Dynamical friction in dark matter spikes: corrections to Chandrasekhar's formula

We consider the intermediate mass-ratio inspiral of a stellar-mass compact object with an intermediate-mass black hole that is surrounded by a dark matter density spike. The interaction of the inspiraling black hole with the dark matter particles in the spike leads to dynamical friction. This can alter the dynamics of the black hole binary, leaving an imprint on the gravitational wave signal. Previous calculations did not include in the evaluation of the dynamical friction coefficient the contribution from particles that move faster than the black hole. This term is neglected in the standard Chandrasekhar's treatment where only slower moving particles contribute to the decelerating drag. Here, we demonstrate that dynamical friction produced by the fast moving particles has a significant effect on the evolution of a massive binary within a dark matter spike. For a density profile $\rho\propto r^{-\gamma}$ with $\gamma\lesssim 1$, the dephasing of the gravitational waveform can be several orders of magnitude larger than estimated using the standard treatment. As $\gamma$ approaches $0.5$ the error becomes arbitrarily large. Finally, we show that dynamical friction tends to make the orbit more eccentric for any $\gamma < 1.8$. However, energy loss by gravitational wave radiation is expected to dominate the inspiral, leading to orbital circularization in most cases.Comment: 6 pages, 4 figures. Submitted. Comments are welcom

Dynamical friction and the evolution of Supermassive Black hole Binaries: the final hundred-parsec problem

The supermassive black holes originally in the nuclei of two merging galaxies will form a binary in the remnant core. The early evolution of the massive binary is driven by dynamical friction before the binary becomes "hard" and eventually reaches coalescence through gravitational wave emission. { We consider the dynamical friction evolution of massive binaries consisting of a secondary hole orbiting inside a stellar cusp dominated by a more massive central black hole.} In our treatment we include the frictional force from stars moving faster than the inspiralling object which is neglected in the standard Chandrasekhar's treatment. We show that the binary eccentricity increases if the stellar cusp density profile rises less steeply than $\rho\propto r^{-2}$. In cusps shallower than $\rho\propto r^{-1}$ the frictional timescale can become very long due to the deficit of stars moving slower than the massive body. Although including the fast stars increases the decay rate, low mass-ratio binaries ($q\lesssim 10^{-3}$) in sufficiently massive galaxies have decay timescales longer than one Hubble time. During such minor mergers the secondary hole stalls on an eccentric orbit at a distance of order one tenth the influence radius of the primary hole (i.e., $\approx 10-100\rm pc$ for massive ellipticals). We calculate the expected number of stalled satellites as a function of the host galaxy mass, and show that the brightest cluster galaxies should have $\gtrsim 1$ of such satellites orbiting within their cores. Our results could provide an explanation to a number of observations, which include multiple nuclei in core ellipticals, off-center AGNs and eccentric nuclear disks.Comment: 18 pages, 13 Figures. Accepted for publication in Ap

Coalescing black hole binaries from globular clusters: mass distributions and comparison to gravitational wave data from GWTC-3

We use our cluster population model, cBHBd, to explore the mass distribution of merging black hole binaries formed dynamically in globular clusters. We include in our models the effect of mass growth through hierarchical mergers and compare the resulting distributions to those inferred from the third gravitational wave transient catalogue. We find that none of our models can reproduce the peak at $m_1\simeq 10M_\odot$ in the primary black hole mass distribution that is inferred from the data. This disfavours a scenario where most of the detected sources are formed in globular clusters. On the other hand, a globular cluster origin can account for the inferred secondary peak at $m_1\simeq 35M_\odot$, which requires that the most massive clusters form with half-mass densities $\rho_{\rm h,0} \gtrsim 10^4 M_\odot \rm pc^{-3}$. Finally, we find that the lack of a high mass cut--off in the inferred mass distribution can be also explained by the repopulation of an initial mass gap through hierarchical mergers. Matching the inferred merger rate above $\simeq 50M_\odot$ requires both initial cluster densities $\rho_{\rm h,0} \gtrsim 10^4 M_\odot \rm pc^{-3}$, and that black holes form with nearly zero spin. A hierarchical merger scenario makes specific predictions for the appearance and position of multiple peaks in the black hole mass distribution, which can be tested against future data.Comment: Submitted to MNRAS; 10 pages, 5 figure

Black Hole Mergers in Galactic Nuclei Induced by the Eccentric Kozai-Lidov Effect

Nuclear star clusters around massive black holes are expected to be abundant in stellar mass black holes and black hole binaries. These binaries form a hierarchical triple system with the massive black hole at the center. Gravitational perturbations from the massive black hole can cause high eccentricity excitation. During this process, the eccentricity may approach unity, and the pericenter distance may become sufficiently small that gravitational wave emission drives the binary to merge. In this paper, we consider a simple proof of concept and explore the effect of the eccentric Kozai-Lidov mechanism for unequal mass binaries. We perform a set of Monte Carlo simulations on BH-BH binaries in galactic nuclei with quadrupole and octupole-level secular perturbations, general relativistic precession, and gravitational wave emission. For a nominal number of steady-state BH-BH binaries, our model gives a total merger rate $\sim 1 - 3$$Gpc^{-3} yr^{-1}$, depending on the assumed density profile. Thus, our model potentially competes with other dynamical mechanisms, such as the dynamical formations and mergers of BH binaries in globular clusters or dense nuclear clusters without a massive black hole. We provide predictions for the distributions of these LIGO sources in galactic nuclei.Comment: 10 pages, 12 figures, accepted to Ap

Formation of counter-rotating and highly eccentric massive black hole binaries in galaxy mergers

Supermassive black hole (SMBH) binaries represent the main target for missions such as the Laser Interferometer Space Antenna and Pulsar Timing Arrays. The understanding of their dynamical evolution prior to coalescence is therefore crucial to improving detection strategies and for the astrophysical interpretation of the gravitational wave data. In this paper, we use high-resolution N-body simulations to model the merger of two equal-mass galaxies hosting a central SMBH. In our models, all binaries are initially prograde with respect to the galaxy sense of rotation. But, binaries that form with a high eccentricity, e ≳ 0.7, quickly reverse their sense of rotation and become almost perfectly retrograde at the moment of binary formation. The evolution of these binaries proceeds towards larger eccentricities, as expected for a binary hardening in a counter-rotating stellar distribution. Binaries that form with lower eccentricities remain prograde and at comparatively low eccentricities. We study the origin of the orbital flip by using an analytical model that describes the early stages of binary evolution. This model indicates that the orbital plane flip is due to the torque from the triaxial background mass distribution that naturally arises from the galactic merger process. Our results imply the existence of a population of SMBH binaries with a high eccentricity and could have significant implications for the detection of the gravitational wave signal emitted by these systems