Pairing of Massive Black Holes in Merger Galaxies

Motivated by the studies of potential LISA sources we develop a semi-analytic model to describe the orbital evolution of massive black hole (MBH) pairs under the influence of stellar and gaseous dynamical friction (DF). The goal of this study is to determine how the properties of the merger remnant galaxy and the MBHs affect the likelihood and timescale for formation of a close MBH pair with separation of less than 1 pc. We compute approximately 40,000 configurations that cover a wide range of host galaxy properties and investigate their impact on the orbital evolution of unequal mass MBH pairs. We find that the remnant galaxies characterized by the fastest formation of close, gravitationally bound MBHs have one or more of the following properties: (1) large stellar bulge, (2) comparable mass MBHs and (3) a galactic gas disk rotating close to the circular speed. In such galaxies, the MBHs with the shortest inspiral times, which are likely progenitors of LISA sources, are either on circular prograde orbits or on very eccentric retrograde orbits. For MBHs evolving in gas-rich backgrounds, the ionizing radiation that emerges from the innermost parts of their accretion flow can affect the surrounding gas in such a way to cause the MBHs to accelerate and gain orbital energy. Our results show that for a wide range of merger galaxy and MBH properties negative DF reduces the MBH pairing probability by 47%. The suppression of MBH pairing is most severe for pairs with mass less than few 10⁸ solar masses, which are the progenitors of merging MBHs targeted by LISA. Therefore, if negative DF operates as described here, the merger rate of MBHs detectable by LISA may be considerably reduced.