Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

Detection strategies for bursts in networks of non-homogeneus gravitational waves detectors

Silvia Poggi*, Lucio Baggio*, Giovanni A.Prodi*, Alessandro Mion*, Francesco

Salemi§

* University of Trento & INFN§ University of Ferrara & INFN

The time coincidence strategy adopted by the International Gravitational Event Collaboration (IGEC) was suited for a network of almost equal and parallel detectors, and assuming a template. (P. Astone et al., Phys Rev D 68 022001 (2003) )

Considerations on the directional sensitivity and sky coverage in bar/interferometer network analysis:

• if gw’s are linearly polarized• If gw’s are circularly polarized

Characteristics of the cross-correlation search (coherent coincidence analysis)

Extension of the classical IGEC analysis (incoherent coincidence analysis)

Outline:

Comparison between coherent and incoherent methods

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

In order to reconstruct the wave amplitude h, any amplitude has to be divided by

Introduction

At any given time, the antenna pattern is:

it is a sinusoidal function of polarization , i.e. any gravitational wave detector is a linear polarizer it depends on declination and right ascension through the magnitude A and the phase )),(2cos(),(),,( AF

),,( F

We will characterize the directional sensitivity of a detector pair by the product of their antenna patterns F1 and F2

F1F2 is inversely proportional to the square of wave amplitude h2 in a cross-correlation search

F1F2 is an “extension” of the “AND” logic of IGEC 2-fold coincidence

This has been extensively used by IGEC: first step is a data selection obtained by putting a threshold F-1 on each detector

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

For linearly polarized signal, does not vary with time.The product of antenna pattern as a function of is given by:

)cos()4cos(

)2cos()2cos(

)()(

21212

121

2121

21

AA

AA

FF

)()( 21 FF

)()( 21 FF

The relative phase 1-2 between detectors affects the sensitivity of the pair.

Linearly polarized signals

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

AURIGA -TAMA sky coverage: (1) linearly polarized signal

)cos()4cos()()( 21212

12121 AAFF

AURIGA2

TAMA2

21 F

22 F

02

21

AURIGA x TAMA 21 FF

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

If:

the signal is circularly polarized:

Amplitude h(t) is varying on timescales longer than 1/f0

Then:

The measured amplitude is simply h(t), therefore it depends only on the magnitude of the antenna patterns. In case of two detectors:

The effect of relative phase 1-2 is limited to a spurious time shift t which adds to the light-speed delay of propagation:

(Gursel and Tinto, Phys Rev D 40, 12 (1989) )

Circularly polarized signals

0

21

2 ft

F

F

tf 02

22

22

12

12

21 FFFFAA

0f

h

)2sin(

)2cos()(

thh

h

04

1

ft

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

)cos()4cos()()( 21212

12121 AAFF

AURIGA2

TAMA2

2221 11 FFA

2222 22 FFA

AURIGA -TAMA sky coverage: (2) circularly polarized signal

AURIGA x TAMA 21 AA

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

AURIGA x TAMA 21AA AURIGA x TAMA 21 FF

AURIGA -TAMA sky coverage

Linearly polarized signalCircularly polarized signal

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

Classical “IGEC style” coincidence search

detector 1

detector 2

detector 2

AND

AND

AND

detector 3

Detectors: PARALLEL, BARS Shh: SIMILAR FREQUENCY RANGE Search: NON DIRECTIONAL Template: BURST = (t)

The search coincidence is performed in a subset of the data such that: the efficiency is at least 50% above the threshold (HS) significant false alarm reduction is accomplished

The number of detectors in coincidence considered is self-adapting

This strategy can be made directional

HS

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

Probability of detection in “IGEC style” coincidence with different antenna patterns

HS = 10 HTHS= 5 HT

51.3 %

22.9 %

In IGEC style non-directional search, the probability of detection of a linearly polarized signal with random polarization is a function of source direction.

The relative amplitude sensitivity of detectors greatly affects the sky coverage of a network search.

Case of LHO – AURIGA assuming AURIGA is 3 times less sensitive. Probability of detection of the non-directional “IGEC style” search.

Threshold of AURIGA HAURIGA= 3 HT Threshold of LHO HLHO= HT

Polarization averagePolarization and time average Sky average

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

Naïve cross-correlation search

Detectors: PARALLEL Shh: SAME FREQUENCY RANGE NEEDED Search: NON DIRECTIONAL Template: NO

Selection based on data quality can be implemented before cross-correlating.

The efficiency is to be determined a posteriori using Montecarlo.

The information which is usually included in cross-correlation takes into account statistical properties of the data streams but not geometrical ones, as those related to antenna patterns.

detector 1

detector 2

detector 1 * detector 2

Threshold crossing after

correlation

Txxwwnj

jj ,1

21)2()1(

T

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

HS2 = 100 THS

2 = 25 T

75.6 %

45.6 %

20.6 %

Probability of detection in cross-correlation strategy

REMARK: the efficiency is not taking into account the contribution of the noise therefore the result of the cross-correlation at threshold T is not directly comparable with that of IGEC at HT=T1/2

Case of LHO – AURIGA assuming AURIGA is 3 times less sensitive. Probability of detection of the cross-correlation search

Signal2 > TT =HAURIGA x HLIGO

Polarization averagePolarization and time average Sky averageHS

2 = 10 T

Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks

Comparison between “IGEC style” and cross-correlation

IGEC style search was designed for template searches. The template guarantees that it is possible to have consistent estimators of signal amplitude and arrival time. A bank of templates may be required to cover different class of signals. Anyway in burst search we don’t know how well the template fits the signalA template-less IGEC search can be easily implemented in case of detectors with equal detector bandwidth. In fact it is possible to define a consistent amplitude estimator. (Karhunen-Loeve, power…)

Cross-correlation among identical detectors is the most used method to cope with lack of templates.

Cross-correlation in general is not efficient with non-overlapping frequency bandwidths, even for wide band signals.

We are working to the extension of IGEC in case of template-less search among different detectors. It is needed to determine spectral weights common to all detectors, setting a balance between efficiency loss and network gain (sky coverage and false alarm rate)

21hh SS

Templatesearch

Template-lesssearch

21hh SkS IGEC

IGEC

cross-

corr

IGEC

cross-

corr

IGEC