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Time calibration of LOFAR-TBB data and cosmic ray wavefront shapes

Dalfsen, March 20, 2012

Arthur Corstanje, Radboud University Nijmegen

for the LOFAR Cosmic Rays KSP

A ‘good’ cosmic ray detection

Characterize radio signal from air shower

•  Footprint and lateral power distribution –  Shower axis direction and location

•  Time of arrival for each antenna –  Found using Hilbert transform or cross correlations –  Direction fitting –  Curvature fit

– Delay calibration! •  Polarization •  Pulse shape

Wavefront curvature

•  Zenith angle theta = 30° •  Superterp diameter d=300m •  Point source at altitude h=4 km !

To lowest orders at the edges:

≈ 250 ns + 6 ns •  1 sample = 5 ns…

c!t = d2sin! + d

2

8hcos3!

Measuring wavefront curvature •  Measure time of arrival for each antenna using maximum of

Hilbert envelope or cross correlation

•  Obtain direction of best-fitting plane wave, by linear regression of arrival times:

•  Parameters A and B give incoming direction •  Subtract plane-wave arrival times to obtain residuals, including

curvature  Compare with simulations to relate to height of shower

maximum, and particle type

ti = A xi + B yi + ni +Ci

Second-order wavefront shape example

Second-order wavefront shape example

Time calibration of LOFAR •  Time calibration is critical for measuring wavefront

shape, especially inter-station clock offsets •  Use LOFAR CalTables (June 2012) as starting point

•  Test given dipole delays using plane-wave fits per station

•  Test given station clock offsets using narrow-band RF transmitters (RFI)

Plane-wave fit residuals

Event from Dec 5, 2012 CS002 LBA-Outer 3 one-sample ‘glitches’, +5 ns Measured minus fitted plane-wave arrival times

Plane-wave fit residuals

Event from Dec 25, 2012 CS002 LBA-Outer 1 more 5 ns shift 2 at different RCUs! Measured minus fitted plane-wave arrival times

Radio transmitter phases •  Use phases of narrowband radio

signals from a known transmitter •  Phases from FFT •  average over ~ 50 blocks of 8000 samples •  Gives time delays modulo ~ 11 ns per frequency

Calibration method •  Use phases of narrowband radio

signals from a known transmitter

•  Gives time delays modulo ~ 11 ns per frequency •  Compare measured phases with calculated phases

from source position •  Use GPS location and distance •  Calibrates delays between LOFAR stations •  Smilde FM tower: 5 detectable radio stations at 88.0, 88.6, 90.8, 91.8, 94.8 MHz

Relative measurements -  Measuring at the edge of the band (filter) and a signal

coming from (essentially) the horizon -  Signal propagation effects not completely known

Relative measurements -  Measuring at the edge of the band (filter) and a signal

coming from (essentially) the horizon -  Signal propagation effects not completely known +  Phase difference between channels takes out the

common filter characteristic at this frequency +  Given a starting calibration (e.g. LOFAR or octocopter),

can take difference between observations to observe trends, drifting, glitches etc.

+  Works on datasets of ~ 2 ms +  Available ‘for free’ in every dataset in our collection!

Spectrum of LOFAR data around cosmic ray

Close-up of FM frequency range

Results for inter-station delays

CS002 CS003 CS005 CS006 CS007

Results for inter-station delays

CS002 CS003 CS005 CS006 CS007

Results for inter-station delays

CS002 CS003 CS005 CS006 CS007

Summary •  Promising results for wavefront shape, for

comparing with simulations •  Cosmic ray pulse arrival times give a rough

timing diagnostic (> 1 ns) •  Time calibration of LOFAR array can be done

using known radio transmitters, e.g. FM –  Per antenna, sigma ~ 0.5 ns but very stable (< ~ 0.2 ns) across datasets –  Inter-station delays with sigma ~ 0.15 ns

•  In good agreement with LOFAR calibration tables – but some differences are significant

•  Improved online radio trigger is needed to select better-quality pulses

Clock offsets from parset Nov 5, 2012

Second-order wavefront shape (bad)