We investigate gravitational instability (GI) of rotating, vertically-stratified, pressure-confined, polytropic gas disks using linear stability analysis as well as analytic approximations. The disks are initially in vertical hydrostatic equilibrium
and bounded by a constant external pressure. We find that GI of a pressure-confined disk is in general a mixed mode of the conventional Jeans and distortional instabilities, and is thus an unstable version of acoustic-surface-gravity waves. The Jeans mode dominates in weakly confined disks or disks with rigid boundaries. When the disk has free boundaries and is strongly pressure-confined, on the other hand, the mixed GI is dominated by the distortional mode that is surface-gravity waves driven unstable under own gravity and thus incompressible. We demonstrate that the Jeans mode is gravity-modified acoustic waves rather than inertial waves and that inertial waves are almost unaffected by self-gravity. We derive an analytic expression for the effective sound speed c_eff of acoustic-surface-gravity waves. We also find expressions for the gravity reduction factors relative to a razor-thin counterpart, appropriate for the Jeans and distortional modes. The usual razor-thin dispersion relation after correcting for c_eff and the reduction factors closely matches the numerical results obtained by solving a full set of linearized equations. The effective sound speed generalizes the Toomre stability parameter of the Jeans mode to allow for the mixed GI of vertically-stratified, pressure-confined disks.
In many astrophysical situations, as in the coalescence of supermassive black hole pairs at gas rich galactic nuclei, the dynamical friction experienced by an object is a combination of its own wake as well as the wakes of its companions. Using a sem
i-analytic approach, we investigate the composite wake due to, and the resulting drag forces on, double perturbers that are placed at the opposite sides of the orbital center and move on a circular orbit in a uniform gaseous medium. The circular orbit makes the wake of each perturber asymmetric, creating an overdense tail at the trailing side. The tail not only drags the perturber backward but it also exerts a positive torque on the companion. For equal-mass perturbers, the positive torque created by the companion wake is, on average, a fraction ~40-50% of the negative torque created by its own wake, but this fraction may be even larger for perturbers moving subsonically. This suggests that the orbital decay of a perturber in a double system, especially in the subsonic regime, can take considerably longer than in isolation. We provide the fitting formulae for the forces due to the companion wake and discuss our results in light of recent numerical simulations for mergers of binary black holes.
Using one-dimensional hydrodynamic simulations including interstellar heating, cooling, and thermal conduction, we investigate nonlinear evolution of gas flow across galactic spiral arms. We model the gas as a non-self-gravitating, unmagnetized fluid
, and follow its interaction with a stellar spiral potential in a local frame comoving with the stellar pattern. Initially uniform gas rapidly separates into warm and cold phases as a result of thermal instability (TI), and also forms a quasi-steady shock that prompts phase transitions. After saturation, the flow follows a recurring cycle: warm and cold phases in the interarm region are shocked and immediately cool to become a denser cold medium in the arm; post-shock expansion reduces the mean density to the unstable regime in the transition zone and TI subsequently mediates evolution back into warm and cold interarm phases. For our standard model with n_0 = 2 cm^-3, the gas resides in the dense arm, thermally-unstable transition zone, and interarm region for 14%, 22%, 64% of the arm-to-arm crossing time. These regions occupy 1%, 16%, and 83% of the arm-to-arm distance, respectively. Gas at intermediate temperatures represents ~25-30% of the total mass, similar to the fractions estimated from HI observations. Despite transient features and multiphase structure, the time-averaged shock profiles can be matched to that of a diffusive isothermal medium with temperature 1,000 K and particle mean free path of l_0 = 100 pc. Finally, we quantify numerical conductivity associated with translational motion of phase-separated gas on the grid, and show that convergence of numerical results requires the numerical conductivity to be comparable to or smaller than the physical conductivity. (Abridged)
We explore tidal interactions of a galactic disk with Toomre parameter Q ~ 2 embedded in rigid halo/bulge with a point mass companion moving in a prescribed parabolic orbit. Tidal interactions produce well-defined spiral arms and extended tidal featu
res such as bridge and tail that are all transient, but distinct in nature. In the extended disks, strong tidal force is able to lock the perturbed epicycle phases of the near-side particles to the perturber, shaping them into a tidal bridge that corotates with the perturber. A tidal tail develops at the opposite side as strongly-perturbed, near-side particles overtake mildly-perturbed, far-side particles. The tail is essentially a narrow material arm with a roughly logarithmic shape, dissolving with time because of large velocity dispersions. Inside the disks where tidal force is relatively weak, on the other hand, a two-armed logarithmic spiral pattern emerges due to the kinematic alignment of perturbed particle orbits. While self-gravity makes the spiral arms a bit stronger, the arms never become fully self-gravitating, wind up progressively with time, and decay after the peak almost exponentially in a time scale of ~ 1 Gyr. The arm pattern speed varying with both radius and time converges to Omega-kappa/2 at late time, suggesting that the pattern speed of tidally-driven arms may depend on radius in real galaxies. We present the parametric dependences of various properties of tidal features on the tidal strength, and discuss our findings in application to tidal spiral arms in grand-design spiral galaxies. (Abridged)
We investigate the gravitational wake due to, and dynamical friction on, a perturber moving on a circular orbit in a uniform gaseous medium using a semi-analytic method. This work is a straightforward extension of Ostriker (1999) who studied the case
of a straight-line trajectory. The circular orbit causes the bending of the wake in the background medium along the orbit, forming a long trailing tail. The wake distribution is thus asymmetric, giving rise to the drag forces in both opposite (azimuthal) and lateral (radial) directions to the motion of the perturber, although the latter does not contribute to orbital decay much. For subsonic motion, the density wake with a weak tail is simply a curved version of that in Ostriker and does not exhibit the front-back symmetry. The resulting drag force in the opposite direction is remarkably similar to the finite-time, linear-trajectory counterpart. On the other hand, a supersonic perturber is able to overtake its own wake, possibly multiple times, and develops a very pronounced tail. The supersonic tail surrounds the perturber in a trailing spiral fashion, enhancing the perturbed density at the back as well as far front of the perturber. We provide the fitting formulae for the drag forces as functions of the Mach number, whose azimuthal part is surprisingly in good agreement with the Ostrikers formula, provided Vp t=2 Rp, where Vp and Rp are the velocity and orbital radius of the perturber, respectively.
