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Register a new userAdapted gauge to a quasilocal measure of the black holes recoil
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We explore different gauge choices in the moving puncture formulation in order to improve the accuracy of a linear momentum measure evaluated on the horizon of the remnant black hole produced by the merger of a binary. In particular, motivated by constant values studies, we design a gauge via a variable shift parameter $meta(vec{r}(t))$ such that it takes a low asymptotic (and at the orbiting punctures) value, while about the standard value of 2 at the final hole horizon. This choice then follows the remnant black hole as it moves due to its net recoil velocity. We find that this choice keeps the accuracy of the binary evolution and, once the asymptotic value of the parameter $meta$ is chosen about or below 1.0, it produces more accurate results for the recoil velocity than the corresponding evaluation of the radiated linear momentum at infinity, for typical numerical resolutions. We also find that the choice of the $partial_t$-gauge (at our working resolutions) is more accurate in this regard of computing recoil velocities than the $partial_0$-gauge. Detailed studies of an unequal mass $q=m_1/m_2=1/3$ nonspinning binary are provided and then verified for other mass ratios $(q=1/2,1/5)$ and spinning $(q=1)$ binary black hole mergers.
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We explore the benefits of adapted gauges to small mass ratio binary black hole evolutions in the moving puncture formulation. We find expressions that approximate the late time behavior of the lapse and shift, $(alpha_0,beta_0)$, and use them as initial values for their evolutions. We also use a position and black hole mass dependent damping term, $eta[vec{x}_1(t),vec{x}_2(t),m_1,m_2]$, in the shift evolution, rather than a constant or conformal-factor dependent choice. We have found that this substantially reduces noise generation at the start of the numerical integration and keeps the numerical grid stable around both black holes, allowing for more accuracy with lower resolutions. We test our choices for this gauge in detail in a case study of a binary with a 7:1 mass ratio, and then use 15:1 and 32:1 binaries for a convergence study. Finally, we apply our new gauge to a 64:1 binary and a 128:1 binary to well cover the comparable and small mass ratio regimes.
Gravitational waves carry energy, angular momentum, and linear momentum. In generic binary black hole mergers, the loss of linear momentum imparts a recoil velocity, or a kick, to the remnant black hole. We exploit recent advances in gravitational waveform and remnant black hole modeling to extract information about the kick from the gravitational wave signal. Kick measurements such as these are astrophysically valuable, enabling independent constraints on the rate of second-generation mergers. Further, we show that kicks must be factored into future ringdown tests of general relativity with third-generation gravitational wave detectors to avoid systematic biases. We find that, although little information can be gained about the kick for existing gravitational wave events, interesting measurements will soon become possible as detectors improve. We show that, once LIGO and Virgo reach their design sensitivities, we will reliably extract the kick velocity for generically precessing binaries--including the so-called superkicks, reaching up to 5000 km/s.
We discuss the merger process of binary black holes with Hawking radiation taken into account. Besides the redshifted radiation to infinity, binary black holes can exchange radiation between themselves, which is first redshifted and then blueshifted when it propagates from one hole to the other. The exchange rate should be large when the temperature-divergent horizons are penetrating each other to form a single horizon with unique temperature. This will cause non-negligible mass and angular momentum transfer between the black holes during the merging process of the horizons. We further argue in the large mass ratio limit that the light hole whose local evaporation is enhanced by the competing redshift-blueshift effects will probably evaporate or decay completely before reaching the the horizon of the heavy one. We also discuss the possibility of testing Hawking radiation and even exploring the information loss puzzle in gravitational wave observations.
Solutions to the two-body problem in general relativity allow us to predict the mass, spin and recoil velocity of a black-hole merger remnant given the masses and spins of its binary progenitors. In this paper we address the inverse problem: given a binary black-hole merger, can we use the parameters measured by gravitational-wave interferometers to tell if the binary components are of hierarchical origin, i.e. if they are themselves remnants of previous mergers? If so, can we determine at least some of the properties of their parents? This inverse problem is in general overdetermined. We show that hierarchical mergers occupy a characteristic region in the plane composed of the effective spin parameters $chi_{rm eff}$ and $chi_{rm p}$, and therefore a measurement of these parameters can add weight to the hierarchical-merger interpretation of some gravitational-wave events, including GW190521. If one of the binary components has hierarchical origin and its spin magnitude is well measured, we derive exclusion regions on the properties of its parents: for example we infer that the parents of GW190412 (if hierarchical) must have had unequal masses and low spins. Our formalism is quite general, and it can be used to infer constraints on the astrophysical environment producing hierarchical mergers.
An accurate and precise measurement of the spins of individual merging black holes is required to understand their origin. While previous studies have indicated that most of the spin information comes from the inspiral part of the signal, the informative spin measurement of the heavy binary black hole system GW190521 suggests that the merger and ringdown can contribute significantly to the spin constraints for such massive systems. We perform a systematic study into the measurability of the spin parameters of individual heavy binary black hole mergers using a numerical relativity surrogate waveform model including the effects of both spin-induced precession and higher-order modes. We find that the spin measurements are driven by the merger and ringdown parts of the signal for GW190521-like systems, but the uncertainty in the measurement increases with the total mass of the system. We are able to place meaningful constraints on the spin parameters even for systems observed at moderate signal-to-noise ratios, but the measurability depends on the exact six-dimensional spin configuration of the system. Finally, we find that the azimuthal angle between the in-plane projections of the component spin vectors at a given reference frequency cannot be well-measured for most of our simulated configurations even for signals observed with high signal-to-noise ratios.
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