Periastron Advance in Black-Hole Binaries

TL;DR

The general relativistic (Mercury-type) periastron advance is calculated here for the first time with exquisite precision in full general relativity and the effective-one-body model is found to be remarkably accurate.

Abstract

The general relativistic (Mercury-type) periastron advance is calculated here for the first time with exquisite precision in full general relativity. We use accurate numerical relativity simulations of spinless black hole binaries with mass ratios 1/8 < m1/m2 < 1 and compare with the predictions of several analytic approximation schemes. We find the effective-one-body model to be remarkably accurate, and, surprisingly, so also the predictions of self-force theory [replacing m1/m2 --> m1m2/(m1+m2)^2]. Our results can inform a universal analytic model of the two-body dynamics, crucial for ongoing and future gravitational-wave searches.

Figures (3)

• Figure 1: The periastron advance $K$ of an equal mass black hole binary, in the limit of zero eccentricity, as a function of the orbital frequency $\Omega_\varphi$ of the circular motion. The NR results are indicated by the cyan-shaded region. The PN and EOB results are valid at 3PN order. The lower panel shows the relative difference $\delta K/K \equiv (K-K_{\rm NR})/K_{\rm NR}$.
• Figure 2: Same as in Fig. \ref{['fig:q=1']}, but for a mass ratio $q={1}/{8}$. Note that for an orbital frequency $m \Omega_\varphi \sim 0.03$, corresponding to a separation $r \sim 10 m$, the periastron advance reaches half an orbit per radial period.
• Figure 3: The relative difference $\delta K/K = (K - K_\text{NR}) / K_\text{NR}$ as a function of the mass ratio $q$, for $m \Omega_\varphi = 0.022$. The PN and EOB results are valid at 3PN order. The shaded area marks the error margin of the NR data. The results are qualitatively identical and quantitatively similar for other values of $\Omega_\varphi$.