Measurement of sub-dominant modes in a BBH population

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1 Measurement of sub-dominant modes in a BBH population Brendan O Brien, Filipe Da Silva, Sergey Klimenko University of Florida 1

2 Outline Introduction: motivation, previous work

3 Outline Introduction: motivation, previous work Synchronization Method: coherent summation of binary black hole (BBH) events

4 Outline Introduction: motivation, previous work Synchronization Method: coherent summation of binary black hole (BBH) events Results: method applied to simulated events, figures of merit

5 Outline Introduction: motivation, previous work Synchronization Method: coherent summation of binary black hole (BBH) events Results: method applied to simulated events, figures of merit Conclusion: upshot, future work

6 Outline Introduction: motivation, previous work Synchronization Method: coherent summation of binary black hole (BBH) events Results: method applied to simulated events, figures of merit Conclusion: upshot, future work

7 Introduction: Background and motivation GW emission from BBH systems is best understood in spherical harmonics: q=2 (SXS:BBH:0169) 2

8 Introduction: Background and motivation GW emission from BBH systems is best understood in spherical harmonics: (2,2) dominates for most systems q=2 (SXS:BBH:0169) 2

9 Introduction: Background and motivation GW emission from BBH systems is best understood in spherical harmonics: (2,2) dominates for most systems all other modes are known as subdominant modes (SDMs) q=2 (SXS:BBH:0169) 2

10 Introduction: Background and motivation GW emission from BBH systems is best understood in spherical harmonics: (2,2) dominates for most systems Ringdown: quasi- normal modes (QNMs) all other modes are known as subdominant modes (SDMs) q=2 (SXS:BBH:0169) 2

11 Introduction: Background and motivation GW emission from BBH systems is best understood in spherical harmonics: (2,2) dominates for most systems Ringdown: quasi- normal modes (QNMs) all other modes are known as subdominant modes (SDMs) study of QNMs is known as black hole spectroscopy q=2 (SXS:BBH:0169) 2

12 Introduction: Background and motivation GW emission from BBH systems is best understood in spherical harmonics: (2,2) dominates for most systems Ringdown: quasi- normal modes (QNMs) all other modes are known as subdominant modes (SDMs) study of QNMs is known as black hole spectroscopy SDMs and QNMs have yet to be observed q=2 (SXS:BBH:0169) 2

13 Introduction: Measuring SDMs/QNMs GW Requires a BBH event with high signal-to-noise ratio 3

14 Introduction: Measuring SDMs/QNMs GW Requires a BBH event with high signal-to-noise ratio During O3: possible we could detect sub-dominant modes, unlikely to measure QNMs 3

15 Introduction: Measuring SDMs/QNMs GW Requires a BBH event with high signal-to-noise ratio During O3: possible we could detect sub-dominant modes, unlikely to measure QNMs Solution: coherent summation of multiple signals = 3

16 Introduction: Previous work and main concept Previous work: 4

17 Introduction: Previous work and main concept Previous work: Synchronizing QNMs using a signal model (Yang et al. 2017, C. Da Silva et al. 2018) 4

18 Introduction: Previous work and main concept Previous work: Synchronizing QNMs using a signal model (Yang et al. 2017, C. Da Silva et al. 2018) This study is a simple approach to an ill-defined problem: 4

19 Introduction: Previous work and main concept Previous work: Synchronizing QNMs using a signal model (Yang et al. 2017, C. Da Silva et al. 2018) This study is a simple approach to an ill-defined problem: Synchronize without the use of a priori knowledge of the signal model 4

20 Introduction: Previous work and main concept Previous work: Synchronizing QNMs using a signal model (Yang et al. 2017, C. Da Silva et al. 2018) This study is a simple approach to an ill-defined problem: Synchronize without the use of a priori knowledge of the signal model Measure sub-dominant modes during merger and ringdown of combined BBH event 4

21 Introduction: Previous work and main concept Previous work: Synchronizing QNMs using a signal model (Yang et al. 2017, C. Da Silva et al. 2018) This study is a simple approach to an ill-defined problem: Synchronize without the use of a priori knowledge of the signal model Measure sub-dominant modes during merger and ringdown of combined BBH event Maximize the overlap between multiple BBH signals by applying a transformation set 4

22 Outline Introduction: motivation, previous work Synchronization Method: coherent summation of binary black hole (BBH) events Results: method applied to simulated events, figures of merit Conclusion: upshot, future work

23 Synchronization Method: Simulated waveforms Numerical relativity waveforms (SXS) including harmonic modes up to (ℓ=5,m=5) 5

24 Synchronization Method: Simulated waveforms Numerical relativity waveforms (SXS) including harmonic modes up to (ℓ=5,m=5) Parameter space chosen to emulate BBH events which have been detected: 5

25 Synchronization Method: Simulated waveforms Numerical relativity waveforms (SXS) including harmonic modes up to (ℓ=5,m=5) Parameter space chosen to emulate BBH events which have been detected: Mass ratio, total mass zero initial spin, zero eccentricity, chirp mass 5

26 Synchronization Method: Simulated waveforms Numerical relativity waveforms (SXS) including harmonic modes up to (ℓ=5,m=5) Parameter space chosen to emulate BBH events which have been detected: Mass ratio, total mass, chirp mass zero initial spin, zero eccentricity Randomly selected source distance, sky location, orientation confined so recovered SNR is less than SNRGW

27 Synchronization Method: Coherent WaveBurst (cwb) Use cwb for unmodeled signal detection and reconstruction GW

28 Synchronization Method: Coherent WaveBurst (cwb) Use cwb for unmodeled signal detection and reconstruction GW strain data 6

29 Synchronization Method: Coherent WaveBurst (cwb) Use cwb for unmodeled signal detection and reconstruction GW strain data wavelet transform/ pixel selection 6

30 Synchronization Method: Coherent WaveBurst (cwb) Use cwb for unmodeled signal detection and reconstruction GW reconstructed waveform strain data wavelet transform/ pixel selection 6

31 Synchronization Method: Transformations Exclusively use the waveforms reconstructed by cwb to synchronize BBH signals Time-frequency representation of waveform reconstructed by cwb 7

32 Synchronization Method: Transformations Exclusively use the waveforms reconstructed by cwb to synchronize BBH signals Apply a transformation set: time rescale, time shift, frequency shift, phase shift Time-frequency representation of waveform reconstructed by cwb 7

33 Synchronization Method: Transformations Exclusively use the waveforms reconstructed by cwb to synchronize BBH signals Apply a transformation set: time rescale, time shift, frequency shift, phase shift rescale Time-frequency representation of waveform reconstructed by cwb 7

34 Synchronization Method: Transformations Exclusively use the waveforms reconstructed by cwb to synchronize BBH signals Apply a transformation set: time rescale, time shift, frequency shift, phase shift time shift Time-frequency representation of waveform reconstructed by cwb 7

35 Synchronization Method: Transformations Exclusively use the waveforms reconstructed by cwb to synchronize BBH signals Apply a transformation set: time rescale, time shift, frequency shift, phase shift frequency shift Time-frequency representation of waveform reconstructed by cwb 7

36 Synchronization Method: Transformations Exclusively use the waveforms reconstructed by cwb to synchronize BBH signals Apply a transformation set: time rescale, time shift, frequency shift, phase shift Time-frequency representation of waveform reconstructed by cwb 7

37 Synchronization Method: Transformations Exclusively use the waveforms reconstructed by cwb to synchronize BBH signals Apply a transformation set: time rescale, time shift, frequency shift, phase shift Optimize a functional using MINUIT: Time-frequency representation of waveform reconstructed by cwb 7

38 Synchronization Method: Maximizing waveform overlap Synchronization method applied to two reconstructed BBH events (black: q = 1.0, Mtot = 75.7M, Mc= 37.0; red: q = 1.5, Mtot = 76.5M, Mc = 42.0) 8

39 Synchronization Method: Maximizing waveform overlap Synchronization method applied to two reconstructed BBH events (black: q = 1.0, Mtot = 75.7M, Mc= 37.0; red: q = 1.5, Mtot = 76.5M, Mc = 42.0) 8

40 Synchronization Method: Maximizing waveform overlap optimization time window Synchronization method applied to two reconstructed BBH events (black: q = 1.0, Mtot = 75.7M, Mc= 37.0; red: q = 1.5, Mtot = 76.5M, Mc = 42.0) 8

41 Outline Introduction: motivation, previous work Synchronization Method: coherent summation of binary black hole (BBH) events Results: method applied to simulated events, figures of merit Conclusion: upshot, future work

42 Results: Summation of simulated waveforms Coherent stacking method applied to 16 BBH simulated waveforms 9

43 Results: Summation of simulated waveforms one simulated BBH waveform Coherent stacking method applied to 16 BBH simulated waveforms 9

44 Results: Summation of simulated waveforms one simulated BBH waveform 16 waveforms stacked Coherent stacking method applied to 16 BBH simulated waveforms 9

45 Results: Summation of simulated waveforms one simulated BBH waveform 16 waveforms stacked Coherent stacking method applied to 16 BBH simulated waveforms 9

46 Results: Summation of simulated waveforms one simulated BBH waveform 16 waveforms stacked x16 Coherent stacking method applied to 16 BBH simulated waveforms 9

47 Results: Summation of simulated waveforms one simulated BBH waveform 16 waveforms stacked FFT of stacked waveform Coherent stacking method applied to 16 BBH simulated waveforms 9

48 Results: Summation of simulated waveforms one simulated BBH waveform 16 waveforms stacked FFT of stacked waveform Coherent stacking method applied to 16 BBH simulated waveforms 9

49 Results: Summation of simulated waveforms one simulated BBH waveform 16 waveforms stacked FFT of stacked waveform Coherent stacking method applied to 16 BBH simulated waveforms 9

50 Results: Extracting sub-dominant modes 10

51 Results: Extracting sub-dominant modes 10

52 Results: Extracting sub-dominant modes cwb 10

53 Results: Extracting sub-dominant modes cwb x16 x16 10

54 Results: Extracting sub-dominant modes cwb x16 x16 synchronization method 10

55 Results: Extracting sub-dominant modes cwb x16 x16 synchronization method cwb 10

56 Results: Extracting sub-dominant modes cwb x16 x16 synchronization method cwb an aggregate waveform is reconstructed without a signal model 10

57 Results: Extracting sub-dominant modes cwb x16 x16 synchronization method cwb an aggregate waveform is reconstructed without a signal model 10

58 Results: Extracting sub-dominant modes Coherent stacking method applied to strain data with injected numerical relativity waveforms, recovered and reconstructed with cwb 11

59 Results: Extracting sub-dominant modes single reconstructed BBH waveform Coherent stacking method applied to strain data with injected numerical relativity waveforms, recovered and reconstructed with cwb 11

60 Results: Extracting sub-dominant modes single reconstructed BBH waveform reconstructed aggregate BBH waveform Coherent stacking method applied to strain data with injected numerical relativity waveforms, recovered and reconstructed with cwb 11

61 Results: Extracting sub-dominant modes single reconstructed BBH waveform reconstructed aggregate BBH waveform x4 Coherent stacking method applied to strain data with injected numerical relativity waveforms, recovered and reconstructed with cwb 11

62 Results: Extracting sub-dominant modes single reconstructed BBH waveform reconstructed aggregate BBH waveform FFT of aggregate BBH waveform Coherent stacking method applied to strain data with injected numerical relativity waveforms, recovered and reconstructed with cwb 11

63 Results: Extracting sub-dominant modes single reconstructed BBH waveform reconstructed aggregate BBH waveform FFT of aggregate BBH waveform Coherent stacking method applied to strain data with injected numerical relativity waveforms, recovered and reconstructed with cwb 11

64 Conclusion: We introduce a method for coherently stacking multiple BBH events 12

65 Conclusion: We introduce a method for coherently stacking multiple BBH events We demonstrate the possibility to extract sub-dominant modes from noise without using signal model 12

66 Conclusion: We introduce a method for coherently stacking multiple BBH events We demonstrate the possibility to extract sub-dominant modes from noise without using signal model Future work: applying this method to BBH events detected by LIGO 12

67 Conclusion: We introduce a method for coherently stacking multiple BBH events We demonstrate the possibility to extract sub-dominant modes from noise without using signal model Future work: applying this method to BBH events detected by LIGO Thank you! 12

68 Extra slides Signals with similar astrophysical parameters are easier to synchronize We use chirp mass as a measure of signal morphology Binary tree for coherent stacking of 16 BBH events

69 Extra slides Need a way to estimate the performance of summation procedure Introduce root-sum-squared amplitude of a waveform: We define the efficiency of stacking as: Can be calculated for entire simulated signal or individual modes

70 Extra slides We stack 16 BBH events by maximizing overlap of cwb reconstructed waveforms We calculate the efficiency for several harmonic modes: Harmonic Mode H1 Efficiency (%) L1 Efficiency (2,2) (3,3) (4,4) Sub-dominant (%)