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

1. 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)) Outline: • 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 Extension of the classicalIGEC analysis (incoherent coincidence analysis) Characteristics of the cross-correlation search (coherent coincidence analysis) Comparison between coherent and incoherent methods Silvia Poggi - GW burst detection strategy in non-homogeneus networks

2. 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  • In order to reconstruct the wave amplitude h, any amplitude has to be divided by • This has been extensively used by IGEC: first step is a data selection obtained by putting a threshold  F-1on each detector • We will characterize the directional sensitivity of a detector pair by theproduct 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 Silvia Poggi - GW burst detection strategy in non-homogeneus networks

3. d1-d2 = p/2 d1-d2 = p/4 d1-d2 = 0 Linearly polarized signals 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. Silvia Poggi - GW burst detection strategy in non-homogeneus networks

4. AURIGA x TAMA AURIGA -TAMA sky coverage: (1) linearly polarized signal AURIGA2 TAMA2 Silvia Poggi - GW burst detection strategy in non-homogeneus networks

5. Circularly polarized signals • 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twhich adds to the light-speed delay of propagation: • (Gursel and Tinto, Phys Rev D 40, 12 (1989) ) y Silvia Poggi - GW burst detection strategy in non-homogeneus networks

6. AURIGA x TAMA AURIGA -TAMA sky coverage: (2) circularly polarized signal AURIGA2 TAMA2 Silvia Poggi - GW burst detection strategy in non-homogeneus networks

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

8. detector 1 AND detector 2 AND detector 2 AND detector 3 Classical “IGEC style” coincidence search • 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 networks

9. Polarization average Polarization and time average HS = 10 HT HS= 5 HT Probability of detection in “IGEC style” coincidence with different antenna patterns • 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 Sky average 51.3 % 22.9 % Silvia Poggi - GW burst detection strategy in non-homogeneus networks

10. Threshold crossing after correlation detector 1 T detector 1 * detector 2 detector 2 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 aposteriori 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. Silvia Poggi - GW burst detection strategy in non-homogeneus networks

11. HS2 = 10 T HS2 = 100 T HS2= 25 T Probability of detection in cross-correlation strategy Case of LHO – AURIGA assuming AURIGA is 3 times less sensitive. Probability of detection of the cross-correlation search Signal2 > T T =HAURIGA x HLIGO Polarization average Polarization and time average Sky average 75.6 % 45.6 % 20.6 % 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 Silvia Poggi - GW burst detection strategy in non-homogeneus networks

12. IGEC IGEC IGEC IGEC cross- corr cross- corr 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 • 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) • 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…) Template search Template-less search • 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. Silvia Poggi - GW burst detection strategy in non-homogeneus networks