High-spin binary black hole mergers

TL;DR

The paper investigates equal-mass binary black hole mergers with spins perpendicular to the orbital plane, exploring initial spins from $s/m^2 = -0.90$ to $0.90$ to push the limits of current data. Using the moving punctures method within the BAM code and Bowen–York initial data anchored by 2PN estimates, the authors perform thorough convergence and validation tests across multiple grid resolutions. They fit a quadratic relation for the remnant spin $J_f/M_f^2$ as a function of total initial spin, combining their results with prior data to estimate extreme remnant spins at $J_f/M_f^2 = 0.951 \pm 0.004$ (maximum) and $0.341 \pm 0.004$ (minimum), though these are extrapolations to near-singular spin values. A notable finding is an artificial angular momentum loss for high spins ($s/m^2 > 0.75$) that complicates long evolutions, highlighting the need for improved initial data beyond Bowen–York to accurately simulate spins approaching unity. These insights impact gravitational-wave template accuracy and the astrophysical interpretation of highly spinning black hole mergers.

Abstract

We study identical mass black hole binaries with spins perpendicular to the binary's orbital plane. These binaries have individual spins ranging from $s/m^2=-0.90$ to 0.90, ($s_1 = s_2$ in all cases) which is near the limit possible with standard Bowen-York puncture initial data. The extreme cases correspond to the largest initial spin simulations to date. Our results expand the parameter space covered by Rezzolla {\it et al.} and, when combining both data sets, we obtain estimations for the minimum and maximum values for the intrinsic angular momenta of the remnant of binary black hole mergers of $J/M^2=0.341 \pm 0.004$ and $0.951 \pm 0.004$ respectively. Note, however, that these values are reached through extrapolation to the singular cases $|s_1| = |s_2| = 1$ and thus remain as {\it estimates} until full-fledged numerical simulations provide confirmation.

Figures (7)

• Figure 1: Mass and angular momentum plots for three different resolutions. The dashed curves have been scaled according to a factor corresponding to 4th order convergence in spatial resolution.
• Figure 2: Spin of the merger remnant as a function of the initial black hole spins measured $500M$ after the black hole merger. The binaries are composed of identical black holes with initial spins of magnitude $s/m^2$ aligned with the orbital angular. The values calculated in Campanelli:2006uy (Pollney:2007ss) are shown as empty circles (square). The solid square represents the remnant spin calculated right after the merger for the case $s/m^2=0.90$, using Grid L. The solid line is a quadratic interpolation of the values corresponding to Grid 2 for $s/m^2<0.75$ plus the Grid L value.
• Figure 3: Evolution of the angular momentum for the binary with $s/m^2=0.90$ obtained using the isolated horizon techniques of Campanelli:2006fy. The top plot corresponds to the angular momentum of the remnant of the merger, while the bottom plot tracks the spin of the individual black holes before the merger (occurring at $265M$).
• Figure 4: Single black hole evolutions with $s/m^2=0.53$ (dashed) and $0.90$ (solid), on Grid 4. The plots present the relative differences with respect to the initial values, denoted with the $0$ sub-index. The bottom plot presents the relative variation of intrinsic angular momentum $j\equiv J_f/M^2_f$.
• Figure 5: Evolution of single black holes with $s/m^2=0.90$ for different spatial resolutions.