Evolution of Binary Supermassive Black Holes in Rotating Nuclei

Abstract

Interaction of a binary supermassive black hole with stars in a galactic nucleus can result in changes to all the elements of the binary's orbit, including the angles that define its orientation. If the nucleus is rotating, the orientation changes can be large, causing large changes in the binary's orbital eccentricity as well. We present a general treatment of this problem based on the Fokker-Planck equation for f , defined as the probability distribution for the binary's orbital elements. First-and second-order diffusion coefficients are derived for the orbital elements of the binary using numerical scattering experiments, and analytic approximations are presented for some of these coefficients. Solutions of the Fokker-Planck equation are then derived under various assumptions about the initial rotational state of the nucleus and the binary hardening rate. We find that the evolution of the orbital elements can become qualitatively different when we introduce nuclear rotation: 1) the orientation of the binary's orbit evolves toward alignment with the plane of rotation of the nucleus; 2) binary orbital eccentricity decreases for aligned binaries and increases for counter-aligned ones. We find that the diffusive (random-walk) component of a binary's evolution is small in nuclei with non-negligible rotation, and we derive the time-evolution equations for the semimajor axis, eccentricity and inclination in that approximation. The aforementioned effects could influence gravitational wave production as well as the relative orientation of host galaxies and radio jets. arXiv:1610.08555v3 [astro-ph.GA] 4 Apr 2017 Fokker-Planck equationThe binary is assumed to interact with stars, causing changes in its orbital elements. 1 In the simplest representation, the binary's orbit would evolve smoothly and deterministically with respect to time. We consider a slightly more complex model, in which a random, or diffusive, component to the binary's evolution is allowed as well.Accordingly, define f (E, L, t) dE dL to be the probability that the binary's energy E and angular momentum L lie in the intervals E to E + dE and L to L + dL, respectively, at time t. Let ∆t denote an interval of time that is short compared with the time over which the orbit of the binary changes due to encounters with stars, but still long enough that many encounters occur. Define the transition probability Ψ(E, L; ∆E, ∆L) that the energy and angular momentum of the binary change by ∆E and ∆L, respectively, in time ∆t. Then

Hypervelocity Stars from a Supermassive Black Hole–Intermediate-mass Black Hole Binary

“…3 shows K for co-and counterrotating stellar environments. For q 10 −2 , we have confirmed the previous findings that the binary eccentricity tends to decrease in a corotating environment and increase in a counterrotating one (Sesana et al 2011;Rasskazov & Merritt 2017), |K| being about an order of magnitude larger compared to the nonrotating case and weakly dependent on a/a h (Fig. 3, top).…”

“…This happens because H becomes negative for sufficiently soft equal-mass binaries, as was discovered in Rasskazov & Merritt (2017). Fig.…”

“…To calculate the ejected star velocities we use scattering experiments analyzed using the method originally presented in Quinlan (1996) and later built upon by Sesana et al (2006) and Rasskazov & Merritt (2017). We assume every star is initially unbound from the SMBH-IMBH binary and approaches it from infinity.…”

“…In the slowest velocity bin, 0.5%-3% and 6%-9% of all simulations fall into categories 2 and 3, respectively. Given the scattering experiment data described above, it is possible to introduce the rotation of the stellar nucleus in the same way as in Rasskazov & Merritt (2017) or Gualandris et al (2012):…”

Evaluating black hole detectability with LISA

“…These MBH binary coalescences result from mergers of their host galaxy haloes. Over time, the two MBHs sink to the centre of the primary halo via different dynamical pro-cesses (Haiman et al 2009, Dosopoulou & Antonini 2017, Kelley et al 2017, Rasskazov & Merritt 2017b.…”