Length requirements for numerical-relativity waveforms

Abstract

One way to produce complete inspiral-merger-ringdown gravitational waveforms from black-hole-binary systems is to connect post-Newtonian (PN) and numerical-relativity (NR) results to create ``hybrid'' waveforms. Hybrid waveforms are central to the construction of some phenomenological models for GW search templates, and for tests of GW search pipelines. The dominant error source in hybrid waveforms arises from the PN contribution, and can be reduced by increasing the number of NR GW cycles that are included in the hybrid. Hybrid waveforms are considered sufficiently accurate for GW detection if their mismatch error is below 3% (i.e., a fitting factor about 0.97). We address the question of the length requirements of NR waveforms such that the final hybrid waveforms meet this requirement, considering nonspinning binaries with q = M_2/M_1 \in [1,4] and equal-mass binaries with \chi = S_i/M_i^2 \in [-0.5,0.5]. We conclude that for the cases we study simulations must contain between three (in the equal-mass nonspinning case) and ten (the \chi = 0.5 case) orbits before merger, but there is also evidence that these are the regions of parameter space for which the least number of cycles will be needed

Post-Newtonian templates for binary black-hole inspirals: the effect of the horizon fluxes and the secular change in the black-hole masses and spins

“…Built on this, the second objective of this work is to quantify the importance of corresponding corrections to observe GW signals from BBHs by Advanced LIGO and LISA. While many results have been obtained along those lines in the past [41,57,65,66,68,69,70,71,72,73,74], they have considered only the correction due to the horizon flux restricted to various special cases and the emphasis of these works are not always on the application to GW detectors. We improve these results with all possible effects of the BH absorption up to the relative 3.5PN order in the context of arbitrary-mass-ratio BBH inspirals by bringing to bear the mindset and tools of GW data analysis.…”

Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal

“…PN inspiral waveforms become less accurate at higher frequencies, and we need to decide at what frequency we need to be able to switch to NR information in order to produce a sufficiently accurate model. Previous work suggests that ∼5-10 orbits will be sufficient to produce models that meet the needs for GW detections with advanced GW detectors [58,59], if we use standard PN approximants for the inspiral. Those works took the largest differences between the highest-order PN waveforms available at that time as a conservative estimate of their overall error.…”

Stability of the puncture method with a generalized Baumgarte-Shapiro-Shibata-Nakamura formulation

“…Stationary data for this gauge has been studied in [27][28][29][30][31]62]. In our numerical evolutions the Γ-driver shift condition…”

“…We consider the densitization parameters (n Q , n K ) = {(0, 0), (0.2, −0.2), (0.4, −0.4), (0.6, −0.6)}, denoted as models HD1 -HD4 in Table I. For models HD1 -HD3 we have chosen the Γ-driver shift conditions (30) with (µ S , ξ 1 , ξ 2 , η) = (1, 0, 0, 1), whereas in case of model HD4 the Γ-driver shift conditions (30) have been taken with (µ s , ξ 1 , ξ 2 , η) = (3/4, 1, 1, 1) [73]. Information about gravitational waves emitted during the plunge has been obtained by the Newman-Penrose scalar Ψ 4 .…”

“…The Moving Puncture method in particular has proven robust in even the most demanding simulations of BBHs involving nearly critical spins and velocities close to the speed of light [23][24][25][26]. Previous investigations of this method have concentrated on the structure near the singularity and the impact of gauge conditions [27][28][29][30][31].…”