Simulations of black-hole binaries with unequal masses or nonprecessing spins: Accuracy, physical properties, and comparison with post-Newtonian results

Abstract

We present gravitational waveforms for the last orbits and merger of black-hole-binary (BBH) systems along two branches of the BBH parameter space: equal-mass binaries with equal non-precessing spins, and nonspinning unequal-mass binaries. The waveforms are calculated from numerical solutions of Einstein's equations for black-hole binaries that complete between six and ten orbits before merger. Along the equal-mass spinning branch, the spin parameter of each BH is.85], and along the unequal-mass branch the mass ratio is q = M 2 /M 1 ∈ [1, 4]. We discuss the construction of low-eccentricity puncture initial data for these cases, the properties of the final merged BH, and compare the last 8-10 GW cycles up to Mω = 0.1 with the phase and amplitude predicted by standard post-Newtonian (PN) approximants. As in previous studies, we find that the phase from the 3.5PN TaylorT4 approximant is most accurate for nonspinning binaries. For equal-mass spinning binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN order) gives the most robust performance, but it is possible to treat TaylorT4 in such a way that it gives the best accuracy for spins χ i > −0.75. When high-order amplitude corrections are included, the PN amplitude of the ( = 2, m = ±2) modes is larger than the NR amplitude by between 2-4%. arXiv:1007.4789v2 [gr-qc] 15 Nov 2010 III. SPECIFICATION OF LOW-ECCENTRICITY INITIAL PARAMETERSPuncture initial data typically consist of the analytic Bowen-York solution to the momentum constraint [20] (which allows for the construction of multiple boosted, spinning black holes), and a numerical solution of the Hamiltonian constraint in puncture form [19]. To produce the data for the simulations that we discuss in this paper we used the single-domain spectral elliptic solver described in [21]. In this approach the black holes' angular and linear momenta may be directly specified,

IsJenough? Comparison of gravitational waves emitted along the total angular momentum direction with other preferred orientations

“…In this approximation, only one complex-valued function is needed to characterize the gravitational wave signature from a binary: either the (l, m) = (2, 2) mode itself or the strain extracted along the binary angular momentum axis. This approach has been broadly adopted when comparing nonspinning numerical relativity simulations to one another [1] and to post-Newtonian [2][3][4][5] and other [6] approximations; when building hybrid waveforms that join systematic postNewtonian approximations to numerical relativity [7,8]; when constructing phenomenological approximations to numerical relativity waveforms [9][10][11]; and when searching for the gravitational wave signature of merging compact binaries with interferometric detectors [12]. For similar reasons, the gravitational wave signature from a nonprecessing unequal-mass binary can also be approximated by h +,× (t,Ĵ ), the radiation along the total angular momentum axisĴ.…”

Mergers of black-hole binaries with aligned spins: Waveform characteristics

“…Nevertheless, we quote the derived eccentricity measure for each run in Table I. This is higher than we would like for serious data-analysis applications, or for generating PN-NR hybrid waveforms, and we could choose to reduce eccentricity through methods similar to those presented in [17]. However, our primary purpose in this paper is to investigate the bulk behavior of the waveform modes across configurations, and very low eccentricity does not appear to be necessary for this.…”

“…Quoted uncertainties are the direct sum of three terms: uncertainties in the highest-resolution fits; differences between best-fit values for rext → ∞ and rext = 45M (40M for X4 00); differences between best-fit values at highest and next-highest resolutions runs. (15), and of A0 and α1 for the amplitude model (17). Unlike in Table V, only t0 and A0 are freely fit; the remaining parameters have been fixed, as given in Eq.…”

“…We consider an explicit waveform model restricted to the (2, ±2) modes, which contain most of the power. The waveform phase is derived from integrating the model IRS frequency given (17). All fits are over a time window from t peak − 40M to t peak + 60M .…”

“…High-accuracy waveforms from such evolutions have been produced and studied by several groups [13][14][15][16]. Such systems have been partially characterized by [17], using a variant of the frequency model from [1]. The frequency-domain phenomenological templates of Ajith et al have been extended to cover both mass ratio and total aligned spin [18,19], at least for the dominant modes, and attempts have been made to extend these to more generic systems [20,21].…”