . . . . . . . . . . . . . . . . . 713.10 Prepfold Pulsar Candidate 2 - Plot #4 . . . . . . . . . . . . . . . . . . . . . . 723.11 Prepfold Pulsar Candidate 2 - Plot #5 . . . . . . . . . . . . . . . . . . . . . . 733.12 Prepfold Pulsar Candidate 3 - Plot #1 . . . . . . . . . . . . . . . . . . . . . . 743.13 Prepfold Pulsar Candidate 3 - Plot #2 . . . . . . . . . . . . . . . . . . . . . . 753.14 Prepfold Pulsar Candidate 4 - Plot #1 . . . . . . . . . . . . . . . . . . . . . . 763.15 Prepfold Pulsar Candidate 4 - Plot #2 . . . . . . . . . . . . . . . . . . . . . . 77

6

3.16 Geometry of J0212+5320 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.17 J0212 Light Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.18 J0212 Light Curve #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

A.1 Prepfold Plot - DM19.56 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91A.2 Prepfold Plot - DM13.52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92A.3 Prepfold Plot - DM26.68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93A.4 Prepfold Plot - DM9.109 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94A.5 Prepfold Plot - DM29.28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95A.6 Prepfold Plot - DM22.71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96A.7 Prepfold Plot - DM3.49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

7

List of Tables

2.1 Estimated Pulsar Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2 Incoherent Dedispersion Plan . . . . . . . . . . . . . . . . . . . . . . . . . . 502.3 Candidate Sifting Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.1 Pulsar Flux Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

8

List of Abbreviations

DM Dispersion MeasureISM Interstellar MediumDFT Discrete Fourier TransformFFT Fast Fourier TransformRFI Radio Frequency InterferenceMSP Millisecond PulsarFIR Finite Impulse Response

9

Physical Constants

Speed of Light c = 2.997 924 58× 108 m s−1

Gravitational Constant G = 6.67408(31)× 10−11 m3kg−1s−2

Solar Mass M = 1.98847± 0.00007× 1030 kgSolar Radius R = 6.955× 108 mParsec pc = 3.0857× 1016 m

10

THE UNIVERSITY OF MANCHESTER

AbstractFaculty of Science and Engineering

Department of Physics and Astronomyin the School of Natural Sciences

Master of Science by Research

Searching for Radio Pulses from the Redback Pulsar Candidate3FGL J0212.1+5320

by Eoin T. O’KELLY

Binary pulsar systems that irradiate or ablate their companion are collectively called ‘spi-der’ pulsars. There are two groups of ‘spider’ pulsars: black widows and redbacks. Thisproject was focused on searching L-band (1.4 GHz) radio data obtained by the Lovelltelescope on the redback pulsar candidate 3FGL J0212.1+5320.

The data were analysed using the pulsar searching software PRESTO within a dispersionmeasure (DM) range of 12.5 - 37.5 pc cm−3, and then an acceleration search was con-ducted as this is a suspected binary system. The resulting candidates were folded andtheir prepfold plots analysed to assess whether a pulsar detection was present. No con-firmed pulsar detections were found by our search within the data.

The data were initially analysed in quarters, each ∼ 1800 s in length. The sensitivity ofthis initial search was Smin = 0.20 mJy. This could be improved by searching the wholedataset utilising the full integration time of 7208.4 s which improved the sensitivity ofthe search to Smin = 0.10 mJy. The lower limit on the flux density enables an upper limiton the radio pseudo-luminosity, assuming that the reason for non-detection is luminosityrather than external factors such as beaming, eclipsing and Radio Frequency Interference(RFI). The radio pseudo-luminosity of our search was L1400 = 0.24 mJy kpc2 for the initialsearch, and L1400 = 0.12 mJy kpc2 for the whole dataset analysis. The sensitivity of oursearch is high enough to have detected the majority of known millisecond pulsars.

The possible explanations for a non-detection are then discussed, such as eclipsing of thesystem, orientation of the radio emission region or the flux density of the target systembeing below the sensitivity limit of our search. The conclusion of this work is that re-observing this system at an optimal phase position is essential.

HTTPS://WWW.MANCHESTER.AC.UK/

http://www.se.manchester.ac.uk/

https://www.physics.manchester.ac.uk/

https://www.physics.manchester.ac.uk/

11

Declaration of AuthorshipThat no portion of the work referred to in the dissertation hasbeen submitted in support of an application for another degreeor qualification of this or any other university or other institute oflearning.

12

Copyright Statement

(i) The author of this dissertation (including any appendices and/or schedules to thisdissertation) owns certain copyright or related rights in it (the “Copyright”) ands/he has given The University of Manchester certain rights to use such Copyright,including for administrative purposes.

(ii) Copies of this dissertation, either in full or in extracts and whether in hard or elec-tronic copy, may be made only in accordance with the Copyright, Designs andPatents Act 1988 (as amended) and regulations issued under it or, where appropri-ate, in accordance with licensing agreements which the University has from time totime. This page must form part of any such copies made.

(iii) The ownership of certain Copyright, patents, designs, trademarks and other intel-lectual property (the “Intellectual Property”) and any reproductions of copyrightworks in the dissertation, for example graphs and tables (“Reproductions”), whichmay be described in this dissertation, may not be owned by the author and maybe owned by third parties. Such Intellectual Property and Reproductions cannotand must not be made available for use without the prior written permission of theowner(s) of the relevant Intellectual Property and/or Reproductions.

(iv) Further information on the conditions under which disclosure, publication andcommercialisation of this dissertation, the Copyright and any Intellectual Propertyand/or Reproductions described in it may take place is available in the UniversityIP Policy, in any relevant Dissertation restriction declarations deposited in the Uni-versity Library, The University Library’s regulations and in The University’s policyon Presentation of Dissertations.

http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=24420

http://www.library.manchester.ac.uk/about/regulations/

13

AcknowledgementsI would like to thank my supervisors Rene Breton and Colin Clark for the assistance, ex-pertise and knowledge. Without your help and guidance I wouldn’t have made it, and Ican’t believe how fast it all went by.

Thank you to the spiders group who welcomed me from the beginning and helped meimmensely.

Thank you to everyone in the pulsar group and JBCA who made me feel welcome andhelped me whenever needed. A huge thank you to the other MSc students who alwayshelped and supported each other. Also to Laura Driessen for making the template I usedfor my dissertation.

To my closest friends - Alex, Ali and Jay, it’s always...interesting with you all!

Finally, thank you to my family for always supporting and believing in me.

14

Chapter 1

Introduction

1.1 Introduction to Pulsars

A star of sufficient mass when it reaches the end of its life explodes via a process calleda supernova (Glendenning, 2005). The supernova can form a neutron star if the grav-itational collapse causes the stellar remnant’s density to exceed a white dwarf’s Chan-drasekhar limit - the electron degeneracy pressure limit (Chandrasekhar, 1967).

Neutron degeneracy pressure supports the neutron star and prevents it from collapsing.Neutron star’s magnetic fields are particularly strong, 108-1015 G, and the rate of rotationincreases as the core of the parent star collapses as a result of angular momentum conser-vation (Lorimer & Kramer, 2005).

Charged particles can be accelerated along the open field lines of the magnetospherewhich results in emission of electromagnetic radiation (Condon & Ransom, 2016). Thisradiation is detected as pulses as the cone shaped region of emission sweeps past our lineof sight similar to a lighthouse. These pulsating neutron stars are called pulsars.

1.1. Introduction to Pulsars 15

1.1.1 P− P Diagram

Pulsar’s period and period derivative are key aspects of their properties and how theyare identified. This is vital when comparing pulsar’s and studying their evolution. Pulsarobservations typically consist in time series analysis, where the interval between pulses(their pulse period) is calculated as well as their long term behaviour.

The P− P diagram plots pulsars by their period and period derivative in seconds ands s−1 respectively as shown in Fig. 1.1 (Lorimer & Kramer, 2005). It shows the varietyof the population of pulsars with young pulsars that can be associated with supernovaremnants plotting in the upper left, normal pulsars plotting towards the centre, magne-tars plotting towards the upper right and millisecond and binary pulsar systems plottingtowards the lower left. Types of pulsars are discussed in Section 1.1.2.

The different values of P−P indicate very different ages and magnetic field strengths be-tween normal and millisecond pulsars. Where normal pulsars have periods of ∼0.5 sand millisecond pulsars have periods of ∼0.01 to 0.001 s. Fig. 1.1 also shows that their Pvalues differ where normal pulsars are∼ 10−15 s s−1 and millisecond pulsars are∼ 10−19

s s−1.

The P−P diagram also shows the ‘graveyard‘ where pulsars are theoretically predictedto not exist (Lorimer & Kramer, 2005). As pulsars spin down and their periods slow,the radiation either becomes too weak to be detected or emission ceases altogether, andthey cross into the ‘graveyard‘ - seen in Fig. 1.1 as the empty space in the right of thediagram (Chen & Ruderman, 1993). Section 1.3 discusses the observation and timingof pulsar’s, discussing properties such as: spin evolution, age and braking index anddispersion measure.

16 Chapter 1. Introduction

FIGURE 1.1: P-P diagram plotting pulsars by their period and periodderivative. Younger pulsars that can be associated with supernova rem-nants plot in the upper left. Normal pulsars plot in the central regionmarked by blue dots, magnetars towards the upper right and millisec-ond pulsars plot towards the bottom left along with the majority of binarysystems marked by green dots. Red triangles mark pulsars detected athigh energies (Condon & Ransom, 2016; Ostriker & Gunn, 1969; Lorimer &Kramer, 2005). Image created using the ATNF catalog: Hobbs et al. (2019)

1.1.2 Types of Pulsars

Normal pulsars are highly magnetised, fast rotating neutron stars. They convert that ro-tational kinetic energy into electromagnetic radiation that can be detected (Pacini, 1967).A diagram of a pulsar can be seen in Fig. 1.2. Over time pulsars lose their rotational ki-netic energy, an effect called spin down (Lorimer & Kramer, 2005). Normal pulsars plotin the central section of the P−P diagram, as seen in Fig. 1.1.

However, there is a phenomenon that causes pulsars to momentarily spin up as they arespinning down (Radhakrishnan & Manchester, 1969). This is called glitching, it is still notfully understood and are primarily observed in younger pulsars. These glitches provideevidence that there is a fluid component within the solid outer crust (Lorimer & Kramer,2005). It is hypothesised that this is due to the superfluid nature of the interior and the


development of vortices, which are pinned to the crust (Ruderman, 1976).

One of the most well known examples of young pulsars is the Crab Pulsar and is theremnant of the supernova SN 1054 (Brecher et al., 1983). The pulsar PSR B0833-45 (com-monly called ‘Vela‘ after the supernova remnant associated with it) is another well knownexample of a young energetic pulsar (Large et al., 1968; Johnston et al., 2001). Youngpulsars are often associated with supernova remnants, as would be expected from theirformation and evolution. Young pulsars and pulsars that are associated with supernovaremnants plot in the upper left of the the P−P diagram, this can be seen in Fig. 1.1.

Pulsars that have millisecond periods were first discovered in 1982 (Backer et al., 1982)and are likely to be binary systems. Roughly 80% of millisecond pulsars are found inbinary systems whereas <1% of normal pulsars are binary systems. The companionstar of these systems can be a main sequence, white dwarf or even another neutron star.Within these systems material sharing can occur via Roche Lobe overflow (Bhattacharya& van den Heuvel, 1991). The infall of material can form an accretion disk, which canalso increase the pulsars spin period which can then form a millisecond pulsar. In theorythere is a correlation between the orbital period and the end state white dwarf’s mass,where the millisecond period of the pulsar is a result of Roche lobe overflow (Rappaportet al., 1995; Ergma et al., 1998; Tauris & Savonije, 1999). Millisecond and binary pulsarsplot in the lower left of the the P−P diagram, as seen in Fig. 1.1.

There are 2 groups of millisecond binary pulsars that ‘devour’ their companions: blackwidows and redbacks (Fruchter et al., 1988; Bhattacharya & van den Heuvel, 1991; Archibaldet al., 2009; Roberts et al., 2015). These pulsar systems are detailed in Section 1.1.3.

The gamma-ray emission from pulsars, Ly ≈ 1033 − 1035 erg s-1, is produced within themagnetosphere and is generally pulsed (An et al., 2018). Although, due to the low pho-ton count it is generally quite challenging to detect gamma-ray pulsations (Watters &Romani, 2011). These pulsars are less luminous in the X-ray band and the X-ray emissionis also generally not pulsed, Lx ≈ 1030 − 1033 erg s-1 (An et al., 2018).

Within an ultra-compact binary system a shock region can form from the pulsar windwhich drives material from the companion; this is called an intrabinary shock, see Fig. 1.3(An et al., 2018; Arons & Tavani, 1993; Roberts et al., 2014). Intrabinary shocks are dis-cussed in Section 1.1.3 and specifically regarding the target in Section 1.4.


FIGURE 1.2: Figure of a pulsar showing the magnetosphere, cone-shapedregion of radio emission, magnetic field lines and rotation axis. Field linesthat do not close are called open field lines and those that do are called closedfield lines. The region where the field lines are open defines the polar capcentred on the magnetic pole. The light cylinder marks the boundary atwhich the co-rotating plasma around the neutron star reaches the speed oflight. Image credit: Condon & Ransom (2016)


FIGURE 1.3: Intrabinary shock within a binary pulsar system - the windfrom the pulsar driving material from the companion forming a shock re-gion. Image credit: Venter et al. (2015).

Magnetars are young neutron stars that are, as the name suggests, highly magnetised.They exhibit varying X-ray activity which includes: short and longer bursts, large flares,periodic oscillations, enhanced spin-down and glitches (Kaspi & Beloborodov, 2017).Younes et al. (2017) shows that for the majority of sources their spin-down rate is ofthe order 10−11 - 10−12 ss−1 and they have particularly strong surface dipole magneticfields of 1014 - 1015 G. Most magnetars have been discovered while emitting short (∼ 0.1s) X-ray bursts that are especially bright (Eburst ≈ 1037 − 1047 erg) (Younes et al., 2017).Magnetars are commonly found in the top right of the P−P diagram dues to their longerperiods and high magnetic field strength, as seen in Fig. 1.1.

1.1.3 Spider Pulsars

The source targeted in this dissertation is suspected to be a binary or ‘spider‘ pulsar sys-tem, therefore this section is focused on the details of these types of systems. Close binarypulsar systems that have a millisecond period and that drive or have driven material offof the companion by the wind from the pulsar are collectively called ‘spider systems’(Roberts et al., 2018).

There are generally two classes of spider system: black widows and redbacks. These aremillisecond pulsars that have a period, P . 1 day. The two spider classes are defined bytheir companion. Black widows have low mass companions M2 0.1 M and redbackshave non-degenerate companions in the range 0.1 < M2 < 0.4 M (Chen et al., 2013;Manchester, 2017).


The first black widow pulsar discovered was PSR B1957+20 by Fruchter et al. (1988). Thematerial that is being driven off by the intrabinary shock causes radio eclipses and emis-sion of X-rays through interaction with the pulsar wind (Roberts et al., 2018). The firstredback discovered was PSR J1023+0038 by Archibald et al. (2009).

The pulsar wind can cause heating of the surface of the companion that is facing the pul-sar (Fruchter et al., 1988), giving rise to orbital modulation of the optical emission. If thecompanion is near Roche lobe filling it will be tidally distorted also causing ellipsoidalmodulation (Breton et al., 2013; Roberts et al., 2018). X-rays have been observed asso-ciated with spider systems that are a result of the intrabinary shock and in the opticalthe companion exhibits variations as a result of tidal distortion and heating (Romani &Sanchez, 2016; Roberts et al., 2018).

Variations of the orbital period of spider systems can also occur, with both positive andnegative period derivatives. These changes are much larger than would be expected forgravitational radiation, and might occur as a result of interaction between the compan-ion’s magnetic field and the pulsar wind via the mechanism described by Applegate &Shaham (1994) (Shaifullah et al., 2016; Roberts et al., 2018).

Some redback systems have been observed to transition between two different ablationand accreting states, usually on a timescale of months to years, which is much shorterthan predicted (Archibald et al., 2009; Papitto et al., 2013; Bassa et al., 2014). When red-back pulsars transition to an accreting state an increase in optical brightness is observedby ∼ 1 magnitude (Archibald et al., 2009; Linares, 2014; Shahbaz et al., 2019). Studyingthese systems in the optical can provide information such as heating of the companion,Roche-lobe filling fraction and possibly the masses of the objects (van Kerkwijk et al.,2011; Breton et al., 2013).

In the X-ray many black widows do not have much shock emission although some havebeen found that do, like ordinary millisecond pulsars they have largely thermal spectra(Roberts et al., 2018). Redbacks however are much brighter in the X-ray regime than blackwidows and exhibit a light curve morphology that does not vary as much, usually witha double peak at pulsar inferior conjunction - see Section 2.2.4, Fig. 2.2 and Fig. 3.16 fordetails of binary motion and positions (Roberts et al., 2018).

The companions of black widows have been observed to be mostly cool and faint withtemperatures down to T ' 2000 K on the side facing away from the pulsar, and magni-tudes in the optical of mv > 23 (Breton et al., 2013). The light curves are almost alwaysdominated by companion heating resulting from irradiation from the pulsar (Sotani &Miyamoto, 2018; Roberts et al., 2018).

Redback’s X-ray spectra are usually quite hard, power law photon indices Γ ∼ 1.0 - 1.3,

1.2. Properties of Pulsars 21

which is harder than would result from shock acceleration (Sironi & Spitkovsky, 2014;Kandel et al., 2019). One possibility is that magnetic reconnection could result in this(Sironi & Spitkovsky, 2011).

Redback’s double peak orbital modulation observed in the X-ray is still not fully under-stood. Models have reproduced a light curve that is observed with a wind-wind shockbetween the companion and the pulsar, but only if the momentum of the pulsar’s windis many times weaker than that of the companion (Romani & Sanchez, 2016; Wadiasinghet al., 2017).

However, it is not very likely that the companion’s wind is this strong and Roche-lobeoverflow is another possibility (Benvenuto et al., 2014), but this leads to another issue thatthe resulting light curve would not be very stable. Another possibility is that a strongmagnetic field of the companion could be resulting in the observed light curves (Robertset al., 2018).

1.2 Properties of Pulsars

This section focuses on introducing and discussing general pulsar properties such as:mass, radius, structure, moment of inertia and magnetic field strength. These generalproperties are important to the fundamental physics of pulsars.

1.2.1 Mass and Radius

The canonical mass of a neutron star of 1.4 M (Oppenheimer & Volkoff, 1939) was calcu-lated from general relativity and quantum mechanics. However, neutron stars and binarypulsar systems have observed masses up to ∼2.0 M (Antoniadis et al., 2013; Demorestet al., 2010). Binary pulsar system’s masses are important to understand as it can revealfurther details of the system and its evolution as described in Section 1.1.3. Fig. 1.4 showsthe mass distribution of 43 neutron stars and pulsars.

However, the equation of state defines the mass-radius relationship and a maximum pos-sible mass - the relationship between density and pressure (Lorimer & Kramer, 2005).Redshifts are observed as neutron stars have strong gravitational effects and thereforethe observed thermal flux and temperature are smaller than the actual values. The mea-sured radius Robs is larger than the intrinsic value R,

Robs =R√

1− 2GM/Rc2=

R√1− RS/R

, (1.1)

where M is the gravitational mass, R is the radius, c is the speed of light, G is Newton’sgravitational constant and RS is the Schwarzschild radius,


RS =2GM

c2 ' 4.2 km(

M1.4M

)(1.2)

(Lorimer & Kramer, 2005).

Neutron stars have atmospheres composed of thin layers of plasma, this modifies theluminosity and results in a spectrum that differs from a black body (Lorimer & Kramer,2005). Cooler and hotter spots can occur because the surface brightness distribution ismodified by the strong magnetic field, this needs to be accounted for or the value of theradii might be incorrect.

A lower limit of the radius can be estimated if it is assumed that in a neutron star thespeed of sound is less than the speed of light and the equation of state is a smooth tran-sition from low to high densities (Lattimer et al., 1990; Glendenning, 1992),

Rmin ' 1.5RS =3GM

c2 = 6.2 km(

M1.4M

). (1.3)

If the neutron star is stable against breakup because of centrifugal forces then an upperlimit can also be calculated,

Rmax '(

GMP2

4π2

)1/3

= 16.8 km(

M1.4M

)1/3 ( Pms

)2/3

. (1.4)

It is possible to measure the mass of a neutron star if it is in a binary system, the fiveKeplerian parameters measured are: binary period Pb, eccentricity e, the projection of thesystem’s semi-major axis on the line of sight x ≡ a1sini

c where i is the inclination, and thetime and longtitude of the periastron (the point at which an orbiting body around a staris nearest to it) - T0 and ω0.

Information obtained from optical observations or relativistic corrections to the orbit isneeded to then solve for the mass. The mass function relates the pulsar and companion’smass to each other (Thorsett & Chakrabarty, 1999),

f =(m2sin)3

M2 = n2x3(

1T

)M, (1.5)

where M ≡ m1 + m2, x is the semimajor axis on the line of sight ≡ a1 sin i/c, n is theorbital angular frequency ≡ 2π/Pb and the constant T ≡ GM/c3 = 4.925490947×10−6 s (Thorsett & Chakrabarty, 1999).

1.2. Properties of Pulsars 23

FIGURE 1.4: The mass distribution of 43 neutron stars and pulsars plottedin increasing order. ‘C’ in parentheses indicates a binary system, thosemarked in red indicate the companion could be a neutron star or massivewhite-dwarf. Image credit: Freire (2019)

1.2.2 Pulsar Structure and Moment of Inertia

A pulsar’s structure and their moment of inertia are fundamental aspects of their studyas their structure assists in understanding their general nature. The moment of inertia isI = kMR2 for a sphere of uniform density , where k = 2/5 = 0.4. The equation of stateor the density profile is what the value of k depends on (Lorimer & Kramer, 2005). Fora mass-radius range M/R = 0.10 - 0.20 M km−1 the value of k is estimated as k = 0.30- 0.45. An average mass density using the canonical values stated above is < ρ > = 6.7x 1017 kg m−3 = 6.7 x 1014 g cm−3, as a comparison the density of nuclear matter is 2.7x 1014 g cm−3. However, it should be noted that a neutron star is not a uniform sphere(Lorimer & Kramer, 2005).


Glitches occurring within young pulsars indicate a solid crust that contains > 1.4% ofthe moment of inertia, which is linked with the density of the liquid interior between thecrust and centre of the neutron star (Link et al., 1999). The crust is a crystalline composi-tion of degenerate electrons and iron nuclei with a density ρ ∼ 106 g cm−3.

As the density increases inward it eventually results in electrons and protons combiningto form neutrons, this forms an inner crust of nuclei that are neutron-rich. At severalhundred metres depth the density is ρ ∼ 4 x 1011 g cm−3 which passes the neutron drippoint and the neutrons released from nuclei increases (Lorimer & Kramer, 2005). Thecrust dissolves when the density reaches ρ ∼ 2 x 1014 g cm−3 and is mainly composed ofa ‘sea’ of free superfluid neutrons and roughly 5% superconducting protons and electrons(Lorimer & Kramer, 2005).

1.2.3 Magnetic Field Strength

It is extremely difficult to directly measure a pulsars magnetic field strength, however itcan be estimated if it is assumed that the dominant force resulting in spin down is dipolebraking. B ≈ |m| / r3 relates the magnetic moment and magnetic field strength, equation1.11 can be rearranged for surface magnetic field strength (Lorimer & Kramer, 2005),

BS ≡ B(r = R) =

√3c3

8π2I

R6sin2αPP. (1.6)

If the moment of inertia is I = 1045 g cm2, the radius is R is 10 km and assuming α = 90degrees,

BS = 3.2× 1019G√

PP ' 1012G(

P10−15

)1/2 (PS

)1/2

. (1.7)

It should be noted that because the moment of inertia and radius are estimates and α

is usually unknown equation 1.7 is an order of magnitude estimate (Lorimer & Kramer,2005). Shapiro & Teukolsky (1986) indicated that equation 1.7 is the magnetic field strengthat the equator and that at the poles it is higher by a factor of two (Lorimer & Kramer,2005).

1.3 Pulsar Timing and Observational Properties

This section focuses on introducing and discussing properties of pulsars that relate totheir timing and observation such as: spin evolution, age and braking index, the radiobeam, dispersion measure and spectral indices. These properties that relate to pulsartiming and observing are important for studying and understanding pulsar’s evolution,and when searching for pulsars.

1.3. Pulsar Timing and Observational Properties 25

1.3.1 Spin Evolution

A pulsar’s spin evolution is important as it reveals the history of the neutron star andits overall evolution. Pulsar’s spin evolution begins in the top left of the P-P diagram -seen in Fig. 1.1. They then begin to rapidly spin-down moving to the central part of theP-P diagram. As spin-down continues the radio emission becomes too weak to detector stops altogether and they cross the ‘death line‘ into the empty section to the right ofFig. 1.1.

Millisecond pulsars spin evolution are especially interesting as they are recycled pulsarsthat have been spun-up, as described in Section 1.1.2. As discussed earlier the loss ofrotational kinetic energy means the pulse period increases (the rate of rotation slows) P =dP / dt. The spin down luminosity is E and is the total power output,

E ≡ −dErot

dt= −d(IΩ2/2)

dt= −IΩΩ = 4π2 IPP−3, (1.8)

where the rotational angular frequency is Ω = 2π/P and the moment of inertia is I(Lorimer & Kramer, 2005). For moment of inertia I = 1045 g cm2,

E ' 3.95× 1031erg s−1(

P10−15

)(Ps

)−3

. (1.9)

Only a small amount of the neutron star’s energy is emitted in the radio spectrum. Mostof its energy is converted into magnetic dipole radiation as well as high-energy radiationand pulsar wind (Lorimer & Kramer, 2005).

1.3.2 Age and Braking Index

A pulsar’s age and braking index are important parameters to understand as they dealwith the pulsar’s kinetic energy and the dissipation of it. Age and braking index arerelated through the pulsar’s spin down as discussed in this section. Binary pulsar’s areespecially interesting as they are recycled, and so are usually older neutron stars as dis-cussed in Section 1.1.2. According to classical electrodynamics a rotating magnetic dipolewith a moment |m| radiates at its rotation frequency (Jackson, 1962).

Therefore, its radiation power is,

Edipole =2

3c3 |m|2 Ω4 sin2α, (1.10)

where the angle between the spin axis and the magnetic moment is α (Lorimer & Kramer,2005). With Edipole equated with the spin-down luminosity the expected evolution of thefrequency of rotation is,

Ω = −(

2 |m|2 sin2α

3Ic3

)Ω3. (1.11)


Equation 1.11 can be expressed generally as a power law in terms of rotational frequencyv = 1/P rather than Ω = 2πν results in,

v = −Kvn, (1.12)

where the braking index is n and K is a constant (Lorimer & Kramer, 2005).

The model of spin down in equation 1.12 can be expressed as pulse period and thereforeP = KP2−n, and assuming that K is a constant and n 6= 1 this first-order differentialequation can be integrated to obtain the age of a pulsar,

T =P

(n− 1)P

[1−

(P0

P

)n−1]

, (1.13)

where P0 is the birth spin period.

Equation 1.13 can be simplified to characteristic age if it is assumed the present value ofspin period is longer than the birth spin period (P0 P) and that the magnetic dipoleradiation results in spin down (n = 3) (Lorimer & Kramer, 2005),

τc ≡P

2P' 15.8 Myr

(Ps

)(P

10−15

)−1

. (1.14)

For a few pulsars estimating their age is simpler as the supernova was witnessed directly.The most well known example is the Crab Pulsar when Chinese astronomers recordedtheir observations of the supernova explosion in AD 1054 (Brecher et al., 1983). However,in some cases the supernova remnant provides an independent estimate of age (Kaspi &Helfand, 2002; Hénault-Brunet et al., 2012; Titus et al., 2019). A good example of this isMCSNR J0513-6724 where the supernova remnant provided an independent estimate ofthe age of the neutron star (Maitra et al., 2019).

1.3.3 The Radio Beam

The radio beam is arguably vitally important when studying pulsar’s radio emission andwhen searching for them within the radio. Studying the radio beam is not just a caseof understanding detection but also modelling the plasma processes that result in emis-sion to begin with. The generally accepted theory is that of a cone shaped beam centredaround the magnetic axis (Lorimer & Kramer, 2005). The region where there are openmagnetic fields lines is a site for stable radio emission. Plasma flows from the surfacealong the open field lines and emission of photons occurs tangentially to the point ofemission and the field lines (Lorimer & Kramer, 2005).

Specifically, electrons within the polar cap are accelerated along the curved open fieldlines resulting in curvature radiation which is polarized in the direction of the curvedfield lines (Condon & Ransom, 2016). The curvature radiation produces higher energy


photons which interact with both lower energy photons and the magnetic field, this re-sults in electron-positron pairs that emit more higher energy photons (Condon & Ran-som, 2016). This cascade process results in bunches of charged particles that are emittingin the radio (Condon & Ransom, 2016). However, there have been other hypotheses re-garding pulsar’s radio emission (Smith, 1970; Smith, 1976).

A diagram of a pulsar’s magnetosphere model can be seen in Fig. 1.5. This is assumingthe generally accepted model of a cone shaped beam centred on the magnetic axis.

The pulse width observed, W, measured in longitude of rotation is,

sin2(

W4

)=

sin2(ρ/2)− sin2(β/2)sin α · sin (α + β)

(1.15)

(Gil et al., 1984; Lorimer & Kramer, 2005),

this can also be written as,

cos ρ = cos α cos(α + β) + sin α sin(α + β) cos(

W2

), (1.16)

where β is the impact angle or impact parameter, which is the closest approach to themagnetic axis of the line of sight (Lorimer & Kramer, 2005).

FIGURE 1.5: The Goldreich-Julian model of a pulsar’s magnetosphere nearthe poles. The electron-positron cascade that results in a pulsar’s coherentemission is shown in the enlarged (right) section. Image credit: Condon &Ransom (2016).


1.3.4 Dispersion Measure

The Dispersion Measure, or DM, is an important factor in observing pulsars as it affectsthe electromagnetic radiation being observed. The interstellar medium (ISM) is com-posed of ionized plasma and affects electromagnetic radiation that travels through it ina number of ways (e.g. scattering and scintillation, frequency dispersion and Faradayrotation).

Therefore, radiation from a pulsar experiences an index of refraction that is frequency-dependent and pulse components at a higher frequency experience a smaller delay thanlower frequencies (higher frequencies are observed before lower frequencies), this effectcan be seen in Fig. 1.6. The refractive index is (Lorimer & Kramer, 2005),

µ =

√1−

(fp

f

)2

. (1.17)

The delay mentioned above is,

t = kDM ×DM

f 2 , (1.18)

where kDM is the dispersion constant, which ≡ e2

2πmec = 4.148808 ± 0.000003×103 MHz2

pc−1 cm3 s (Lorimer & Kramer, 2005).

Integrating the column density of the free electrons over the path of the photon throughthe ISM is the dispersion measure,

DM =∫ d

0ne dl. (1.19)

where d is the distance to the pulsar and ne is the electron density of the plasma.

This delay between two frequencies f1 and f2 is,

∆t ' 4.15× 106ms× ( f−21 − f−2

2 )×DM. (1.20)

If the arrival time of the pulse is measured at two or more frequencies, the DM can beinferred and can then be used to estimate the distance to the pulsar. DM is found by in-tegrating an assumed Galactic electron density distribution ne (Lorimer & Kramer, 2005).However, a model of ne is required. The NE2001 model was created by Cordes & Lazio(2002) and Yao et al. (2017) created a more recent model called YMW16, this is shown inFig. 1.7.


FIGURE 1.6: Pulsar dispersion shown as a function of frequency for pulsarB1356-60. This figure illustrates the dispersion delay by the curved lines inthe upper part of the figure; this is uncorrected observational data centredat 1380 MHz with a bandwidth of 288 MHz. The dispersion measure (DM)for this pulsar is DM = 295 pc cm−3. The curved lines show the affectdispersion has and when corrected the lines will be straight. Image credit:Lorimer & Kramer (2005).


FIGURE 1.7: Diagram representing the YMW16 Galactic electron densitymodel (Yao et al., 2017). The figure is centred on the centre of the MilkyWay and the Sun is located at x = 0 y = +8.3 kpc. The Galactic molecularring can be seen by the “thin disk", the dense area at 4kpc. The spiral armsof the galaxy have a pre-determined logarithmic form and decay at largerradii except in the Carina-Sagittarius arm where dense regions associatedwith Carina and less dense regions associated with Sagittarius are located(Yao et al., 2017). Distance to 189 pulsars were used to create this model,these distances were independently calculated using: distance estimatesfor binary companions, annual parallax, globular cluster associations, HIabsorption coupled with kinematic models of Galactic rotation and super-nova remnants. Image credit: Yao et al. (2017).


1.3.5 Spectral Index

Pulsar’s spectral indices are useful not only for understanding their flux densities butalso for comparing observations, detections, searches and sky surveys. In radio astron-omy flux densities are measured with the unit Jansky (Jy), where 1 Jy ≡ 10−26 W m−2

Hz−1. The mean flux densities of pulsars typically have an inverse dependence with thefrequency of observations. For pulsars that are observed over 100 MHz this dependenceis approximately the power law,

Smean( f ) ∝ f α, (1.21)

where f is the frequency of observations and α is the spectral index (Lorimer & Kramer,2005).

Fig. 1.8 below shows a sample flux density spectra for two different pulsars, and Fig. 1.9shows spectral indices for 228 pulsars.

Maron et al. (2000) collected flux density data and fitted spectra on 281 pulsars betweenfrequencies of 39 MHz to 43 GHz. Their results show that for observations above a fre-quency of 100 MHz the majority of pulsar’s spectra can be described by a power law withan average value < α > = -1.8 ± 0.2.

Kramer et al. (1998) analysed flux densities and fitted spectra of 23 millisecond pulsars.Their results showed that for those 23 MSPs the indices were between α = -1.0 to -2.0which is a narrower range than for normal pulsars. Han et al. (2017) also analysed fluxdensities and fitted spectra of 228 pulsars and found their spectra were distributed be-tween α = -4.8 to -0.5 peaking at -2.2, the spectral indices plot can be seen in Fig. 1.9.

FIGURE 1.8: Sample flux density spectra. This figure shows two pul-sars with different spectra. Left shows a low-frequency turnover in PSRB0329+54, right shows a broken power law fit indicating a high-frequencyturn over in PSR B1929+10. Image credit: Lorimer & Kramer (2005).


FIGURE 1.9: Figure showing spectral indices for 228 pulsars, which arein the range -4.8 to -0.5 and peaks at -2.2. These are at 4 subbands andfitted with a power law; 200 of these pulsars have had their spectral indicesnewly determined. Image credit: Han et al. (2017).

1.4 Background of 3FGL J0212.1+5320

So far this chapter has focused on the general and observational properties of pulsarsand binary pulsars. This section will be focused on the target system of this work,its background and previous results. The unidentified Fermi gamma-ray object 3FGLJ0212.1+5320 has been the target of observations and studies in the optical, gamma andX-ray (Li et al., 2016). An r‘ band image of J0212+5320 is seen in Fig. 1.10 and a broadband spectral energy plot in Fig. 1.11.

Properties of this system have been derived from these observations, including: orbitalperiod of the companion, X-ray luminosity, mass ratio, spectroscopic data and radialvelocity semi-amplitude (Linares et al., 2016; Shahbaz et al., 2017). This system has avariable optical counterpart identified by Li et al. (2016) and Linares et al. (2016). Theseprevious studies by Shahbaz et al. (2017) all reach a conclusion that this system is highlylikely to be a redback millisecond pulsar.

It was detected by Chandra as a bright X-ray source: F(0.5-7keV) = 1.4 × 1012 erg cm2

s and has a low mass optical counterpart: M < 0.4 M and T ∼ 6000 K (Li et al., 2016).Li et al. (2016) reached a conclusion that the gamma-ray properties are consistent with amillisecond pulsar with a companion that is ' 64% Roche-lobe filling.

The gamma-ray properties of this system are within the top 15% brightest sources within3FGL (Li et al., 2016), these gamma-ray properties are: Fγ = (1.71± 0.16) × 10−11 ergcm−2 s−1 in 0.1-100 GeV, seen in Fig. 1.11. Gamma-rays from pulsars usually exhibit lowvariability and a curved spectral shape; J0212+5320 exhibits both (Li et al., 2016). The

1.4. Background of 3FGL J0212.1+5320 33

spectroscopic data obtained by Li et al. (2016) show no strong emission lines which indi-cates that accretion is inactive.

FIGURE 1.10: r’ band image of J0212+5320 field from IAC-80-CAMELOT.The 95% error ellipse is seen from three Fermi-LAT point source catalogs.Right is zoomed in showing the location of the target of this project, sus-pected redback pulsar, (Porb ' 20.9 hr and r′ ' 14.3 mag, marked by redarrow). The red circle is Swift X-ray counterpart, a nearby W UMa contactbinary is marked by the purple arrow, a nearby galaxy ZOAG G134.92-07.63 is marked by the black diamond and Chandra 3-sigma location ismarked by the brown ellipse. Image credit: Linares et al. (2016).

FIGURE 1.11: J0212+5320 broad band spectral energy distribution whichranges from infrared to gamma-ray. Optical fluxes are at a phase of 0.X-ray data is Chandra spectrum. Infrared to UV fluxes are corrected forinterstellar absorption. The black line is a best-fit model of a power-law.Red line is Fermi-LAT spectrum log-parabola fit. Image credit: Linareset al. (2016)


Linares et al. (2016) reached a conclusion suggesting this is a semi-detached system withan orbital period of 0.86955 ±0.00015 d (∼21 hr). The companion is an F6±2 type star ata distance D = 1.1±0.2 kpc, has a projected rotational velocity Vsin(i) = 73.2±1.6 km s−1

and a radial velocity curve semi-amplitude K2 = 214.1±5.0 km s−1.

Linares et al. (2016) identified the target system as an X-ray source of 0.5-10 keV luminos-ity LX = 2.6 × 1032 (D/1.1 kpc)2 erg s−1, this also supports that it could be a millisecondpulsar. Light curves fitted by Shahbaz et al. (2017) exhibit unequal maxima and minimumsuggesting either off centre heating as a result of an intrabinary shock (a characteristic ofa spider pulsar system) or a dark solar-type star spot. The light curves that were fitted forboth of these models can be seen in Fig. 1.12. The effective temperature of the companiondetermined from the hot spot model also fits with the observed F6±2 spectral type classi-fication of the companion star. Shahbaz et al. (2017) estimate a neutron star mass of M1 =1.85 +0.32

−0.26 M and companion star mass of M2 = 0.50 +0.22−0.19 M with an orbital inclination

angle i = 69.

Shahbaz et al. (2017) quotes the X-ray photon index for the target system as Γ ∼ 1.3,which corresponds to a spectral index α ∼ 2.3. The intrabinary shock is thought to bewhat is powering the X-ray emission. Photon indices for redback pulsars that are cur-rently in the accreting or pulsar state are generally between 0.9 to 1.8 (Linares, 2014).

1.5 Aim of the Project

The aim of this work is to search radio data acquired with the Lovell Telescope for pulsedradio emission in an attempt to confirm the suspected pulsar nature of J0212+5320. Thesearching was conducted using PRESTO, a pulsar searching and analysis software (Ran-som, 2018). A pipeline that was initially created by the main supervisor and a previousstudent (Sett, 2019) has been adopted and altered to conduct this work. The main de-velopment made to the search pipeline is the addition of coherent dedispersion stagesinterspersed between finer incoherent dedispersion steps. This techniques is not com-monly used to search for new pulsars due to storage and computational requirementsand was adopted to ensure high enough sensitivity to effectively search the data and aredescribed in detail in sections 2.1, 2.4.2 and 2.6.

1.5. Aim of the Project 35

(A) Dark spot model - light curve and radial velocity

(B) Hot spot model - light curve and radial velocity

FIGURE 1.12: J0212+5320 light curves showing g’ (blue), r’ (red), i’ (yellow)and Hα absorption line radial velocity curve (black), the correspondingresiduals in each band are shown in bottom left (Shahbaz et al., 2017). (a)the dark spot model - parameters of f =0.80, q=0.18 and i=65o. (b) the hotspot model - best fit parameters of f =0.76, q=0.28 and i=69o. This figureshows the unequal maxima and minimum, an increase or decrease in lightat phase 0.25 or 0.75 suggests a source from the surface of the companioneither a dark spot or hot spot Shahbaz et al. (2017).

36

Chapter 2

Pulsar Search Techniques

In theory, searching for pulsars is a somewhat straightforward task - to search forpulse emission within data that has a lot of noise. However, as pulsars are fairlyfaint objects it requires sensitive instruments. Studying and searching for pulsarswill aid in furthering our knowledge and understanding of not just neutron stars,but also the interstellar medium, binary systems and orbital physics.

This section will layout and discuss the standard procedure and techniques usedwhen conducting pulsar searching. The details of the observations and data arefirst discussed followed by an explanation of the standard pulsar search proce-dure, the software used for this work, the dedispersion plan, details of filterbank-ing the data and then followed by the steps involved in our search.

Our search adopted a novel technique of utilising the baseband data, filterbank-ing and coherent dedispersion at intermediate steps, followed by finer steps ofincoherent dedispersion to ensure the sensitivity is high enough and that thesmearing is kept to a minimum. This searching technique is usually not em-ployed for most L-band searches. However, it has recently gained more use dueto increased computational power, and enables higher sensitivities especially tomillisecond pulsars as is the case here. Although, similar techniques have beenutilised for LOFAR searches (Bassa et al., 2017).

2.1. Observation and Data 37

2.1 Observation and Data

The data were acquired by the Lovell telescope - a 76 metre radio telescope at JodrellBank Observatory. The telescope has a parabolic surface and an altitude-azimuth mount,the primary focus is an L-band receiver which is cryogenically cooled with a system tem-perature of 25 K and observes at a 500 MHz wide bandwidth between frequencies of 1.3to 1.8 GHz (Bassa et al., 2016).

The data were initially stored as baseband data (raw Nyquist sampled voltages) as thetarget system is suspected to be a millisecond pulsar. This allowed the data to be coher-ently dedispersed before filterbanking the data - converting the raw baseband data ton-bit numbers that corresponds to frequency channels. Coherent dedispersion and filter-banking results in important increase of sensitivity, the data were processed through thepipeline which searches for Radio Frequency Interference (RFI), creates subbands andthen incoherently dedisperses the data before it can be searched.

This novel strategy involved coherent dedispersion at a number of steps followed byfiner incoherent sub-steps. This is all to ensure the highest sensitivity and lowest smear-ing so that a millisecond pulsar can be searched for and detected.

The data are 7208.4 s or ∼ 2 hr in length. This was to ensure a large enough portion ofthe system’s orbit is covered (∼ 2 hr is ∼ 10% of the 21 hr orbit). The data are betweenfrequencies of f = 1348 and 1732 MHz with a bandwidth of ∆ f = 512 MHz. The centralfrequency of the observations is therefore fcentral = 1540 MHz. The raw baseband datahas a sample time of 6.25 x 10−8 s and each raw baseband file was 10 s in length. Thedata were coherently dedispersed between a range of DM = 12.5 to 37.5 pc cm−3, andthen converted to filterbank files which have a sample time of 4 microseconds (4 x 10−6

s), the data were channelised so each filterbank file has 384 channels and a channel sizeof 1 MHz, with 32 bits per sample.

The phase of the system during observation is important to estimate as it gives an initialidea of whether eclipses are likely to be a factor in the search. Therefore, phases werecalculated to determine if eclipses were likely to have occurred and to determine if ac-celeration would be an important factor. Linares et al. (2016) quotes T0 = 57408.539 ±0.003 MJD, using the MJD value of the start and end of the observation times the phaseposition of the companion during the observation can be calculated,

φi = (Ti − T0)/Porb. (2.1)

38 Chapter 2. Pulsar Search Techniques

Using equation 2.1,

φstart = (57643.1762962963 - 57408.539) / 0.86955 = 269.8376128989703

φend = (57643.24155092592 - 57408.539) / 0.86955 = 269.91265703631257

Therefore, the phase position of the observation is φstart = 0.838± 0.004 and φend = 0.913±0.004. These are optical astronomy phase positions where φ = 0.0 is inferior conjunctionof the companion, in radio astronomy phase positions these would be φstart = 0.088 ±0.004 and φend = 0.163 ± 0.004. Explanations of phase positions see Section 2.2.4, Fig. 2.2and Fig. 3.16.

The pulsar parameters of the target system are unknown as there has not been previousradio studies of this system. Therefore, only a range of expected parameters of the pulsarcan be estimated based on previous MSP detections and their derived parameters.

Table 2.1 shows the expected ranges of parameters of the target system. P is the period,P is the spin-down, fspin is the spin frequency, the age of the system, E is the spin-downenergy loss (see Section 1.3.1), Bsur f is the surface magnetic flux density (see Section 1.2.3and equation 1.7) and DM is the dispersion measure (see Section 1.3.4 and 2.6). P is ex-pected to be negative as the phase positions estimated indicate that the pulsar’s radialvelocity is decreasing as it approaches superior conjunction - that the pulsar is accelerat-ing towards the observer, see Section 2.2.4, Fig. 2.2 and Fig. 3.16.

Parameter RangeP 1 - 10 msP −10−12 - −10−15 s s−1

fspin 100 - 800 HzAge 107 - 1010 YrE 1033 - 1035 erg s−1

Bsur f 108 - 1010 GDM ∼25 pc cm−3

TABLE 2.1: Table showing the estimated ranges of parameters for millisec-ond pulsars. The specific paramaters of the target system are unknown as ithas not been observed in the radio before this work. Therefore, we can onlyestimate a range in which the target would be expected. These parameterswere estimated by utilising the pulsar ATNF catalogue(Hobbs et al., 2019)and the Handbook of Pulsar Astronomy (Lorimer & Kramer, 2005). TheDM for this system was estimated using the NE2001 and YMW16 modelsat ∼ 25 pc cm−3 this is detailed in Section 2.6 (Cordes & Lazio, 2002; Yaoet al., 2017).

2.2. Standard Pulsar Search Procedure 39

2.2 Standard Pulsar Search Procedure

Firstly, the data needs to be searched for Radio Frequency Interference (RFI), that is in-terference from radio sources that are not celestial in origin such as from mobile phones,wireless computer networks, satellites and even from airports if the radio observatory iswithin close proximity.

The data then needs to be dedispersed forming a number of time series that span a rangeof trial DM values. The resulting time series can then be searched for periodic signals.The standard procedure involves searching the amplitude or power spectra after it hasbeen Fourier transformed. This results in a list of best candidates which can then be anal-ysed, this is then repeated for another trial dispersion measure (DM) value resulting in afinal list of candidates that can then be folded modulo each candidate period (Lorimer &Kramer, 2005).

2.2.1 Radio Frequency Interference

Radio Frequency Interference (RFI) presents a persistent challenge for radio astronomy.Radio sources are very weak so RFI impacts the ability to observe in the radio spectrumand therefore also to pulsar searching. It is possible that RFI could result in a pulsarbeing missed. Broadband signals can mimic periodic signals and are especially prob-lematic. This issue can be resolved usually either by time domain clipping or frequencydomain masking (Lorimer & Kramer, 2005).

Time domain clipping involves analysing the time series for sporadic bursts of RFI, com-paring them to the standard deviation and mean of a zero DM time series to indicate ifit differs by more than two standard deviations from the mean. If it does then it is ex-cluded. This is especially vital for pulsars that have a longer period as RFI can result in abias in their integrated profiles (Lorimer & Kramer, 2005).

RFI is usually persistent and independent of the area being observed, therefore if a listof potential RFI signals is created a spectral mask can be made. This list is composed ofFourier bins that the RFI is found in, it can be flagged and then ignored by the analysissoftware. This technique is an effective way of resolving RFI issues (Lorimer & Kramer,2005).

2.2.2 Dedispersion Stage

Dispersion when uncorrected causes broadening of the pulse profile which results in areduced S/N (signal-to-noise ratio). Fig. 1.6 shows the effect of smearing on a signal of afinite bandwidth as a result of dispersion.


Incoherent dedispersion is the simplest method of correction and involves compensatingfor the delay in the pulse signal by splitting it into frequency channels, taking chunks ofthose channels called subbands and then shifting them by applying a time delay to ac-count for the effects of dispersion (Lorimer & Kramer, 2005). An incoherent dedispersionplan is seen in Fig. 2.1.

If the raw data is considered as a two-dimensional array of time samples and frequencychannels, the jth time sample of the lth frequency channel is Rjl . For nchans frequencychannels the jth sample of the dedispersed time series Tj is,

Tj =nchans

∑l=1

Rj+k(l),l , (2.2)

where k(l) is the nearest integer of time samples corresponding to the dispersion delayof the lth frequency channel relative to a reference frequency. If the lth frequency channelof the data was taken, fl , and the dispersion relation, k(l) can be written as,

k(l) =(

tsamp

4.15× 106 ms

)−1 ( DMcm−3 pc

) [(fl

MHz

)−2

−(

f1

MHz

)−2]

. (2.3)

If the order of channels in R starts at the highest frequency (l = 1) and proceeds in de-scending order the frequencies are,

fl = f1 − (l − 1) ∆ fchans. (2.4)

The interval between trial DM values needs to be considered carefully; it should not belarge enough to significantly broaden causing loss of sensitivity. It also should not betoo small so as to result in unnecessarily producing and searching identical time series.The ideal option is for the DM stepsize to be between the highest and lowest frequencychannels that are equivalent to the data sampling interval. DM step is also dependenton number of channels, subbands, centre frequency and bandwidth (Lorimer & Kramer,2005).

Fig. 2.1 shows a sample plot which is used to decide the specifics of the dedispersionplan. This plot is from the PRESTO tutorial and was created using sample data on PSRJ1643-1224 from the Green Bank Telescope provided as part of the tutorial for PRESTO.


The most fundamental source of smearing is the Channel Smearing, which arises due tothe unremovable dispersion delay arising between the top and bottom of a frequencychannel. Then, it is also possible that the smearing across a channel spans more than asingle time sample. This is called the Sample Time smearing. In principle, this also im-plies that data can be downsampled in time to reduce compute efforts in the case whereit oversamples the possible time smearing while still enabling pulsations at a short pe-riod to be recovered. The computations can be further optimised by grouping blocks ofchannels into ‘subbands’, and then only shift necessary blocks to dedisperse the signal.A similar effect to the Channel Smearing therefore arises and is called Subband StepsizeSmearing. Finally, the overall dedispersion needs to be performed in discrete steps, andthus introduces a DM Stepsize Smearing which corresponds to the smearing of a pulse forwhich the actual DM is exactly halfway between two steps (Lazarus et al., 2015).

The smearing time, tDM, can be estimated by rearranging equation 1.20 and assumingthat ∆ f f ,

tDM ' 8.3× 106 ms×DM× ∆ f × f−3, (2.5)

where the smearing time is within individual channels at frequency f and bandwidth ∆ fin MHz.

The total broadening of a signal is estimated as,

τtot =√

τ2chan + τ2

samp + τ2sub + τ2

BW, (2.6)

where τchan is the channel smearing, τsamp is the sample time, τsub is the subband smear-ing and τBW is the bandwidth smearing.

Coherent dedispersion involves removing the effects of dispersion by de-convolving us-ing the complex conjugate of the transfer function of the interstellar medium which re-moves the effects of dispersion before filterbanking the data (filterbank files are detailedin Section 2.7). This method retains the instrumental/Nyquist time resolution allowingthe sensitivity to be high enough and smearing low enough to detect a millisecond pul-sar (Lorimer & Kramer, 2005; Condon & Ransom, 2016). This method was pioneered byHankins & Rickett (1975).


FIGURE 2.1: The dispersion measure for the sample pulsar data set on PSRJ1643-1224 used for the tutorial within PRESTO. It illustrates the smearingof the data caused by interstellar propagation. The smearing at DM = 50pc cm−3 is ∼ 0.5 ms. This type of plot is used to create the dedispersionplan. Image created using PRESTO software: Ransom (2018).

2.2.3 Searching for period pulses using Fourier Transforms

If necessary a time series Tj can be corrected for the motion and rotation of the Eartharound the Sun (barycentred) by correcting for the travel time of the light to the barycen-tre of the Solar System (Lorimer & Kramer, 2005). An algorithm is needed for the periodicsignal searching. The most common method is to Fourier transform and examine the fre-quency domain. Tj - the time series that has been dedispersed is a set of N data pointsand the discrete Fourier transform (DFT) is computed. The kth Fourier component of theDFT is (Lorimer & Kramer, 2005),

Fk =N−1

∑j=0

Tj exp (−2πijk/N), (2.7)

where i is√−1, N is number of elements within time series.

Equation 2.7 shows that for the N-point DFT to be computed it requires N2 floating-pointoperations. However, this requires a large amount of time to compute. One method thatcan reduce the computing time is the Fast Fourier Transform (FFT). This requires N log2

N operations for an N-sample time series to be transformed. The highest frequency in theFourier domain is 1/tsamp, the discrete Fourier transform is symmetric about the Nyquist


frequency, which is the highest frequency component, νNyq = 1/(2 tsamp). Fourier com-ponents above νNyq

1 are just the complex conjugates of their low-frequency counterparts(Lorimer & Kramer, 2005). This can be used to DFT the two N-point real data sets at thesame time, or one at a time of length N/2 (Press et al., 1992).

Looking at the amplitude of the Fourier components (AK = |FK|) or powers (PK = |FK|2)as a function of frequency results in higher sensitivity and therefore an effective tech-nique of searching for periodic signals (Lorimer & Kramer, 2005). However, the DFT’sfrequency response is not uniform and only ideal if they match the central frequency ofthe Fourier bins. This can result in a loss of sensitivity which can be accounted for sev-eral ways: Fourier domain interpolation and interbinning, and zero padding (Lorimer &Kramer, 2005).

The addition of elements in the time series that are zero-valued is the simplest option,this is called zero padding, and is advantageous as it adds no noise or signal into thetime domain data (Lorimer & Kramer, 2005).

To remove low frequency noise it is standard to whiten the data and then attempt toestimate the signal level. This can be done by splitting the spectrum into pieces and thencalculating the mean and root mean square values for each part. This results in a responseto noise of the spectrum being as uniform as possible (Lorimer & Kramer, 2005).

2.2.4 Binary Searching

The search techniques discussed so far have reduced sensitivity to binary system pulsarsthat have shorter or millisecond periods. The motion of binary pulsar systems causes achange in the apparent pulse frequency and the result is a spread of the power of thesignal across several Fourier bins (Ng et al., 2015). A diagram of pulsar binary motioncan be seen in Fig. 2.2. This results in the sensitivity, sharpness and signal-to-noise ratioof the search to be reduced.

A technique that is used to account for this is the acceleration search, at first it assumesfor a fraction of the orbital period a constant acceleration, then constant acceleration fordifferent values which can show increased detection at various trial values of a pulsarthat is accelerated (Dimoudi & Armour, 2015).

The two methods that utilise acceleration searching are a frequency domain techniquecalled the correlation method and time domain resampling.

The correlation method requires the creation of a set of finite impulse response (FIR) fil-ters within the Fourier domain, this spreads the power across several spectral bins by

1Due to the circular symmetry, frequencies above νNyq are the same as negative frequencies.


FIGURE 2.2: A simplified diagram of pulsar binary orbit with the pulsarin the centre (marked by the black circle), the companion orbiting aroundit (marked by the blue circle) and the observer marked in the lower partof the diagram. Indicating the positions of: inferior conjunction of thecompanion, pulsar descending node, superior conjunction of the compan-ion, pulsar ascending node. The radio astronomy phase positions are alsomarked where inferior conjunction of the companion = 0.25.

the acceleration. The FIR filter describes this resulting spreading of the power. Thenthe power is put into a single Fourier bin, it therefore describes the effect of constant ac-celeration and correlates it to the signal. This search method cross correlates the powerspectrum with the FIR filter to attempt to find a signal that has been spread in a way con-sistent with acceleration. This method is less computer intensive as the filters associatedwith it are smaller and require shorter Fourier transforms and convolutions (Dimoudi &Armour, 2015).

The time domain resampling method involves resampling the time series to a rest frameof inertial observation to recover the signal, and then searching would reveal a pulsar asa solitary object. This method can be quite computer intensive as an FFT is needed aftereach correction and with large datasets it becomes more intensive (Lorimer & Kramer,2005).

2.3. Time Domain Searching 45

2.2.5 Pulsar Candidates

The results after dedispersing and Fourier transforming is a list of periods and DM valuesof pulsar candidates and the S/N ratio of the folds. A pulsar will appear in this listmultiple times with varying S/N ratio and a fairly close DM to the actual value. Oncethis list has been created, the dedispersed time series can be folded at the candidate’s DMvalue and period, and then plotted to visually inspect (Lorimer & Kramer, 2005).

2.3 Time Domain Searching

The most effective techniques to search for periodic signals are the frequency domainones discussed in previous sections, however time domain techniques can also be used,mainly: single pulse algorithms and fast folding.

2.3.1 Fast Folding

One of the most essential steps is to fold the dedispersed data modulo the candidate pe-riod and examine the pulse profile. Another method is to fold each time series after dedis-persion for different trial periods and examine for significant pulse profiles (Lorimer &Kramer, 2005). Folding can be summarised as:

1. Data is dedispersed, the time series has a sampling time tsamp.

2. An array is created for the folded profile that has equally spaced elements nbins

across the pulse period. The centre of phase bin i is (i – 0.5) / nbins.

3. Calculate the phase of a sample time series relative to its period, if a constant pulseperiod, P, the phase of the jth sample is jtsamp / P, tsamp is the interval of data sam-pling.

4. Locate the bin in the profile array that has the closest phase and add the sample binto it.

(Lorimer & Kramer, 2005).

Finally, take the phase bin within the folded profile, normalise it and the integrated pulseprofiles that result indicate averaged emission as a function of phase.

2.3.2 Single Pulse Searches

To find some pulsars is more complex than simply searching for their periodic nature,such as searching for nulling pulsars or giant-pulse emitters requires single pulse searcheswhich is basically matched filtering. If a time series has Gaussian noise of a known meanand standard deviation searching for single events that deviate from its mean can revealsingle pulses and therefore a pulsar (Lorimer & Kramer, 2005).


2.4 Adopted Search Strategies

The previous section focused on the techniques utilised for pulsar searching, this sectionwill discuss the strategies for pulsar searching. Specifically, focusing on the strategiesused when searching for millisecond pulsars.

2.4.1 Sky Surveys

The Fermi Large Area Telescope (LAT) has aided in a large amount of millisecond pul-sar discoveries (∼30%) and about half of pulsars that emit gamma-rays are millisecondpulsar (Abdo et al., 2009). LAT has aided by highlighting where radio observations tar-geting pulsars should be focused. It was possible to search for gamma-ray source pulsarsbefore LAT, however, it has aided greatly due to its improved angular resolution whichincreases the efficieny of searches within the Galactic disk (Cromartie et al., 2016). Thetarget system of this work (3FGL J0212+5320) was listed within the third Fermi catalogsource (Acero et al., 2015).

There have been successful studies of pulsar populations through all sky searches forMSPs in Galactic latitudes. These studies started with the detection of PSR B1257+12(Wolszczan, 1992) and B1534+12 (Wolszczan, 1991). Since dispersion decreases awayfrom the Galactic plane and is frequency dependent a frequency of less than 1 GHz isoptimal for studies such as these (Lorimer & Kramer, 2005).

All sky searches for millisecond pulsars focused on higher galactic latitudes, since thedispersion is less in this area, has been very successful at finding and studying millisec-ond pulsars. The shorter integration times involved with searches such as this also meanthat the acceleration searches can be conducted fairly easily (Lorimer & Kramer, 2005).

2.4.2 J0212+5320 Search

The search conducted for this work involved utilising the baseband data to ensure ahigh enough sensitivity and low enough smearing. The baseband data were filterbankedand coherently dedispersed as described in sections 2.1, 2.6 and 2.7. The data were thensearched for RFI and a mask was then created followed by subbanding and finer inco-herent dedispersion steps as described in sections 2.1 and 2.9. The data were then fastFourier transformed before an acceleration search was conducted to search for periodicsignals which were then sifted through to create a list of potential candidates.

As discussed in Section 2.7 the data were split into quarters when filterbanked and ini-tially the analysis was conducted on each quarter individually. This was due to harddrive storage limitations within the hard drive array used and considering computa-tional times as it was unknown where a pulsar signal might be discovered. This had anadvantage of lowering the risk of overlooking a transient signal but the disadvantage is

2.5. PRESTO Software 47

that the sensitivity is lower. Therefore, a more sensitive analysis of the whole dataset thatutilised all the integration time was also conducted.

This search technique of utilising the baseband data for coherent dedispersion at interme-diate steps followed by finer incoherent dedispersion steps for L-band data is not usuallyemployed. Although, as mentioned at the beginning of this chapter it has been utilisedfor LOFAR searches (Bassa et al., 2017). A typical pulsar search is described in Section2.2, other pulsar searches such as Oostrum et al. (2020); Titus et al. (2019); Sett (2019) alsodescribe pulsar searching techniques. Ransom et al. (2002) also describes the basics ofPRESTO and standard pulsar searching.

2.5 PRESTO Software

PRESTO is a pulsar search pipeline written in ANSI C and python. It was written primar-ily to search for binary millisecond pulsars in globular clusters, such as the work doneby Menezes et al. (2018). However, it can be effectively utilised for searching for otherpulsar types (Ransom, 2001; Ransom, 2018). The pipeline being utilised for this projectwas written by the primary supervisor and another student but was altered to allow theanalysis for this work to be conducted (Sett, 2019). It calls the various functions withinPRESTO to analyse the data with the preset parameters.

A general outline of a PRESTO search is to:

1. use ‘readfile’ to examine the data by printing the meta-data,

2. use ‘rfifind’ to search the raw data for RFI in both the time and frequency domains,

3. create a topocentric time series with a DM of 0 pc cm−3 with ‘prepdata’ and ‘ex-ploredat’. ‘prepdata’ dedisperses a single time series, if multiple need to be donethen ‘prepsubband’ is used to create a dedispersed time series.

4. use ‘realfft’ to Fast-Fourier Transform the dedispersed time series,

5. identify “birdies" to zap (“birds" are periodic interference within the power spectra,zapping them zeroes them out) done with ‘explorefft’ and ‘accelsearch’,

6. use ‘makezaplist.py’ to create the zap list,

7. use ‘DDplan.py’ to create a dedispersion plan,

8. use ‘accelsearch’ to search for periodic and single pulses,

9. if periodic signals are found fold the time series and time it using ‘prepfold’ and‘get_TOAs.py’

(Ransom, 2018).


2.6 Dedispersion Plan

As J0212+5320 is suspected to be a millisecond pulsar having as much time resolutionand keeping the smearing as low as possible is key to being sensitive to a potential MSP.Therefore, coherent dedispersion before filterbanking followed by incoherent dedisper-sion when run through the pipeline was necessary. Section 1.3.4 explains dispersion mea-sure and Section 2.2.2 explains the dedispersion stage including: the novel two dedisper-sion techniques, DM trial values and the smearing time.

A DM value for the system was obtained from both the NE2001 model and the YMW16model. For these estimates a distance was assumed of D = 1.1±0.2 kpc (Linares et al.,2016). The distance was also estimated using Gaia to ensure accuracy which gave D =1.19±0.28 kpc (van Leeuwen et al., 2018). The NE2001 model gave a value of DM = 27.12pc cm−3 (Cordes & Lazio, 2002) and YMW16 gave a value of DM = 23.08 pc cm−3 (Yaoet al., 2017). Therefore, having the coherent dedispersion centred on DM = 25 pc cm−3

was ideal for an initial search.

The DDplan.py routine within PRESTO estimates the channel smearing utilising the pa-rameters passed: central frequency (MHz), sample time (µs), bandwidth (MHz), numberof channels and number of subbands, the dedispersion plan plot can be seen in Fig. 2.3.Dedispersion and smearing are discussed in Section 2.2.2. A search of a range betweenDM values of 12.5 to 37.5 pc cm−3 was chosen as this was centred on DM = 25 pc cm−3.

Fig. 2.3 shows that the smearing is lowest at the point where the coherent dedispersionhas been applied (at DM = 25 pc cm−3) and increases as the DM value increases or de-creases away from this point (to the left and right of this central point). If the amountof smearing exceeds the period of the pulsar being observed then it will become unde-tectable against background noise.

However, an ideal scenario would be for the smearing to not exceed a few percent ofthe period value. As the target of this study is likely a millisecond pulsar and the fastestperiod of a known MSP is∼1.5 ms the maximum smearing value should be under∼3% ofthe period value. A smearing value of 0.0288 ms seen in Fig. 2.3 is an acceptable amount(∼2% of period value) when searching for a millisecond pulsar. As stated in Section 2.2.2smearing of the pulse profile results in reduced S/N which also reduces the sensitivity ofthe search.

2.6. Dedispersion Plan 49

FIGURE 2.3: Dedispersion plan for J0212.1+5320 showing dispersion mea-sure (pc cm−3) against smearing (ms). Smearing is the amount of broad-ening of a signal per frequency channel, keeping this to a minimum is keyto being sensitive to a MSP. Ideally, the smearing should be around or be-low a few percent of the period of a MSP, the maximum smearing betweenDM = 12.5 and 37.5 pc cm−3 is kept below 0.03 ms or 3%, which is an ac-ceptable amount. This range was chosen as the DM value is expected tobe ∼ 25 pc cm−3. This plot was generated using PRESTO and it should benoted that the right side of the curve should be similar to the left side, thiswas manually accounted for in the dedispersion plan shown in Table 2.2.It shows the maximum smearing value of 0.0288 ms which is sufficient forthis search. Image created using PRESTO: Ransom (2018)

The DDplan.py routine parameters to produce Fig. 2.3 were: the central frequency of theobservation fctr = 1540 MHz, the sample time of the data dt = 4 µs, the bandwidth of thedata BW = 384 MHz, the number of channels Nchan = 384 and the number of subbandsNsub = 96. The frequency channels are therefore 1 MHz in width to reduce smearingacross channels, as having larger channel widths could result in unwanted pulse smear-ing. Knispel et al. (2013) illustrates this in the discovery plot of the millisecond pulsarJ1748-3009 where channel widths of 3 MHz were utilised and the pulse profile is quitewide as a result of channel smearing.

The incoherent dedispersion plan was created also between the DM search range of 12.5to 37.5 pc cm−3, which is centred on 25 pc cm−3. The specifics of that plan can be seen inTable 2.2.


subDM dDM downsamp dmspercall13.0 0.02 2 5014.0 0.02 2 5015.0 0.02 2 5016.0 0.02 2 5017.0 0.02 2 5018.0 0.01 1 10019.0 0.01 1 10020.0 0.01 1 10021.0 0.01 1 10022.0 0.01 1 10023.0 0.01 1 10024.0 0.01 1 10025.0 0.01 1 10026.0 0.01 1 10027.0 0.01 1 10028.0 0.01 1 10029.0 0.01 1 10030.0 0.01 1 10031.0 0.01 1 10032.0 0.01 1 10033.0 0.02 2 5034.0 0.02 2 5035.0 0.02 2 5036.0 0.02 2 5037.0 0.02 2 51

TABLE 2.2: Showing the specifics of the dedispersion plan: the subDMsteps, the dDM which is the DM stepsize, the downsampling rate andthe number of DMs per call. The incoherent dedispersion plan was con-structed to maximise sensitivity between the initial DM search range ofDM = 12.5 to 37.5 pc cm−3, centred on DM = 25 pc cm−3. The DM for thissystem was estimated using the NE2001 and YMW16 models at ≈ 25 pccm−3 (Cordes & Lazio, 2002; Yao et al., 2017).

2.7. Filterbank Files 51

2.7 Filterbank Files

The data were coherently dedispersed and then filterbanked to create .fil files which area 2D stream of n-bit numbers corresponding to radio frequency channels and time, thatcould be analysed by the pipeline. The raw baseband data were intially converted tofilterbank files that corresponded to their frequency and timestamp, however there wasan issue with that format as they were not sequential and PRESTO did not accept fileswith a gap in time. This gap in time was a result of the way the data was written duringobserving.

The solution was to delete a small amount of the data to align them so they could be putinto the pipeline, the amount of data to be deleted was up to 24 microseconds (2.4 x 10−5

s). This aligned the files as needed and then they were merged using ‘filmerge’ to create4 larger .fil files each corresponding to the timestamp of the data, and which represent aquarter of the data. They were named from their respective timestamps: 041248, 044503,051622, 054741. These files cover the whole frequency range of the observation. Thesecould then be put through the pipeline.

2.8 Radio Frequency Interference Masking

Removal of RFI from the data was done using the routine ‘rfifind’ within PRESTO (Ran-som, 2018). This searches the dataset for interference in both the frequency and timedomains. It analyses each channel throughout the dataset for short time intervals andconsiders 1 second long blocks of data in each frequency channel separately. Time do-main statistics are computed: mean of block data and standard deviation of the values(Lorimer & Kramer, 2005; Ransom, 2018). Then blocks where the value of one or more aresufficiently far from the mean value are marked as RFI. The standard deviation cut-offvalue is 4σ, if a signal is found at this cut-off value it is flagged.

The data were then masked based on the marked RFI. The blocks that are masked haveconstant data added that is chosen based on the median bandpass. Where channels are≥ 30% corrupted by the RFI they are masked completely. The RFI mask outputted by‘rfifind’ can be seen in Figure 2.4 (Ransom, 2018).


FIGURE 2.4: RFI mask output plot from ‘rfifind’ for the J0212.1+5320dataset. This output plot shows the RFI that has been found in the dataand will mask it. It shows the profile of the RFI in the upper left, specificsof the mask in the upper right and the mask data plotted in lower section- channel on the lower x-axis, time in seconds on the y-axis and showsfrequency along the upper x-axis. The far left section shows max power,middle left is data sigma, middle right is data mean and far right is all ofthem plotted together. Image created using PRESTO: Ransom (2018)

2.9 Incoherent Dedispersion

After ‘rfifind’ the data needs to be incoherently dedispersed by creating subbands, inco-herent dedispersion is discussed in Section 2.9. To summarise - this technique increasesthe computational efficiency, as the subbands are corrected rather than individual chan-nels. The full bandwidth is split into larger chunks (subbands) and these are shifted tocorrect for dispersion, the amount of delay needs to result in the subbands aligning ap-propriately (Lorimer & Kramer, 2005). This technique does not correct for dispersiondelay inherent in each subband.

The PRESTO routine ‘prepsubband’ is used for incoherent dedispersion (Ransom, 2018).It uses the parameters given within the dedispersion plan to dedisperse and then pad thedata into time series over a range of trial DMs which are defined within the dedispersionplan (Ransom, 2018). The dedispersion plan is discussed in Section 2.6. This stage of theanalysis results in the subbanded data.

2.10. Fast Fourier Transform 53

This part of the data analysis can also barycentre the data if needed. However, if barycen-tering is not conducted this can be accounted for within the ‘prepfold‘ stage of the anal-ysis.

2.10 Fast Fourier Transform

A Fast Fourier Transform (FFT) is an algorithm that is used to compute the DiscreteFourier Transform (DFT) of the time series. The next step after ‘rfifind’ and ‘prepsub-band’ is to use the ‘realfft’ routine. This results in summed dedispersed subbands of thetime series, which can then be searched for periodic signals (Ransom, 2018). UtilisingFourier transforms for searching is discussed in Section 2.2.3. This stage, therefore, re-sults in Fourier transformed data which can then be searched.

As discussed in Section 2.2.3 FFT results in reduced computation time as it requires onlyNlog2N operations for a series of N-samples (Lorimer & Kramer, 2005).

2.11 Acceleration Search

Acceleration searching is done using the routine ‘accelsearch’ in PRESTO. It searches thetime series for periodic signals by taking the number of harmonics to sum and the high-est Fourier frequency derivative, the results are then used to optimise candidate selec-tion (Ransom et al., 2002). The acceleration search was introduced in Section 2.2.4, thespecifics for this work are detailed here. When searching for pulsar binary systems, likethe target system of this project, a non zero value for the acceleration search is needed.As the precise value is an unknown, a range of accelerations will be searched (Lorimer &Kramer, 2005).

Here we describe how the acceleration search can be estimated as constant if the obser-vation spans a fraction (∼ 10%) of the orbit. We also relate it to the physical parametersof the system and determine the range of acceleration to be searched using PRESTO.

The phase (φ) of the system is,

φ = fspin tPSR, (2.8)

where fspin is the spin frequency and tPSR is the time of emission at the pulsar.

The centre of the observation (t0) is,

t0 = tPSR +d(t0)

c, (2.9)


where d(t) is the travel time for light from the pulsar for a photon that is emitted at timetPSR,

tPSR = t0 −d(t0)

c. (2.10)

Therefore,

φ = fspin

(t0 −

d (t0)

c

), (2.11)

φ = fspin

(t0 −

asinic

sin(

2π(t− tASC)

PB

)). (2.12)

A Taylor Series can be used to approximate:

f (x) '∞

∑n=0

f n(a)n!

(x− a)n, (2.13)

sin(x)→ a = 0, (2.14)

ddx

sin(x) = cos(x). (2.15)

The Taylor series approximation to sin(x) around x = a is,

sin(x) ' sin(a) + cos(a)(x− a)− sin(a)2

(x− a)2 + ... (2.16)

Therefore the phase φ(t) is,

φ(t) = fspin

(t0 −

asinic

[sin(2π(t0 − tASC)

PB

)+

2π

PBcos(2π(t0 − tASC)

PB

)(t− t0)

− 2π2

P2B

sin(2π(t0 − tASC)

PB

)(t− t0)

2])

.

(2.17)

Therefore, the phase of a pulsar with a constant rate of spin-down is,

φ(t) = f 1t0 +f2(t− t0)

2, (2.18)

comparing coefficients between equation 2.17 and equation 2.18 gives the following:f2 = fspin

asinic A.

2.11. Acceleration Search 55

Therefore,

f = fspin ·asini

c· 4π2

P2B· sin

(2π(t0 − tASC)

PB

), (2.19)

where f is the spin down. This indicates that over a small time interval a binary pulsarappears to spin-down at a constant rate.

asini =k2PB

2πq, (2.20)

where q = mass ratio which is MPSRMcomp

.

The Fourier spacing, that is the interval between adjacent frequency bins produced bythe FFT, for an observation of length TOBS is,

TOBS → ∆ f =1

TOBS, (2.21)

The acceleration parameter z is,

z =f TOBS

∆ f' f T2

OBS. (2.22)

The acceleration parameter, z, is the number of Fourier bins in which the signal is smeareddue to acceleration.

The estimation that the acceleration is assumed to be constant has been justified. Thenumber of bins (acceleration parameter) that is required by PRESTO has been related tophysical quantities, we will now attempt to use expected constraints on the system inorder to determine the range of z to be searched.

Starting with the mass ratio, q, was estimated using the values from Li et al. (2016);Linares et al. (2016); Shahbaz et al. (2017) which gave a range of masses for both thepulsar and companion of: MPSR ∼ [1.4, 2.0] M and MCOMP ∼ [0.3, 0.77] M. Therefore,by combining them we obtain a mass ratio in the range q ∼ [1.82, 6.67].

The period is quoted by Shahbaz et al. (2017) as PB = 0.86955 ± 0.00015 d.The radial velocity semi-amplitude, K2, is quoted by Shahbaz et al. (2017) as K2 = 214.1 ±5 kms−1.

Using equation 2.20 a range for asinic can be obtained ∼ [1.25, 4.81] s.

Then using equation 2.19 a range for f can be calculated using a range of fspin of 100 to800 Hz, as this covers the range of values for known MSPs. Therefore, f ∼ [2.696 x 10−8

s s−1, 1.268 x 10−5 s s−1].


Finally, utilising the range of parameters stated above and using equation 2.22, a mini-mum and maximum value for z can be calculated giving the acceleration search range.Where z is the highest harmonic in the search that can drift linearly within the powerspectrum due to the binary orbital motion (Ransom, 2001).

The time required to conduct the acceleration search increases by a factor of 2 witheach additional level added to the acceleration search - linearly proportional to zmax.This needs careful consideration when planning the acceleration search ranges (Ransom,2001). Equation 2.22 gives zmin = 1.4 and zmax = 658.6. However, the PRESTO documen-tation states that a zmax of over 200 is usually not necessary for an acceleration search, asbeyond that value acceleration that is non-linear begins to appear which is not wanted(Ransom, 2018). This recommended upper limit of zmax has also been used within otherpulsar radio searches such as Camilo et al. (2015) and Andersen & Ransom (2018).

Therefore, to be certain that an effective range is searched and taking into account theincrease in time by a factor of 2, considering the range of fspin used within the accel-eration search calculations (100 to 800 Hz) and the advised limit of zmax, rounding toa range of zmin = 0 and zmax = 300 is an acceptable z range considering the values thatwere calculated. This will sufficiently search an acceleration range for the expected spinfrequencies.

2.12 Harmonic Summing

To establish the significance of a candidate signal one or more metrics are useful. Thesemetrics typically test the significance of the signal against the null hypothesis assumingthe noise statistics should be normally distributed. Two metrics are produced by PRESTOthese are the signal-to-noise ratio and chi-squared.

The power of a pulsar is spread across multiple peaks or harmonics within the Fourierspectrum, therefore, to increase sensitivity to a pulsar the power from all harmonicsshould be summed. The pulse profile shape dictates the number of harmonics whichscale as, NHARM ≈ P

W , P is the period and W the width of the profile (Lorimer & Kramer,2005).

Harmonic summing is performed on each Fourier series that is produced for each DM,this increases the S/N. The harmonic signal is directly added and the noise increases by√

2, this results in an increase in the S/N (Lorimer & Kramer, 2005). The specifics ofharmonic summing used in this work is detailed in Section 2.12 and Table 2.3.

2.13. Signal-to-Noise Ratio and Chi-Square 57

2.13 Signal-to-Noise Ratio and Chi-Square

The signal-to-noise ratio is commonly used to determine the significance of a pulse. Asmentioned in Section 2.12 this is the first significance metric that PRESTO produces whichis defined as,

S/N =1

σp√

Weq

nbins

∑i=1

(pi − p), (2.23)

where Weq is the width in bins of a top-hat function that has an equivalent area and peakas the pulse that is observed (Lorimer & Kramer, 2005).The confidence level of the detection is denoted by σ and is the uncertainty within thedata points. It is given by,

σ2 =1

nbins − 1

nbins−1

∑i=0

(pi − p)2. (2.24)

A signal can also be harmonically summed to increase the strength of the pulse and there-fore detection. Pulse significance can also be analysed by its deviation from Gaussiannoise with a mean, p, and variance σ2

p . This chi-squared test is the second significancemetric that PRESTO produces and was initially developed to analyse X-ray data by Leahyet al. (1983),

χ2 =1σ2

p

nbins

∑i=1

(pi − p)2. (2.25)

where for this model nbins - 1 degrees of freedom.

Standard deviation was used within PRESTO for RFI masking within the ‘rfifind‘ routineas explained in Section 2.8 and when sifting the candidates using ‘ACCEL_search.py’after analysis was complete as explained in Section 2.17. A chi-squared test was usedwithin PRESTO when plotting the reduced χ2 sections seen in the prepfold plots withinchapter 3. The time domain plot, DM plot, period and period derivative plots andthe colour plot section of the prepfold plots seen in Section 3.1 have a χ2 plot section.P(noise) is also quantified within the prepfold plots and is the probability of obtaininga chi-squared value for a random pulse profile. The statistical significance of a signal isrepresented by σ. The prepfold plots are described in Section 2.15.

2.14 Candidate Optimisation

The result from the acceleration search is a list of acceleration candidates for each trialDM that contain any significant peaks within the time series. These can then be searchedfor the best candidates based on their harmonics, period, power and to determine if it isRFI or a detection (Lorimer & Kramer, 2005).


One of the first steps is to reject any signals that could not be a millisecond pulsar, P <

0.5 ms. After that, signals can be grouped based on their periods. In those that haveduplicate period values but at different DM values, the one that is less significant can beexcluded.

If signals are found that do not occur at multiple DM values they can be excluded, aswell as any detected at too low DM values and those that are not found consecutively. Apulsar detection would be found consistently across multiple DM values. Once a list ofthe best candidates has been created, the detected signals can be folded to then be furtheranalysed (Lorimer & Kramer, 2005).

2.15 Prepfold Analysis

Once a list of the candidate detections is created they can be folded. Adding or foldingpotential pulsar detection signals is important, as pulsars are generally fairly weak radiosources and this allows them to be visible even with the background noise (Lorimer &Kramer, 2005).

Folding is conducted using the PRESTO routine ‘prepfold’, which conducts a search overthe signals period, period derivative and DM value resulting in the maximum signifi-cance for the detection (Ransom, 2018).

As noted in Section 2.9 if barycentering is not conducted during the incoherent dedis-persion and subbanding stage of the analysis it can be accounted for by adding ‘-topo‘to the prepfold command. This folds the data topocentrically (not barycentred). Thisalso results in the prepfold plots not having the celestial co-ordinates of the system be-ing studied (the prepfold plots will show 0’s for the system’s RA and Dec). An example‘prepfold’ plot from the PRESTO tutorial can be seen in Fig. 2.5.

The prepfold plot shows: integrated pulse profile, time domain plot, frequency and sub-band plot, dispersion measure, period and period derivatives, period and period deriva-tives combined (colour plot). The header information portion also shows informationand parameter values of the signal such as: telescope, celestial co-ordinates of target,period, period derivative, dispersion measure and significance (in sigma). The exam-ple shown in Fig. 2.5 has a high significance at 63.1σ. The following subsections detaileach component of the prepfold diagnostic plot and the expected features that separatesa likely pulsar detection from noise and RFI.

2.15. Prepfold Analysis 59

FIGURE 2.5: An example of a prepfold output plot from the PRESTO tuto-rial showing a pulsar detection for PSR 1643-1224 from Green Bank Tele-scope data. Each section of the plot is labelled in red: integrated pulseprofile upper left, header information upper right, time domain plot farlower left, subband plot centre, DM plot lower centre, period and periodderivative centre far right and colour plot lower far right. Original imagecredit: Ransom (2018)

2.15.1 Subintegration

The time domain or subintegration portion of the prepfold plot shows the signal strengthat a certain point in the timeseries. This is used to plot the time domain section whichrepresents the average emission of the pulsar as a function of its phase. Every point orbin is shaded in greyscale, white signifies no signal and the darker the colour the strongerthe signal (Ransom, 2018). Plotted on the x-axis is the phase of the system up to a phaseof 2 so two full rotations, and the y-axis is time in seconds.

2.15.2 Pulse Profile

The pulse profile portion of the prepfold plot shows the signal power. This representsthe integration of the results of the time domain plot. If the plot is of a real pulsar signalthen the peak represents when the pulsar’s beam is pointing at the observer (Lorimer &Kramer, 2005). Sharp peaks indicate a higher probability of detection, whereas no sharppeaks could indicate RFI.


2.15.3 Subbands

The subband portion of the plot shows the signal strength across the frequency range bysubband (Ransom, 2018). Similar to the subintegration plot darker colours represent astronger signal. The x-axis plots phase, left part of the y-axis is subbands and right partof the y-axis is the frequency range. Darker lines indicate a stronger signal and shouldcorrelate with those seen in the time domain plot.

2.15.4 Dispersion Measure

The dispersion measure portion shows the dispersion measure on the x-axis in pc cm−3

and reduced chi-squared (χ2) on the y-axis. The χ2 is the statistical goodness of fit ofa model to the observation and indicates how well the dedispersion is at a specific DMvalue (Leahy et al., 1983). This plot shows which DM value is best for dedispersing thedata (the one that corresponds to the peak). The better the dedispersion is, the higher theχ2 value. If the peak is at DM = 0 pc cm−3 then it is most likely RFI.

2.15.5 Period and Period Derivative

The period and period derivative section plots a combination of data.The first plot shows the period and how well constrained it is, and the period derivative,P, shows the change in acceleration of the measured period. As the target system is abinary pulsar candidate if there is a detection it would be expected to fluctuate as a resultof the binary motion (Lorimer & Kramer, 2005).

The final section of the period and period derivative plot shows a combination of theprevious two plots. It is a colour plot representing the χ2 value where red represents astrong signal. If a single fairly well defined region of red is seen in the plot, it indicates apossibly pulsar detection.

2.16 Candidate Selection

Alongside the plot output from ‘prepfold’ there are other methods to analysing pulsarsignal candidates. For example, candidates that are found to peak at a DM of 0 pc cm−3

have not experienced any refraction from dispersion and therefore are most likely to beRFI. Checking the time domain and subband plots for dark vertical tracks is a strongindicator that a pulsar has been detected. The reduced χ2 vs DM plot should have aGaussian-like peak. The values of period, period-derivative and spin frequency are alsogood indicators. If these parameters of the signal are not within the ranges discussed inSection 2.1 then it is likely not a pulsar detection.

Checking candidates with the method described assists in searching through all the po-tential detections, finding the most optimal candidates for further analysis and thereforemaximises the chances of finding a real pulsar signal.

2.17. Candidate Sifting 61

2.17 Candidate Sifting

Candidate sifting is important to analyse the large amount of candidates and becausemany candidates will appear across the data multiple times, usually they are harmoni-cally related. It also allows a threshold for the parameters to be applied. This is doneusing a routine called ‘ACCEL_search.py’, which is used to analyse candidates and rejectthose which are not a pulsar detection e.g. duplicate candidates or ones that have issueswith the DM (Ransom, 2018). The specific parameters that the sift routine uses are givenby the user.

The specifics of the parameters used for this project are given in Table 2.3.

Parameter Parameter ValueNumber of Harmonics 16Minimum DM value 2 pc cm−3

Minimum sigma value 4.0 σMinimum coherent power 100.0Candidate proximity (in Fourier bins) 1.1Shortest period value 0.0005 sLongest period value 15.0 sHarmonic power cutoff 8.0

TABLE 2.3: Table of the candidate sifting parameters showing: the numberof harmonics, minimum sigma value, minimum DM and coherent power,candidate proximity in Fourier bins (this indicates if it is the same can-didate), shortest and longest period values and the harmonic power cutoffused for the candidate sifting. These values are user defined and are inputswithin the sifting routine used.

The sifting routine creates a text file with the potential candidates listed. This includes thecandidate’s DM, S/N, harmonics summed, sigma and period (Ransom, 2018). After thecreation of the text file from the sifting routine the potential pulsar detection candidatescan be folded using the ACCEL files and the subband files. Their resulting prepfold plotscan then be inspected and analysed.

62

Chapter 3

Results and Discussion

This section is focused on the results and discussion of our analysis and presentsthe prepfold output after dedispersion, FFT, acceleration searches and candidateselection. The sifting routine resulted in several hundred candidates per quarterto be plotted as well as several hundred from the whole dataset analysis. Themost significant of those are presented in this chapter and those that are less sig-nificant presented in Appendix A.

The analysis resulted in a large number of candidates - the first quarter (041248)had 57,874 which was sifted to 106, the second quarter (044503) had 67,213 whichwas sifted to 110, the third quarter (051622) had 80,094 which was sifted to 120,the fourth quarter (054741) had 98,952 which was sifted to 145 and finally thewhole dataset analysis had 163,997 which was sifted to 341 candidates. Scatterplots of the number of candidates can be seen in Fig. 3.1 and Fig. 3.2, where thedata points size are proportional to S/N. There were several candidates that weremore significant and therefore analysed in depth utilising the diagnostic prepfoldplots. The result of the analysis of these diagnostic plots was that there was noconfirmable radio pulsar detections found.

Chapter 3. Results and Discussion 63

FIGURE 3.1: Scatter plot showing the number of candidates from the indi-vidual quarters after sifting plotted by DM (pc cm−3) vs period (ms). Thedata points size are proportional to S/N and coloured to represent whichquarter of the data they were found in. The first quarter (041248) is blueand has 106 candidates, the second quarter (044503) is red and has 110 can-didates, the third quarter (051622) is green and has 120 candidates and thefourth quarter (054741) is orange and has 145 candidates. The total num-ber of candidates from all quarters is 481. This plot aided in visualising thenumber of candidates and to seek out candidates that are possibly signifi-cant as candidates that occur in more than one quarter could be potentialdetections.

64 Chapter 3. Results and Discussion

FIGURE 3.2: Scatter plot showing the number of candidates from the wholedataset analysis after sifting plotted by DM (pc cm−3) vs period (ms). Thedata points size are proportional to S/N. The number of candidates fromthe whole dataset analysis was 341. This plot aided in visualising the num-ber of candidates and in analysing potential significant candidates. As theDM and period range of the target system have been estimated the candi-dates that plot within the expected area could be potential detections.

3.1. Prepfold Results 65

3.1 Prepfold Results

The results from candidate selection and prepfold should indicate whether a pulsar haslikely been detected. The prepfold plot will be used to analyse any potential pulsar sig-nal detection, and will be used to ascertain whether further analysis is justified. Of theseveral hundred candidates mentioned at the beginning of the chapter there are severalwhich were noteworthy (∼10 to 20 per quarter) and the few of those that were significantenough to justify further analysis are presented in this chapter. An example of a pulsardetection in a prepfold plot can be seen in Fig. 3.3, which shows the discovery plot forPSR J2214+3000 (Ransom et al., 2011; Ransom, 2018). This plot is a useful comparison asit shows a different pulsar detection to that seen in Fig. 2.5. Further prepfold plots arepresented in Appendix A.

FIGURE 3.3: An example of the output plot of prepfold of a pulsar dis-covery. Showing the pulse profile in upper left, header information upperright, time domain plot far lower left, subband plot upper middle, DM plotlower middle, period and period derivative plots far right and the colourplot lower right. This is the discovery plot for PSR J2214+3000 taken withthe Green Bank Telescope. It shows what a pulsar detection might look like- strong prominent peaks within the pulse profile, darker vertical trackswithin the time domain and subband plots, a Gaussian-like peak at a non-zero DM value in the reduced χ2 vs DM plot, peaks in the period andperiod derivative plots and a point like source in the colour plot. Imagecredit: Ransom (2018)


3.1.1 Prepfold - RFI

Figure 3.4 shows a result prepfold plot from the analysis of the first quarter (041248) ofdata that could be mis-identified as a pulsar. In this example the summed signal profileand the time domain plot are consistent with a pulsar signal. However, the DM plot(reduced χ2 vs DM) peaks at a DM of 0 pc cm−3, indicating that it originated from Earthand the subband plot indicates it occurred only across a few frequency bins and thereforeis RFI. Even though the analysis and prepfold results indicate that this could be a pulsarsignal, careful analysis of the plot is required to confirm the nature and origin of thesignal. It should be noted that the RA and Dec of the system are 0’s; this is a result offolding topocentrically as discussed in Section 2.15.

FIGURE 3.4: A prepfold plot of RFI from the first quarter (041248) of thedataset. This is a result prepfold from the initial analysis and was chosenas it has pulsar like characteristics. At first glance this is a very promisingpulsar candidate, the pulse profile and time domain plots could indicatea pulsar detection. However, the subband and DM plots show that it isRFI. The subband plot shows that the signal only occurred across a fewfrequency bins, and the DM plot shows that it peaks at a DM value of 0 pccm−3, meaning that the signal has experienced no dispersion and thereforeoriginated from Earth. Also note that the RA and Dec of the system are 0’s;this is a result of folding topocentrically as discussed in Section 2.15.


3.1.2 Pulsar Candidates

This section will focus on presenting the result prepfold plots of potential pulsar detec-tions from the data analysis. This section will start with the initial analysis of each quarterof the data. Each candidate has been given a simple designation such as ’Candidate 1’.

Candidate 1

FIGURE 3.5: A prepfold plot of a potential pulsar candidate in the secondquarter of the dataset (044503) given the designation Candidate 1. Thiscandidate is at DM = 21.605 pc cm−3. The time domain plot shows slightlydarker vertical lines at φ ∼ 0.5 and 1.5, the subband plot also shows slightlydarker vertical tracks. The period of∼ 1.63 ms and spin frequency of∼ 614Hz are consistent with a millisecond pulsar. The DM plot does not peak at0 pc cm−3. All of this indicates a potential pulsar detection, although thisplot is not definitive as the signal significance is not high at 5.4σ.


This promising candidate seen in Fig. 3.5 is a potential pulsar detection which has beengiven the designation ’Candidate 1’ whose parameters are what would be expected -peaks in the pulse profile, darker vertical tracks in the time domain and subband plots,the DM plot does not peak at 0 (DM = 21.605 pc cm−3), peaks in the period and periodderivative plots, structure within the colour plot, a period of ∼1.63 ms, spin frequencyof ∼614 Hz, a P that is negative and within the expected range (P = -2.663 ×10−12 s/s).Although the significance is low at 5.4σ.

FIGURE 3.6: A prepfold plot showing Candidate 1 refolded with the orig-inal .fil file rather than the subbanded files used within the search. As the.fil file is not subbanded the level of smearing within the folded plot islower as more channels are available for the dedispersion and should im-prove the significance of a pulsar detection. However, the significance inthis plot has decreased from 5.4 to 3σ. Some of the features in the timeplot have become more localised (darker horizontal lines at∼200 s, ∼600 sand ∼1300 s) and therefore RFI is most likely the underlying cause of thiscandidate.

The significance is not that high but the parameters and features seen within the prepfoldplot justify further analysis, therefore this candidate was re-folded using the filterbank(.fil) file rather than the dedispersed subband file, as a pulsar detection should becomemore significant as smearing from subbanding is not present in the .fil file which containsthe original channels post-dedispersion (the .fil file is not subbanded which is explained


in sections 2.2.2 and 2.7).

Fig. 3.6 shows Candidate 1 but refolded with the .fil file rather than the subband file.The original channels of the .fil file have allowed features within the frequency and timedomain to be resolved. These were likely random fluctuations. The significance hasdecreased to 3.0σ and darker horizontal lines have become more pronounced in both thetime domain and subband plots indicating this is most likely RFI.

Candidate 2

The candidate plot seen in Fig. 3.7 is a potential pulsar detection which has been giventhe designation ’Candidate 2’.

FIGURE 3.7: A prepfold plot showing a promising candidate from the 4thquarter of the data (054741) given the designation Candidate 2. There areclear peaks in the pulse profile, darker vertical lines in the time domainplot as well as the subband plot, the DM peaks at DM = 25.445 pc cm−3,the spin period is ∼ 2.23 ms and spin frequency is ∼ 448 Hz. These are allconsistent with a millisecond pulsar. The significance, however, is low atonly 4.9σ.


Fig. 3.7 shows a promising pulsar candidate whose parameters fit with a pulsar detection(discussed in Section 2.1) - a period of ∼2.23 ms, a P that is negative (as discussed in Sec-tion 2.1) and close to the expected range, a spin frequency of ∼448 Hz, clear peaks in thepulse profile plot, darker tracks in both the time domain and subband plots (at φ ∼0.8and 1.8), the DM plot peaks at DM = 25.445 pc cm−3 and there are peaks in the period andperiod derivative plots. The colour plot structure is not that prominent and the signifi-cance is only 4.9σ. However, the parameters and characteristics of this candidate justifyfurther analysis.

FIGURE 3.8: A prepfold plot showing Candidate 2 which was refolded us-ing the .fil file. As mentioned previously a pulsar detection should becomemore significant when refolded with the .fil file. The significance decreasedfrom the original plot seen in Figure 3.7 to 2.9σ. However, this plot alsoshows darker vertical lines within the time domain plot and the subbandplot that corresponds to the peaks in the pulse profile.

Fig. 3.8 shows Candidate 2 refolded using the filterbank (.fil) file. As with the previouscandidate refolding with the .fil file should result in the signal becoming more signifi-cant. Fig. 3.8 shows that the darker vertical tracks in the time domain and subband plotsare still present as are the peaks in the DM plot and the period and period derivativeplots. However, the significance has decreased from 4.9σ as seen in Fig. 3.7 to 2.9σ seenin Fig. 3.8. However, this plot still retains some pulsar-like features although the signifi-cance is quite low some further investigation is required to be thorough in our analysis


and results.

FIGURE 3.9: A prepfold plot showing Candidate 2 but re-folded usingspecified parameters of period, period derivative, DM, the number of binsin the profile (32) and the number of sub-integrations in the search (32).These parameters were chosen in an attempt to further constrain and viewthe candidate signal to try and reveal if this is a pulsar detection. However,the significance has decreased to 3.6σ.

Therefore, Candidate 2 was refolded with parameters that allow a different view of thesignal - the number of bins in the profile as 32 (previously 64), and the number of sub-integrations in the search as 32, this can be seen in Fig. 3.9. These parameters werechanged to further constrain and view this signal in an attempt to discern if it was apulsar detection. This aided in the analysis of this signal by allowing a different view tothat in Fig. 3.7.

The view of Candidate 2 seen in Fig. 3.9 is also pulsar-like in nature, with the darkertracks in the time domain and subband plots still visible and a prominent peak in theDM plot at DM = 25.445 pc cm−3. However, the significance of the signal has decreasedto 3.6σ.


FIGURE 3.10: A prepfold plot showing Candidate 2 which was refoldedusing the subband file from the previous quarter of the dataset (from051622). It shows no features that suggest it is a pulsar detection - there areno prominent peaks against the noise in the pulse profile plot, the time do-main and subband plots lack the vertical tracks that would be expected andthere is a dark horizontal line in the time domain plot (∼1400 s), the DM,period and period derivative plots have no prominent peaks, the colourplot lacks structure and the significance is 0σ.

Fig. 3.10 shows Candidate 2 refolded with the subband data from the previous quarter(051622) to see if the signal is still present. Fig. 3.10 shows no features that indicate a pul-sar detection, no darker tracks in the time domain or subband plot, no prominent peaksin the DM plot or period and period derivative plots, no obvious structure in the colourplot and the significance has decreased to a small enough value to be estimated withinthe plot as 0σ. However, as this is a binary system and could have a transient naturefurther analysis is justified to be certain a pulsar detection has not been overlooked.

Therefore, further analysis of Candidate 2 was required and this involved creating sub-band data focused on a narrow DM range centred on the DM value of this candidate(DM = 25.445 pc cm−3) utilising the whole dataset rather than a single quarter of thedata. Utilising the whole dataset in this manner should not only increase the significanceof a pulsar detection but also reveal any transient nature of the signal.


FIGURE 3.11: A prepfold plot showing Candidate 2 which was refoldedusing subband data from the whole dataset over a narrow range of DMvalues. The candidate’s DM = 25.445 pc cm−3 so subband data over a rangeof DM values of 25 to 26 pc cm−3 was used. As this plot utilises subbanddata from the whole dataset it would reveal a pulsar detection and showif it has a transient nature. This plot lacks a prominent peak in the pulseprofile, no tracks can be seen in the time domain or subband plots, the DMplot exhibits not prominent peak, the period and period derivative plotsalso lack prominent peaks and the colour plot lacks the expected structure.The significance has also decreased to 0σ.

Fig. 3.11 shows Candidate 2 refolded with the subband data of the whole dataset over anarrow range of DM values of 25 to 26 pc cm−3. Fig. 3.11 lacks a prominent peak in thepulse profile, there are no vertical tracks in the time domain or subband plots, the DMplot lacks a prominent peak, the period and period derivative plots also lack prominentpeaks, there is no structure seen in the colour plot and the significance has decreased toa value small enough that it is estimated as 0σ. Fig. 3.11 shows no features that indicate apulsar detection is present. Therefore, it is highly likely that Candidate 2 is RFI.


Candidate 3

This section will now be focused on presenting the candidates from the whole datasetanalysis. These are the result prepfolds from the analysis of the whole dataset utilisingthe whole integration time.

Fig. 3.12 shows a result prepfold of a potential pulsar detection from the whole datasetanalysis which has been given the designation ’Candidate 3’.

FIGURE 3.12: A prepfold plot of a potential pulsar detection from thewhole dataset analysis given the designation Candidate 3. It has a periodof ∼1.42 ms and a spin frequency of ∼704 Hz. It has peaks in the pulseprofile. Vertical tracks in the time domain plot that corresponds to thepeaks in the pulse profile (at phase φ ∼7 and 1.7). Vertical tracks are alsopresent in the subband plot although they are difficult to discern. Thereare clear peaks in the DM (at DM = 18.519 pc cm−3) and period and pe-riod derivative plots, and there is some structure visible in the colour plot.However, the P value is positive, as discussed in Section 2.1 it is expectedto be negative, and the significance is not that high at 5.0σ.


Fig. 3.12 does exhibit some pulsar characteristics consistent with the parameters expected- period of∼1.42ms, spin frequency of∼704 Hz, DM = 18.519 pc cm−3, peaks in the pulseprofile, DM and period and period derivative plots. Vertical tracks in the time domainand subband plots are also present. Despite the low significance and positive P value(1.325 × 10−13 s/s) this candidate does exhibit some pulsar characteristics. Therefore,further analysis to be thorough and certain that a pulsar detection has not been over-looked is justified.

Therefore, Candidate 3 was refolded utilising the .fil files for the whole dataset. As men-tioned with previous candidates refolding with the .fil file will result in the significanceincreasing if it is a pulsar detection.

FIGURE 3.13: A prepfold plot of Candidate 3 but refolded utilising the .filfiles. The peaks in the pulse profile, DM and period and period deriva-tive plots are still present, as are the vertical tracks in the time domainand subband plots. However, the significance of the signal has decreasedto 2.4σ. It should be noted that in the bottom left of the figure it states"J0212_041248.fil" despite this it has folded with all 4 .fil files from thedataset as seen from the length of the time domain plot, ∼7200 s is ∼2hrs.

Fig. 3.13 shows Candidate 3 refolded with the .fil file. The peaks in the pulse profile,


DM and period and period derivative plots are still present. The tracks in the time do-main and subband plots are also still present. However, the significance of the signal hasdecreased to 2.4σ indicating Candidate 3 is most likely RFI.

Candidate 4

Fig. 3.14 shows a potential pulsar detection candidate from the whole dataset analysiswhich has been given the designation ’Candidate 4’.

FIGURE 3.14: A prepfold plot of a potential pulsar detection from thewhole dataset analysis given the designation Candidate 4. It has a periodof∼1.90 ms, a spin frequency of∼527 Hz and DM = 24.378 pc cm−3. It hasprominent peaks in the pulse profile, darker vertical tracks in the time do-main and subband plots (at phase φ ∼0.9 and 1.9). The DM plot peaks atDM = 24.378 pc cm−3. There are prominent peaks in the period and periodderivative plots, and structure within the colour plot. However, as withthe previous candidate the P value is positive and the significance is quitelow at 4.5σ.

Candidate 4 seen in Fig. 3.14 does exhibit some characteristics that are consistent with apulsar detection. It has a period of ∼1.90 ms, a spin frequency of ∼ 527 Hz and DM =24.378 pc cm−3. There are clear peaks in the pulse profile, and darker tracks in the timedomain and subband plots at phase φ ∼0.9 and 1.9. Peaks are also visible in the DM,period and period derivative plots. There is also some structure seen within the colour


plot. However, the significance is quite low at 4.5σ and the P value is positive.

This candidate does exhibit characteristics that justify further analysis to be thorough inour results, and to ensure a pulsar detection has not been overlooked. Therefore, Candi-date 4 was refolded using the 4 .fil files. As with previous candidates this should resultin a higher significance if it is a pulsar detection.

FIGURE 3.15: A prepfold plot of Candidate 4 but refolded using the 4 .filfiles of the whole dataset. The signal has retained the peaks seen in thepulse profile, although they are slightly less prominent. The darker tracksin the time domain and subband plots are still present (at phase φ ∼0.9and 1.9). The peaks in the DM, period and period derivative plots arealso still present, as is the structure seen in the colour plot. However, thesignificance has decreased from 4.5σ to 3.6σ.

Fig. 3.15 shows Candidate 4 refolded with the 4 .fil files. It still retains some of the pulsar-like features - peaks in the time domain plot, somewhat visible darker tracks in the timedomain and subband plots (at phase φ ∼0.9 and 1.9), peaks in the DM, period and periodderivative plots and structure within the colour plot. However, the significance of thesignal has decreased from 4.5σ to 3.6σ, indicating this is most likely RFI.


3.2 Discussion

Potential pulsar detections can be seen in Section 3.1.2. Candidate 1 is a promising can-didate seen in Fig. 3.5. However, when Candidate 1 was re-folded using the .fil file itshowed no obvious features within the plot and the significance decreased from 5.4 to3.0σ. A pulsar detection should become more significant when folding with the filter-bank (.fil) file as smearing from subbanding is not present. The filterbank files contain theoriginal channels post-dedispersion - they are not subbanded. This means that there aremore channels available for the dedispersion and therefore the smearing is lower. There-fore, this is unlikely to be a pulsar detection and most likely is RFI. The significance islow when compared with other candidates (as in they have similar sigma values) withinour search which suggests these fall into the lower end of statistical fluctuations.

A further potential pulsar detection is seen in Fig. 3.7 which shows Candidate 2, this plotshows clear darker vertical tracks in the time domain and subband plot, a DM plot thatdoes not peak at 0 pc cm−3 (DM of this candidate = 25.445 pc cm−3), a P that is negativeand a period of P = 2.23 ms. This is all consistent with the expected properties a redbackpulsar should have. However, when Candidate 2 was refolded using the subband datafrom the previous quarter of the data it showed no obvious features that would indicateit is a pulsar detection, this can be seen in Fig. 3.10.

However, taking into account that this is a binary system and the possible transient na-ture of a redback pulsar, Candidate 2 does appear pulsar like enough to justify furtheranalysis. Therefore, subband data were created from all 4 of the .fil files covering thewhole 2 hr integration time, this subband data covered a small limited range of DM val-ues. This range was 25 to 26 pc cm−3 as Candidate 2’s DM = 25.445 pc cm−3.

The period also had to be corrected before folding can occur as this is an acceleratedcandidate. The original period of Candidate 2 seen in Fig. 3.7 is from a single quarter ofthe data (4th quarter 054741) and the new subband data covers the whole 2 hr integrationtime. Therefore, P had to be accounted for. Where Pold is the old period value, P is thespin-down and Epochold is the Epoch value of the original candidate, these values can beseen in Fig. 3.7, and finally Epochnew is the new Epoch value of the candidate. ThereforePnew is,

Pnew = Pold + P× (Epochnew − Epochold), (3.1)

Pnew = 0.0022342774810679054 s.

Candidate 2 was then refolded using the corrected period value and the subband data.As this data covers the whole 2 hr integration time a pulsar detection would be visibleeven if it has a transient nature. Fig. 3.11 shows the resulting prepfold plot. This plotlacks a prominent peak in the pulse profile. The time domain and subband plots lack the

3.2. Discussion 79

dark vertical tracks that would be expected with a pulsar detection even if it was a tran-sient signal. The DM plot and the period and period derivative plots also lack prominentpeaks. The significance is also now a value small enough to be estimated as 0σ. Thisprepfold plot lacks any significant features that would indicate a pulsar detection. There-fore, Candidate 2 is most likely statistical fluctuations.

A secondary more sensitive analysis was also conducted that analysed the whole datasetacross the whole integration time rather than focusing on individual quarters. This analy-sis utilised the same techniques and dedispersion plan as the initial analysis, as describedin Section 2.6 and seen in Fig. 2.3. The resulting candidates after analysis of the data weresifted using the same sifting routine and then folded using prepfold in PRESTO.

There were some candidates from the more sensitive whole dataset analysis that exhib-ited characteristics that could be possible pulsar detections, these are Candidate 3 seenin Fig. 3.12 and Candidate 4 seen in Fig. 3.14. However, the significance of both thesecandidates is quite low at 5.0σ and 4.5σ respectively. These candidates also had positiveP values, which as discussed in Section 2.1 is not what is expected.

However, to be thorough in our analysis and ensure a potential pulsar detection is notoverlooked both of these candidates were refolded with all 4 of the .fil files from thedataset. As discussed previously if a candidate is refolded with the .fil files it shouldincrease the significance as the .fil files do not have smearing from subbanding the dataas the .fil files are not subbanded. These can be seen in Fig. 3.13 and Fig. 3.15. The sig-nificance of both of these candidates has decreased to 2.4σ and 3.6σ respectively. Thisindicates that both of these candidates are most likely statistical fluctuations.

The initial analysis was conducted on each quarter of the data individually as the datawere split into 4 quarters corresponding to the time stamps of the observation (041248,044503, 051622, 054741). A more sensitive analysis of the data across the whole integra-tion time rather than on individual quarters was also completed. The overall result ofour analyses was a non-detection of radio pulses from J0212+5320.

3.2.1 Non-detection of a Pulsar

The analysis of the data has shown that there is no confirmed radio detection of a pulsarwithin the dataset analysed for this work. The optical data and work presented by Liet al. (2016); Linares et al. (2016); Shahbaz et al. (2017) all reached a conclusion that it ishighly likely that J0212+5320 is a redback pulsar. Therefore, it is unlikely that there areno pulsations from J0212+5320, this is supported by γ-ray detections. There are severalexplanations as to why our analysis did not detect a radio pulsar signal.


It is possible that the configuration of this system is such that the radio emission regionis not beamed towards the observer resulting in our non-detection - refer to Fig. 1.2 andFig. 1.5 for a diagram of the emission region of a pulsar. If this is the case, that the radioemission is not beamed towards the observer, then detection of radio pulses from the tar-get system is not possible (Clark et al., 2018).

A possible scenario is that J0212+5320 is a radio-quiet gamma-ray pulsar (Lorimer &Kramer, 2005; Smith et al., 2017). These types of gamma-ray pulsars are known to beradio quiet such as J1826-1256 (Karpova et al., 2019) and J1932+1916 (Medvedev et al.,2019). Gamma-ray pulsars commonly have wider γ-ray beams than radio beams mean-ing that detecting γ-rays is a common feature but not necessarily γ-ray pulsations dueto the generally low γ-ray photon count (Watters & Romani, 2011; Caraveo, 2014). Ingeneral, gamma-ray pulsars cannot be detected in the same way that radio pulsars canusing a simple Fourier analysis of the data. The small number of photons required tointegrate data that span weeks or, usually, years in order to build enough sensitivity. Fora binary, this process involves removing effects of the orbital motion, which is a priorunknown and therefore requires a brute force search of the full parameter space, whichis not computationally feasible (Caraveo, 2014).

Therefore, if J0212+5320 is a gamma-ray pulsar then much more data will need to beacquired to confirm this potential scenario. It is also not unheard of for previously radio-quiet gamma-ray pulsars to eventually be detected in the radio, one such example isJ1732-3131 (Maan et al., 2017). However, the radio pulses detected from J1732-3131 re-quired extensive observation with the Ooty telescope, the detections reported in Maanet al. (2017) were at 327 MHz and with an integration time of ∼60 hr.

Another possibility is that the companion or ablation of the companion has resulted inany radio signals from J0212+5320 to be eclipsed, therefore resulting in our non-detection(Fruchter et al., 1988; Crawford et al., 2013; D’Amico et al., 2001). The presence of ionisedmaterial within the binary system that is larger than the Roche lobe of the companion isa possibility and could explain the non-detection as the system is being eclipsed due tothis (Zharikov et al., 2019). Eclipsing binary pulsar systems are not uncommon as statedin Gusinskaia et al. (2019). There is parochial evidence from a number of searches con-ducted by the Fermi pulsar consortium that some redback discoveries required multiplere-observations of a candidate due to extreme variability caused by eclipses.

A possible solution is for any future observations to be conducted at different phases tothe observations for the dataset analysed in this work. This could increase the chancesof a detection as it maximises the possibility that the observation would occur when thesystem is not eclipsing. A schematic of the binary geometry of J0212+5320 can be seenin Fig. 3.16. For example, the pulsar studied by Hessels et al. (2006) eclipses for a largepercentage & 70% of its orbit. Some eclipsing binary pulsars have also exhibited quite

3.2. Discussion 81

irregular eclipses (Nice et al., 2000; Possenti et al., 2003) and therefore reobserving thissystem might be essential.

FIGURE 3.16: Predicted projection of J0212+5320 on the sky assuming aninclination angle of 69 (Shahbaz et al., 2017). The schematic indicates theconfigurations of the system at 5 different phase positions. The black dotsrepresent the pulsar, blue circles the companion and the red dots markthe centre of the night-side of the companion star. The schematic doesnot account for gravitational distortion of the companion. The companionpasses closest to the observer at phase φ = 0.25 (inferior conjunction ofcompanion). Image created using work by Polzin (2019).

It is also a possibility that the pulsar’s flux density is less than the sensitivity of the searchresulting in it not being detectable. The sensitivity of our search and MSP flux densitiesare discussed and compared in sections 3.2.2 and 3.2.3.

Another possibility is that J0212+5320 could belong to a peculiar class of redback pul-sars known as transitional MSPs, where these systems can swing back and forth over thecourse of years or decades between a ‘low-mass X-ray binary’ (LMXB) state powered byaccretion and a ‘radio pulsar’ state powered by the pulsar’s rotation. There are only a fewredbacks where this change in state has been observed: PSR J1023+0038, XSS J12270-4859and PSR J1824-2452I (Archibald et al., 2009; Papitto et al., 2013; Bassa et al., 2014; Shahbazet al., 2019). In the LMXB state, pulsed radio emission is quenched by an accretion discwhich dominates the energy output of the system and makes it a brighter X-ray source.On the other hand, in the radio pulsar state the accretion disc disappears and radio pul-sations can be detected.


It could therefore be that our observations took place while J0212+5320 was experienc-ing such a state change, therefore making radio pulsations impossible to detect. We canexamine this option using available optical data as typical transitional MSPs brighten upby ∼1.5-2 mag in the LMXB state compared to the pulsar state (Bassa et al., 2014). Firstly,Li et al. (2016) concluded from spectroscopic observations that accretion was not takingplace at the time of acquiring their data in 2010 due to the absence of emission lines.Linares et al. (2016) also reached the same conclusion - their data was acquired in August2014, and in February and December 2015. We can also conclude that the system was ina pulsar state during the period July 2018 to February 2020 using weekly monitoring ob-servations acquired via my supervisors’ ERC team and their colleague at the Universityof Sheffield with the pt5m, a robotic 0.5 metre optical telescope located at the Roque delos Muchachos Observatory in La Palma (Dhillon et al., 2020).

Fig. 3.17 shows an optical light curve made with the pt5m data and folded at the orbitalperiod of the system. While some outlier points seem to stand out, a look at the unfoldedtime series (Fig. 3.18) shows that the outliers are not correlated in time and are most likelyspurious outputs from the automated pipeline, which is known to misbehave when theseeing is poor. Given that our radio observations were obtained in the gap between theobservations from Linares et al. (2016) and those from my supervisors, we cannot com-pletely exclude a state transition as the explanation for the lack of pulsations. However,given that the gap is only 18 months, it is extremely unlikely that the system would haveswitched back and forth between radio, LMXB and then radio state again.

3.2. Discussion 83

FIGURE 3.17: Optical light curve of J0212+5320 plotting r magnitudeagainst phase, folded at the orbital period (0.86955±0.00015 d). As seenin Li et al. (2016); Linares et al. (2016); Shahbaz et al. (2017) the light curveexhibits an orbital modulation with unequal maxima and minima. Thereare several outlying points that are most likely artefacts from weather orshort flares from the companion, this is supported by the unfolded opticallight curve seen in Fig. 3.18. This light curve does not exhibit any brighten-ing features that would be expected from a transition of state from a radiopulsar to a low-mass X-ray binary. Data credit: Dhillon et al. (2020).


FIGURE 3.18: Optical light curve of J0212+5320 plotting r magnitudeagainst MJD, this is an unfolded light curve. This unfolded light curveshows that the outlying points seen in Fig. 3.17 are most likely artefactsdue to weather or short flares and not events associated with a state transi-tion. This light curve does not exhibit any brightening features that wouldbe expected from a transition of state from a radio pulsar to a low-massX-ray binary. Data credit: Dhillon et al. (2020).

3.2. Discussion 85

3.2.2 Radio Search Sensitivity

The sensitivity of the search is important to understand how effective it has been, andcan be estimated using the radiometer equation (Lorimer & Kramer, 2005),

Smin =S/Nmin(Tsys + Tsky)

G√

2Bτint

√W

P−W, (3.2)

where Tsys is the system temperature of the L-band receiver of the Lovell telescope is25 K (Bassa et al., 2016), Tsky is the sky temperature and is estimated as Tsky = Ts0λ2.55

(Haslam et al., 1982), G is the gain of the telescope and is 1 K Jy−1 (Bassa et al., 2016), B isthe bandwidth of the observations of 384 MHz, τint is the integration time, W is the pulsewidth of 0.1 ms and P is the period of 1 ms which both had to be assumed.

Equation 3.2 can be used to estimate the sensitivity of the search by calculating the min-imum flux density that can be detected at a given signal to noise ratio. Using the valuesdetailed above and an integration time of one quarter of the observation, τint = 1861.4 s,the estimated sensitivity of the initial search is Smin = 0.20 mJy.

However, the sensitivity was improved by analysing and searching the whole datasettogether, using the full integration time τint = 7208.4 s the estimated sensitivity would beSmin = 0.10 mJy.

3.2.3 Flux Comparison with Millisecond Pulsars

Having estimated the sensitivity of the search in Section 3.2.2 using equation 3.2, wecan now compare the flux density Smin value and the radio pseudo-luminosity L1400 forour search with known flux density values for millisecond pulsars. The radio pseudo-luminosity L1400 allows a comparison that takes distance of the pulsar into account andtherefore is more indicative of flux density, as defined in equation 3.3.

The radio pseudo-luminosity L1400 is,

L1400 = S1400 × d2, (3.3)

where S1400 is the flux density at a frequency of 1400 MHz and d is the distance whichfor J0212+5320 is 1.1 ±0.2 kpc (Clark et al., 2018). Therefore, L1400 = 0.24 mJy kpc2 for theinitial analysis and L1400 = 0.12 mJy kpc2 for the whole dataset analysis.

A good example of comparisons using L1400 is for J0437-4715 which is the closest knownMSP at 0.16 kpc, which has an S1400 value of 150.2 mJy but an L1400 value of 3.69 mJykpc2. These pulsars were searched for using the ATNF Pulsar Catalogue (Hobbs et al.,2019) and were chosen as they are all millisecond pulsars with similar parameters to what


would be expected of the target system J0212+5320.

To further compare the radio pseudo-luminosity with other similar MSPs - J0023+0923has a period of 3.05 ms, S1400 = 0.48 mJy, distance = 1.11 kpc and L1400 = 0.59 mJy kpc2.Our search would therefore detect this pulsar. J0034-0534 is also a similar MSP to whatwould be expected of J0212+5320. J0034-0534 has a period of 1.88 ms, S1400 = 0.61 mJy,distance = 1.35 kpc and L1400 = 1.11 mJy kpc2. Our search would therefore also detect thispulsar.

This brief comparison of the flux densities of MSPs indicates that their flux are somewhatvariable. Most of these MSPs have fluxes above the sensitivity limit of our search andwould have been detected, however, a few are below our sensitivity limit. Therefore,the sensitivity of our search is good enough that it would detect the majority of MSPs,although there are a few that would not have been detected. This section is summarisedin Table 3.1.

3.3 Significance of Pulsar Detection

The previous work by Li et al. (2016); Linares et al. (2016); Shahbaz et al. (2017), as dis-cussed in Section 1.4, strongly suggest that J0212+5320 is a redback pulsar, and detectingpulsed emission would confirm this.

This system has quite a wide orbit at ∼ 21 hrs or 0.86955(15) d (Linares et al., 2016; Shah-baz et al., 2017), and there are not many spider pulsars with similarly wide orbits. Thusconfirming its existence would contribute to widening the parameter space within whichevolutionary models can form these systems.

The optical brightness of J0212+5320 is one of the highest known at r’ ' 14.3 mag dueto being comparatively close to us. This allows high precision measurements althoughthe parameters derived by Li et al. (2016) and Linares et al. (2016) are limited due touncertainties and degeneracies with the mass ratio of the system. These parameters couldbe well determined with an independent measurement of the pulsar’s orbital velocityfrom timing eventual pulsations. In turn, this would enable the mass to be measured tohigh precision.

3.3. Significance of Pulsar Detection 87

Nam

ePe

riod

(ms)

Orb

ital

Peri

od(d

)D

M(p

ccm−

3 )S 1

400

(mJy

)L 1

400

(mJy

kpc2 )

Dis

tanc

e(k

pc)

J002

3+09

233.

050.

1414

.30.

480.

591.

11J0

030+

0451

4.87

-4.

340.

60.

060.

32J0

034-

0534

1.88

1.59

13.7

0.61

1.11

1.35

J010

1-64

222.

571.

7911

.93

0.28

0.28

1.00

J021

8+42

322.

322.

0361

.25

0.9

8.93

3.15

J034

0+41

303.

3-

49.5

90.

310.

791.

60J0

437-

4715

5.76

5.74

2.64

150.

23.

690.

16J0

509+

0856

4.06

4.91

38.3

20.

80.

540.

82J0

557+

1551

2.56

4.85

102.

60.

050.

171.

83J0

610-

2100

3.86

0.29

60.6

70.

44.

253.

26J0

613-

0200

3.06

1.2

38.7

82.

251.

370.

78J0

645+

5158

8.86

-18

.25

0.29

0.45

1.25

J075

1+18

073.

480.

2630

.25

3.2

3.94

1.11

J101

2+53

075.

260.

69.

023.

21.

570.

70J1

024-

0719

5.16

-6.

482.

33.

421.

22J1

035-

6720

2.87

-84

.16

0.04

0.09

1.46

J104

8+23

394.

660.

2516

.65

0.17

50.

72.

00J1

101-

6424

5.11

9.61

207

0.27

1.27

2.17

J110

3-54

033.

39-

104

0.18

0.51

1.68

J112

5-58

253.

176

.412

4.8

0.86

2.60

1.74

J112

5-60

142.

638.

7553

.00.

050.

050.

99J1

216-

6410

3.53

4.04

47.4

0.05

0.06

1.10

J143

1-47

152.

00.

4559

.40.

731.

781.

56J1

723-

2837

1.86

0.62

19.7

1.1

0.95

0.93

J180

1-14

173.

63-

57.2

60.

170.

211.

10J2

241-

5236

2.19

0.15

11.4

11.

951.

800.

96J2

322-

2650

3.46

0.32

6.15

0.16

0.01

0.23

TAB

LE

3.1:

Tabl

esu

mm

aris

ing

Sect

ion

3.2.

3-

com

pari

son

ofkn

own

MSP

ssh

owin

gva

riou

spa

ram

eter

s,in

clud

ing

the

flux

dens

ity

valu

esan

dps

eudo

-lum

inos

ity

both

at14

00M

Hz.

88

Chapter 4

Conclusion

This section is focused on the conclusion of the work and discussing any futurestudies of this target system.

4.1 Conclusion and Future Study

In this project, radio data obtained by the 76 metre Lovell telescope on the redback pulsarcandidate J0212+5320 were searched for pulsed emission. The data is at a frequency of1.4 GHz (L-band) with a bandwidth of 512 MHz.

The data were searched and corrected for radio frequency interference, and then anal-ysed through a pipeline which was created by the primary supervisor and a previousstudent which utilises the pulsar searching software PRESTO (Sett, 2019; Ransom, 2001).The data were then coherently dedispersed followed by incoherent dedispersion, andsearched in a DM range of 12.5 to 37.5 pc cm−3 as the expected DM value of the systemis ∼ 25 pc cm−3 (Cordes & Lazio, 2002; Yao et al., 2017).

An acceleration search was conducted between acceleration parameter values of z = 0 to300 as the system is a suspected binary redback pulsar. The resulting candidates werethen folded and analysed through diagnostic prepfold plots. Any potential pulsar de-tection candidates were refolded using the filterbank file or the subband file from theprevious quarter of the dataset.

The initial search resulted in no confirmed pulsar detection. The initial search involvedanalysing each quarter of the dataset individually. Analysing the whole dataset, utilisingthe whole integration time of τint = 7208.4 s, increased the sensitivity of the search. Thiswas also conducted resulting in no confirmable pulsar detection.

The reasons for a non-detection are discussed in detail in Section 3.2.1. To summarise -the system may be eclipsed due to the companion or ablation of the companion, the radioemission may not be beamed towards the observer or the pulsar’s flux density may be

4.1. Conclusion and Future Study 89

less than the sensitivity of the search.

The sensitivity of the search was calculated using the radiometer equation as Smin = 0.20mJy for the initial search, and Smin = 0.10 mJy for the whole dataset analysis. The radiopseudo-luminosity was also calculated using equation 3.3, L1400 = 0.24 mJy kpc2 for theinitial analysis and L1400 = 0.12 mJy kpc2 for the whole dataset analysis. This was thencompared to known binary pulsar systems - see sections 3.2.3 and 3.2.4. In general thesensitivity of our search was good enough to detect the majority of millisecond pulsarsalthough a small number of known MSPs are faint enough that they would not have beendetected by our search.

For future study or observations, it is recommended based on this project’s findings thatthe system is observed at a different phase position to the observation conducted for thedataset analysed here to maximise the possiblity of a detection. An estimation of the ge-ometry of J0212+5320 can be seen in Fig. 3.16. The observation for the dataset analysedhere occured at radio phase values φstart = 0.088± 0.004 and φend = 0.163± 0.004, with anoverall offset ± 0.004 due to uncertainties in TASC.

An ideal scenario would be to re-observe J0212+5320 at a phase position φ ∼0.75 (supe-rior conjunction of companion) - when the companion is behind the pulsar.Although, it should be noted that as discussed in Section 3.2.1 eclipsing binary pulsarscan have unpredictable and irregular eclipses.

One final consideration for future work is to utilise a newly developed search methodthat is more sensitive to binary pulsars called a ’Jerk’ search (Andersen & Ransom, 2018).This method accounts for acceleration that changes linearly and improves the sensitivityof the search if the data covers 5-15% of the orbital period (Andersen & Ransom, 2018).However, the ’jerk’ search results in longer computation times although Adámek et al.(2019) reports achieving a 90x performance increase by utilising GPU CUDA acceleration.

90

Appendix A

Prepfold Plots

This appendix presents some of the resulting prepfold plots and discussion fromthe analysis of the J0212+5320 dataset. Some are potential, but unconfirmed, can-didates and some are RFI. The range of expected parameters for J0212+5320 isshown in Section 2.1. The candidates presented here are ones that were not sig-nificant enough to justify further analysis.

Appendix A. Prepfold Plots 91

FIGURE A.1: Prepfold of a candidate at DM = 19.44 pc cm−3. This candi-date is from the first quarter of the data (041248) and is a potential pulsardetection candidate. There are dark vertical lines that can just be seen inthe time domain plot, the DM plot peaks at a non-zero value, the spin pe-riod of ∼ 7.47 ms and spin frequency of ∼ 134 Hz are consistent with amillisecond pulsar (Papitto et al., 2014). However, the time domain andsubband plots are not definitive and the dark horizontal lines in the sub-band plot (at subbands ∼ 0 and 61) indicate that this could be narrowbandRFI.

Fig. A.1 is a prepfold plot of a 7.47 ms candidate from the first quarter of the data (041248).This candidate is a potential pulsar detection. There are just visible vertical tracks in thetime domain and subband plots at ∼0.8 and 1.8 φ, the DM plot does not peak at 0 (DM =19.437 pc cm−3) and peaks in the period and period derivative plots. The period is 7.47ms and the spin frequency is ∼134 Hz. The P value is within the expected range (P = -1.6×10−12 s/s). All these parameters are within the expected range for an MSP. The colourplot is not centred but some structure can just been seen. However, the significance ofthis candidate is quite low at 5.7σ and there are dark horizontal lines in both the timedomain (at ∼1600 s) and subband (at subband ∼ 60) plots.

92 Appendix A. Prepfold Plots

FIGURE A.2: Prepfold of a candidate at DM = 10.57 pc cm−3. This candi-date is from the first quarter of the data (041248) and is a potential pulsarcandidate. There are darker vertical lines in the time domain plot that canjust be seen at φ ∼ 0.6 and 1.6 that correspond to the peaks in the pulseprofile. The DM plot peaks at DM = 10.565 pc cm−3 and there are also justvisible vertical lines in the subband plot. The spin period of ∼ 2.55 ms andspin frequency of ∼ 392 Hz is consistent with a millisecond pulsar. How-ever, it is clearly not a definitive detection as the vertical lines in the timedomain and subband plots are not clear enough. There are also dark hor-izontal lines in both these plots which could indicate this is narrowbandRFI.

Fig. A.2 is a prepfold plot of a 2.55 ms candidate that is a potential pulsar detection fromthe first quarter (041248). The period is 2.55 ms and the spin frequency is ∼392 Hz.The P value is within the expected range (P = -1.504 ×10−11 s/s). There are just visibletracks in the time domain and subband plots (although they are quite vague and onlyjust discernible). The DM plot does not peak at 0 (DM = 10.565 pc cm−3) and the periodand period derivative plots have noticeable peaks. All these parameters are within theexpected range for an MSP. However, the colour plot lacks the expected structure, thesignificance of this candidate is quite low at 5.3σ and there are darker horizontal lines inboth the time domain (at∼100, 400, 700, 1200 and 1800 s) and subband (at subband∼ 15)plots.


FIGURE A.3: Prepfold of a candidate at DM = 26.83 pc cm−3. This can-didate is from the first quarter of the data (041248) and at first glance isa potential pulsar candidate - the DM plot does not peak at 0, there arejust visible vertical lines in the time domain plot at φ ∼ 0.6 and 1.6. Thespin period of ∼ 1.01 ms and spin frequency of ∼ 989 Hz is faster thanthe fastest currently known pulsar which is PSR J1748-2446ad which has aspin frequency of ∼ 716 Hz and a period of ∼ 1.4 ms (Hessels et al., 2006;Koliogiannis & Moustakidis, 2019) and the dark horizontal lines in boththe time domain and subband plots all indicate this is most likely RFI.

Fig. A.3 is a prepfold of a potential pulsar detection from the first quarter of the data(041248). However, further scrutiny of this signal shows it is most likely RFI. The peaksin the pulse profile plot are not definitive (it appears quite noisy), the time domain plothas vaguely visible vertical tracks but the subband plot lacks the expected tracks. The DMplot peaks at 26.825 pc cm−3, and the period and period derivative plots have prominentpeaks. However, the significance is quite low at 5.8σ, the positive P value of 6.491×10−12

s/s is outside the expected range and the period of 1.01 ms and spin frequency of ∼989Hz is faster than the currently fastest known MSP (PSR J1748-2446ad). Therefore, this ismost likely to be RFI.


FIGURE A.4: Prepfold of a candidate at DM = 9.11 pc cm−3. This candidateis from the fourth quarter of the data (054741) and is a potential pulsardetection. This is indicated by the prominent peaks, darker vertical linesin the time domain plot, a period of 3.26 ms, spin frequency of ∼ 307 Hzand a DM plot that does not peak at 0. However, the signal significanceis not high and the DM value is much lower than expected for the targetsystem.

Fig. A.4 is a prepfold of a 3.26 ms potential pulsar detection from the fourth quarter ofthe data (054741). There is a prominent double peak in the pulse profile plot and verticaltracks that corresponds to those peaks in the time domain plot (at ∼0.2 and 1.2 φ). Theperiod is ∼3.26 ms and the spin frequency is ∼3.07 Hz. The subband plot has visibletracks at these phase positions too, although they are not that prominent. The DM plotpeaks at 9.109 pc cm−3 which is a lot lower than would be expected (the expected DM ofJ0212+5320 is ∼ 25 pc cm−3). The P value is positive (P = 2.174 ×10−11 s/s) which is notconsistent with the expected range. The time domain and subband plots both have darkhorizontal lines, at ∼1200 s and subbands ∼75 to 80. This indicates this is most likelyRFI.


FIGURE A.5: Prepfold of a candidate at DM = 243 pc cm−3. This candidateis from the second quarter of the data (044503) and is clearly RFI. This isindicated by the subband plot which shows dark horizontal lines acrossonly a few subbands (∼ 46 to 55) indicating this is a narrowband signal.The DM plot also does not have the expected peak shape as seen in Fig. 3.3and peaks at a DM which is much higher than would be expected for thetarget system.

Fig. A.5 is a prepfold from the second quarter of the data (044503) and is clearly RFI. Theperiod is ∼71.11 ms and the spin frequency is ∼14 Hz which are both outside the ex-pected range. The time domain plot has clear vertical tracks but also has dark horizontallines at ∼1400 s. The subband plot has clear dark horizontal lines around subbands 45 to55, the DM plot has a very broad peak at DM = 243 pc cm−3 which is much higher thanexpected. This plot is clearly RFI.


FIGURE A.6: Prepfold of a candidate at DM = 22.678 pc cm−3. This candi-date is from the whole dataset analysis. It has a period of ∼2.35 ms and aspin frequency of ∼425 Hz. There are prominent peaks in the pulse pro-file and darker vertical tracks in the time domain plot. There are also clearpeaks in the DM, period and period derivative plots. The significance ofthe signal is not too low at 11.9σ. However, the subband plot lacks the ver-tical tracks that are expected and has dark horizontal lines indicating thisis most likely RFI.

Fig. A.6 is a prepfold plot from the whole dataset analysis and at first glance appears tobe a promising candidate. It has a period of ∼2.35 ms and a spin frequency of ∼425Hz. It has clear prominent peaks in the pulse profile, darker vertical tracks in the timedomain plot, peaks in the DM, period and period derivative plots. The colour plot showssome structure. The significance of the signal is not that low at 11.9σ. However, the darkhorizontal lines and spots in the subband plot indicate this is most likely RFI.


FIGURE A.7: Prepfold of a candidate at DM = 3.492 pc cm−3. This candi-date is from the whole dataset analysis. It has a period of ∼6.13 ms anda spin frequency of ∼163 Hz. This candidate has prominent peaks in thepulse profile and darker vertical tracks in the time domain plot. The periodand period derivative plots also have prominent peaks. The significance is8.0σ. The DM plot, however, lacks a prominent peak and the DM value of3.492 pc cm−3 is very low. The subband plot has darker lines that are slop-ing to the right indicating that the DM has been overestimated. Therefore,this signal is likely RFI.

Fig. A.7 is a prepfold plot from the whole dataset analysis. It has a period of ∼6.13 msand a spin frequency of ∼163 Hz. There are prominent peaks in the pulse profile anddarker vertical tracks in the time domain plot. The period and period derivative plotsalso have prominent peaks, and the colour plot shows some structure. The significance is8.0σ. However, the DM plot lacks a prominent peak and the DM value of 3.492 pc cm−3

is very low. The subband plot also exhibits darker tracks that are sloping to the rightindicating that the DM value has been overestimated - the DM plot peaks at 0. Therefore,this signal is most likely RFI.

98

Bibliography

Abdo A., Ackermann M., Ajello M., 2009, Science, Vol. 325, Issue 5942, pp. 848-852

Acero F., et al., 2015, Astrophysical Journal, Supplement, 218, 23

Adámek K., Novotný J., Dimoudi S., Armour W., 2019, arXiv e-prints, p. arXiv:1911.01353

An H., Romani R., Kerr M., 2018, Astrophysical Journal Letters, Volume 868, Issue 1,article ID. L8, 5 pp.

Andersen B. C., Ransom S. M., 2018, Astrophysical Journal, Letters, 863, L13

Antoniadis J., Freire P., Wex N., Tauris T., 2013, Science, 340:448, April 2013.

Applegate J., Shaham J., 1994, Astrophysical Journal, Part 1, vol. 436, no. 1, p. 312-318

Archibald A. E., et al., 2009, Science, Volume 324, Issue 5933, pp. 1411

Arons J., Tavani M., 1993, Astrophysical Journal, 403:249–255.

Backer D., Kulkarni S., Heiles C., Davis M., Goss W., 1982, Nature volume 300, pages615–618

Bassa C., Patruno A., Hessels J., Keane E., 2014, Monthly Notices of the RAS, Volume 441,Issue 2, p.1825-1830

Bassa C. G., et al., 2016, Monthly Notices of the RAS, 456, 2196

Bassa C. G., Pleunis Z., Hessels J. W. T., 2017, Astronomy and Computing, 18, 40

Benvenuto O. G., Vito M. A. D., Horvath J. E., 2014, Astrophysical Journal, 798, 44

Bhattacharya D., van den Heuvel E. P. J., 1991, Physics Reports, 203:1–124.

Brecher K., Fesen R. A., Maran S. P., Brandt J. C., 1983, The Observatory, 103, 106

Breton R. P., et al., 2013, Astrophysical Journal, 769, 108

Camilo F., et al., 2015, Astrophysical Journal, 810, 85

Caraveo P. A., 2014, Annual Review of Astron and Astrophys, 52, 211

Chandrasekhar S., 1967, An introduction to the study of stellar structure. Dover Publica-tions

http://dx.doi.org/10.1126/science.1176113

http://dx.doi.org/10.1088/0067-0049/218/2/23

https://ui.adsabs.harvard.edu/abs/2015ApJS..218...23A

https://ui.adsabs.harvard.edu/abs/2019arXiv191101353A

http://dx.doi.org/10.3847/2041-8213/aaedaf

http://dx.doi.org/10.3847/2041-8213/aaedaf

http://dx.doi.org/10.3847/2041-8213/aad59f

https://ui.adsabs.harvard.edu/abs/2018ApJ...863L..13A


http://dx.doi.org/10.1086/174906


http://dx.doi.org/10.1086/172198

http://dx.doi.org/10.1038/300615a0

http://dx.doi.org/10.1038/300615a0

http://dx.doi.org/10.1093/mnras/stu708

http://dx.doi.org/10.1093/mnras/stu708

http://dx.doi.org/10.1093/mnras/stv2755

https://ui.adsabs.harvard.edu/abs/2016MNRAS.456.2196B

http://dx.doi.org/10.1016/j.ascom.2017.01.004

https://ui.adsabs.harvard.edu/abs/2017A&C....18...40B

http://dx.doi.org/10.1088/0004-637x/798/1/44

http://dx.doi.org/https://doi.org/10.1016/0370-1573(91)90064-S

https://ui.adsabs.harvard.edu/abs/1983Obs...103..106B

http://dx.doi.org/10.1088/0004-637X/769/2/108

http://dx.doi.org/10.1088/0004-637X/810/2/85

https://ui.adsabs.harvard.edu/abs/2015ApJ...810...85C

http://dx.doi.org/10.1146/annurev-astro-081913-035948

https://ui.adsabs.harvard.edu/abs/2014ARA&A..52..211C

BIBLIOGRAPHY 99

Chen K., Ruderman M., 1993, Astrophysical Journal, 402, 264

Chen H., Chen X., Tauris T., Han Z., 2013, Astrophysical Journal, Volume 775, Number 1.

Clark C. J., et al., 2018, Science Advances, 4, eaao7228

Condon J., Ransom S., 2016, Essential Radio Astronomy, Pulsars, Astr 534, https://www.cv.nrao.edu/course/astr534/Pulsars.html

Cordes M., Lazio W., 2002, arXiv e-prints, NE2001 Galactic Free Electron Density Model,U.S. Naval Research Laboratory, pp astro–ph/0207156

Crawford F., et al., 2013, Astrophysical Journal, 776, 20

Cromartie H. T., Camilo F., Kerr M. 2016, Astrophysical Journal, 819:34.

D’Amico N., Possenti A., Manchester R. N., Sarkissian J., Lyne A. G., Camilo F., 2001,Astrophysical Journal, Letters, 561, L89

Demorest P., Pennucci T., Ransom S., Roberts M., 2010, Nature, 467:1081–1083, October2010.

Dhillon V. S., Breton R. P., Clark C. J., 2020, Private communication - pt5m telescope data.Roque de los Muchachos Observatory, La Palma, https://www.iac.es/en

Dimoudi S., Armour W., 2015, arXiv e-prints, Proceedings of the 25th Annual Astronom-ical Data Analysis Software and Systems Conference, p. arXiv:1511.07343

Ergma E., Sarna M., J. A., 1998, Monthly Notices of the RAS, 300, 352

Freire 2019, Pulsar mass measurements and tests of general relativity, https://www3.mpifr-bonn.mpg.de/staff/pfreire/NS_masses.html

Fruchter A., Stinebring D., Taylor J., 1988, Nature, vol. 333, May 19, 1988, p. 237-239.

Gil J., Gronkowski P., W. R., 1984, Astronomy & Astrophysics, 132, 312

Glendenning N. K., 1992, American Physical Society, 46: 4161-4168.

Glendenning N. K., 2005, Compact Stars: Nuclear Physics, Particle Physics and GeneralRelativity. Springer-Verlag

Gusinskaia N. V., et al., 2019, Accepted for publication in Monthly Notices of the RAS,arXiv e-prints, p. arXiv:1909.02323

Han J., Wang C., Xu J., Ji. H., 2017, eprint arXiv:1703.05988, Astrophysics - High En-ergy Astrophysical Phenomena; Astrophysics - Solar and Stellar Astrophysics, p.arXiv:1703.05988

Hankins T. H., Rickett B. J., 1975, Pulsar signal processing. Vol. 14, https://ui.adsabs.harvard.edu/abs/1975mcpr...14...55H

http://dx.doi.org/10.1086/172129

https://ui.adsabs.harvard.edu/abs/1993ApJ...402..264C

http://dx.doi.org/10.1088/0004-637X/775/1/27

http://dx.doi.org/10.1126/sciadv.aao7228

https://ui.adsabs.harvard.edu/abs/2018SciA....4.7228C

https://www.cv.nrao.edu/course/astr534/Pulsars.html

https://www.cv.nrao.edu/course/astr534/Pulsars.html

https://ui.adsabs.harvard.edu/abs/2002astro.ph..7156C

http://dx.doi.org/10.1088/0004-637X/776/1/20

https://ui.adsabs.harvard.edu/abs/2013ApJ...776...20C

http://dx.doi.org/10.3847/0004-637X/819/1/34

http://dx.doi.org/10.1086/324562

https://ui.adsabs.harvard.edu/abs/2001ApJ...561L..89D

http://dx.doi.org/10.1038/nature09466


https://www.iac.es/en

https://ui.adsabs.harvard.edu/abs/2015arXiv151107343D

https://www3.mpifr-bonn.mpg.de/staff/pfreire/NS_masses.html

https://www3.mpifr-bonn.mpg.de/staff/pfreire/NS_masses.html

http://dx.doi.org/10.1038/333237a0

http://dx.doi.org/10.1103/PhysRevD.46.4161

https://ui.adsabs.harvard.edu/abs/2019arXiv190902323G

https://ui.adsabs.harvard.edu/abs/2017arXiv170305988H

https://ui.adsabs.harvard.edu/abs/2017arXiv170305988H

https://ui.adsabs.harvard.edu/abs/1975mcpr...14...55H

https://ui.adsabs.harvard.edu/abs/1975mcpr...14...55H

100 BIBLIOGRAPHY

Haslam C. G. T., Salter C. J., Stoffel H., Wilson W. E., 1982, Astronomy and Astrophysics,Supplement, 47, 1

Hénault-Brunet V., et al., 2012, Monthly Notices of the RAS, 420, L13

Hessels J. W. T., Ransom S. M., Stairs I. H., Freire P. C. C., Kaspi V. M., Camilo F., 2006,Science, 311, 1901

Hobbs G., Manchester R., Teoh A., M. H., J. A., 2019, ATNF Pulsar Database 129, 1993-2006 (2005), http://www.atnf.csiro.au/research/pulsar/psrcat

Jackson J. D., 1962, Classical Electrodynamics.. Wiley & Sons

Johnston S., van Straten W., Kramer M., Bailes M., 2001, Astrophysical Journal, Letters,549, L101

Kandel D., Romani R. W., An H., 2019, AAS/High Energy Astrophysics Division, 17,112.13

Karpova A. V., Zyuzin D. A., Shibanov Y. A., 2019, Monthly Notices of the RAS, 487, 1964

Kaspi V. M., Beloborodov A. M., 2017, Annual Review of Astronomy and Astrophysics(2017) 55:1, 261-301

Kaspi V. M., Helfand D. J., 2002, Constraining the Birth Events of Neutron Stars. p. 3

Knispel B., et al., 2013, Astrophysical Journal, 774, 93

Koliogiannis P. S., Moustakidis C. C., 2019, Phys. Rev. C 101, 015805 – Published 29 Jan-uary 2020,

Kramer M., Xilouris K. M., Lorimer D. R., Doroshenko O., Jessner A., Wielebinski R.,Wolszczan A., Camilo F., 1998, Astrophysical Journal, 501, 270

Large M. I., Vaughan A. E., Mills B. Y., 1968, Nature, 220, 340

Lattimer J., Prakash M., Masak D., A. Y., 1990, Astrophysical Journal, 355: 241-254.

Lazarus P., et al., 2015, Astrophysical Journal, 812, 81

Leahy D. A., Darbro W., Elsner R. F., Weisskopf M. C., Sutherland P. G., Kahn S., GrindlayJ. E., 1983, Astrophysical Journal, 266, 160

Li K.-L., Kong A. K. H., Hou X., Mao J., Strader J., Chomiuk L., Tremou E., 2016, Astro-physical Journal, 833, 143

Linares M., 2014, Astrophysical Journal, 795, 72

Linares M., Miles-Páez P., Rodríguez-Gil P., Shahbaz T., Casares J., Fariña C., KarjalainenR., 2016, Oxford University Press, Royal Astronomical Society.

Link B., Epstein R. I., Lattimer J. M., 1999, Physical Review Letters, 83, 3362

https://ui.adsabs.harvard.edu/abs/1982A%26AS...47....1H

http://dx.doi.org/10.1111/j.1745-3933.2011.01183.x

https://ui.adsabs.harvard.edu/abs/2012MNRAS.420L..13H


https://ui.adsabs.harvard.edu/abs/2006Sci...311.1901H

http://www.atnf.csiro.au/research/pulsar/psrcat

http://dx.doi.org/10.1086/319154

https://ui.adsabs.harvard.edu/abs/2001ApJ...549L.101J

https://ui.adsabs.harvard.edu/abs/2019HEAD...1711213K

https://ui.adsabs.harvard.edu/abs/2019HEAD...1711213K

http://dx.doi.org/10.1093/mnras/stz1387

https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.1964K

http://dx.doi.org/https://doi.org/10.1146/annurev-astro-081915-023329

http://dx.doi.org/https://doi.org/10.1146/annurev-astro-081915-023329

http://dx.doi.org/10.1088/0004-637x/774/2/93

http://dx.doi.org/10.1103/PhysRevC.101.015805

http://dx.doi.org/10.1103/PhysRevC.101.015805

http://dx.doi.org/10.1086/305790

http://dx.doi.org/10.1038/220340a0

https://ui.adsabs.harvard.edu/abs/1968Natur.220..340L

http://dx.doi.org/http://adsbit.harvard.edu/full/1990ApJ...355..241L

http://dx.doi.org/10.1088/0004-637X/812/1/81

https://ui.adsabs.harvard.edu/abs/2015ApJ...812...81L

http://dx.doi.org/10.1086/160766

https://ui.adsabs.harvard.edu/abs/1983ApJ...266..160L

http://dx.doi.org/10.3847/1538-4357/833/2/143

http://dx.doi.org/10.3847/1538-4357/833/2/143

https://ui.adsabs.harvard.edu/abs/2016ApJ...833..143L

http://dx.doi.org/10.1088/0004-637X/795/1/72

https://ui.adsabs.harvard.edu/abs/2014ApJ...795...72L

http://dx.doi.org/10.1093/mnras/stw3057

http://dx.doi.org/10.1103/PhysRevLett.83.3362

https://ui.adsabs.harvard.edu/abs/1999PhRvL..83.3362L

BIBLIOGRAPHY 101

Lorimer D. R., Kramer M., 2005, Handbook of Pulsar Astronomy.. Cambridge UniversityPress.

Maan Y., Krishnakumar M. A., Naidu A. K., Roy S., Joshi B. C., Kerr M., Manoharan P. K.,2017, Monthly Notices of the RAS, 471, 541

Maitra C., et al., 2019, Monthly Notices of the RAS, 490, 5494

Manchester R. N., 2017, Journal of Astrophysics and Astronomy, 38:42

Maron O., Kijak J., Kramer M., Wielebinski R., 2000, Astronomy and Astrophysics, Sup-plement, 147, 195

Medvedev O. D., Karpova A. V., Shibanov Y. A., Zyuzin D. A., Pavlov G. G., 2019, inJournal of Physics Conference Series. p. 022018 (arXiv:2002.11958), doi:10.1088/1742-6596/1400/2/022018

Menezes R., Cafardo F., R. N., 2018, Monthly Notices of the RAS, Volume 486, 1, pp.851-867

Ng C., et al., 2015, Monthly Notices of the RAS, 450, 2922

Nice D. J., Arzoumanian Z., Thorsett S. E., 2000, in Kramer M., Wex N., Wielebinski R.,eds, Astronomical Society of the Pacific Conference Series Vol. 202, IAU Colloq. 177:Pulsar Astronomy - 2000 and Beyond. p. 67 (arXiv:astro-ph/9911211)

Oostrum L. C., van Leeuwen J., Maan Y., Coenen T., Ishwara-Chandra C. H., 2020,Monthly Notices of the RAS, 492, 4825

Oppenheimer J. R., Volkoff G. M., 1939, Physical Review, 55:374–381.

Ostriker J. P., Gunn J. E., 1969, Nature, Volume 223, Issue 5208, pp. 813-814

Pacini F., 1967, Nature, 216, 567

Papitto A., Ferrigno C., Bozzo E., Rea N., 2013, Nature, Volume 501, Issue 7468, pp. 517-520 (2013)

Papitto A., Torres D. F., Rea N., Tauris T. M., 2014, Astronomy and Astrophysics, 566, A64

Polzin E. J., 2019, PhD thesis, University of Manchester, https://www.research.

manchester.ac.uk/portal/files/102605021/FULL_TEXT.PDF

Possenti A., D’Amico N., Manchester R. N., Camilo F., Lyne A. G., Sarkissian J., CorongiuA., 2003, Astrophysical Journal, 599, 475

Press W., Teukolsky S., Vetterling W., Flannerly B., 1992, Numerical Recipes: The Art ofScientific Computing, 2nd Edition. Cambridge University Press.

Radhakrishnan V., Manchester R. N., 1969, Nature, 222, 228

http://dx.doi.org/10.1093/mnras/stx1615

https://ui.adsabs.harvard.edu/abs/2017MNRAS.471..541M


https://ui.adsabs.harvard.edu/abs/2019MNRAS.490.5494M

http://dx.doi.org/https://doi.org/10.1007/s12036-017-9469-2

http://dx.doi.org/10.1051/aas:2000298

http://dx.doi.org/10.1051/aas:2000298

https://ui.adsabs.harvard.edu/abs/2000A&AS..147..195M

http://arxiv.org/abs/2002.11958

http://dx.doi.org/10.1088/1742-6596/1400/2/022018

http://dx.doi.org/10.1088/1742-6596/1400/2/022018



http://dx.doi.org/10.1093/mnras/stv753

https://ui.adsabs.harvard.edu/abs/2015MNRAS.450.2922N

http://arxiv.org/abs/astro-ph/9911211

http://dx.doi.org/10.1093/mnras/staa146

https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.4825O

http://dx.doi.org/https://doi.org/10.1103/PhysRev.55.374

http://dx.doi.org/10.1038/223813a0

http://dx.doi.org/10.1038/216567a0

https://ui.adsabs.harvard.edu/abs/1967Natur.216..567P



http://dx.doi.org/10.1051/0004-6361/201321724

https://ui.adsabs.harvard.edu/abs/2014A&A...566A..64P

https://www.research.manchester.ac.uk/portal/files/102605021/FULL_TEXT.PDF


http://dx.doi.org/10.1086/379190

https://ui.adsabs.harvard.edu/abs/2003ApJ...599..475P

http://dx.doi.org/10.1038/222228a0

https://ui.adsabs.harvard.edu/abs/1969Natur.222..228R

102 BIBLIOGRAPHY

Ransom S. M., 2001, PhD thesis, Harvard University, https://www.cv.nrao.edu/

~sransom/ransom_thesis_2001.pdf

Ransom S., 2018, PRESTO - Pulsar Exploration and Search Toolkit, https://www.cv.nrao.edu/~sransom/presto/

Ransom S. M., Eikenberry S. S., Middleditch J., 2002, Astronomical Journal, 124, 1788

Ransom S. M., et al., 2011, Astrophysical Journal, Letters, 727, L16

Rappaport S., Podsiadlowski P., Joss P., Di Stefano R., Han Z., 1995, Monthly Notices ofthe RAS, Volume 273, Issue 3, 1 April 1995, Pages 731–741

Roberts M., Mclaughlin M., Gentile P., Aliu E., Hessels J., Ransom S., Ray P., 2014, As-tronomische Nachrichten, 335:313–317.

Roberts M., McLaughlin M., Gentile P., 2015, arXiv e-prints, 2014 Fermi Symposium pro-ceedings, p. arXiv:1502.07208

Roberts M., et al., 2018, International Astronomical Union, Volume 13, Symposium S337(Pulsar Astrophysics the Next Fifty Years) September 2017 , pp. 43-46

Romani R. W., Sanchez N., 2016, Astrophysical Journal, 828, 7

Ruderman M. A., 1976, Astrophysical Journal, 203:213-222.

Sett S., 2019, Master’s thesis, University of Manchester, https://www.research.

manchester.ac.uk/portal/files/87763534/FULL_TEXT.PDF

Shahbaz T., Linares M., Breton R. P., 2017, Monthly Notices of the RAS, 472, 4287

Shahbaz T., Linares M., Rodríguez-Gil P., Casares J., 2019, Monthly Notices of the RAS,488, 198

Shaifullah G., et al., 2016, Monthly Notices of the RAS, 462, 1029

Shapiro S., Teukolsky S., 1986, Wiley-Interscience

Sironi L., Spitkovsky A., 2011, Astrophysical Journal, 741, 39

Sironi L., Spitkovsky A., 2014, Astrophysical Journal, 783, L21

Smith F., 1970, Monthly Notices of the RAS, 149, 1-15

Smith F. G., 1976, Quarterly Journal of the RAS, 17, 383

Smith D. A., Guillemot L., Kerr M., Ng C., Barr E., 2017, arXiv e-prints, p.arXiv:1706.03592

Sotani H., Miyamoto U., 2018, Physical Review D, 98, 103019

Tauris T., Savonije G., 1999, Astronomy and Astrophysics, v.350, p.928-944 (1999)

https://www.cv.nrao.edu/~sransom/ransom_thesis_2001.pdf

https://www.cv.nrao.edu/~sransom/ransom_thesis_2001.pdf

https://www.cv.nrao.edu/~sransom/presto/

https://www.cv.nrao.edu/~sransom/presto/

http://dx.doi.org/10.1086/342285

https://ui.adsabs.harvard.edu/abs/2002AJ....124.1788R

http://dx.doi.org/10.1088/2041-8205/727/1/L16

https://ui.adsabs.harvard.edu/abs/2011ApJ...727L..16R

http://dx.doi.org/10.1002/asna.201312038

http://dx.doi.org/10.1002/asna.201312038

https://ui.adsabs.harvard.edu/abs/2015arXiv150207208R

http://dx.doi.org/10.1017/S1743921318000480

http://dx.doi.org/10.1017/S1743921318000480

http://dx.doi.org/10.3847/0004-637x/828/1/7

http://dx.doi.org/10.1086/154069



http://dx.doi.org/10.1093/mnras/stx2195

https://ui.adsabs.harvard.edu/abs/2017MNRAS.472.4287S


https://ui.adsabs.harvard.edu/abs/2019MNRAS.488..198S

http://dx.doi.org/10.1093/mnras/stw1737

https://ui.adsabs.harvard.edu/abs/2016MNRAS.462.1029S

http://dx.doi.org/10.1002/9783527617661

http://dx.doi.org/10.1088/0004-637X/741/1/39

https://ui.adsabs.harvard.edu/abs/2011ApJ...741...39S

http://dx.doi.org/10.1088/2041-8205/783/1/L21

https://ui.adsabs.harvard.edu/abs/2014ApJ...783L..21S

http://dx.doi.org/10.1093/mnras/149.1.1

https://ui.adsabs.harvard.edu/abs/1976QJRAS..17..383S

https://ui.adsabs.harvard.edu/abs/2017arXiv170603592S

https://ui.adsabs.harvard.edu/abs/2017arXiv170603592S

http://dx.doi.org/10.1103/PhysRevD.98.103019

https://ui.adsabs.harvard.edu/abs/2018PhRvD..98j3019S

BIBLIOGRAPHY 103

Thorsett S., Chakrabarty D., 1999, Astrophysical Journal, 512:288–299.

Titus N., et al., 2019, Monthly Notices of the RAS, 487, 4332

Venter C., Kopp A., Harding A., Gonthier P., Büsching I., 2015, Astrophysical Journal,Volume 807, Issue 2, article id. 130, 19 pp.

Wadiasingh Z., Harding A. K., Venter C., Böttcher M., Baring M. G., 2017, AstrophysicalJournal, 839, 80

Watters K. P., Romani R. W., 2011, Astrophysical Journal, 727, 123

Wolszczan A., 1991, Nature, vol. 350, April 25, 1991, p. 688-690.

Wolszczan A.; Frail D. A., 1992, Nature, vol. 355, Jan. 9, 1992, p. 145-147.

Yao J. M., Manchester R. N., Wang N., 2017, Astrophysical Journal, 835, 29

Younes G., et al., 2017, Astrophysical Journal, 847:85

Zharikov S., Kirichenko A., Zyuzin D., Shibanov Y., Deneva J. S., 2019, Monthly Noticesof the RAS, Volume 489, Issue 4, p.5547-5555,

van Kerkwijk M., Breton R., Kulkarni S., 2011, Astrophysical Journal, Volume 728, Issue2, article id. 95, 8 pp. (2011)

van Leeuwen F., et al., 2018, Gaia DR2 documentation, https://ui.adsabs.harvard.edu/abs/2018gdr2.reptE....V

http://dx.doi.org/10.1086/306742


https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4332T

http://dx.doi.org/10.1088/0004-637X/807/2/130

http://dx.doi.org/10.1088/0004-637X/807/2/130

http://dx.doi.org/10.3847/1538-4357/aa69bf

http://dx.doi.org/10.3847/1538-4357/aa69bf

http://dx.doi.org/10.1088/0004-637X/727/2/123

https://ui.adsabs.harvard.edu/abs/2011ApJ...727..123W

http://dx.doi.org/10.1038/350688a0

http://dx.doi.org/10.1038/355145a0

http://dx.doi.org/10.3847/1538-4357/835/1/29

https://ui.adsabs.harvard.edu/abs/2017ApJ...835...29Y

http://dx.doi.org/10.3847/1538-4357/aa899a



http://dx.doi.org/10.1088/0004-637X/728/2/95

http://dx.doi.org/10.1088/0004-637X/728/2/95

https://ui.adsabs.harvard.edu/abs/2018gdr2.reptE....V

https://ui.adsabs.harvard.edu/abs/2018gdr2.reptE....V

searching for radio pulses from the redback pulsar

Documents