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.