Using self-consistent three-dimensional (3D) N-body simulations, we investigate the physical properties of non-axisymmetric features in a disk galaxy created by a tidal interaction with its companion. The primary galaxy consists of a stellar disk, a
bugle, and a live halo, corresponding to Milky-Way type galaxies, while the companion is represented by a halo alone. We vary the companion mass and the pericenter distance to explore situations with differing tidal strength parameterized by either the relative tidal force P or the relative imparted momentum S. We find that the formation of a tidal tail in the outer parts requires P > 0.05 or S > 0.07. A stronger interaction results in a stronger, less wound tail that forms earlier. Similarly, a stronger tidal forcing produces stronger, more loosely wound spiral arms in the inner parts. The arms are approximately logarithmic in shape, with both amplitude and pitch angle decaying with time. The derived pattern speed decreases with radius and is close to the Omega-kappa/2 curve at late time, with Omega and kappa denoting the angular and epicycle frequencies, respectively. This suggests that the tidally-induced spiral arms are most likely kinematic density waves weakly modified by self-gravity. Compared to the razor-thin counterparts, arms in the 3D models are weaker, have a smaller pitch angle, and wind and decay more rapidly. The 3D density structure of the arms is well described by the concentrated and sinusoidal models when the arms are in the nonlinear and linear regimes, respectively. We demonstrate that dynamical friction between interacting galaxies transfers the orbital angular momentum of one galaxy to the spin angular momentum of the companion halo.
The Kohn-Nireberg domains are unbounded domains in the complex Euclidean space of dimension 2 upon which many outstanding questions are yet to be explored. The primary aim of this article is to demonstrate that the Bergman and Caratheodory metrics of
any Kohn-Nirenberg domains are positive and complete.
The purpose of this paper is to present a solution to perhaps the final remaining case in the line of study concerning the generalization of Forellis theorem on the complex analyticity of the functions that are: (1) $mathcal{C}^infty$ smooth at a poi
nt, and (2) holomorphic along the complex integral curves generated by a contracting holomorphic vector field with an isolated zero at the same point.
The first result is the semicontinuity of automorphism groups for the collection of complex two-dimensional bounded pseudoconvex domains with smooth boundary of finite DAngelo type. The method of proof is new so that it simplifies the previous proof
of earlier semicontinuity theorems on bounded strongly pseudoconvex daomains by Greene and Krantz in the early 1980s.
Nuclear rings in barred galaxies are sites of active star formation. We use hydrodynamic simulations to study temporal and spatial behavior of star formation occurring in nuclear rings of barred galaxies where radial gas inflows are triggered solely
by a bar potential. The star formation recipes include a density threshold, an efficiency, conversion of gas to star particles, and delayed momentum feedback via supernova explosions. We find that star formation rate (SFR) in a nuclear ring is roughly equal to the mass inflow rate to the ring, while it has a weak dependence on the total gas mass in the ring. The SFR typically exhibits a strong primary burst followed by weak secondary bursts before declining to very small values. The primary burst is associated with the rapid gas infall to the ring due to the bar growth, while the secondary bursts are caused by re-infall of the ejected gas from the primary burst. While star formation in observed rings persists episodically over a few Gyr, the duration of active star formation in our models lasts for only about a half of the bar growth time, suggesting that the bar potential alone is unlikely responsible for gas supply to the rings. When the SFR is low, most star formation occurs at the contact points between the ring and the dust lanes, leading to an azimuthal age gradient of young star clusters. When the SFR is large, on the other hand, star formation is randomly distributed over the whole circumference of the ring, resulting in no apparent azimuthal age gradient. Since the ring shrinks in size with time, star clusters also exhibit a radial age gradient, with younger clusters found closer to the ring. The cluster mass function is well described by a power law, with a slope depending on the SFR. Giant gas clouds in the rings have supersonic internal velocity dispersions and are gravitationally bound.
Using hydrodynamic simulations, we investigate the physical properties of gaseous substructures in barred galaxies and their relationships with the bar strength. The gaseous medium is assumed to be isothermal and unmagnetized. The bar potential is mo
deled as a Ferrers prolate with index n. To explore situations with differing bar strength, we vary the bar mass fbar relative to the spheroidal component as well as its aspect ratio. We derive expressions as functions of fbar and the aspect ratio for the bar strength Qb and the radius r(Qb) where the maximum bar torque occurs. When applied to observations, these expressions suggest that bars in real galaxies are most likely to have fbar=0.25-0.5 and n<1. Dust lanes approximately follow one of x1-orbits and tend to be more straight under a stronger and more elongated bar, but are insensitive to the presence of self-gravity. A nuclear ring of a conventional x2 type forms only when the bar is not so massive or elongated. The radius of an x2-type ring is generally smaller than the inner Lindblad resonance, decreases systematically with increasing Qb, and slightly larger when self-gravity is included. This evidences that the ring position is not determined by the resonance but by the amount of angular momentum loss at dust-lane shocks. Nuclear spirals exist only when the ring is of the x2-type and sufficiently large in size. Unlike the other features, nuclear spirals are transient in that they start out as being tightly-wound and weak, and then due to the nonlinear effect unwind and become stronger until turning into shocks, with an unwinding rate higher for larger Qb. The mass inflow rate to the galaxy center is found to be less than 0.01 Msun/yr for models with Qb<0.2, while becoming larger than 0.1 Msun/yr when Qb>0.2 and self-gravity is included.
Barred galaxies are known to possess magnetic fields that may affect the properties of bar substructures such as dust lanes and nuclear rings. We use two-dimensional high-resolution magnetohydrodynamic (MHD) simulations to investigate the effects of
magnetic fields on the formation and evolution of such substructures as well as on the mass inflow rates to the galaxy center. The gaseous medium is assumed to be infinitesimally-thin, isothermal, non-self-gravitating, and threaded by initially uniform, azimuthal magnetic fields. We find that there exists an outermost x1-orbit relative to which gaseous responses to an imposed stellar bar potential are completely different between inside and outside. Inside this orbit, gas is shocked into dust lanes and infalls to form a nuclear ring. Magnetic fields are compressed in dust lanes, reducing their peak density. Magnetic stress removes further angular momentum of the gas at the shocks, temporarily causing the dust lanes to bend into an L shape and eventually leading to a smaller and more centrally distributed ring than in unmagnetized models. The mass inflow rates in magnetized models correspondingly become larger, by more than two orders of magnitude when the initial fields have an equipartition value with thermal energy, than in the unmagnetized counterparts. Outside the outermost x1-orbit, on the other hand, an MHD dynamo due to the combined action of the bar potential and background shear operates near the corotation and bar-end regions, efficiently amplifying magnetic fields. The amplified fields shape into trailing magnetic arms with strong fields and low density. The base of the magnetic arms has a thin layer in which magnetic fields with opposite polarity reconnect via a tearing-mode instability. This produces numerous magnetic islands with large density which propagate along the arms to turn the outer disk into a highly chaotic state.
The inner regions of barred galaxies contain substructures such as off-axis shocks, nuclear rings, and nuclear spirals. These substructure may affect star formation, and control the activity of a central black hole (BH) by determining the mass inflow
rate. We investigate the formation and properties of such substructures using high-resolution, grid-based hydrodynamic simulations. The gaseous medium is assumed to be infinitesimally-thin, isothermal, and non-self-gravitating. The stars and dark matter are represented by a static gravitational potential with four components: a stellar disk, the bulge, a central BH, and the bar. To investigate various galactic environments, we vary the gas sound speed c_s as well as the mass of the central BH M_BH. Once the flow has reached a quasi-steady state, off-axis shocks tend to move closer to the bar major axis as c_s increases. Nuclear rings shrink in size with increasing c_s, but are independent of M_BH, suggesting that ring position is not determined by the Lindblad resonances. Rings in low-c_s models are narrow since they are occupied largely by gas on x2-orbits and well decoupled from nuclear spirals, while they become broad because of large thermal perturbations in high-c_s models. Nuclear spirals persist only when either c_s is small or M_BH is large; they would otherwise be destroyed completely by the ring material on eccentric orbits. The shape and strength of nuclear spirals depend sensitively on c_s and M_BH such that they are leading if both c_s and M_BH are small, weak trailing if c_s is small and M_BH is large, and strong trailing if both c_s and M_BH are large. While the mass inflow rate toward the nucleus is quite small in low-c_s models because of the presence of a narrow nuclear ring, it becomes larger than 0.01 Msun/yr when c_s is large, providing a potential explanation of nuclear activity in Seyfert galaxies.
We use three-dimensional hydrodynamic simulations to investigate the nonlinear gravitational responses of gas to, and the resulting drag forces on, very massive perturbers moving on circular orbits. This work extends our previous studies that explore
d the cases of low-mass perturbers on circular orbits and massive perturbers on straight-line trajectories. The background medium is assumed to be non-rotating, adiabatic with index 5/3, and uniform with density rho0 and sound speed a0. We model the gravitating perturber using a Plummer sphere with mass Mp and softening radius rs in a uniform circular motion at speed Vp and orbital radius Rp, and run various models with differing R=rs/Rp, Mach=Vp/a0, and B=G*Mp/(a0^2*Rp). A quasi-steady density wake of a supersonic model consists of a hydrostatic envelope surrounding the perturber, an upstream bow shock, and a trailing low-density region. The continuous change in the direction of the perturber motion makes the detached shock distance reduced compared to the linear-trajectory cases, while the orbit-averaged gravity of the perturber gathers the gas toward the center of the orbit, modifying the background preshock density to rho1=(1 + 0.46B)*rho0 depending weakly on Mach. For sufficiently massive perturbers, the presence of a hydrostatic envelope makes the drag force smaller than the prediction of the linear perturbation theory, resulting in F = 4*pi*rho1*(G*Mp/Vp)^2 * (0.7/etaB) for etaB = B/(Mach^2 -1) > 0.1; the drag force for low-mass perturbers with etaB < 0.1 agrees well with the linear prediction. The nonlinear drag force becomes independent of R as long as R < etaB/2, which places an upper limit on the perturber size for accurate evaluation of the drag force in numerical simulations.
The mass-loss rate of donor stars in cataclysmic variables (CVs) is of paramount importance in the evolution of short-period CVs. Observed donors are oversized in comparison with those of isolated single stars of the same mass, which is thought to be
a consequence of the mass loss. Using the empirical mass-radius relation of CVs and the homologous approximation for changes in effective temperature T_2, orbital period P, and luminosity of the donor with the stellar radius, we find the semi-empirical mass-loss rate M2_dot of CVs as a function of P. The derived M2_dot is at ~10^(-9.5)-10^(-10) Msun/yr and depends weakly on P when P > 90 min, while it declines very rapidly towards the minimum period when P < 90 min, emulating the P-T_2 relation. Due to strong deviation from thermal equilibrium caused by the mass loss, the semi-empirical M2_dot is significantly different from, and has a less-pronounced turnaround behavior with P than suggested by previous numerical models. The semi-empirical P-M2_dot relation is consistent with the angular momentum loss due to gravitational wave emission, and strongly suggests that CV secondaries with 0.075 Msun < M_2 < 0.2 Msun are less than 2 Gyrs old. When applied to selected eclipsing CVs, our semi-empirical mass-loss rates are in good agreement with the accretion rates derived from the effective temperatures T_1 of white dwarfs, suggesting that M2_dot can be used to reliably infer T_2 from T_1. Based on the semi-empirical M2_dot, SDSS 1501 and 1433 systems that were previously identified as post-bounce CVs have yet to reach the minimal period.
