On formation rate of close binaries consisting of a super-massive black hole and a white dwarf

P. B. Ivanov

doi:10.1046/j.1365-8711.2002.05733.x

paper

On formation rate of close binaries consisting of a super-massive black hole and a white dwarf

arXiv:astro-ph/0112317 · doi:10.1046/j.1365-8711.2002.05733.x

Abstract

The formation rate of a close binary consisting of a super-massive black hole and a compact object (presumably a white dwarf) in galactic cusps is calculated with help of the so-called loss cone approximation. For a power low cusp of radius $r_{a}$ , the black hole mass $M \sim 1 0^{6} M_{⊙}$ , this rate $\dot N_{wd}\sim 4\cdot 10^{-5}K(p}\sqrt{{GM\over r_{a}^{3}}}\approx 3\cdot 10^{-9}K(p){({M\over 10^{6}M_{\odot}})}^{1/2}{({r_{a}\over 1pc})}^{-3/2}yr^{-1}$. The function $K (p)$ depends on parameter $p$ determining the cusp profile, and for the standard cusp profiles with $p = 1/4$ $K (p) \sim 2$ . We estimate the probability $Pr$ of finding of a compact object orbiting around a black hole with period $P$ in one particular galaxy to be $Pr \sim 1 0^{- 7} (\frac{P /1 0 ^{3} s}{M /1 0 ^{6} M _{⊙}})^{8/3} (\frac{M /1 0 ^{6} M _{⊙}}{r _{a} /1 p c})^{3/2}$ . The object with the period $P \sim 1 0^{3} s$ emits gravitational waves with amplitude sufficient to be detected by LISA type gravitational wave anatenna from the distance $\sim 1 0^{3} M p c$ . Based on estimates of masses of super-massive black holes in nearby galaxies, we speculate that LISA would detect several such events during its mission.

This version is to be published in MNRAS

On formation rate of close binaries consisting of a super-massive black hole and a white dwarf

Abstract

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