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Register a new userExploring the small mass ratio binary black hole merger via Zenos dichotomy approach
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We perform a sequence of binary black hole simulations with increasingly small mass ratios, reaching to a 128:1 binary that displays 13 orbits before merger. Based on a detailed convergence study of the $q=m_1/m_2=1/15$ nonspinning case, we apply additional mesh refinements levels around the smaller hole horizon to reach successively the $q=1/32$, $q=1/64$, and $q=1/128$ cases. Roughly a linear computational resources scaling with $1/q$ is observed on 8-nodes simulations. We compute the remnant properties of the merger: final mass, spin, and recoil velocity, finding precise consistency between horizon and radiation measures. We also compute the gravitational waveforms: its peak frequency, amplitude, and luminosity. We compare those values with predictions of the corresponding phenomenological formulas, reproducing the particle limit within 2%, and we then use the new results to improve their fitting coefficients.
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We present the results of 14 simulations of nonspinning black hole binaries with mass ratios $q=m_1/m_2$ in the range $1/100leq qleq1$. For each of these simulations we perform three runs at increasing resolution to assess the finite difference errors and to extrapolate the results to infinite resolution. For $qgeq 1/6$, we follow the evolution of the binary typically for the last ten orbits prior to merger. By fitting the results of these simulations, we accurately model the peak luminosity, peak waveform frequency and amplitude, and the recoil of the remnant hole for unequal mass nonspinning binaries. We verify the accuracy of these new models and compare them to previously existing empirical formulas. These new fits provide a basis for a hierarchical approach to produce more accurate remnant formulas in the generic precessing case. They also provide input to gravitational waveform modeling.
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.
The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at $scri$. However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction.
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The LIGO Scientific Collaboration
, the Virgo Collaboration: Then LIGO Scientific Collaboration
, the Virgo Collaboration: B. P. Abbott
2016
On September 14, 2015, the Laser Interferometer Gravitational-wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterize the properties of the source and its parameters. The data around the time of the event were analyzed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general relativity. GW150914 was produced by a nearly equal mass binary black hole of $36^{+5}_{-4} M_odot$ and $29^{+4}_{-4} M_odot$; for each parameter we report the median value and the range of the 90% credible interval. The dimensionless spin magnitude of the more massive black hole is bound to be $<0.7$ (at 90% probability). The luminosity distance to the source is $410^{+160}_{-180}$ Mpc, corresponding to a redshift $0.09^{+0.03}_{-0.04}$ assuming standard cosmology. The source location is constrained to an annulus section of $610$ deg$^2$, primarily in the southern hemisphere. The binary merges into a black hole of $62^{+4}_{-4} M_odot$ and spin $0.67^{+0.05}_{-0.07}$. This black hole is significantly more massive than any other inferred from electromagnetic observations in the stellar-mass regime.
We evolve a binary black hole system bearing a mass ratio of $q=m_1/m_2=2/3$ and individual spins of $S^z_1/m_1^2=0.95$ and $S^z_2/m_2^2=-0.95$ in a configuration where the large black hole has its spin antialigned with the orbital angular momentum, $L^z$, and the small black hole has its spin aligned with $L^z$. This configuration was chosen to measure the maximum recoil of the remnant black hole for nonprecessing binaries. We find that the remnant black hole recoils at 500km/s, the largest recorded value from numerical simulations for aligned spin configurations. The remnant mass, spin, and gravitational waveform peak luminosity and frequency also provide a valuable point in parameter space for source modeling.
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