S. Frasca

INFN – Virgo and “La Sapienza” Rome University

Baton Rouge, March 2007

Whole sky blind hierarchical search (P.Astone, SF, C.Palomba - Roma1)

Targeted search (F.Antonucci, F. Ricci – Roma1)

Binary source search (T.Bauer , J.v.d.Brand, S.v.d.Putten – Amsterdam)

Our method is based on the use of Hough maps, built starting from peak maps obtained taking the absolute value of the SFTs.

4

h-reconstructed data

Data quality

SFDB

Average spect rum estimation

peak map

hough transf.

candidates

peak map

hough transf.

candidates

coincidences

coherent step

events

Here is a rough sketch of our

pipeline

Data quality

SFDB

Average spect rum estimation

The software is described in the document at http://grwavsf.roma1.infn.it/pss/docs/PSS_UG.pdf

It is in C (mainly the high CP procedures) and in Matlab. Some procedure were written in both the environment (for check).

Time-domain big event are removed

Non-linear adaptive estimation of the power spectrum is performed (these estimated p.s. are saved together with the SFTs and the peak maps).

Only relative maxima are taken (little less sensitivity in the ideal case, much more robustness in practice)

Periodogram of 222 (= 4194304 ) data of C7

Seconds in abscissa. Note on the full piece the slow amplitude variation and in the zoom the perfect synchronization with the deci-second.

17

1kHz band analysis: peak maps

• On the peak maps there is a further cleaning procedure consisting in putting a threshold on the peaks frequency distribution

• This is needed in order to avoid a too much large number of candidates which implies a reduction in sensitivity.

C7: peaks frequency distribution before and after cleaning

Now we are using the “standard” (not “adaptive”) Hough transform

Here are the results

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Parameter space

• observation time

• frequency band

• frequency resolution

• number of FFTs

• sky resolution

• spin-down resolution

Hz 00095367.0f

(@1050Hz) deg 3.0)50(@ deg5.7, Hz

Hz/s1058.1

(@1050Hz)yr 2100(@50Hz)yr 100 8

max

f

Hz/s1076.1 10N :C7

Hz/s1006.4 40N :C69

sd

10sd

f

f

HzHz 105050

daysTCdaysTC obsobs 37.3:7 87.13:6

556 :7

2286 :6

FFT

FFT

NC

NC

f

1

~1013 points in the parameter space are explored for each data set

sTFFT 576.1048

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• On each Hough map (corresponding to a given frequency and spin-down) candidates are selected putting a threshold on the CR

• The choice of the threshold is done according to the maximum number of candidates we can manage in the next steps of the analysis

Candidates selection

• In this analysis we have used 8.3thrCR

• Number of candidates found:

C6: 922,999,536 candidates

C7: 319,201,742 candidates

map

mapnCR

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1kHz band: candidates analysis

C6: frequency distribution of candidates (spin-down 0)

f [Hz]

22

C7: frequency distribution of candidates (spin-down 0)

f [Hz]Sky distribution of candidates (779.5Hz)

[deg]

[deg]

peaks frequency distribution

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red line: theoretical distribution

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‘quiet’ band

‘disturbed’ band

Many candidates appear in ‘bumps’ (at high latitude), due to the short observation time, and ‘strips’ (at low latitude), due to the symmetry of the problem

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Coincidences

• Number of coincidences: 2,700,232

• Done comparing the set of parameter values identifying each candidate

• To reduce the false alarm probability; reduce also the computational load of the coherent “follow-up”

• False alarm probability: 7102.2 band 1045-1050 Hz

• Coincidence windows: 2 ,2 ,0 ,1 ff

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‘Mixed data’ analysis

• Let us consider two set of ‘mixed’ data:

• Produce candidates for data set A=A6+A7

• Produce candidates for data set B=B6+B7

• Make coincidences between A and B

• Two main advantages:

• larger time interval -> less ‘bunches’ of candidates expected

• easier comparison procedure (same spin-down step for both sets)

A6 B6 A7 B7

time

C6 C7

There are three basic methods to use the data from more antenna in order to better detect periodic sources:

coherent linear combination of the data (with delays), in priciple the “best” method

construction of single Hough (or Radon) maps from data from more antennas (non-coherent combinations)

coincidences between candidate lists

With today ratio of sensitivities between Ligo and Virgo, both a coherent and incoherent approach should be ineffectual (except, maybe, at very high frequency). But the situation is improving…

Non-coherent combination can combine data taken at distant times, so we can combine, e.g., “future” better Virgo data with today Ligo data

The Ligo candidates can be used as triggers for the Virgo data, allowing a much lower theshold (on the Hough map). This enhances the reliability of the detection.

Another point is: what is the probability to detect a source with a lower sensitivity antenna ? (if it was detected by a higher sensitivity detector)

If we suppose that the distribution of the sources amplitude A be a power law, of power m, the probability that A is over a value x is

1( 1) m

kP A x

m x

and the probability that A>x, if A>x0, is

1

00|

mx

P A x A xx

So, if m= 2~3, an antenna with half the sensitivity of another, has a probability 0.5~0.25 to detect the source.