On the distribution of stellar remnants around massive black holes: slow mass segregation, star cluster inspirals and correlated orbits

We study the long term dynamical evolution of stellar mass black holes (BHs) at the Galactic center (GC) and put constraints on their number and central mass distribution. Models of the GC are considered that have not yet achieved a steady state under the influence of random gravitational encounters. Contrary to some recent claims that mass-segregation can rapidly rebuild a density cusp in the stars, we find that time scales associated with cusp regrowth are longer than the Hubble time. These results cast doubts on standard models that postulate high densities of BHs near the GC and motivate studies that start from initial conditions which correspond to well-defined physical models. For the first time, we consider the distribution of BHs in a dissipationless formation model for the Milky Way nuclear cluster (NC), in which massive stellar clusters merge in the GC to form a nucleus. We simulate the successive inspiral of massive clusters containing an inner dense cluster of BHs. The pre-existing mass segregation is not completely erased as the clusters are disrupted by the massive black hole tidal field. As a result, after 12 inspiral events a NC forms in which the BHs have higher central densities than the stars. After evolving the model for 5-10 Gyr, the BHs do form a steep central cusp, while the stellar distribution maintains properties that resemble those of the Milky Way NC. Finally, we investigate the effect of BH perturbations on the motion of the GC S-stars, as a means of constraining the number of the perturbers. We find that reproducing the S-star orbital distribution requires >~1000 BHs within 0.1 pc of Sgr A*. A dissipationless formation scenario for the Milky Way NC is consistent with this lower limit and therefore could reconcile the need for high central densities of BHs (to explain the orbits of the S-stars), with the missing-cusp problem of the GC giant star population.Comment: 23 pages, 21 Figures. Accepted for publication in Ap

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

Massive binary star mergers in galactic nuclei: implications for blue stragglers, binary S-stars and gravitational waves

Galactic nuclei are often found to contain young stellar populations and, in most cases, a central supermassive black hole (SMBH). Most known massive stars are found in binaries or higher-multiplicity systems, and in a galactic nucleus the gravitational interaction with the SMBH can affect their long-term evolution. In this paper, we study the orbital evolution of stellar binaries near SMBHs using high precision $N$-body simulations, and including tidal forces and Post-Newtonian corrections to the motion. We focus on the Lidov-Kozai (LK) effect induced by the SMBH on massive star binaries. We investigate how the properties of the merging binaries change with varying the SMBH mass, the slope of the initial mass function, the distributions of the binary orbital parameters and the efficiency in energy dissipation in dissipative tides. We find that the fraction of merging massive binary stars is in the range $\sim 4\%$--$15\%$ regardless of the details of the initial distributions of masses and orbital elements. For a Milky Way-like nucleus, we find a typical rate of binary mergers $\Gamma\approx 1.4\times 10^{-7}$ yr$^{-1}$. The merger products of massive binaries can be rejuvenated blue-straggler stars, more massive than each of their original progenitors, and G2-like objects. Binary systems that survive the LK cycles can be source of X-rays and gravitational waves, observable with present and upcoming instruments.Comment: 13 pages, 7 figures, 1 table, accepted by MNRA

The final-parsec problem in the collisionless limit

A binary supermassive black hole loses energy via ejection of stars in a galactic nucleus, until emission of gravitational waves becomes strong enough to induce rapid coalescence. Evolution via the gravitational slingshot requires that stars be continuously supplied to the binary, and it is known that in spherical galaxies the reservoir of such stars is quickly depleted, leading to stalling of the binary at parsec-scale separations. Recent N-body simulations of galaxy mergers and isolated nonspherical galaxies suggest that this stalling may not occur in less idealized systems. However, it remains unclear to what degree these conclusions are affected by collisional relaxation, which is much stronger in the numerical simulations than in real galaxies. In this study, we present a novel Monte Carlo method that can efficiently deal with both collisional and collisionless dynamics, and with galaxy models having arbitrary shapes. We show that without relaxation, the final-parsec problem may be overcome only in triaxial galaxies. Axisymmetry is not enough, but even a moderate departure from axisymmetry is sufficient to keep the binary shrinking. We find that the binary hardening rate is always substantially lower than the maximum possible, "full-loss-cone" rate, and that it decreases with time, but that stellar-dynamical interactions are nevertheless able to drive the binary to coalescence on a timescale <=1 Gyr in any triaxial galaxy.Comment: 17 pages, 10 figures; matches published versio

Dynamical processes near the super massive black hole at the galactic center

Observations of the stellar environment near the Galactic center provide the strongest empirical evidence for the existence of massive black holes in the Universe. Theoretical models of the Milky Way nuclear star cluster fail to explain numerous properties of such environment, including the presence of very young stars close to the super massive black hole (SMBH) and the more recent discovery of a parsec-scale core in the central distribution of the bright late-type (old) stars. In this thesis we present a theoretical study of dynamical processes near the Galactic center, strongly related to these issues. Using different numerical techniques we explore the close environment of a SMBH as catalyst for stellar collisions and mergers. We study binary stars that remain bound for several revolutions around the SMBH, finding that in the case of highly inclined binaries the Kozai resonance can lead to large periodic oscillations in the internal binary eccentricity and inclination. Collisions and mergers of the binary elements are found to increase significantly for multiple orbits around the SMBH. In collisions involving a low-mass and a high-mass star, the merger product acquires a high core hydrogen abundance from the smaller star, effectively resetting the nuclear evolution clock to a younger age. This process could serve as an important source of young stars at the Galactic center. We then show that a core in the old stars can be naturally explained in a scenario in which the Milky Way nuclear star cluster (NSC) is formed via repeated inspiral of globular clusters into the Galactic center. We present results from a set of N-body simulations of this process, which show that the fundamental properties of the NSC, including its mass, outer density profile and velocity structure, are also reproduced. Chandrasekhar’s dynamical friction formula predicts no frictional force on a test body in a low-density core, regardless of its density, due to the absence of stars moving more slowly than the local circular velocity. We have tested this prediction using large-scale N-body experiments. The rate of orbital decay never drops precisely to zero, because stars moving faster than the test body also contribute to the frictional force. When the contribution from the fast-moving stars is included in the expression for the dynamical friction force, and the changes induced by the massive body on the stellar distribution are taken into account, Chandrasekhar’s theory is found to reproduce the rate of orbital decay remarkably well. However, this rate is still substantially smaller than the rate predicted by Chandrasekhar’s formula in its most widely-used forms, implying longer time scales for inspiral. Motivated by recent observations that suggest a parsec-scale core around the Galactic center SMBH, we investigated the evolution of a population of stellar-mass black holes (BHs) as they spiral in to the center of the Galaxy. After ! 10 Gyr, we find that the density of BHs can remain substantially less than the density in stars at all radii; we conclude that it would be unjustified to assume that the spatial distribution of BHs at the Galactic center is well described by steady-state models

Dynamical constraints on the origin of hot and warm Jupiters with close friends

Gas giants orbiting their host star within the ice line are thought to have migrated to their current locations from farther out. Here we consider the origin and dynamical evolution of observed Jupiters, focusing on hot and warm Jupiters with outer friends. We show that the majority of the observed Jupiter pairs (twenty out of twenty-four) will be dynamically unstable if the inner planet was placed at >~1AU distance from the stellar host. This finding is at odds with formation theories that invoke the migration of such planets from semi-major axes >~1AU due to secular dynamical processes (e.g., secular chaos, Lidov-Kozai oscillations) coupled with tidal dissipation. In fact, the results of N-body integrations show that the evolution of dynamically unstable systems does not lead to tidal migration but rather to planet ejections and collisions with the host star. This and other arguments lead us to suggest that most of the observed planets with a companion could not have been transported from further out through secular migration processes. More generally, by using a combination of numerical and analytic techniques we show that the high-e Lidov-Kozai migration scenario can only account for less than 10% of all gas giants observed between 0.1-1 AU. Simulations of multi-planet systems support this result. Our study indicates that rather than starting on highly eccentric orbits with orbital periods above one year, these "warm" Jupiters are more likely to have reached the region where they are observed today without having experienced significant tidal dissipation.Comment: Accepted to AAS journals (AJ). 15 pages, 9 figure

Millisecond pulsars and the gamma-ray excess in Andromeda

The Fermi Gamma-Ray Space Telescope has provided evidence for diffuse gamma-ray emission in the central parts of the Milky Way and the Andromeda galaxy. This excess has been interpreted either as dark matter annihilation emission or as emission from thousands of millisecond pulsars (MSPs). We have recently shown that old massive globular clusters may move towards the center of the Galaxy by dynamical friction and carry within them enough MSPs to account for the observed gamma-ray excess. In this paper we revisit the MSP scenario for the Andromeda galaxy, by modeling the formation and disruption of its globular cluster system. We find that our model predicts gamma-ray emission $\sim 2-3$ times larger than for the Milky Way, but still nearly an order of magnitude smaller than the observed Fermi excess in the Andromeda. Our MSP model can reproduce the observed excess only by assuming $\sim 8$ times larger number of old clusters than inferred from galaxy scaling relations. To explain the observations we require either that Andromeda deviates significantly from the scaling relations, or that a large part of its high-energy emission comes from additional sources.Comment: 5 pages, 2 figures, 1 Table, accepted by ApJ Let