Gravitational-Wave Constraints on GWTC-2 Events by Measuring Tidal

15:00-15:15, July 8 (Thu.), 2021

Gravitational-Wave Constraints on GWTC-2 Events by Measuring Tidal Deformability and Spin-Induced Quadrupole Moment Λ arXiv:2106.09193 δκ Tatsuya Narikawa (ICRR, The Univ. of Tokyo)

Nami Uchikata (ICRR), Takahiro Tanaka (Kyoto Univ.)

KIW8

1 Introduction spin-induced quadrupole moment Λ δκ Measuring tidal deformability Λ and SIQM δκ by GW → Tests of GR

We report constraints on Λ for low-mass GWTC-2 events (long-inspiral regime): GW151226, GW170608, GW190707, GW190720, GW190728, GW190924 Related works - Tidal tests: Johnson-McDaniel+2018 (Constraints on Boson stars Λ by future BBH detections) - SIQM tests: ① Krishnendu+2019 (GW151226 & GW170608); δκ ② O3 TGR paper 2020 (GWTC-2 events) 2 Exotic compact objects (ECOs) ECO: Alternatives to BH in GR 1.3 NatureMotivation: of Dark Matter. Avoidance spacial singularity in BH, solution for 5 information loss problem of BH [GWIC-3G_science-case]

neutron star

fuzzball, gravastar, wormhole, 2-2 hole, collapsed polymer, quantum isotropic fluid star star/bounce/condensate, … black hole limit strongly anisotropic star boson star

1020 10 3 2 surface redshift Planck scale clean photosphere photosphere Buchdahl Compactness

Figure 1.3: Schematic classification of dark compact objects. Compactness of ECOs is expressed as the gravitational ECO modify GWs and tidal deformability and SIQM is useful to test redshift at the surface: objects with a photon-sphere have z & 1.7, the Buchdhal’s limit corresponds to z = 3, the clean photon-spheredeviation condition from [86] requires BBH zin& GR7.9, Planck-scale(Λ=0 & δκ=0). corrections correspond to z & 1020, and a BH has infinite redshift. Objects in the same category have similar dynamical properties. Boxes refer to known ECO models and the case of anIf ordinary we find NS (deviationz 1) is reported from as aBBH, reference. which provides evidence for existence ⇡ of ECO and hint for new physics. 3 interact electromagnetically or any electromagnetic (EM) signal from the surface of the compact object might be highly redshifted [86]. Example GW signatures from the inspiral epoch include dipole radiation as well as the variety of matter effects as in the case of NSs [96] (see, Chapter 2). An ECO could be parameterized by the gravitational redshift zg near its surface (see Fig. 1.3). This parameter can change by several orders of magnitude depending on the model. BHs have z • while g ! NSs and the most compact theoretically constructed boson stars have z O(1). Thus, for sufficiently g ⇠ large values of zg compact objects could behave like BHs with increasing precision. Studies of geodesic motion and quasi-normal modes indicate that ECOs with zg . 1.4 display internal structure effects that can be discerned in future GW observations. For larger values of zg, ECOs mimic BHs [99, 86, 100] as departures are redshifted to ever smaller values. Interestingly, models of near-horizon quantum structures—motivated by various scenarios [75–77, 82]—can reach redshifts as high as z O(1020) for ECOs in the frequency band g ⇠ of ground-based detectors. GWs could be our only hope to detect or rule them out. Additionally, while the ringdown signal can be qualitatively similar to that of a BH, quasi-normal modes of, e.g., gravastars, axion stars and boson stars, are different from Kerr BHs [10]. 3G detectors will have unprecedented ability to extract such modes. In addition to gravitational modes, matter modes might be excited in the ringdown of an extremely compact object, akin to fluid modes excited in a remnant NS [96]. In the case of certain BH mimickers the prompt ringdown signal is identical to that of a BH; however, these objects generically support quasi-bound trapped modes which produce a modulated train of pulses at late time. These modes appear after a delay time whose characteristics are key to test Planckian corrections at the horizon scale that could be explored with 3G detectors [86].

1.3 Nature of Dark Matter. The exquisite ability of 3G detectors to probe the population and dynamics of electromagnetically dark objects throughout the Universe and harness deep insights on gravity can help reveal the nature of dark matter and answer key questions about its origin. Black holes as dark matter candidates: LIGO and Virgo discoveries have revived interest in the possibility that dark matter could be composed, in part, of BHs of masses 0.1–100M [101–103]. Such BHs might ⇠ have been produced from the collapse of large primordial density fluctuations in the very early Universe or during inflation [104, 105]. The exact distribution of masses depends on the model of inflation, and might be further affected by processes in the early Universe such as the quantum-chromodynamic phase transition [106]. SYSTEMATIC AND STATISTICAL ERRORS IN A … PHYSICAL REVIEW D 89, 103012 (2014) decreases. The deformation of each body will have an effect The total mass is M m1 m2, where m1 and m2 are ¼ þ 2 on the rate at which the bodies coalesce. BNS systems the component masses, η m1m2=M is the symmetric SYSTEMATIC AND STATISTICAL ERRORS IN A … ¼ 3 2=3 PHYSICAL REVIEW D 89, 103012 (2014) therefore depart from the point-particle approximation at mass ratio, x πGMfgw=c is the PN expansion high frequencies and require an additional correction to the ¼ð Þ decreases. The deformationparameter, of each bodyf willgw have2f anorb effectis the GWThe frequency, total massf isorbMis them1 m2, where m1 and m2 are energy and luminosity of the system relativeon the rate to the at which point- the bodies coalesce.¼ BNS systems the component masses,¼η mþ m =M2 is the symmetric binary’s orbital frequency, and χ1 m1=M and χ2 1 2 therefore depart from the point-particle approximation at ¼ ¼ 3 2=3 particle terms. m =M are the two mass fractions.mass Note ratio, thatx theπ PNGMf ordergw=c is the PN expansion high frequencies and require an2 additional correction to the ¼ð Þ Since a NS in a binary system will deform under the tidal is labeled by the exponent on x insideparameter, the squarefgw 2 brackets,forb is the GW frequency, forb is the energy and luminosity of the system relative to the point- ¼ influence of its companion, its quadrupole moment Qij which is why these terms are referredbinary’s to orbital as 5PN frequency, and 6PN and χ1 m1=M and χ2 particle terms. ¼ ¼ must be related to the tidal field E caused by its m2=M are the two mass fractions. Note that the PN order ijSince a NS in a binary systemcorrections. will deform Since under the the tidal 5PN and 6PN tidal correction companion. For a single NS, to leading order in the 5 6 is labeled by the exponent on x inside the square brackets, influence of its companion,coefficients its quadrupole multiply momentx andQ x , respectively, these effects quasistationary approximation and ignoring resonance, ij which is why these terms are referred to as 5PN and 6PN must be related to the tidalwill be field insignificantEij caused at by low its frequenciescorrections. and Since increasingly the 5PN and 6PN tidal correction 2=3 companion. For a singlemore NS, to significant leading order at higher in the frequenciescoefficients (x ∼ f multiply), asx antici-5 and x6, respectively, these effects Qij −λEij; (1) orb ¼ quasistationary approximationpated. and The ignoring Appendix resonance, derives eachwill be tidally insignificant corrected at low PN frequencies and increasingly 5 2=3 where λ 2=3 k2R =G parametrizes the amount that a Q waveform−λE ; family from Eqs.(1) (2)moreand (3) significant. at higher frequencies (x ∼ forb ), as antici- ¼ð Þ ij ¼ ij NS deforms [10]. The i and j are spatial tensor indices, k2 is The point-particle energy and luminositypated. The are Appendix only known derives each tidally corrected PN 5 the second Love number, and R is thewhere NS’s radius.λ 2= Since3 k2Rλ=G parametrizesto 3.5 PN order the amount[14]. However, that a wewaveform add tidal family corrections from Eqs. to(2) and (3). ¼ð Þ parametrizes the severity of a NS’s deformationNS deforms [10] under. The ai andthej are energy spatial tensor and luminosity indices, k2 is that appearThe point-particle at 5 PN and energy 6 PN and luminosity are only known given tidal field, it must depend on thethe NS second EOS. Love NSs number, with andordersR is the without NS’s radius. knowing Since theλ higher-orderto 3.5 PN order point-particle[14]. However, we add tidal corrections to parametrizes the severity ofterms. a NS The’s deformation justification under for a includingthe energy the tidal and luminosity corrections that appear at 5 PN and 6 PN large radii will more easily be deformed by the external orders without knowing the higher-order point-particle given tidal field, it must dependhas typically on the NS been EOS. that NSs they with are always associated with the tidal field, because there will be a morelarge extreme radii will gravita- more easily be deformed by the external terms. The justification for including the tidal corrections tional gradient over their radius. For a fixed mass, NSs with large coefficient Gλ c2= Gm 5 ∼ c2R = Gm 5 ∼ 105 tidal field, because there will be a more extremeA½ gravita-ð AÞhas typically½ A ð beenA thatÞ they are always associated with the large radii are also referred to as havingtional a stiff gradient EOS, over and, their radius.[10]. For Therefore, a fixed mass, although NSs with they appearlarge at coefficient high PNG orders,λ c2= theGm 5 ∼ c2R = Gm 5 ∼ 105 A½ ð AÞ ½ A ð AÞ for the same mass, NSs with small radiilarge have radii a are soft also EOS. referredeffect to as of having the tidal a stiff terms EOS, on and, the binary[10].’s Therefore, orbit are although comparable they appear at high PN orders, the Therefore, NSs that have large valuesfor of λ thewill same have mass, large NSs withto small the effects radii have of the a soft 3 PN EOS. and 3.5effect PN of point-particle the tidal terms terms. on the binary’s orbit are comparable radii, a stiff EOS, and become severelyTherefore, deformed NSs in that BNS have largeHowever, values this of λ claimwill have was large contradictedto the effects in Ref. of[24] the 3because PN and 3.5 PN point-particle terms. systems; on the other hand, NSs that haveradii, small a stiff values EOS, of andλ becomethe severely tidal corrections deformed in are BNS actuallyHowever, associated this claim with was contradicted the in Ref. [24] because systems; on the other hand, NSs that have small2 values5 of λ 3 the tidal2 corrections5 are actually associated with the will have small radii, a soft EOS, and will be less severely coefficient c R= GM ∼ 10 ≪ c RA= Gm2 A , which5 3 2 5 will have small radii, a softis EOS, apparent and will½ from be less theð formseverelyÞ of Eqs.coefficient(2)½ and ð(3)c .R= WeÞGM show∼ in10 ≪ c RA= GmA , which deformed in these systems. is apparent½ from theð formÞ of Eqs. (2)½ and ð(3). WeÞ show in deformed in these systems.Sec. VA that not knowing the higher-order PN point- Tidal effects are most important at smallTidal separations effects are and most important at small separations and Sec. VA that not knowing the higher-order PN point- particle terms leads to significant systematic error when therefore at high frequencies in BNS systems.therefore Tidal at high correc- frequencies in BNS systems. Tidal correc- particle terms leads to significant systematic error when tions to the energy δEtidal and tidaltions corrections to the energy to theδE recoveringand tidal tidal corrections parameters. to the Yagirecovering and Yunes tidal in parameters. Ref. [24] Yagi and Yunes in Ref. [24] tidaland Favata in Ref. [25] also discussed the importance of luminosity δLtidal add linearly to the point-particleluminosity δLtidal energyadd linearly to the point-particle energy and Favata in Ref. [25] also discussed the importance of EPP and luminosity LPP. Though theEPP leading-orderand luminosity tidalLPP. Thoughthese unknown the leading-order point-particle tidal terms.these unknown point-particle terms. correction is a Newtonian effect, it is oftencorrection referred is a Newtonian to as a effect, it is often referred to as a B. Reparametrization of tidal parameters 5 PN correction, because it appears at 55 PN PN order correction, relative because to it appearsB. at 5 Reparametrization PN order relative to of tidal parameters the leading-order point-particle term. Inthe this leading-order work, we keep point-particleIt term. becomes In this convenient work,Interpreting we keep to Binary reparametrizeIt Neutron becomes the Star convenient tidal Mergers param- to reparametrize the tidal param- 7 the leading-order (5 PN) and next-to-leading-order (6 PN) eters λ1; λ2 in terms of purely dimensionless parameters, the leading-order (5 PN) and next-to-leading-order (6 PN) eters λ1; λ2 in terms of purely dimensionlessð Þ parameters,~ ~ corrections to the energy and luminosityð Þ[28]: ~ ~ which we call Λ; ~δΛ [25]. Inspired by the λ~ from corrections to the energy and luminosity [28]: whichTidal we call deformationΛ; δΛ [25]. Inspired by~ theð ~λ 2fromÞ 5 ð 2Þ Ref.5 [10], Λ 32Gλ c = GM is essentially the entire Ref. [10], Λ~ 10 32Gλ~ c = GM is essentially¼ the½ entireð Þ 1 9 c λ1 5 PN tidal correction in all of the PN waveform families, 10 δE c2Mηx When9 binary¼ x 5orbital½ ð Þ 1 2 9 c λ1 tidal5 − 5− PN tidal− correction4 5 in all of the PN waveform families, ~ δE − c Mηx − − 9 x ¼ 2 χ1 G M while the 6 PN tidal correction is a linear combination of Λ tidal 2 χ 4 5 while separations the 6 PN tidal are correction small, each is a star linear~ combination of Λ~ ¼ 1 G M 33 11 11 33 and δΛ. For example, the tidal corrections to the TaylorF2 is~ tidally 2distorted by its − − and δΛχ.1 For− example,χ1 the tidal correctionsphase later to derived the TaylorF2 in Eq. (A26) of the Appendix can 33 11 11 33 2 2χ1 2 þ 2 2 − − χ1 − χ1 phasecompanion. later derived in Eq. (A26)equivalentlyof the Appendixbe expressed can as follows: 2χ1 2 þ 2 2 c10 λ × 1 x6equivalently1⟷2 ; be expressed(2) as follows: 3 39 10 4 5 Q = δψ− λE Λ~ x5 c λ1 6 G M þð Þ tidal 5=2 − × x 1⟷2 ; (2) 3 39 ¼ [Dietrich,128ηx Hinderer,2 Samajdar 2020] G4 M5 þð Þ δψ − Λ~ x5 32 c5 18 tidalc10 λ 5=2 3115 6595 2 5 ¼ 1281 5ηx 2 Λ~ 1 4ηδΛ~ x6 ; (4) δLtidal η x − 12 4 5 x Q: (tidal induced)− quadrupole moment− 5 10 ¼ 5 G χ G M Fig. 3 Cartoon depicting theþ definition64 ofþ tidal364 deformability. The tidal field due to the 32 c 18 c λ 1 tidal deformability:3115 λ=-6595 E 2 5 1 5 spacetime curvature~ ofε: the companion's companion~ 6 causes tidal the field NS to deform as the matter adjusts to a δLtidal η x − 12 x 176 1803 643 155 − Λ 1 − 4ηδΛ x ; (4) p ffiffiffiffiffiffiffiffiffiffiffiffiffi 5 G χ G4 M5 þ 2 64 þ 364where ¼ 1 − − χ1 newχ1 equilibrium configuration. The relevant quantity influencing the GWs is the induced 7χ 28 4 2 8 2 1 þ binaryþ tidalchange deformability in the multipole, mass-weightedp ffiffiffiffiffiffiffiffiffiffiffiffiffiΛ~ structure1 of the7 combinationη − NS’s31η exteriorΛ ofΛ spacetime Λ1,2 . The multipoles are also 176 1803 643 155 where 1 2 Q χ χ2 c10 λ impacted by spin effects, and¼ 13 dynamicalð þ tidalÞð effects.þ Þ − − 1 1 1 6 8 h 7χ1 þ 28 4 þ 2 × x 1⟷2~ : (3) 2 2 G4 M5 þð ΛÞ 1 7η − 31η Λ1 Λ2 1 − 4η 1 9η − 11η Λ1 − Λ2 (5) c10 λ ¼ 13 ð þ Þð þ Þþ ð þ Þð Þ 1 6 h p ffiffiffiffiffiffiffiffiffiffiffiffiffi i × 4 5 x 1⟷2 : (3) 2 G M þð Þ the1 − presence4η 1 9η of− 11 aη companionΛ1 − Λ2 5 is small,(5) with a description of the interaction [Flanaganþ & Hindererð þ2007; ΛÞð1,2 = λ1,2/mÞ1,2 : individual ones zone where the NSs behave almost as point masses with small corrections due Damour, Nagar,p ffiffiffiffiffiffiffiffiffiffiffiffiffi Villain 103012-32012] i to their finite size [2134 ,442], see also [184,513,281,303,302,535]. For weakly self-gravitating bodies described by PN gravity see also the seminal series of 103012-3 papers by Damour, Soffel, Xu [164]. As will be discussed in detail in Sec. 4,the multipole moments defined for the spacetime in the vicinity of the NSs play akeyroleforcommunicatinginformationaboutNSmatterbetweenthese descriptions. The multipole structure is affected by a variety of tidal effects, spins, and more complicated spin-tidal interactions. In addition to affecting the dynamics, the NS’ multipole moments also give rise to additional imprints on the asymptotic gravitational radiation. The radiation can be described by double perturbation expansion around flat spacetime and an infinite series of radiative multipole moments, as explained in detail in the review article [86]. The radiative moments are related in a complicated way, i.e., nonlinearly and non-locally in retarded time, to the total multipole moments of the binary system, which comprise contributions from the orbital motion and the NSs’ multipoles. Problems such as the relativistic two-body problem that involve different scales can also efficiently be treated with effective-field-theory meth- ods, see [335,436,466,219] for comprehensive reviews and references.

2.2.1 Dominant tidal eﬀects

In Newtonian gravity, tidal effects arise from the response of the NS to the gradient of the companion’s gravitational field across its matter distribution. From the perspective of the NS, the companion is orbiting and produces a time- varying tidal field that slowly sweeps up in frequency. This quasi-periodic tidal forcing can excite characteristic oscillation modes in the NS that depend on the properties of matter in its interior. These concepts carry over to a General Relativistic description, where the modes are the NS’s quasi-normal modes. A NS has a broad spectrum of modes [300], several of which have sufficiently low frequencies to be relevant for the inspiral. The tidal excitation can either be a Tidal deformability Λ Λ=0: BH in GR (Schwarzschild BH [Binnington&Poisson2009; Damour&Nagar2009], Kerr BH [Poisson2015; Pani+2015; Landry&Poisson2015]), Λ=100-1000: Neutron Stars (NSs) [Lattimer&Prakash2004]. (<900 by GW170817 [LVC 2018]) Λ≠0: exotic compact objects (ECOs), boson stars, gravastars, wormhole, quantum correction to BH

For gravastar Λ<0. [Uchikata, Yoshida, Pani 2016]

Tidal tests: Johnson-McDaniel+2018 (Constraints on Boson stars by future BBH detections)

5 Spin-induced quadrupole moment (SIQM) deformation due to compact object’s spin δκ Q = − (1 + δκ)χ2m3

δκ=0: BH [Poisson 1998], δκ~2-20: spinning NS [Laarakkers 1997; Pappas 2012], δκ~10-150: spinning boson stars [Ryan 1997], For gravastar δκ< 0 is possible [Uchikata+2016].

δκs = (δκ1 + δκ2)/2

SIQM tests: ① Krishnendu+2019 (GW151226 & GW170608); ② O3 TGR paper 2020 (GWTC-2 events)

6 Our analysis - Post-Newtonian inspiral waveform model: TaylorF2-5.5PN (TF2g) + Tidal + SIQM Λ δκ - Phase Ψ( f ) = ΨBBH + ΨSIQM + Ψtidal adding higher-order PN terms - Point-particle (TF2g): 0-5.5 PN, to prevent Λ˜ biasing - Spin (aligned-spin): 1.5-3 PN, SIQM: 2-3PN, - Tides: 5-7.5 PN. spin terms at other PN orders help to break degeneracies, e.g., q− χeﬀ

- Amplitude up to 3PN for BBH (PP & spin)

- Priors: uniform in [-3000, 3000] on Λ˜ and δΛ˜ , uniform in [-200, 200] on δκ1,2

- Bayesian inference library: Nested sampling in LALSUITE

Refs. - TF2-5.5PN [Messina, Dudi, Nagar, Bernuzzi, 2019] - SIQM [Krishnendu+ 2017] - PNTidal [Damour, Nagar, Villain, 2012; Henry, Faye, Blanchet, 2020] 7 Event selection Low-mass events: higher cutoﬀ frequency > 120 Hz and larger inspiral SNR > 9

Event fhigh [Hz] ρinsp

GW151226 150 11.1

GW170608 180 14.8

GW190707 160 12.2

GW190720 125 9.2 fhigh denotes the cutoﬀ frequency GW190728 160 11.4 divide the inspiral and post-inspiral regimes. GW190924 175 11.8

See Table V in O3a Test of GR paper 2010.14529

8 Results for the largest SNR event GW170608

9 Tidal constraints on GW170608 Λ

˜ fhigh=180 Hz Almost no change for Λ by adding SIQM parameters

Consistent with GR, Λ˜ = 0 at the 90% CR

The 90% symmetric credible range of Λ˜ : [-1213, 523]

10 SIQM constraints on GW170608 δκ

The median of δκs is shifted fhigh=180 Hz zero by adding tidal deformability, since spins become unmeasurable.

PDF

Consistent with GR, δκs = 0 at the 90% CR ̶̶- TF2g They are weighted by dividing the ̶ - - TF2g_Tidal - - - - TF2g_SIQM original prior: uniform on δκ1,2. 11 ̶ ̶ TF2g_Tidal_SIQM Tidal and SIQM constraints on GW170608 Λ δκ The corner plots of Λ˜ and δκs from GW170608

with uniform priors on Λ˜ , δΛ˜ and δκ1,2.

Consistent with GR, Λ˜ = 0

and δκs = 0 at the 90% CR

δκs-Λ˜ degeneracy: slightly negative correlation ̶- TF2g_Tidal_SIQM fhigh=180 Hz

12 Results for low-mass GWTC-2 events: GW151226, GW170608, GW190707, GW190720, GW190728, and GW190924 13 8 8

FIG. 5.FIG. The 5. same The as same Fig. 1 as but Fig. for 1 GW151226 but for GW151226 (red (red dashed),dashed), GW170608 GW170608 (green solid), (green GW190707 solid), GW190707 (blue dot- (blue dot- dashed), GW190720dashed), GW190720 (cyan dash-dotdotted), (cyan dash-dotdotted), GW190728 GW190728 (ma- (ma- FIG. 6. The same as Fig. 3 but for GW151226 genta looselygenta dashed), loosely GW190924 dashed), GW190924 (orange dotted), (orange using dotted), the usingFIG. the 6. The same as Fig. 3 but for GW151226 (red), GW170608 (green), GW190707 (blue), GW190720 TF2g TidalTF2gSIQMTidalwaveformSIQM waveform model by modelsetting byf setting=150,180,fhigh =150,180,(red), GW170608 (green), GW190707 (blue), GW190720 high (cyan), GW190728 (magenta), GW190924 (orange) using the 160, 125,160, 160, 125, and 160, 175 Hz, and respectively. 175 Hz, respectively. These constraints These constraints(cyan), GW190728 (magenta), GW190924 (orange) using the ˜ TF2g Tidal SIQM waveform model for fhigh =150,180,160, show thatshow all events that all are events consistent are consistent with BBH with in GR BBH (⇤˜ in=0). GR (⇤TF2g=0).Tidal SIQM waveform model for fhigh =150,180,160, 125, 160, and125, 175 160, Hz, and respectively. 175 Hz, respectively. These constraints These constraints show show ˜ that all eventsthat are all events consistent are consistentwith BBH within GR BBH (⇤˜ = in GRs =0). (⇤ = s =0).

˜ TABLE II.TABLE The 90% II. The symmetric 90% symmetric credible ranges credible of ⇤ ranges˜,thelog- of ⇤,thelog- arithm ofarithm the Bayes of the factors Bayes between factors binary between ECO binary and ECO BBH, and BBH, ECO ECO 2.0 except2.0 for except GW151226 for GW151226 and GW190728, and GW190728, thus favoring thus favoring Tidal constraints oni.e., six log eventsi.e.,BF log10,BF andBBH SNRs, and for SNRs GW151226, for GW151226, GW170608, GW170608, 10 BBH the BBH in GR compared to binary ECO by Bayesian ˜ δκ GW190707,GW190707, GW190720, GW190720, GW190728, GW190728, GW190924, GW190924, and the re- and thethe re- BBH in GR compared to binary ECO by Bayesian The corner plots of Λ and s from six low-mass events. Λ sult combiningsult combining six events six using events the usingTF2g theTidalTF2gSIQMTidalwave-SIQM wave-model selection.model selection. The combined The combined logarithmic logarithmic Bayes factor Bayes factor ECO ECO form modelAllform events with model are respective consistent with respectivefhigh with.Forindividualevents, fhigh.Forindividualevents,between binarybetween ECO binary and ECO BBH and is log BBH10 BF isBBH log,total10 BF=BBH,total = ECO ECO log BF log10 areBFBBH negative,˜ are negative, thus favoring thus favoring the BBH the in BBH10 in.1, which10.1, means which that means the ECOthat the or non-GR ECO or model non-GR model 10 BBHBBH in GR (Λ = 0), no evidence GR comparedofGR deviation compared to from binary GR to ECO. binary For ECO. the Forcombined the combined case, (with case, Tidal(with and Tidal SIQM and parameters) SIQM parameters) is also disfavored is also disfavored ECO ECO log10 BFBBHlog10,totalBFBBHis also,total negative,is also negative, thus disfavoring thus disfavoring binary binarycomparedcompared to BBH in to GR. BBH in GR. ECO. ECO. In this paper,In this we paper, used we the used inspiral-only the inspiral-only waveform waveform model asmodel templates as templates because there because is no there robust is no predic- robust predic- ˜ ˜ ECO ECO Event Eventfhigh [Hz]fhigh [Hz]⇤ log⇤ 10 BFBBHlog10 SNRBFBBH tionSNR waveformtion waveform of the merger-ringdown of the merger-ringdown regimes of regimes binary of binary GW151226GW151226 150 [ 1501466, 623] [ 1466, 623] -0.52 -0.52 10.7 ECO 10.7 merger.ECO It merger. might be It interestingmight be interesting to use a toy to model use a toy model GW170608GW170608 180 [ 1801213, 522] [1213, 522] -2.1 -2.1 14.7 14.7 for post-contactfor post-contact regimes of regimes binary ECOs, of binary which ECOs, has which been has been GW190707GW190707 160 [ 160593, 1556] [ 593, 1556] -2.1 -2.1 11.2 recently 11.2 derivedrecently [30]. derived Also, [30]. GW Also, echoes GW could echoes be used could to be used to GW190720GW190720 125 [ 1251366, 1880] [ 1366, 1880] -1.2 -1.2 9.2 9.2 examine post-merger regime. Such extensions including GW190728GW190728 160 [ 1601250, 1159] [1250, 1159] -1.9 -1.9 12.1 12.1 examine post-merger regime. Such extensions including GW190924GW190924 175 [ 1752022, 1210] [2022, 1210] -2.2 -2.2 11.4 the 11.4 waveformthe waveform after the inspiral after the regime inspiral would regime allow would us to allow us to CombinedCombined - - - - -10.1 -10.1 - analyze - heavy-massanalyze heavy-mass events and events to put and a di to↵erent put a type di↵erent of type of TF2g_Tidal_SIQM constraintsconstraints on ECO hypothesis. on ECO hypothesis. 14

TF2g TidalTF2gSIQMTidalwaveformSIQM waveform model as model templates. as templates. The ob- The ob- ACKNOWLEDGMENTACKNOWLEDGMENT tained resultstained are results the first are the constraints first constraints on the tidal on the de- tidal de- formabilityformability of the events of the classified events classified as BBH asin GWTC- BBH in GWTC-T. NarikawaT. Narikawa thanks Chris thanks van Chris den Broeck van den and Broeck Anu- and Anu- 2 events,2 motivated events, motivated by ECO by hypotheses. ECO hypotheses. We found We foundradha Samajdarradha Samajdar for useful discussions,for useful discussions, and he also and thanks he also thanks that allthat events all that events we that have we analyzed have analyzed are consistent are consistenthospitalityhospitality of Chris’s of group, Chris’s in group, particular in particular Khun Sang Khun Sang with BBHwith mergers BBH mergers in GR. The in GR. logarithmic The logarithmic Bayes fac- BayesPhukon, fac- ArchismanPhukon, Archisman Gosh, and Gosh, Tim Dietrich, and Tim during Dietrich, his during his tor log BFECO forECO individual events are less than - stay at Nikhef. We thank Aditya Vijaykumar, Nathan K. 10torBBH log10 BFBBH for individual events are less than - stay at Nikhef. We thank Aditya Vijaykumar, Nathan K. 8 8

FIG. 5. The same asFIG. Fig. 5. 1 but The for same GW151226 as Fig. (red 1 but for GW151226 (red dashed), GW170608 (greendashed), solid), GW170608 GW190707 (green (blue solid), dot- GW190707 (blue dot- dashed), GW190720 (cyandashed), dash-dotdotted), GW190720 GW190728 (cyan dash-dotdotted), (ma- GW190728 (magenta loosely dashed), GW190924genta loosely (orange dashed), dotted), GW190924 using the (orangeFIG. dotted), 6. using The the sameFIG. as Fig. 6. 3 The but same for GW151226 as Fig. 3 but for GW151226 TF2g Tidal SIQM waveformTF2g modelTidal by settingSIQM waveformfhigh =150,180, model by setting(red),fhigh GW170608=150,180, (green),(red), GW190707 GW170608 (blue), (green), GW190720 GW190707 (blue), GW190720 160, 125, 160, and 175 Hz,160, respectively. 125, 160, and These 175 Hz, constraints respectively.(cyan), These GW190728 constraints (magenta),(cyan), GW190924 GW190728 (orange) (magenta), using GW190924 the (orange) using the show that all events are consistentshow that with all events BBH are in GR consistent (⇤˜ =0). with BBHTF2g Tidal in GRSIQM (⇤˜ =0).waveformTF2g modelTidal forSIQMfhighwaveform=150,180,160, model for fhigh =150,180,160, 125, 160, and 175 Hz, respectively.125, 160, and These 175 constraints Hz, respectively. show These constraints show that all events are consistentthat with all events BBH in are GR consistent (⇤˜ =  withs =0). BBH in GR (⇤˜ = s =0).

TABLE II. The 90% symmetricTABLE credible II. The ranges 90% symmetric of ⇤˜,thelog- credible ranges of ⇤˜,thelog- arithm of the Bayes factorsarithm between of the binary Bayes ECO factors and between BBH, binary ECO and BBH, ECO ECO 2.0 except for GW1512262.0 and except GW190728, for GW151226 thus favoring and GW190728, thus favoring i.e., log10 BFBBH, and SNRsi.e., log for10 BF GW151226,BBH, and GW170608, SNRs for GW151226, GW170608, GW190707, GW190720, GW190728,GW190707, GW190924, GW190720, and GW190728, the re- GW190924,the BBH and in GR the re- comparedthe BBH to binary in GR ECO compared by Bayesian to binary ECO by Bayesian sult combining six eventssult using combining the TF2g sixTidal eventsSIQM usingwave- the TF2gmodelTidal selection.SIQM wave- The combinedmodel selection. logarithmic The Bayes combined factor logarithmic Bayes factor ECO ECO form model with respectiveformf modelhigh.Forindividualevents, with respective fhigh.Forindividualevents,between binary ECO andbetween BBH binary is log10 ECOBFBBH and,total BBH= is log10 BFBBH,total = Tidal and SIQMECO constraints on sixECO events log10 BFBBH are negative,log10 BF thusBBH favoringare negative, the BBH thus in favoring10.1, the which BBH means in that10. the1, which ECO means or non-GR that model the ECO or non-GR model ˜ The corner plotsGR of compared Λ and δκs from to six binarylow-massGR ECO.events. compared For the to combinedbinary ECO. case, For(with the combined Tidal and case, SIQM(with parameters) Tidal and is alsoSIQM disfavored parameters) is also disfavored ECO ECO δκ log10 BFBBH,total is alsoAlllog negative,events10 BF BBHare thus ,consistenttotal disfavoringΛis also with negative, binary thuscompared disfavoring to binary BBH in GR.compared to BBH in GR. ECO. ECO. BBH in GR (Λ˜ = 0 and δκs = 0) In this paper, we usedIn the this inspiral-only paper, we used waveform the inspiral-only waveform model as templates becausemodel there as templates is no robust because predic- there is no robust predic- ˜ ECO ˜ ECO Event fhigh [Hz] Event⇤ fhighlog10[Hz]BFBBH SNR⇤ tionlog10 waveformBFBBH SNR of the merger-ringdowntion waveform of regimes the merger-ringdown of binary regimes of binary GW151226 150 [GW1512261466, 623] 150 -0.52 [ 1466 10.7, 623] -0.52 10.7 ECO merger. It mightECO be interesting merger. It to might use a toy be interesting model to use a toy model GW170608 180 [GW1706081213, 522] 180 -2.1 [1213 14.7, 522] -2.1 14.7 for post-contact regimesfor of post-contact binary ECOs, regimes which hasof binary been ECOs, which has been GW190707 160 [GW190707593, 1556] 160 -2.1 [593 11.2, 1556] -2.1 11.2 recently derived [30]. Also,recently GW derived echoes could [30]. Also, be used GW to echoes could be used to GW190720 125 [ GW1907201366, 1880] 125 -1.2 [ 1366 9.2, 1880] -1.2 9.2 examine post-merger regime. Such extensions including GW190728 160 [ GW1907281250, 1159] 160 -1.9 [1250 12.1, 1159] -1.9 12.1 examine post-merger regime. Such extensions including GW190924 175 [ GW1909242022, 1210] 175 -2.2 [2022 11.4, 1210]the waveform -2.2 11.4 after thethe inspiral waveform regime after would the allow inspiral us to regime would allow us to Combined -Combined - - -10.1 - - analyze -10.1 heavy-mass - eventsanalyze and heavy-mass to put a di↵ eventserent type and of to put a di↵erent type of constraints on ECO hypothesis.constraints on ECO hypothesis. The non-GR model (with Tidal and SIQM) is disfavored TF2g_Tidal_SIQMTF2g Tidal SIQM waveformcomparedTF2g modelTidal to asGR.SIQM templates.waveform The model ob- as templates. TheACKNOWLEDGMENT ob- ACKNOWLEDGMENT 15 tained results are the firsttained constraints results are on the the first tidal constraints de- on the tidal deformability of the eventsformability classified of as the BBH events in GWTC- classified as BBHT. Narikawa in GWTC- thanks ChrisT. Narikawa van den Broeck thanks Chrisand Anu- van den Broeck and Anu- 2 events, motivated by2 events, ECO hypotheses. motivated by We ECO found hypotheses.radha Samajdar We found for usefulradha discussions, Samajdar and for he useful also discussions, thanks and he also thanks that all events that wethat have all analyzed events that are we consistent have analyzedhospitality are consistent of Chris’s group,hospitality in particular of Chris’s Khun group, Sang in particular Khun Sang with BBH mergers inwith GR. The BBH logarithmic mergers in Bayes GR. The fac- logarithmicPhukon, Bayes Archisman fac- Gosh,Phukon, and Tim Archisman Dietrich, Gosh, during and his Tim Dietrich, during his ECO ECO tor log10 BFBBH for individualtor log10 BF eventsBBH arefor less individual than - eventsstay are at Nikhef. less than We - thankstay Aditya at Nikhef. Vijaykumar, We thank Nathan Aditya K. Vijaykumar, Nathan K. Conclusion Λ δκ - We are implementing the tidal deformability, Λ, and spin-induced quadrupole moments (SIQMs), δκ, in TF2g. - Analysis on six low-mass GWTC-2 events: GW151226, GW170608, GW190707, GW190720, GW190728, and GW190924 with TF2g_Tidal_SIQM. - We find that all events that we have analyzed to be consistent with BBH mergers in GR (Λ˜ = 0 and δκs = 0). - The non-GR model (with Tidal and SIQM parameters) is disfavored compared to GR.

Future work - Improvement of waveform model by extension to post-inspiral regimes of binary ECOs

16 Back up slides

17 Tidal and SIQM constraints

logBFECOvsBBH fhigh TF2g_Amp TF2_Amp

GW151226 150 -0.52 -0.67

GW170608 180 -2.11 -1.65

GW190707 160 -2.1 -1.95

GW190720 125 -1.24 -1.31

GW190728 160 -1.92 -1.89

GW190814 140 × -3.81

GW190924 175 -2.18 -2.13

Combined - -10.07 -13.41 9 9

Johnson-McDaniel,Johnson-McDaniel, Rahul Kashyap, Rahul Kashyap, Arunava Mukherjee, Arunava Mukherjee,tical uncertainty.tical uncertainty. and Parameswaran Ajith for sharing and discussing their We show the Bayes factor between the binary ECO and Parameswaran Ajith for sharing and discussing their We show the Bayes factor between theECO binary ECO results on a similar study [91]. We would like to thank and BBH waveform model,ECO BFBBH in Table III. The results on a similar study [91]. We would like to thank and BBH waveform model, BFBBH in Table III. The SoichiroSoichiro Morisaki, Morisaki, Kyohei Kawaguchi, Kyohei Kawaguchi, and Hideyuki and Hideyukibinary ECObinary hypothesis ECO hypothesis (the TF2 Tidal (the TF2SIQMTidalwaveformSIQM waveform Tagoshi forTagoshi fruitful for discussions. fruitful discussions. T. Narikawa T. Narikawa was sup- wasmodel) sup- ismodel) disfavored is disfavored compared compared to BBH (the to BBHTF2g (thewave-TF2g wave- ported inported part by in a part Grant-in-Aid by a Grant-in-Aid for JSPS for Research JSPS Research Fel- form Fel- model)form for model) all events. for all The events. combined The combined Bayes factor Bayes factor lows. This work is supported by Japanese Society for the ECO lows. This work is supported by Japanese Society for the of seven eventsof seven are events log BF areECO log10 BF=BBH13,total.4 shows= 13 that.4 shows that Promotion of Science (JSPS) KAKENHI Grant Numbers 10 BBH,total Promotion of Science (JSPS) KAKENHI Grant Numbers BBH hypothesisBBH hypothesis is preferred is preferred to the binary to the ECO binary hypoth- ECO hypoth- JP21K03548,JP21K03548, JP17H06361, JP17H06361, JP17H06358, JP17H06358, JP17H06357, JP17H06357,esis as shownesis as for shownTF2g Tidal for TF2gSIQMTidal. SIQM. and JP20K03928.and JP20K03928. We would We also would like to also thank like to Comput- thank Comput- ing Infrastructureing Infrastructure ORION in ORION Osaka in City Osaka University. City University. We We are also gratefulare also to grateful the LIGO-Virgo to the LIGO-Virgo collaboration collaboration for the for the public releasepublic of release gravitational-wave of gravitational-wave data of GW151226, data of GW151226, GW170608,GW170608, GW190707 GW190707093326, and093326, GW190924 and GW190924021846. 021846. This researchThis research has made has use made of data, use software, of data, software, and web and web tools obtainedtools obtained from the from Gravitational the Gravitational Wave Open Wave Sci- Open Sci- ence Centerence (https://www.gw-openscience.org), Center (https://www.gw-openscience.org), a service a service of LIGOof Laboratory, LIGO Laboratory, the LIGO the Scientific LIGO Scientific Collaboration Collaboration and theand Virgo the Collaboration. Virgo Collaboration. LIGO is LIGO funded is by funded the by the U. S. NationalU. S. National Science Foundation. Science Foundation. Virgo is funded Virgo is by funded by the Frenchthe Centre French National Centre National de la Recherche de la Recherche Scientifique Scientifique (CNRS),(CNRS), the Italian the Istituto Italian Nazionale Istituto Nazionale di Fisica di Nucle- Fisica Nucle- are (INFN),are and(INFN), the Dutch and the Nikhef, Dutch with Nikhef, contributions with contributions by by Polish andPolish Hungarian and Hungarian institutes. institutes.

AppendixAppendix A: Results A: by Results using byTF2 usingwaveformTF2 waveform model model

WhileWhile we show we the show results the results by using by using TF2g TidalTF2gSIQMTidalwaveformSIQM waveform model in model Sec. in III, Sec. we III, we show theshow results the for results seven for events seven added events GW190814 added GW190814FIG. 7. TheFIG. same 7. asThe Fig. same 5 but as Fig. for the 5 butTF2 forTidal the TF2SIQMTidalwave-SIQM wave- by usingbyTF2 usingTidalTF2SIQMTidalwaveformSIQM waveform model in model this Ap- in thisform Ap- modelform and model GW190814 and GW190814 (purple loosely (purple dotted) loosely is added. dotted) is added. pendix. Forpendix. highly For unequal highly mass unequal ratio mass events ratio GW190814, events GW190814,These constraintsThese constraints show that show all events that all are events consistent are consistent with with TF2g waveformTF2g waveform model do model not work do not well work due well to setting due to settingBBH in GRBBH (⇤˜ =0). in GR (⇤˜ =0). the uncalculatedthe uncalculated terms at terms high PN-order at high PN-order to zero. to We zero. We take thetake low frequency the low frequency cuto↵ flow cuto=↵ 20flow Hz= for 20 Hanford Hz for Hanford data anddata 30 Hz and for 30 Livingston Hz for Livingston data for data GW190814 for GW190814 by by followingfollowing the papers the which papers reported which reported theTidal detection constraints the detection [90] with [90] TF2_Tidal_SIQM The corner plots of Λ˜ and δκTABLE from seven low-massTABLE III. The events. III. same The as same Table as II Table but for II but the for the and the highand the frequency high frequency cuto↵ f cuto=↵ 140f Hz.= 140 Hz. s Λ high high TF2 TidalTF2SIQMTidalwaveformSIQM waveform model and model GW190814 and GW190814 is added. is added. We presentWe posteriors present posteriors of binary of tidal binary deformability tidal deformabilityFor bothAll theFor events individual both are the consistent individual events and with events the combined and the case, combined the log case, the log and the SIQMsand the for SIQMs GW151226, for GW151226, GW170608, GW170608, GW190707, GW190707, ECO ECO Bayes factorBBHBayes login GR10 factorBF (Λ˜ BBH= log0),, totalno10 BFevidenceisBBH negative,,total is thus negative, disfavoring thus disfavoring GW190720,GW190720, GW190728, GW190728, GW190814 GW190814 and GW190924 and GW190924 by binary by ECO.ofbinary deviation ECO. from GR using theusingTF2 Tidal the TF2SIQMTidalwaveformSIQM waveform model. model. Figure 7 shows posteriors of ⇤˜ for seven˜ events using ˜ ˜ ECO ECO Figure 7 shows posteriors of ⇤ for seven events usingEvent Eventfhigh [Hz] fhigh [Hz]⇤ log⇤ 10 BFBBHlog10SNRBFBBH SNR the TF2 Tidalthe TF2SIQMTidalwaveformSIQM waveform model. Figure model. 8 Figure shows 8 showsGW151226GW151226 150 [ 1501580, 471] [ 1580, -0.67471] -0.67 10.7 10.7 the posteriorthe posterior distribution distribution on ⇤˜- onplane.⇤˜- Theplane. 90% TheGW170608 90% GW170608 180 [ 1801336, 344] [1336, 344] -1.7 -1.7 14.7 14.7 s s symmetric credible ranges of ⇤˜ are summarized˜ in GW190707GW190707 160 [ 160691, 1313] [691, 1313] -2.0 -2.0 11.2 11.2 symmetric credible ranges of ⇤ are summarized in GW190720GW190720 125 [ 1251506, 1557] [ 1506, 1557] -1.3 -1.3 9.3 9.3 Table III,Table which III, are which [ 1580 are, [471]1580 for, 471] GW151226, for GW151226, GW190728GW190728 160 [ 1601341, 807] [ 1341, 807] -1.9 -1.9 12.1 12.1 [ 1336, [ 344]1336, for344] GW170608, for GW170608, [ 691, [1313]691, for1313] for GW190814GW190814 140 [ 140475, 1268] [475, 1268] -3.8 -3.8 22.1 22.1 GW190707,GW190707, [ 1506, 1557] [ 1506 for, 1557] GW190720, for GW190720, [ 1341, 807] [ 1341, 807] GW190924GW190924 175 [ 1752005, 1111] [ 2005, 1111] -2.1 -2.1 11.4 11.4 for GW190728,for GW190728, [ 475 , 1268] [ 475, for1268] GW190814, for GW190814, and and CombinedCombined - - - - -13.4 -13.4 - - [ 2005, [1111]2005 for, 1111] GW190924. for GW190924. Except for Except GW190814, for GW190814, TF2_Tidal_SIQM systematicsystematic uncertainty uncertainty between betweenTF2g TidalTF2gSIQMTidalandSIQM and 19 TF2 TidalTF2SIQMTidalresultsSIQM remainsresults subdominant remains subdominant to statis- to statis- 9 9

Johnson-McDaniel, Rahul Kashyap, Arunava Mukherjee, tical uncertainty. Johnson-McDaniel, Rahul Kashyap, Arunava Mukherjee, tical uncertainty. and Parameswaran Ajith for sharing and discussing their We show the Bayes factor between the binary ECO and Parameswaran Ajith for sharing and discussing their We showECO the Bayes factor between the binary ECO results on a similar study [91]. We would like to thank and BBH waveform model, BF in Table III. TheECO results on a similar study [91]. We would like to thank and BBHBBH waveform model, BF in Table III. The TF2 Tidal SIQM BBH Soichiro Morisaki, KyoheiSoichiro Kawaguchi, Morisaki, and Kyohei Hideyuki Kawaguchi,binary and ECO Hideyuki hypothesisbinary (the ECO hypothesiswaveform (the TF2 Tidal SIQM waveform TF2g Tagoshi for fruitful discussions.Tagoshi for T. fruitful Narikawa discussions. was sup- T.model) Narikawa is disfavored was sup- comparedmodel) to is disfavored BBH (the comparedwave- to BBH (the TF2g wave- ported in part by a Grant-in-Aidported in for part JSPS by a Research Grant-in-Aid Fel- forform JSPS model) Research for Fel- all events.form The model) combined for all Bayes events. factor The combined Bayes factor lows. This work is supported by Japanese Society for the ECO lows. This work is supported by Japaneseof seven Society events for are the log10ofBF sevenBBH,total events= are13 log.4 showsBFECO that = 13.4 shows that Promotion of Science (JSPS) KAKENHI Grant Numbers 10 BBH,total Promotion of Science (JSPS) KAKENHIBBH Grant hypothesis Numbers is preferredBBH to hypothesis the binary is ECO preferred hypoth- to the binary ECO hypoth- JP21K03548, JP17H06361, JP17H06358, JP17H06357, JP21K03548, JP17H06361, JP17H06358,esis as JP17H06357, shown for TF2g Tidalesis asSIQM shown. for TF2g Tidal SIQM. and JP20K03928. We wouldand JP20K03928. also like to thank We would Comput- also like to thank Comput- ing Infrastructure ORIONing in Infrastructure Osaka City University. ORION in We Osaka City University. We are also grateful to the LIGO-Virgoare also grateful collaboration to the LIGO-Virgo for the collaboration for the public release of gravitational-wavepublic release data of gravitational-wave of GW151226, data of GW151226, GW170608, GW190707 093326,GW170608, and GW190707 GW190924 093326,021846. and GW190924 021846. This research has madeThis use of research data, software, has made and use web of data, software, and web tools obtained from thetools Gravitational obtained Wave from the Open Gravitational Sci- Wave Open Sci- ence Center (https://www.gw-openscience.org),ence Center (https://www.gw-openscience.org), a service a service of LIGO Laboratory, theof LIGO LIGO Scientific Laboratory, Collaboration the LIGO Scientific Collaboration and the Virgo Collaboration.and the LIGO Virgo is Collaboration. funded by the LIGO is funded by the U. S. National Science Foundation.U. S. National Virgo Science is funded Foundation. by Virgo is funded by the French Centre Nationalthe de French la Recherche Centre National Scientifique de la Recherche Scientifique (CNRS), the Italian Istituto(CNRS), Nazionale the Italian di Fisica Istituto Nucle- Nazionale di Fisica Nucle- are (INFN), and the Dutchare Nikhef, (INFN), with and contributions the Dutch Nikhef, by with contributions by Polish and Hungarian institutes.Polish and Hungarian institutes.

Appendix A: Results byAppendix using TF2 A:waveform Results by model using TF2 waveform model

While we showWhile the results we show by using the results by using TF2g Tidal SIQM waveformTF2g Tidal modelSIQM in Sec.waveform III, we model in Sec. III, we show the results for sevenshow events the results added for GW190814 seven eventsFIG. added 7. The GW190814 same as Fig. 5FIG. but 7. for The the sameTF2 Tidal as Fig.SIQM 5 butwave- for the TF2 Tidal SIQM wave- by using TF2 Tidal SIQMbywaveform using TF2 modelTidal inSIQM thiswaveform Ap- form model model in and this GW190814 Ap- form (purple model loosely and GW190814 dotted) is (purple added. loosely dotted) is added. pendix. For highly unequalpendix. mass ratio For highly events unequal GW190814, mass ratioThese events constraints GW190814, show thatThese all constraints events are show consistent that all with events are consistent with ˜ TF2g waveform model doTF2g notwaveform work well model due to do setting not workBBH well in due GR to (⇤ setting=0). BBH in GR (⇤˜ =0). the uncalculated termsthe at high uncalculated PN-order terms to zero. at high We PN-order to zero. We take the low frequency cutotake↵ theflow low= 20frequency Hz for Hanfordcuto↵ flow = 20 Hz for Hanford data and 30 Hz for Livingstondata and data 30 Hz for for GW190814 Livingston by data for GW190814 by following the papers whichfollowing reported the the papers detection which [90] reported the detection [90] TABLE III. The sameTABLE as Table III. The II but same for as the Table II but for the and the high frequency cutoand↵ thefhigh high= frequency 140 Hz. cuto↵ f = 140 Hz. Tidalhigh andTF2 SIQMTidal constraintsSIQM waveformTF2 modelwithTidal TF2_Tidal_SIQM andSIQM GW190814waveform is model added. and GW190814 is added. We present posteriors ofWe binary present tidal posteriors deformability of binary tidal deformability The cornerFor plots both of Λ˜ and the δ individualκs from seven events low-massFor both and events. the the combined individual case, events the and log the combined case, the log and the SIQMs for GW151226,and the GW170608, SIQMs for GW151226, GW190707, GW170608,Bayes factor GW190707, log BFECO is negative, thusECO disfavoringδκ 10 BBHAllBayes,total events factor are logconsistent10 BFΛBBH with,total is negative, thus disfavoring GW190720, GW190728,GW190720, GW190814 GW190728, and GW190924 GW190814 by binary and GW190924 ECO. by binary ECO. ˜ using the TF2 Tidal SIQMusingwaveform the TF2 model.Tidal SIQM waveform model. BBH in GR (Λ = 0 and δκs = 0) Figure 7 shows posteriors of ⇤˜ for seven events using˜ ˜ ECO ˜ ECO Figure 7 shows posteriors of ⇤ forEvent seven eventsfhigh using[Hz] Event⇤ fhighlog10[Hz]BFBBH SNR⇤ log10 BFBBH SNR the TF2 Tidal SIQM waveformthe TF2 model.Tidal SIQM Figurewaveform 8 shows model.GW151226 Figure 8 shows 150 [ GW1512261580, 471] 150 -0.67 [ 1580 10.7, 471] -0.67 10.7 the posterior distributionthe on posterior⇤˜- plane. distribution The on 90%⇤˜- GW170608plane. The 180 90% [ GW1706081336, 344] 180 -1.7 [1336 14.7, 344] -1.7 14.7 s s symmetric credible rangessymmetric of ⇤˜ are credible summarized ranges of in ⇤˜ areGW190707 summarized 160 in [ GW190707691, 1313] 160 -2.0 [691 11.2, 1313] -2.0 11.2 Table III, which are [ 1580, 471] for GW151226, GW190720 125 [ GW1907201506, 1557] 125 -1.3 [ 1506 9.3, 1557] -1.3 9.3 Table III, which are [ 1580, 471] for GW151226, [ 1336, 344] for GW170608,[1336, 344] [ 691 for, 1313] GW170608, for [GW190728691, 1313] 160 for [ GW1907281341, 807] 160 -1.9 [ 1341 12.1, 807] -1.9 12.1 GW190814 140 [GW190814475, 1268] 140 -3.8 [475 22.1, 1268] -3.8 22.1 GW190707, [ 1506, 1557]GW190707, for GW190720, [ 1506 [, 1557]1341, for807] GW190720, [ 1341, 807] for GW190728, [ 475,for1268] GW190728, for GW190814, [ 475, 1268] and forGW190924 GW190814, 175 and [ GW1909242005, 1111] 175 -2.1 [ 2005 11.4, 1111] -2.1 11.4 Combined -Combined - - -13.4 - - -13.4 - [ 2005, 1111] for GW190924.[ 2005, Except1111] for for GW190924. GW190814, Except for GW190814, systematic uncertaintysystematic between TF2g uncertaintyTidal SIQM betweenand TF2g Tidal SIQM and The non-GR model (with Tidal TF2 Tidal SIQM resultsTF2 remainsTidal subdominantSIQM results to remains statis- subdominant to statis- and SIQM) is disfavored TF2_Tidal_SIQM compared to GR. 20 5

Next, we show the results for other events and model selection by the Bayes factor combining six events.

FIG. 2. Marginalized posterior PDFs of s for GW170608 using the TF2g SIQM (green, dotted) and TF2g Tidal SIQM (red, solid) waveform models. We set FIG. 1. Marginalized posterior PDFs of ⇤˜ for low-mass fhigh = 180 Hz. They are weighted by dividing the original event GW170608 with the TF2g Tidal (blue, dashed) and prior: uniform on 1,2. The original prior is also shown by TF2g Tidal SIQM (red, solid) waveform models. We set solid yellow curve. The peak of s is shifted toward zero by Results of GW170608 withadding theTF2g_Tidal_SIQM tidal terms, since the spin becomes unmeasurable. fhigh = 180 Hz. Adding the SIQM terms do not a↵ect the constraint on the tidal deformability ⇤˜.

TABLE I. The logarithm of the Bayes factors for a signal compared to Gaussian noise log10 BFs/n and SNRs for GW170608 using the TF2g, TF2g Tidal, TF2g SIQM,and TF2g Tidal SIQM waveform models. The tidal and SIQM terms do not a↵ect the Bayes factor and SNR.

log10 BFs/n SNR TF2g (BBH in GR) 71.3 14.7 TF2g Tidal 69.9 14.7 TF2g SIQM 70.4 14.7 TF2g Tidal SIQM 69.2 14.7

The tidal and SIQM terms do not aﬀect the Bayes factor A. Estimating tidal deformability and SIQMs for and SNR. GW170608

We show the results of low mass presumed BBH event GW170608. We present posteriors of binary tidal deformability and the SIQM for GW170608. Figure 1 shows ˜ 21 posteriors of ⇤ for GW170608. We set fhigh = 180 Hz. FIG. 3. Corner plot on the ⇤˜-s plane for GW170608 us- The posterior distribution of ⇤˜ for the TF2g Tidal wave- ing the TF2g Tidal SIQM waveform model by setting fhigh = form model (blue dot-dashed) is consistent with the one 180 Hz. The contours correspond to 50% and 90% credible TF2g Tidal SIQM regions. The constraints show that GW170608 is consistent for the waveform model (red solid). ˜ Adding the SIQM terms do not a↵ect the constraint on with BBH in GR (⇤ = s =0). the tidal deformability ⇤˜. Results of GW170608 with TF2g

GR log10BFs/n SNR

PhenomD 71.51 14.71 fhigh180

TF2g_Amp 71.34 14.67 fhigh180