Equilibrium Sequences and Gravitational Instability of Rotating Isothermal Rings

Nuclear rings at centers of barred galaxies exhibit strong star formation activities. They are thought to undergo gravitational instability when sufficiently massive. We approximate them as rigidly-rotating isothermal objects and investigate their gravitational instability. Using a self-consistent field method, we first construct their equilibrium sequences specified by two parameters: alpha corresponding to the thermal energy relative to gravitational potential energy, and R_B measuring the ellipticity or ring thickness. Unlike in the incompressible case, not all values of R_B yield an isothermal equilibrium, and the range of R_B for such equilibria shrinks with decreasing alpha. The density distributions in the meridional plane are steeper for smaller alpha, and well approximated by those of infinite cylinders for slender rings. We also calculate the dispersion relations of nonaxisymmetric modes in rigidly-rotating slender rings with angular frequency Omega_0 and central density rho_max. Rings with smaller alpha are found more unstable with a larger unstable range of the azimuthal mode number. The instability is completely suppressed by rotation when Omega_0 exceeds the critical value. The critical angular frequency is found to be almost constant at ~ 0.7 sqrt(G*rho_c) for alpha > 0.01 and increases rapidly for smaller alpha. We apply our results to a sample of observed star-forming rings and confirm that rings without a noticeable azimuthal age gradient of young star clusters are indeed gravitationally unstable.Comment: 17 figures and 2 tables; Accepted for publication in the Ap

Hydrodynamical Simulations of Nuclear Rings in Barred Galaxies

Dust lanes, nuclear rings, and nuclear spirals are typical gas structures in the inner region of barred galaxies. Their shapes and properties are linked to the physical parameters of the host galaxy. We use high-resolution hydrodynamical simulations to study 2D gas flows in simple barred galaxy models. The nuclear rings formed in our simulations can be divided into two groups: one group is nearly round and the other is highly elongated. We find that roundish rings may not form when the bar pattern speed is too high or the bulge central density is too low. We also study the periodic orbits in our galaxy models, and find that the concept of inner Lindblad resonance (ILR) may be generalized by the extent of $x_2$ orbits. All roundish nuclear rings in our simulations settle in the range of $x_2$ orbits (or ILRs). However, knowing the resonances is insufficient to pin down the exact location of these nuclear rings. We suggest that the backbone of round nuclear rings is the $x_2$ orbital family, i.e. round nuclear rings are allowed only in the radial range of $x_2$ orbits. A round nuclear ring forms exactly at the radius where the residual angular momentum of infalling gas balances the centrifugal force, which can be described by a parameter $f_{\rm ring}$ measured from the rotation curve. The gravitational torque on gas in high pattern speed models is larger, leading to a smaller ring size than in the low pattern speed models. Our result may have important implications for using nuclear rings to measure the parameters of real barred galaxies with 2D gas kinematics.Comment: ApJ accepted version; we expanded the discussion of the limitations of this work in Section 4.7, and included a new subsection (Section 4.8) to demonstrate the convergence test for the resolution effects; 15 pages; emulateapj format. A movie showing the gas evolution in the canonical model is available on the ApJ website and at http://hubble.shao.ac.cn/~shen/nuclear_rings/canonicalmodel2.gi

Three Dimensional Hydrodynamic Simulations of Multiphase Galactic Disks with Star Formation Feedback: II. Synthetic HI 21 cm Line Observations

We use three-dimensional numerical hydrodynamic simulations of the turbulent, multiphase atomic interstellar medium (ISM) to construct and analyze synthetic HI 21 cm emission and absorption lines. Our analysis provides detailed tests of 21 cm observables as physical diagnostics of the atomic ISM. In particular, we construct (1) the "observed" spin temperature, $T_{s,obs}(v_{ch})\equiv T_B(v_{ch})/[1-e^{-{\tau}(v_{ch})}]$, and its optical-depth weighted mean T_s,obs; (2) the absorption-corrected "observed" column density, $N_{H,obs}\propto \int dv_{ch} T_B(v_{ch}){\tau}(v_{ch})/[[1-e^{-{\tau}(v_{ch})}]$; and (3) the "observed" fraction of cold neutral medium (CNM), $f_{c,obs}\equiv T_c/T_{s,obs}$ for T_c the CNM temperature; we compare each observed parameter with true values obtained from line-of-sight (LOS) averages in the simulation. Within individual velocity channels, T_s,obs(v_ch) is within a factor 1.5 of the true value up to ${\tau}(v_{ch})\approx10$. As a consequence, N_H,obs and T_s,obs are respectively within 5% and 12% of the true values for 90% and 99% of LOSs. The optically thin approximation significantly underestimates N_H for ${\tau}>1$. Provided that T_c is constrained, an accurate observational estimate of the CNM mass fraction can be obtained down to 20%. We show that T_s,obs cannot be used to distinguish the relative proportions of warm and thermally-unstable atomic gas, although the presence of thermally-unstable gas can be discerned from 21 cm lines with 200K<$T_{s,obs}(v_{ch})$<1000K. Our mock observations successfully reproduce and explain the observed distribution of the brightness temperature, optical depth, and spin temperature in Roy et al. (2013a). The threshold column density for CNM seen in observations is also reproduced by our mock observations. We explain this observed threshold behavior in terms of vertical equilibrium in the local Milky Way's ISM disk.Comment: 34 pages, 12 figures. Accepted for publication in ApJ. For Paper I, see http://arxiv.org/abs/1308.323