Lecture 3. Alex Nielsen Max Planck Institute for Gravitational Physics Hanover, Germany. How can we detect gravitational wave signals?

Transcription

1 Lecture 3 Alex Nielsen Max Planck Institute for Gravitational Physics Hanover, Germany How can we detect gravitational wave signals? 2015 International Summer School on Numerical Relativity and Gravitational Waves, KAIST, Daejeon Tuesday 28 July,

2 Lecture 1 - What are gravitational waves? Linearised approximation Energy carried by gravitational waves Generation of gravitational waves Evidence for gravitational waves in binaries Detecting gravitational waves Lecture 2 What are the sources of gravitational waves? Neutron stars Black holes Tidal disruption The data analysis challenge Lecture 3 How can we detect gravitational wave signals? Template banks Non-Gaussian noise Estimating the background Detection pipelines and PyCBC 2

3 (Simulated signal)

4 Matched filtering Source: Babak et al. (2013) Matched filter is the optimal linear filter (it maximises the signal to noise) if the data is Gaussian stationary and the signal is known. 4

5 Beware statistics... (and grammar and quotations) If you torture the data enough, it will confess - Ronald Coase (NP Econ 1991) 5

6 Chirp signals Time domain signal from inspiral is a chirp (increasing frequency, increasing amplitude) 5 /4 t c t 1 M h(t) cos 5/ 4 DL (t c t) M M= 5/8 ( ) (m 1 m 2 )3 / 5 1 /5 (m1 +m2) Source: Adrian Webb 6

7 Newtonian order SN HB At Newtonian order, only the chirp mass is measured. It is impossible to tell neutron stars and black holes apart. NS BH (Ohme, AN, Keppel, Lundgren 2013)7

8 Initial LIGO ignored spin effects Stationary black holes are characterised by mass and spin only (black hole no hair theorems). General relativity predicts that binary orbits are effected by spin. [ ] 2E 3 η 2 = 1 + v ηmv [ ( 2 i 8m2i 3M ) ] 3 4 ( ) +2η χ. L v +O v ( ) i N 2 Van Den Broeck et al., Phys.Rev. D80 (2009) We recommend the continued use of the non-spinning stationary phase template bank until the false alarm rate associated with templates which include spin effects can be substantially reduced. 8

9 Post-Newtonian expansion For an expansion parameter v 2 M x (π M t f ) c r 2 /3 () 9

10 Waveform calculation methods Taylor pn - post-newtonian expansion in v/c EOB Effective One Body NR - Numerical Relativity IMRPhenom Inspiral Merger Ringdown Phenomenological 10 Source: Frank Ohme

11 Inspiral, merger, ringdown (IMR) gravitational waveforms 11 Source: Mohapatra et al. (2014)

12 Match and fitting factor s h m(s,h)= s s h h * s (f ) h (f ) s h =4 ℜ df Sn ( f ) Fitting Factor (FF)= max over template bank of m (s, h) 12

13 13 Source: S. Hild (2012)

14 Fitting factors in template banks without spin

15 Orbits, precession and disruption Source: Thorne based on Chen and Foucart 15

16 Projected precessing BH spin Alex Nielsen: NSBH Challenges and Prospects 16

17 Non-Gaussian noise 17

18 Using reweighted SNR Signal to Noise Ratio (SNR) e 2πift s (f ) h * (f ) ρ=4 ℜ df S n (f ) N Reduced chi squared New SNR (reweighted SNR) ρ N ρ j N 2 j=1 χr = 2N 2 ( 2 ) ρ ρ = /6 [(1+( χ r ) )/2] 18

19 Using reweighted SNR Signal to Noise Ratio (SNR) e 2πift s (f ) h * (f ) ρ=4 ℜ df S n (f ) N Reduced chi squared ρ N ρ j N 2 j=1 χr = 2 N 2 ( 2 ) Reweighted SNR ρ = ρ /6 [(1+( χ r ) )/ 2] 19

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21 GW (Blind injection Big Dog ) 21

22 Background rate 22 Source:Abadie et al. PRD85, (2012)

23 False Alarm Rate (FAR) False Alarm Rate background triggers above threshold λ= total length of time slides Inverse False Alarm Rate (IFAR) 1 = FAR k Poisson distribution False Alarm Probability λ T (λ T ) e P( X =k ) = k! λ T = 1 e λt 23

24 ROCs Receiver Operating Characteristic Cyan: Aligned-spin bank Magenta: Non-spinning bank Alex Nielsen: NSBH Challenges and Prospects 24

25 Detection pipelines software PyCBC offline frequency domain Germany, USA GSTLAL-SVD online and offline time domain - USA GSTLAL-SPIIR online time domain - Australia MBTA online time domain - France, Italy cohptf offline GRBs - UK cwb bursts, time-frequency wavelets X-pipeline - bursts Powerflux continuous waves, all sky TwoSpect continuous waves, all sky, targeted (Sco X-1) CrossCorr continuous waves, targeted (Sco X-1) Radiometer stochastic background 25

26 PyCBC - aims Python based code Create a flexible, extensible software for CBC analysis that can be released for the public Enable simple, easy and transparent access for various many-core architectures like GPUs Ultimately become the data analysis tool of the advanced era 26

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28 FINDCHIRP and pycbc_inspiral 28 Allen et al. FINDCHIRP (2011)

29 GPU running Identical runs ~x50 faster on GPUs (Nvidia Tesla C2050) compared to CPUs, (Intel Xeon E5420) 29

30 PyCBC files and documentation PyCBC is freely available for download and should be installed along with LALsuite pycbc/workflow/ini_files pycbc/examples/banksim 30

31 End of lecture 3 31