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Gravitational recoil velocities from eccentric binary black hole mergers

Carlos F. Sopuerta, Nicolas Yunes, Pablo Laguna

TL;DR

This work addresses gravitational recoil velocities from mergers of unequal-mass binary black holes with small eccentricities. It combines the Close Limit Approximation (CLA), valid in the last merger stages, with post-Newtonian (PN) estimates to bound the total kick, and introduces an explicit fit for the CLA recoil as a function of symmetric mass ratio $\eta$ and eccentricity $e$. The study finds that the maximum recoil occurs near $\eta \approx 0.19$ and that small eccentricities enhance the kick roughly by a factor of $1+e$ (for $e \lesssim 0.1$); by blending CLA with PN results, it provides lower and upper bounds and a best estimate for the total recoil, with a most likely range around $1.7\times 10^2$ km s$^{-1}$ for typical eccentricities. The results, consistent with recent quasi-circular NR simulations, have implications for SMBH retention in galaxies and for understanding dynamical processes during galaxy mergers, while highlighting the need to incorporate spins and higher multipoles in future work.

Abstract

The formation and growth of supermassive black holes is a key issue to unveil the secrets of galaxy formation. In particular, the gravitational recoil produced in the merger of unequal mass black hole binaries could have a number of astrophysical implications, such as the ejection of black holes from the host galaxy or globular cluster. We present estimates of the recoil velocity that include the effect of small eccentricities. The approach is specially suited for the last stage of the merger, where most of the emission of linear momentum in gravitational waves takes place. Supplementing our estimates with post-Newtonian approximations, we obtain lower and upper bounds that constrain previous recoil velocities estimates as well as a best estimate that agrees with numerical simulations in the quasi-circular case. For eccentricities e <= 0.1, the maximum recoil is found for mass ratios of M_1/M_2 ~ 0.38 with a best estimate of ~ 167 (1 + e) km/s and upper and lower bounds of 79 (1 + e) km/s and 216 (1 + e) km/s respectively.

Gravitational recoil velocities from eccentric binary black hole mergers

TL;DR

This work addresses gravitational recoil velocities from mergers of unequal-mass binary black holes with small eccentricities. It combines the Close Limit Approximation (CLA), valid in the last merger stages, with post-Newtonian (PN) estimates to bound the total kick, and introduces an explicit fit for the CLA recoil as a function of symmetric mass ratio and eccentricity . The study finds that the maximum recoil occurs near and that small eccentricities enhance the kick roughly by a factor of (for ); by blending CLA with PN results, it provides lower and upper bounds and a best estimate for the total recoil, with a most likely range around km s for typical eccentricities. The results, consistent with recent quasi-circular NR simulations, have implications for SMBH retention in galaxies and for understanding dynamical processes during galaxy mergers, while highlighting the need to incorporate spins and higher multipoles in future work.

Abstract

The formation and growth of supermassive black holes is a key issue to unveil the secrets of galaxy formation. In particular, the gravitational recoil produced in the merger of unequal mass black hole binaries could have a number of astrophysical implications, such as the ejection of black holes from the host galaxy or globular cluster. We present estimates of the recoil velocity that include the effect of small eccentricities. The approach is specially suited for the last stage of the merger, where most of the emission of linear momentum in gravitational waves takes place. Supplementing our estimates with post-Newtonian approximations, we obtain lower and upper bounds that constrain previous recoil velocities estimates as well as a best estimate that agrees with numerical simulations in the quasi-circular case. For eccentricities e <= 0.1, the maximum recoil is found for mass ratios of M_1/M_2 ~ 0.38 with a best estimate of ~ 167 (1 + e) km/s and upper and lower bounds of 79 (1 + e) km/s and 216 (1 + e) km/s respectively.

Paper Structure

This paper contains 4 sections, 5 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Recoil velocities and the Close Limit approximation
  3. Estimating the total recoil
  4. Summary and Discussion

Figures (3)

  • Figure 1: Best estimate of the recoil velocity in $\hbox{km s}^{-1}\,$ as a function of symmetric mass ratio $\eta$ for the quasi-circular case $e = 0\,$, calculated by combining the CLA calculation with a $2$ PN approximation. Also plotted are the results from a full numerical relativistic simulation Gonzalez:2006md.
  • Figure 2: Recoil velocity in $\hbox{km s}^{-1}\,$ as a function of symmetric mass ratio $\eta$ for eccentricities in the range $e = 0-0.25\,$.
  • Figure 3: Upper and lower limits (dashed and dotted lines) and best estimate (solid lines) to the total recoil velocity in $\hbox{km s}^{-1}\,$ as a function of symmetric mass ration $\eta$ for eccentricities in the range $e=0-0.1\,$.