Focus issue: Astrophysics and general relativity of dense stellar systems

Observations of the innermost parsec surrounding Sgr A*—the supermassive black hole in the center of our Galaxy—have revealed a diversity of structures whose existence and characteristics apparently defy the fundamental principles of dynamics. In this article, we review the challenges to the dynamics theories that have been brought forth in the past two decades by the observations of the galactic center. We outline the theoretical framework that has been developed to reconcile the discrepancies between the theoretical predictions and the observational results. In particular, we highlight the role of the recently discovered sub-parsec stellar disk in determining the dynamics and resolving the inconsistencies. We also discuss the implications for the recent activity of Sgr A*.

Conventional approaches to incorporating general relativistic effects into the dynamics of N-body systems containing central black holes, or of hierarchical triple systems with a relativistic inner binary, may not be adequate when the goal is to study the evolution of the system over a timescale related to relativistic secular effects, such as the precession of the pericenter. For such problems, it may be necessary to include post-Newtonian (PN) 'cross terms' in the equations of motion in order to capture relativistic effects consistently over the long timescales. Cross terms are PN terms that explicitly couple the two-body relativistic perturbations with the Newtonian perturbations due to other bodies in the system. In this paper, we show that the total energy of a hierarchical triple system is manifestly conserved to Newtonian order over the relativistic pericenter precession timescale of the inner binary if and only if PN cross-term effects in the equations of motion are taken carefully into account.

We consider the problem of star consumption by supermassive black holes in non-spherical (axisymmetric, triaxial) galactic nuclei. We review the previous studies of the loss-cone problem and present a novel simulation method that allows us to separate out the collisional (relaxation-related) and collisionless (related to non-conservation of angular momentum) processes and determine their relative importance for the capture rates in different geometries. We show that for black holes more massive than ${{10}^{7}}\;{{M}_{\odot }}$, the enhancement of the capture rate in non-spherical galaxies is substantial, with even modest triaxiality being capable of keeping the capture rate at the level of a few percent of black hole mass per Hubble time.

Stars around a massive black hole (MBH) move on nearly fixed Keplerian orbits, in a centrally-dominated potential. The random fluctuations of the discrete stellar background cause small potential perturbations, which accelerate the evolution of orbital angular momentum by resonant relaxation. This drives many phenomena near MBHs, such as extreme mass-ratio gravitational wave inspirals, the warping of accretion disks, and the formation of exotic stellar populations. We present here a formal statistical mechanics framework to analyze such systems, where the background potential is described as a correlated Gaussian noise. We derive the leading order, phase-averaged 3D stochastic Hamiltonian equations of motion, for evolving the orbital elements of a test star, and obtain the effective Fokker–Planck equation for a general correlated Gaussian noise, for evolving the stellar distribution function. We show that the evolution of angular momentum depends critically on the temporal smoothness of the background potential fluctuations. Smooth noise has a maximal variability frequency ${{\nu }_{{\rm max} }}$. We show that in the presence of such noise, the evolution of the normalized angular momentum $j=\sqrt{1-{{e}^{2}}}$ of a relativistic test star, undergoing Schwarzschild (in-plane) general relativistic precession with frequency ${{\nu }_{GR}}/{{j}^{2}}$, is exponentially suppressed for $j\lt {{j}_{b}}$, where ${{\nu }_{GR}}/j_{b}^{2}\sim {{\nu }_{{\rm max} }}$, due to the adiabatic invariance of the precession against the slowly varying random background torques. This results in an effective Schwarzschild precession-induced barrier in angular momentum. When j_b is large enough, this barrier can have significant dynamical implications for processes near the MBH.

Accretion disks occur in a wide variety of astrophysical contexts, from planet formation to accretion onto black holes. For simplicity, they are generally imagined as thin and flat. However, whenever the diskʼs angular momentum is oblique to the angular momentum of the central object(s), a torque causes rings within the disk to precess, twisting and warping it. Because the torque weakens rapidly with increasing radius, it has long been thought that some unspecified 'friction' brings the inner portions of such disks into alignment, while the outer parts remain in their original orientation. Nearly all previous work on this topic has assumed that such a diskʼs internal stresses can be described by an isotropic viscosity, even though it has been known for more than four decades that fluid viscosity is far too weak to be significant in accretion disks, and for two decades that accretion stresses are actually due to anisotropic MHD turbulence. This paper reviews recent numerical simulation work showing how twisted disks align when their mechanics are described only in terms of real forces, including MHD turbulence. The detailed mechanisms of alignment are identified, the rate at which it occurs is quantified, and the isotropic viscosity model is shown to be in drastic disagreement with the simulation data.

The formation mechanism of supermassive black holes (SMBHs) in general, and of $\sim {{10}^{9}}\ {{{\rm m}}_{\odot }}$ SMBHs observed as luminous quasars at redshifts $z\gt 6$ in particular, remains an open fundamental question. The presence of such massive BHs at such early times, when the Universe was less than a billion years old, implies that they grew via either super-Eddington accretion, or nearly uninterrupted gas accretion near the Eddington limit; the latter, at first glance, is at odds with empirical trends at lower redshifts, where quasar episodes associated with rapid BH growth are rare and brief. In this work, I examine whether and to what extent the growth of the $z\gt 6$ quasar SMBHs can be explained within the standard quasar paradigm, in which major mergers of host galaxies trigger episodes of rapid gas accretion below or near the Eddington limit. Using a suite of Monte Carlo merger tree simulations of the assembly histories of 40 likely $z\gt 6$ quasar host halos, I investigate (i) their growth and major merger rates out to $z\sim 40$, and (ii) how long the feeding episodes induced by host mergers must last in order to explain the observed $z\gtrsim 6$ quasar population without super-Eddington accretion. The halo major merger rate scales roughly as $\propto \;{{(1+z)}^{5/2}}$, consistent with cosmological simulations at lower redshifts, with quasar hosts typically experiencing $\gtrsim 10$ major mergers between $15\gt z\gt 6$ ($\approx 650\ {\rm Myr}$), compared to ∼1 for typical massive galaxies at $3\gt z\gt 0$ ($\approx 11\ {\rm Gyr}$). The high rate of major mergers allows for nearly continuous SMBH growth if (for example) a merger triggers feeding for a duration comparable to the halo dynamical time. These findings suggest that the growth mechanisms of the earliest quasar SMBHs need not have been drastically different from their counterparts at lower redshifts.

The formation of globular clusters (GCs) remains one of the main unsolved problems in star and galaxy formation. The past decades have seen important progress in constraining the physics of GC formation from a variety of directions. In this article, we discuss the latest constraints obtained from studies of present-day GC populations, the formation of young massive clusters (YMCs) in the local Universe, and the observed, large-scale conditions for star and cluster formation in high-redshift galaxies. The main conclusion is that the formation of massive, GC progenitor clusters is restricted to high-pressure environments similar to those observed at high redshift and at the sites of YMC formation in the local Universe. However, the correspondingly high gas densities also lead to efficient cluster disruption by impulsive tidal shocks, which limits the survival of GCs progenitor clusters. As a result, the long-term survival of GC progenitor clusters requires them to migrate into the host galaxy halo on a short time-scale. It is proposed that the necessary cluster migration is facilitated by the frequent galaxy mergers occurring at high redshift. We use the available observational and theoretical constraints to condense the current state of the field into a coherent picture of GC formation, in which regular star and cluster formation in high-redshift galaxies naturally leads to the GC populations observed today.

This article intends to provide a concise overview, from an observational point-of-view, of the current state of our knowledge of the most relevant properties of the Milky Wayʼs nuclear star cluster (MWNSC). The MWNSC appears to be a typical specimen of nuclear star clusters, which are found at the centers of the majority of all types of galaxies. Nuclear clusters represent the densest and most massive stellar systems in the present-day Universe and frequently coexist with central massive black holes. They are therefore of prime interest for studying stellar dynamics, and the MWNSC is the only one that allows us to obtain data on milli-parsec scales. After discussing the main observational constraints, we start with a description of the overall structure and kinematics of the MWNSC, then focus on a comparison to extragalactic systems, summarize the properties of the young, massive stars in the immediate environment of the Milky Wayʼs central black hole, Sagittarius A*, and finally focus on the dynamics of stars orbiting the black hole at distances of a few to a few tens of milli parsecs.