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Tests of General Relativity Through the Direct Detection of Gravitational Waves

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Tests of General Relativity Through the Direct Detection of Gravitational Waves Tests of general relativity through the direct detection of gravitational waves Chris Van Den Broeck Virtual Conference of the Polish Society on Relativity 2020 24-25 September 2020 Coalescing binary neutron stars and black holes: inspiral-merger-ringdown • 13 published binary black hole detections so far: GW150914, GW151012, GW151226, GW170104, GW170608, GW170729, GW170809, GW170814, GW170818, GW170823, GW190412, GW190814, GW190521 • Binary neutron star GW170817; possible binary neutron star GW190425 Access to strongly curved, dynamical spacetime Curvature of spacetime spacetime of Curvature Characteristic timescale Yunes et al., PRD 94, 084002 (2016) Fundamental physics with gravitational waves (from coalescing binaries) 1. The strong-field dynamics of spacetime 2. The propagation of gravitational waves 3. The nature of compact objects 1. The strong-field dynamics of spacetime Ø Inspiral-merger-ringdown process • Post-Newtonian description of inspiral phase • Merger-ringdown governed by additional parameters βn, ⍺n Ø Look for possible deviations in these parameters: LIGO + Virgo, PRL 118, 221101 (2017) Ø Rich physics: Dynamical self-interaction of spacetime, spin-orbit and spin-spin interactions, … 1. The strong-field dynamics of spacetime Ø Inspiral-merger-ringdown process • Post-Newtonian description of inspiral phase • Merger-ringdown governed by additional parameters βn, ⍺n Ø Combine information from multiple sources: LIGO + Virgo, PRD 100, 104036 (2019) 1. The strong-field dynamics of spacetime Ø Consistency between inspiral and merger-ringdown? • Masses and spins during inspiral can be used to predict mass and spin of the final object • Compare prediction from inspiral with what follows from merger-ringdown Ø Here too, combine information from multiple sources LIGO + Virgo, PRD 100, 104036 (2019) 1. The strongR.- ABBOTTfieldet al.dynamics of spacetime PHYS. REV. D 102, 043015 (2020) energy to be detectable in the data; no further modeling Ø Full structure of a gravitational wave signal: input is needed, although we do not require phase coher- h+ ih = h`m(t) 2Y`m(✓, φ) ence along each track. − ⇥ − The resulting Y α for GW190412 is shown in the h+ ih = h`m(t) `2Y2`m`(✓m, φ`) ð Þ − ⇥ −X≥ − X h+ ih = bottom panelh`m of(t) Fig.28Y.` Itm has(✓, aφ global) peak at α 1, ` 2 ` m ` h+ ih− ⇥= correspondingh` tom the−(t) dominant2Y` (2,2)m(✓ multipole,, φ) and¼ a ≥ − h ih = ⇥h (t`) 2 Y` m(✓`, φ) − X X + − `m ≥ 2−prominent`m local peak at α 1.5, corresponding to the − ⇥ `X−2 X` m ` ¼ • ` 2 ` m ` X≥ −mX3 multipoles. We also calculate Y α from different Dominant harmonic: ` = m =2 f22(t)=2X≥ forb− X segments¼ surrounding, but not includingð Þ GW190412, to • Frequency as function of time of higher-order` = mmodes:=2 f`m(t)=(capturem the/2) detectorf22(t noise) characteristics;↵ f22(t) in this case we call| the| quantity N α . The⇥ ensemble average μ α h+ ih = h`m(t) 2Y`m(✓, φ) ð Þ ð Þ¼ ⇥ • hSearch+ ih for= sub`−=-dominantm =2`h`=m(tfm )modes`m2=2(Yt)=(`m( ✓with, φmf)` m/frequency2)(tf)=(22(t) m ↵ f / 22 2) ( t ) f 22, mwhere(2t/m)N α1 ↵ and f 0is22 standard. 3left(t)m free deviation2/mm21/mσ α01.of1 N α0.are3 alsom2/m1 0.1 − − ⇥ − | | h+ ih =plottedh ð Þi for⇠ referenceh and`m to( highlightt) ⇠2ðYÞ the`m relative(✓ð, Þφ) strength ` 2 ` m ` ` 2 ` m ` h+ |ih | =− ⇥ h`m(t) 2Y`m−(✓, φ)⇠ ⇠ X≥ − X X≥ − X − ⇥ of` the2 GW` signalm present` − in the on-source segment. Ø Sub-dominant modes more prominent when strongly unequal` 2component` XInsteadm≥ `− ofX estimatingmasses the significance of the m 3 X≥ − multipolesX from comparing Y α to its background¼ at α 1.5, we perform a more powerfulð Þ statistical analysis ` = m =2 f`m(`t)=(= m =2m R./2) ABBOTT•ff`m22((tGW190412:t)=(et) al. ↵mf22/(2)t)f 22 m ( t 2 ) /m ↵ 1 f 22 ( 0t .) 3 m; GW190814:m2/m2/m1 1 0.3PHYS.0. 1 m REV.2/m D1102, 0430150.1 (2020) | | ⇠ ⇠ in¼ which we test the hypotheses that the data contain either | | ⇠ ` = ⇠m =2 f`m(t)=(m /2) f22(t) ↵f22(t) m2/m1 0.3 m2/m1 0.1 only noise (H0), or noise and a dominant-multipole ` = energym =2 to be detectablef`m in(t the)=( data; nom further/2) modelingf| 22|(t)maximum↵f22 likelihood(t) signalm2/m (H ),1 or noise0 and.3⇠ a maximumm2/m1 0.⇠1 input is needed, although we do not require| | phase coher- 1 ⇠ ⇠ ence along each track. likelihood signal that includes m 2 and m 3 multipoles Ø(HIn). both By maximizing cases the likelihood¼ of observing¼ Y α The resulting Y α for GW190412 is shown in the 2 ð Þ bottom panel of Fig.ð Þ 8. It has a global peak at α 1, given each hypothesis over a free amplitude parameter for ¼ strong evidence corresponding to the dominant (2,2) multipole, and a each multipole, we obtain likelihood ratios for H1 and H2, prominent local peak at α 1.5, corresponding to the andfor their modes difference at is in turn incorporated into a detection m 3 multipoles. We also calculate¼ Y α from different statistic β [see Eq. (7) in [153] ]. segments¼ surrounding, but not includingð Þ GW190412, to ↵From=1 the on-source.5 m data=3 segment taken from the LIGO capture the detector noise characteristics; in this case we Livingston detector, we found the detection statistic β call the quantity N α . The ensemble average μ↵α =1.i.e.5 m =3 −4 ¼ ð Þ ð Þ¼ 6.1 with a p-value of 6.4 × 10 for EOBNR HM model; N α and standard deviation σ α of N α are also −4 plottedh ð Þi for reference and to highlightð Þ the relativeð Þ strength and β 6.2 with a p-value < 6.4 × 10 for Phenom HM model,¼ which strongly supports the presence of m 3 of the GW signal present in the on-source segment. ¼ Instead of estimating the significance of the m 3 modes in the signal. The full distribution of β from off- multipoles from comparing Y α to its background¼ at source data segments from the LIGO Livingston detector α 1.5, we perform a more powerfulð Þ statistical analysis surrounding the trigger time of GW190412 is shown in the in¼ which we test the hypotheses that the data contain either inset of Fig. 8. only noise (H0), or noise and a dominant-multipoleLIGO + Virgo, PRD 102, 043015 (2020) maximum likelihood signal (H1), or noise and a maximumLIGO + Virgo, ApJ Lett.D. 896 Signal, L44 reconstructions (2020) FIG.likelihood 8. Top panel: signal Time-frequencythat includes m spectrogram2 and m 3 ofmultipoles data con- (H ). By maximizing the likelihood¼ of observing¼ Y α As an additional test of consistency, and an instructive taining GW190412,2 observed in the LIGO Livingston detector.ð Þ The horizontalgiven each axis hypothesis is time (in over seconds) a free relative amplitude to the parameter trigger time for visual representation of the observed GW signal, we (1239082262.17).each multipole, The we amplitude obtain likelihood scale of ratios the detector for H1 outputand H2 is, compare the results of two signal reconstruction methods. normalizedand their by differencethe PSD of is the in noise.turn incorporated To illustrate into the method,a detection the One is derived from the parameter-estimation analysis predictedstatistic trackβ for[see the Eq.m (7)3 inmultipoles[153] ]. is highlighted as a dashed presented in Sec. III, the second uses the model-agnostic ¼ line, aboveFrom the the track on-source from the datam segment2 multipoles taken that from are the visible LIGO in wavelet-based burst analysis BayesWave [154] which was the spectrogram.Livingston detector, Bottom panel: we found¼ The the variation detection of Y statisticα , i.e.,β the also used to generate PSDs. A detailed discussion of such −4 ð Þ ¼ energy6.1 inwith the pixelsa p-value of the of top6.4 × panel,10 alongfor EOBNR the track HM defined model; by signal comparisons for previous BBH observations can be and β 6.2 with a p-value < 6.4 × 10−4 for Phenom HM fα t αf22 t , where f22 t is computed from the Phenom HM found in [155]. ð Þ¼model,¼ð whichÞ stronglyð Þ supports the presence of m 3 analysis. Two consecutive peaks at α 1.0 and α 1.5 (thin For GW190412, both signal reconstruction methods modes in the signal. The full distribution¼ of β¼from¼ off- dashed line) indicate the energy of the m 2 and m 3 multi- agree reasonably well as illustrated in Fig. 9. To quantify poles,source respectively. data segments Inset: The from distribution the LIGO of¼ the Livingston detection¼ detector statistic β in noise,surrounding used to the quantify trigger timep-values of GW190412 for the hypothesis is shown that in the the the agreement for each signal model from the Phenom and data containsinset of Fig.m 82. and m 3 multipoles (red dashed line). EOB families, we compute the noise-weighted inner ¼ ¼ product [128,151] between 200 parameter-estimation sam- Δf 1=5 Hz alongD. the Signal frequency reconstructions axis. By doing so, we ples and the BayesWave median waveform. The BayesWave FIG. 8. Top panel: Time-frequency spectrogram of data con-can¼ decouple the energy in individual multipoles of the waveform is constructed by computing the median values at taining GW190412, observed in the LIGO Livingston detector. As an additional test of consistency, and an instructive signal.visual Once representationf22 t is defined, of the this observed is a computationally GW signal, we every time step across samples.
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