Related papers: Potential-Density Basis Sets for Galactic Disks
A set of bi-orthogonal potential-density basis functions is introduced to model the density and its associated gravitational field of three dimensional stellar systems. Radial components of our basis functions are weighted integral forms of…
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…
We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential--density basis functions. The potential and density functions of the new set have finite central…
We introduce a class of eccentric discs with "strong" density cusps whose potentials are of St\"ackel form in elliptic coordinates. Our models exhibit some striking features: sufficiently close to the location of the cusp, the potential and…
We present a new systematic way of setting up galactic gas disks based on the assumption of detailed hydrodynamic equilibrium. To do this, we need to specify the density distribution and the velocity field which supports the disk. We first…
Potential-density pair basis sets can be used for highly efficient N-body simulation codes, but they suffer from a lack of versatility, i.e. a basis set has to be constructed for each different class of stellar system. We present numerical…
We present axially symmetric analytical potential-density pairs with surface density similar to the Miyamoto-Nagai model, but with more realistic vertical structure. Our models closely approximate an exponential, a sech$^2$, or a cored…
Two dimensional realizations of self-consistent models for the ``perfect elliptic disks'' were tested for global stability by gravitational N-body integration. The family of perfect elliptic disk potentials have two isolating integrals;…
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,…
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…
We have previously explored cylindrical packings of disks and their relation to sphere packings. Here we extend the analytical treatment of disk packings, analysing the rules for phyllotactic indices of related structures and the variation…
The Kuzmin-Toomre family of discs is used to construct potential-density pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a…
Calculations of the hyperpolarizability are typically much more difficult to converge with basis set size than the linear polarizability. In order to understand these convergence issues and hence obtain accurate ab initio values, we compare…
New families of exact general relativistic thick disks are constructed using the ``displace, cut, fill and reflect'' method. A class of functions used to ``fill'' the disks is derived imposing conditions on the first and second derivatives…
We construct simple triaxial generalisations of Navarro-Frenk-White haloes. The models have elementary gravitational potentials, together with a density that is cusped like 1/r at small radii and falls off like 1/r^3 at large radii. The…
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…
In this work, we present an analytical study of the electrostatic potential generated by a charged disk with a surface charge distribution that possesses radial axial symmetry. We express the potential in cylindrical coordinates and apply a…
We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, and cutoff…
A family of analytical potential-density pairs for flat galaxies with spheroidal halos is presented. The potential are obtained by means of the sum of two independent terms: a potential associated with a thin disc and a potential associated…
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…