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Register a new userGravitational-wave echoes from spinning exotic compact objects: numerical waveforms from the Teukolsky equation
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We present numerical waveforms of gravitational-wave echoes from spinning exotic compact objects (ECOs) that result from binary black hole coalescence. We obtain these echoes by solving the Teukolsky equation for the $psi_4$ associated with gravitational waves that propagate toward the horizon of a Kerr spacetime, and process the subsequent reflections of the horizon-going wave by the surface of the ECO, which lies right above the Kerr horizon. The trajectories of the infalling objects are modified from Kerr geodesics, such that the gravitational waves propagating toward future null infinity match those from merging black holes with comparable masses. In this way, the corresponding echoes approximate to those from comparable-mass mergers. For boundary conditions at the ECO surface, we adopt recent work using the membrane paradigm, which relates $psi_0$ associated with the horizon-going wave and $psi_4$ of the wave that leaves the ECO surface. We obtain $psi_0$ of the horizon-going wave from $psi_4$ using the Teukolsky-Starobinsky relation. The echoes we obtain turn out to be significantly weaker than those from previous studies that generate echo waveforms by modeling the ringdown part of binary black hole coalescence waveforms as originating from the past horizon.
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Exotic compact objects (ECOs) have recently become an exciting research subject, since they are speculated to have a special response to the incident gravitational waves (GWs) that leads to GW echoes. We show that energy carried by GWs can easily cause the event horizon to form out of a static ECO --- leaving no echo signals towards spatial infinity. To show this, we use the ingoing Vaidya spacetime and take into account the back reaction due to incoming GWs. Demanding that an ECO does not collapse into a black hole puts an upper bound on the compactness of the ECO, at the cost of less distinct echo signals for smaller compactness. The trade-off between echoes detectability and distinguishability leads to a fine tuning of ECO parameters for LIGO to find distinct echoes. We also show that an extremely compact ECO that can survive the gravitational collapse and give rise to GW echoes might have to expand its surface in a non-causal way.
The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from non-spinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test-particle in equatorial orbit around a Kerr black hole parameterized by a spin parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, T-approximant templates obtain an effectualness of ~ 0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q>0. For q<0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family.
It has recently been claimed, with a $4.2 sigma$ significance level, that gravitational wave echoes at a frequency of about $72$ Hz have been produced in the GW170817 event. The merging of compact stars can lead to the emission of gravitational waves echoes if the post-merger object features a photon-sphere capable of partially trapping the gravitational waves. If the post-merger source is a black hole, a second internal reflection surface, associated to quantum effects near the black hole horizon, must be present to avoid the gravitational wave capture. Alternatively, gravitational wave echoes can be produced by ultracompact stars crossing the photon-sphere line in the mass-radius diagram during the neutron star merging. In this case, the second reflection surface is not needed. A recently proposed preliminary analysis using an incompressible (and so unphysical) equation of state suggests that gravitational wave echoes at a frequency of tens of Hz can be produced by an ultracompact star. Since strange stars are extremely compact, we examine the possibility that strange stars emit gravitational wave echoes at such a frequency. Using parameterized models of the equation of state of ultra-stiff quark matter we find that a strange star can emit gravitational wave echoes, but the corresponding frequencies are of the order of tens of kHz, thus not compatible with the $72$ Hz signal.
Teukolsky equations for $|s|=2$ provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an in-going (out-going) wave boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the Membrane Paradigm, by considering a family of fiducial observers (FIDOs) that float right above the horizon of a linearly perturbed Kerr black hole. From the reference frame of these observers, the ECO will experience tidal perturbations due to in-going gravitational waves, respond to these waves, and generate out-going waves. As it also turns out, if both in-going and out-going waves exist near the horizon, the Newman Penrose (NP) quantity $psi_0$ will be numerically dominated by the in-going wave, while the NP quantity $psi_4$ will be dominated by the out-going wave. In this way, we obtain the ECO boundary condition in the form of a relation between $psi_0$ and the complex conjugate of $psi_4$, in a way that is determined by the ECOs tidal response in the FIDO frame. We explore several ways to modify gravitational-wave dispersion in the FIDO frame, and deduce the corresponding ECO boundary condition for Teukolsky functions. We subsequently obtain the boundary condition for $psi_4$ alone, as well as for the Sasaki-Nakamura and Detweilers functions. As it also turns out, reflection of spinning ECOs will generically mix between different $ell$ components of the perturbations fields, and be different for perturbations with different parities. We also apply our boundary condition to computing gravitational-wave echoes from spinning ECOs, and solve for the spinning ECOs quasi-normal modes.
Gravitational waves (GWs) from presumed binary black hole mergers are now being detected on a regular basis with the Advanced LIGO and Advanced Virgo interferometers. Exotic compact objects (ECOs) have been proposed that differ from Kerr black holes, and which could leave an imprint upon the GW signal in a variety of ways. Here we consider excitations of ECOs during inspiral, which may occur when the monotonically increasing GW frequency matches a resonant frequency of an exotic object. This causes orbital energy to be taken away, leading to a speed-up of the orbital phase evolution. We show that resonances with induced phase shifts $lesssim 10$ radians can be detectable with second-generation interferometers, using Bayesian model selection. We apply our methodology to detections in the GWTC-1 catalog from the first and second observing runs of Advanced LIGO and Advanced Virgo, finding consistency with the binary black hole nature of the sources.
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