1. Silvia 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

2. Silvia 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  We will characterize the directional sensitivity of a detector pair by the product of their antenna patterns F 1 and F 2  F 1 F 2 is inversely proportional to the square of wave amplitude h 2 in a cross-correlation search  F 1 F 2 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

3. Silvia 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:               The relative phase  1 -  2 between detectors affects the sensitivity of the pair. Linearly polarized signals

4. Silvia Poggi - GW burst detection strategy in non-homogeneus networks AURIGA -TAMA sky coverage: (1) linearly polarized signal AURIGA 2 TAMA 2 AURIGA x TAMA

5. Silvia 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/f 0 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 

6. Silvia Poggi - GW burst detection strategy in non-homogeneus networks AURIGA 2 TAMA 2 AURIGA -TAMA sky coverage: (2) circularly polarized signal AURIGA x TAMA

7. Silvia Poggi - GW burst detection strategy in non-homogeneus networks AURIGA x TAMA AURIGA -TAMA sky coverage Linearly polarized signal Circularly polarized signal

8. Silvia Poggi - GW burst detection strategy in non-homogeneus networks Classical “IGEC style” coincidence search detector 1 detector 2 AND detector 3  Detectors: PARALLEL, BARS  S hh : 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 (H S )  significant false alarm reduction is accomplished The number of detectors in coincidence considered is self- adapting This strategy can be made directional HSHS

9. Silvia Poggi - GW burst detection strategy in non-homogeneus networks Probability of detection in “IGEC style” coincidence with different antenna patterns H S = 10 H T H S = 5 H T 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 H AURIGA = 3 H T Threshold of LHO H LHO = H T Polarization average Polarization and time average Sky average

10. Silvia Poggi - GW burst detection strategy in non-homogeneus networks Naïve cross-correlation search  Detectors: PARALLEL  S hh : 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 T

11. Silvia Poggi - GW burst detection strategy in non-homogeneus networks H S 2 = 100 T H S 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 H T =T 1/2 Case of LHO – AURIGA assuming AURIGA is 3 times less sensitive. Probability of detection of the cross-correlation search Signal 2 > T T =H AURIGA x H LIGO Polarization average Polarization and time averageSky average H S 2 = 10 T

12. Silvia 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 signal A 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) Template search Template-less search IGEC cross- corr IGEC cross- corr IGEC