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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. - PowerPoint PPT Presentation
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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()()(
212121
21
2121
21
AA
AAFF
)()( 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()()( 212121
2121 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(
)(
thhh
041f
t
Silvia Poggi - GW burst detection strategy in non-homogeneus networksSilvia Poggi - GW burst detection strategy in non-homogeneus networks
)cos()4cos()()( 212121
2121 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
ANDAND
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 average Polarization 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-
corrIGEC
cross-
corrIGEC