Related papers: Finite Disks with Power-Law Potentials
The first-order ordinary differential equation (ODE) that describes the mid-plane gravitational potential in flat finite size discs in which the surface density is a power-law function of the radius R with exponent s (Hur\'e & Hersant 2007)…
Exact analytical solutions are given for the three finite disks with surface density $\Sigma_n=\sigma_0 (1-R^2/\alpha^2)^{n-1/2} \textrm{with} n=0, 1, 2$. Closed-form solutions in cylindrical co-ordinates are given using only elementary…
We report a simple method to generate potential/surface density pairs in flat axially symmetric finite size disks. Potential/surface density pairs consist of a ``homogeneous'' pair (a closed form expression) corresponding to a uniform disk,…
An infinite family of axially symmetric thin disks of finite radius is presented. The family of disks is obtained by means of a method developed by Hunter and contains, as its first member, the Kalnajs disk. The surface densities of the…
We investigate the gravitational potentials generated by axisymmetric, razor-thin disks. Within certain limitations, the potential on one side of the disk is shown to be equivalent to the potential produced by a linear mass distribution…
A closed-form expression is obtained for the density of a simple layer, equipotential to an oblate level ellipsoid of revolution in an outer space. The potential of any level spheroid of positive mass with the inward direction of attracting…
Previously, we showed that surface density profiles of the form of a power-law times a Sersic function satisfy the hydrostatic Jeans equations, a variety of observational constraints, and the condition of a minimal radial entropy profile in…
Galactic disks in triaxial dark matter halos become deformed by the elliptical potential in the plane of the disk in such a way as to counteract the halo ellipticity. We develop a technique to calculate the equilibrium configuration of such…
We show that the gravitational potential in the plane of an axisymmetrical flat disk where the surface density varies as a power of the radius obeys an inhomogeneous first-order Ordinary Differential Equation (ODE) solvable by standard…
A new method is developed which permits the reconstruction of the surface-density distribution in the galactic disk of finite radius from an arbitrary smooth distribution of the angular velocity via two simple quadratures. The existence of…
We present accurate models of the gravitational potential produced by a radially exponential disk mass distribution. The models are produced by combining three separate Miyamoto-Nagai disks. Such models have been used previously to model…
Mestel determined the surface mass distribution of the finite disk for which the circular velocity is constant in the disk and found the gravitational field for points in the $z=0$ plane. Here we find the exact closed form solutions for the…
We study the kinematics of gaseous disks in triaxial dark matter halos using the closed-loop orbit solutions in non-axisymmetric potentials. The orbits are in general non-circular and, for given triaxiality, their ellipticity depends on the…
We present a new family of spherically symmetric models for the luminous components of elliptical and spiral galaxies and their dark matter haloes. Our starting point is a general expression for the logarithmic slope $\alpha(r) =…
The one-dimensional, ordinary differential equation (ODE) by Hur\'e & Hersant (2007) that satisfies the midplane gravitational potential of truncated, flat power-law disks is extended to the whole physical space. It is shown that thickness…
We use a set of cosmological N-body simulations to investigate the structural shape of galaxy-sized cold dark matter (CDM) halos. Unlike most previous work on the subject - which dealt with shapes as measured by the inertia tensor - we…
Apparent exponential surface density profiles are nearly universal in galaxy discs across Hubble types, over a wide mass range, and a diversity of gravitational potential forms. Several processes have been found to produce exponential…
The power-law disks are a family of infinitesimally thin, axisymmetric stellar disks of infinite extent. The rotation curve can be rising, falling or flat. The self-consistent power-law disks are scale-free, so that all physical quantities…
A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials A*r^{-alpha} take the simple form (l/r)^k = 1 + e cos(m*phi), where k = 2 - alpha > 0 and 'l' and 'e' are…
Aims. Galaxy mass models based on simple and analytical functions for the density and potential pairs have been widely proposed in the literature. Disk models constrained by kinematic data alone give information on the global disk structure…