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

A Fast Poisson Solver of Second-Order Accuracy for Isolated Systems in Three-Dimensional Cartesian and Cylindrical Coordinates

We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.Comment: 24 pages, 13 figures; accepted for publication in ApJ

Symmetric negative differential resistance in a molecular nanosilver chain

The electrical transport properties of the molecular nanosilver chain have been investigated. We observed the symmetric negative differential resistance (NDR) in the current-voltage characteristics. The peak voltage (V P) increased but the peak current (I P) decreased upon cooling. The self-capacitance effect of the silver chain crystal is suggested to explain this unconventional NDR phenomenon.open0

Bis[μ-N-(pyridin-2-ylmeth­yl)pyridin-2-amine-κ2 N:N′]disilver(I) bis(trifluoro­methane­sulfonate)

In the binuclear title compound, [Ag2(C11H11N3)2](CF3O3S)2, the complex cation is centrosymmetric, with the unique Ag+ cation coordinated by two pyridine N atoms from two symmetry-related N-(pyridin-2-ylmeth­yl)pyridin-2-amine ligands in a geometry slightly distorted from linear [N—Ag—N 161.02 (7)°]. This set-up leads to the formation of a 14-membered cyclic dimer. The two pyridine rings coordinated to the Ag+ cation are tilted by 80.19 (7)° with respect to each other. Inter­molecular N—H⋯O hydrogen-bonding inter­actions between the cyclic dimer and the anion exist. A two-dimensional network parallel to the ac plane is constructed by three weak Ag⋯(O,N) inter­actions as well as an F⋯F contact of 2.890 (4) Å