Circular orbits and spin in black-hole initial data

TL;DR

This paper analyzes initial data construction for black-hole binaries, comparing criteria for orbital frequency, measuring spins, and refining models to accurately represent non-spinning and spinning black holes in quasi-circular orbits.

Contribution

It compares two methods for setting orbital frequency, calibrates spin measures, and improves the modeling of non-spinning black-hole binaries by including higher-order effects.

Findings

Excellent agreement between Komar-mass and effective-potential criteria.

Higher-order effects are crucial for accurate spin and orbit modeling.

New sequence of quasi-circular orbits and the innermost stable orbit are computed.

Abstract

The construction of initial data for black-hole binaries usually involves the choice of free parameters that define the spins of the black holes and essentially the eccentricity of the orbit. Such parameters must be chosen carefully to yield initial data with the desired physical properties. In this paper, we examine these choices in detail for the quasiequilibrium method coupled to apparent-horizon/quasiequilibrium boundary conditions. First, we compare two independent criteria for choosing the orbital frequency, the "Komar-mass condition" and the "effective-potential method," and find excellent agreement. Second, we implement quasi-local measures of the spin of the individual holes, calibrate these with corotating binaries, and revisit the construction of non-spinning black hole binaries. Higher-order effects, beyond those considered in earlier work, turn out to be important. Without those, supposedly non-spinning black holes have appreciable quasi-local spin; furthermore, the Komar-mass condition and effective potential method agree only when these higher-order effects are taken into account. We compute a new sequence of quasi-circular orbits for non-spinning black-hole binaries, and determine the innermost stable circular orbit of this sequence.