Long‐Term Evolution of Massive Black Hole Binaries

Abstract

The long-term evolution of massive black hole binaries at the centers of galaxies is studied in a variety of physical regimes, with the aim of resolving the '' final parsec problem,'' i.e., how black hole binaries manage to shrink to separations at which emission of gravity waves becomes efficient. A binary ejects stars by the gravitational slingshot and carves out a loss cone in the host galaxy. Continued decay of the binary requires a refilling of the loss cone. We show that the standard treatment of loss cone refilling, derived for collisionally relaxed systems like globular clusters, can substantially underestimate the refilling rates in galactic nuclei. We derive expressions for nonequilibrium loss cone dynamics and calculate timescales for the decay of massive black hole binaries following galaxy mergers, obtaining significantly higher decay rates than heretofore. Even in the absence of two-body relaxation, decay of binaries can persist as a result of repeated ejection of stars returning to the nucleus on eccentric orbits. We show that this recycling of stars leads to a gradual, approximately logarithmic dependence of the binary binding energy on time. We derive an expression for the loss cone refilling induced by the Brownian motion of a black hole binary. We also show that numerical N-body experiments are not well suited to probe these mechanisms over long times as a result of spurious relaxation.

Efficient Merger of Binary Supermassive Black Holes in Nonaxisymmetric Galaxies

“…N-body simulations (Makino & Funato 2004;Szell et al 2005;Berczik et al 2005) show that continued hardening of the binary takes place at a rate that depends strongly on the number N of "star" particles used in the simulation. As N increases, the hardening rate falls, as expected if the binary's loss cone is repopulated by star-star gravitational encounters (Yu 2002;Milosavljević & Merritt 2003). When extrapolated to the much larger N of real galaxies, these results suggest that binary evolution would generally stall (the "final-parsec problem").…”

Detecting Eccentric Supermassive Black Hole Binaries With Pulsar Timing Arrays: Resolvable Source Strategies

“…If we can include parametrized models of the rate of binary evolution in constructing full Earth and pulsar term signal models in a Bayesian or frequentist search, then we will be able to make statements about the relative importance of the aforementioned mechanisms. This in itself may provide clues as to how binaries are driven to sub-parsec orbital separations after dynamical friction in post-merger galaxies becomes inefficient, thereby adding to our knowledge of how the final parsec problem (Milosavljević & Merritt 2003) is ameliorated.…”

The puzzling case of the radio-loud QSO 3C 186: a gravitational wave recoiling black hole in a young radio source?

“…How the two BHs reach the distance at which GW emission becomes important is a process that is still poorly understood, and it is possible that the binary may stall. This is the so-called final parsec problem (Milosavljević & Merritt 2003). However, a gas-rich environment may significantly help to overcome this problem.…”