Data Analysis Pipeline: The Search for Gravitational Waves in Real life

Transcription

1 Data Analysis Pipeline: The Search for Gravitational Waves in Real life Romain Gouaty LAPP - Université de Savoie - CNRS/IN2P3 On behalf of the LIGO Scientific Collaboration and the Virgo Collaboration 2010 International School on Numerical Relativity and Gravitational Waves July 26 30, 2010 APCTP Pohang, Korea 1

2 References (I) [1] B.Schutz, Nature 323 (1986) [2] V. Kalogera et al., Astrophys. J 601 (2004) erratum-ibid. 604 (2004) R. O Shaughnessy et al., Astrophys. J 672 (2008) [3] LIGO Scientific Collaboration and Virgo Collaboration, Class. Quantum Grav. 27, (2010) [4] L. Blanchet et al., Class. Quantum Grav. 13 (1996) [5] LSC, Tuning matched filtering searches for compact binary systems (2007), Short overview of CBC pipeline [6] C. Van Den Broeck, A. S. Sengupta, Class. Quantum Grav. 24 (2007) [7] T.Damour et al., Phys. Rev. D 57 (1998) [8] A.Buonanno et al., Phys. Rev. D 59 (1999) A.Buonanno et al., Phys. Rev. D 62 (2000) [9] A.Buonanno et al., Phys. Rev. D 67 (2003) A.Buonanno et al., Phys. Rev. D 70 (2004) A.Buonanno et al., Phys. Rev. D 72 (2005) Implementation of the matched-filter algorithm [10] B. Allen et al., «FINDCHIRP: an algorithm for detection of gravitational waves from inspiraling compact binaries» (2005), arxiv:gr-qc/

3 References (II) [11] B. Owen, Phys. Rev. D 53 (1996) Template Placement to B. Owen et al., Phys. Rev. D 60 (1999) cover search parameter [12] D. Buskulic et al., Class. Quant. Grav. 22 (2005) space [13] D. Brown, PhD. Dissertation, University of Wisconsin Milwaukee (2004), arxiv: Details on LIGO CBC pipeline [14] C. Hanna, PhD. Dissertation, Louisiana State University (2008), [15] F. Marion et al., Moriond Proceedings (2003) [16] F Beauville et al., Class. Quantum Grav. 25, (2008) [17] K. G. Arun et al., Phys. Rev. D 71 (2005) [18] C. Robinson et al., GWDAW 11 (2006) C. Robinson et al., A geometric algorithm for efficient coincident detection of gravitational waves (2008), arxiv: [19] T. Cokelaer et al., LSC, GWDAW 11 (2006) LIGO Scientific Collaboration, Phys. Rev. D 77, (2008) [20] B. Allen, Phys. Rev. D 71 (2005) Signal-based veto ( ² test) Elliptical coincidence test for network analysis 3

4 References (III) [21] F. Robinet, for the LSC and Virgo Collaboration, GWDAW 14 (2010) F. Robinet, for the LSC and Virgo Collaboration, proceedings of GWDAW 14, accepted for publication in Class. Quantum Grav. [22] J. Slutsky et al., Methods for Reducing False Alarms in Searches for Compact Binary Coalescences in LIGO Data (2010), arxiv: Instrumental vetoes [23] D. Keppel, The Combined IFAR Statistic, LIGO-T (2010) Detection ranking statistics [24] LIGO Scientific Collaboration, Phys. Rev. D 79, (2009) [25] LIGO Scientific Collaboration and Virgo Collaboration, Search for Gravitational Waves from Compact Binary Coalescence in LIGO and Virgo Data from S5 and VSR1 (2010), arxiv: [26] P. Jaranowski et al., Phys. Rev. D 58, (1998) [27] A. Pai et al., Phys. Rev. D 64, (2001) 4

5 Outline CH1: Introduction to the Search for Gravitational Waves emitted during Compact Binary Coalescences ( CBC searches ) the detectors, the sources, the waveforms, the analysis technique CH2: CBC pipeline Matched filtering and coincident analysis parameter space and template banks, matched filtering, coincidences CH3: CBC pipeline Separating signals from background Signal-based vetoes Instrumental vetoes Ranking statistics Review of interesting candidate-events 5

6 Chapter 2: CBC pipeline: Matched Filtering and Coincidence Analysis Waveforms Matched filter Template Banks Coincidence analysis Background estimation c 6

7 The waveform (1/4) Effect of sky location and polarization The gravitational-wave signal is a combination of two polarizations: F + and F x : detector response functions Depend on sky location (, ) and polarization angle Detector response versus sky location z x y For ground-based detectors: CBC signals spend up to 1 min in the detector bandwidth F + and F x approximated as constant over the duration of the signal! This approximation is no longer valid for long duration signals such as in the pulsar searches 7

8 The waveform (2/4) Post-Newtonian Restricted waveforms h + and h x are obtained from post-newtonian developments Up to 2.5 PN order in amplitude: [REF 6] A ( m k, m/ 2( t) [2 MF( t) ] 2)/3 (t) G = c = 1 F(t) is the instantaneous orbital frequency (t) is the orbital phase of the binary F( t) 1 2 d dt h(t) is a linear combination of harmonics of the orbital phase. k runs over harmonics, and m/2 is PN order in amplitude. Usual searches use restricted waveforms, namely waveforms where all terms with k 2 are neglected other harmonics of the orbital frequency are ignored OK from the detection point of view, at least for initial detectors May reduce the accuracy of parameter estimation, especially for high mass systems 8

9 The waveform (3/4) General formulation The restricted waveform at the detector can be written: 1Mpc h( t) A( t)cos(2 ( t) 2 0) D eff Physical distance to the source : Inclination angle between the rotation axis of the binary system and the direction of observation Effective distance = distance of an optimally located and oriented source that would produce the same signal strength Distance to the source, sky location and inclination angle are replaced by one single parameter 9

10 Signal frequency: At Newtonian order: The waveform (4/4) The Newtonian order 1Mpc h( t) A( t)cos(2 ( t) 2 0) D eff 5/3 4M A( t) ( f ( t)) r 2/3 f(t) = 2 x F(t) ( t) Instantaneous orbital frequency 16 f f ( t) 1 f 0 5/3 Amplitude and phase are function of the chirp mass: ( m1m2 ) ( m m ) Post-Newtonian developments add extra terms that depend on the symmetric mass ratio [REF 4] 10 M 1 2 3/5 1/5

11 [REF 4] Post-Newtonian waveforms Waveform families (1/2)» Known up to order 2.5PN for the amplitude and order 3.5PN for the phase 1Mpc h( t) A( t)cos(2 ( t) 2 0) D eff» Spin effects appear from order 1.5PN (spin-orbit) and 2PN (spin-spin) Expected to be negligible for Neutron Stars, may be significant for Black Holes 1+25 M Spinning Injections CBC Low Mass Search (1-35 M ) used restricted 2 PN waveforms during S5/VSR1 and is now using 3.5 PN waveforms (S6/VSR2) 3.5PN Spin Taylor Spinning Kludge! PN expansion become inaccurate for high mass systems 11

12 Waveform families (2/2) EOBNR waveforms [REF 8] The Effective-One-Body method provides complete analytic IMR waveforms with an attached ring-down Waveforms tuned to agree with NR simulations of non-spinning binaries Horizon distance = maximum distance at which an optimally located and oriented source is detectable EOB NR PN templates CBC High Mass Search ( M ) uses EOBNR waveforms 12

13 Matched filter in theory: In practice: Matched filtering: From theory to practice (1/4) S( t) The bounds of the integral are limited: 4 Re 0 ~ d ( ~ * f ) T ( f ) S ( f ) Expected waveform Detector reconstructed data (=template) One-sided noise power spectrum S( t) 4 Re - choice of f low : mainly a trade-off between computational cost and detector sensitivity - f final is limited by the sampling frequency and the template ending frequency (ISCO) f f final low n ~ d ( n e ~ * f ) T ( f ) S ( f ) 2 i f t e 2 df i f t df f low f final 13

14 In practice: Expected waveform: Matched filtering: From theory to practice (2/4) h F( M,, t c, 0, Deff )! Here we consider waveforms without spin! h Two intrinsic mass parameters, characteristic of the template 1Mpc T( M, D eff, t Time of Coalescence: c, 0 ) Extrinsic parameters: - Effective Distance - Time of coalescence - Initial orbital phase How do we extract them? SNR will be inversely proportional to the effective distance S( t) 4 Re f f final low ~ d ( FFT allows to extract S(t) for all possible arrival times. The maximum will give the time of coalescence ~ * f ) T ( f ) S ( f ) n e 2 i f t df 14

15 In practice: Matched filtering: From theory to practice (3/4) Initial orbital phase: The phase of the chirp signal is unknown: h( t) A[ hc ( t)cos 0 hs ( t)sin 0] cosine and sine phases of the waveform The SNR has to be maximized over all possible values of 0 This can be achieved by filtering the data with two orthogonal templates Filter with T 0 and T 90 and take quadratic sum This is equivalent to calculate the modulus of the complex matched filter output (instead of calculating the real part): f final S c ( t) 4 f low ~ d ( ~ * f ) T ( f ) S ( f ) n e 2 i f t df 15

16 Matched filtering: From theory to practice (4/4) Definition of the Signal to Noise Ratio (SNR): S SNR N 2 SNR : ( t) S c ( t) Signal To Noise Ratio threshold Trigger = Signal above analysis threshold Matched filter complex output: Matched filter noise: S c ( t) 2 4 f f final low 4Re ~ d ( The templates are normalized so that the effective distance can be extracted as: D eff ( 1Mpc) f final low ~ * f ) T ( f ) 2 i f t e Sn( f ) ~ ~ * T ( f ) T ( f ) df S ( f f n ) df 16

17 Scanning the parameter space (1/5) The template T depends on two mass parameters ( 1, 2) (we are neglecting spin) When filtering the data with a template, only one point of the parameter space is tested: Let us call this point 1 = ( 1, 2) It is necessary to try a family of templates sampling the parameter space! Templates should be placed over the parameter space in order to: Achieve coverage of space (no «holes») Preserve search efficiency: keep number of templates as low as possible Optimal SNR is obtained when the signal present in the data perfectly matches the template 1 = ( 1, 2) What is the SNR loss if the signal present in the data correspond to a different point in the parameter space? 2 = ( 1 + 1, 2+ 2) The recovered fraction of the optimal SNR is given by the Match M: M ( 1, 2) max, ( T( 1), T( 2)) 0 t c M is defined as the matched filter between the templates T( 1 ) and T( 2 ) maximized over extrinsic parameters 17

18 Scanning the parameter space (2/5) M ( 1, 2) max, ( T( 1, 2), T( 1 1, 2 2)) 0 t c S opt S Sopt S M S opt 18

19 Scanning the parameter space (3/5) M is defined as the matched filter between the templates T( 1 ) and T( 2 ) maximized over extrinsic parameters 1-M gives a distance between templates One can define a Minimal Match MM: Match corresponding to an acceptable loss of SNR M 1 M 1 Isomatch contour: boundary of the space where M > MM 19

20 Scanning the parameter space (4/5) From the match, define a metric on the parameter space In the regime 1-M << 1 the match can be approximated by [REF 11] Instead of the masses m 1, m 2, it is more convenient to use as parameters: For matches above ~95%, isomatch contours are ellipses In the 0, 1 space, the metric components g ij are constant at 1PN order, and have small variations at higher order. 20

21 Scanning the parameter space (5/5)» Each isomatch contour defines a region of the parameter space which overlaps with the template in the center with a match better than some minimal match value (one choose typically MM = 0.97 for CBC searches)» The template in the center can be used to search for signals in that region of the parameter space, at the price of a controlled loss of SNR (< 1 M ) [REF 12] Example of coverage Typical number of templates 21

22 An example of template bank CBC Low Mass search, M tot [2 ; 35M ] Request Minimum Match = 0.97 Coming back to m 1, m 2 variables Low Mass region is more densely populated than high mass region This is related to the duration and the number of cycles of the templates 2PN 1.4/1.4M f low = 50 Hz High Mass templates are short and contain few cycles It is easier to match different templates in the high mass region 0 14s (~1100 cycles) 17.5/17.5M s (~14 cycles) 22

23 Template bank in practice (1/3) Examples of template bank sizes (a week in S6/VSR2) Low Mass [2; 35 M ] High Mass [25; 100 M ] 7 days 7 days Template Bank Size: varies between 1,000 and 12,000 templates depending on type of search and detector noise curve. 23

24 Template bank in practice (2/3) Examples of template bank sizes (a week in S6/VSR2) Low Mass [2; 35 M ] 7 days Template Bank Size: varies between 1,000 and 12,000 templates depending on type of search and detector noise curve. Differences between detectors: due to different shapes of the Noise Power Spectrum 24

25 Template bank in practice (3/3) Examples of template bank sizes (a week in S6/VSR2) Low Mass [2; 35 M ] 7 days [REF 13] Estimate power spectrum from the median of fifteen 256s data segments Template Bank Size: varies between 1,000 and 12,000 templates depending on type of search and detector noise curve. Differences between detectors: due to different shapes of the Noise Power Spectrum Fluctuation in times: due to non-stationary detector noise 25

26 Matched filtering and computing cost (1/2) The computing cost of a matched filter search is due to: The number of templates (N) detector bandwidth The size of the FFT (N samples) involved in the matched filtering operation (to compute the SNR time series) Template duration Sampling frequency dominated by the low frequency evolution imposed by the high frequency content of the signal Example in LIGO CBC pipeline: Segment duration for FFT calculation = 256s (need to be at least four times larger than the longest template of the bank) Sampling Freq = 4096 Hz FFT size: N = 256 x 4096 = 1.05 x 10 6 Example of low mass template bank: N 8000 [REF 13] [REF 14] Number of operations Ο(N x N x log 2 [N]) 5 x N x N x log 2 *N+ 8.4 x

27 Matched filtering and computing cost (2/2) Number of operations Ο(N x N x log 2 [N]) 5 x N x N x log 2 *N+ 8.4 x With a 2 GHz CPU: Computing Time 420 s This is the computing time needed to filter 128 seconds of data (the edges of the FFT are corrupted) Need to use several computers in parallel to perform matched filter analyses Matched filtering is only a piece of the CBC analysis pipeline:! Need additional CPU for template placement, coincident tests, applying vetoes, recording triggers, Signal based vetoes are more expensive than matched filtering (CH3) Main CBC pipeline runs on clusters of hundreds or thousands of computing nodes (LIGO Data Grid) For the CBC low latency search a slightly different approach is chosen: Multi-Band Template Analysis 27

28 Multi-Band Template Analysis (used in CBC low latency search) The analysis can be split in a few bands Build one bank of real templates per frequency band Fewer templates in each bank Short templates in high frequency band Data can be down-sampled for the low frequency bands filtering Fewer and shorter FFTs [REF 15] duration sampling f final ~ 1 final * * * d ( f ) ~ Q ( f ) df f ~ d ( f ) ~ Q ( f ) df f ~ d ( f ) ~ Q ( f ) df flow flow f1 28

29 Background is not Gaussian!!! Outcome of matched filtering on LIGO and Virgo data An example on LIGO data An example on quiet Virgo data (WSR7)» Basic data quality cuts already applied Virgo VSR2 Loudest triggers Population of glitches [REF 21] SNR threshold Long tails of high SNR background triggers due to non-stationary and non- Gaussian detector noise! Can think of real data as Gaussian noise plus nuisance signals that leak into h(t) from the instrumental and environmental sub-systems (plus possible GW signals ) 29

30 How to reduce the false alarm rate? Matched filter produces elevated false alarm rates due to non-gaussian noise Need analysis techniques to reduce the false alarm rate or better distinguish background triggers from potential detections Require coincidence between several detectors (also allow to estimate the expected non-gaussian background) Get rid of bad quality data and instrumental glitches - Signal-based vetoes - Data Quality vetoes Develop a ranking statistics to select the most promising triggers Perform final sanity checks of interesting triggers with a detection checklist (follow-ups) See Chapter 3 30

31 Coincident analysis (1/3) Main Goals: - Combining triggers from different detectors - Reducing rate of background triggers / Estimating the background CBC pipeline requires coincident triggers between at least two detectors Check parameter consistency within allowed windows in time and in masses: t, M, η Smaller coincidence windows larger reduction of False Alarm Rate - Window size depends on parameter accuracy for single detector triggers (estimated with simulated signals) - t Must allow for time of flight between detector: LIGO Hanford LIGO Livingston: 10 ms Timing precision: typically a few ms [REF 16] Chirp mass very well determined Virgo LIGO: 30 ms less precisely determined 31 31

32 (ms) Coincident analysis (2/3)! Fixed coincidence windows are not optimal Errors on parameters vary across the parameter space Parameters are correlated [REF 17] 32

33 Coincident analysis (3/3) Use ellipsoids to define coincidences Ellipsoid is built using parameter space metric Takes into account correlations and parameter accuracy One tunable scale parameter in the pipeline ( ethinca tuning) Achieves background reduction of a factor 10 [REF 18] 33

34 Background estimation (1/4) Expected distribution of background triggers is estimated by using time shifts A zero-lag trigger (true coincidence) IFO 1 t IFO 2 t 34

35 Background estimation (2/4) Expected distribution of background triggers is estimated by using time shifts A time-slide trigger (accidental coincidence) IFO 1 t T IFO 2 t 35

36 Background estimation (3/4) Expected distribution of background triggers is estimated by using time shifts 100 time slide experiments are performed Background distribution is obtained by counting the number of time-slide triggers found in each slide experiment Works well for distant sites! Co-located detectors (LIGO H1-H2) usually show excess coincident background with respect to time slides estimates (evidence for correlated noise) [REF 24] [REF 19] 36

37 Background estimation (4/4) Expected distribution of background triggers is estimated by using time shifts Ex: S4 Binary Neutron Star search [REF 19] Total analyzed time = 576 hrs (Feb 22 March 24, 2005) injections Histogram of coincident triggers versus combined SNR Region where outlier triggers would appear candidates Background distribution (time-slides) 37