An infinite family of self-consistent models for axisymmetric flat galaxies

Abstract

We present the formulation of a new infinite family of self-consistent stellar models, designed to describe axisymmetric flat galaxies. The corresponding density-potential pair is obtained as a superposition of members belonging to the generalized Kalnajs family, by imposing the condition that the density can be expressed as a regular function of the gravitational potential, in order to derive analytically the corresponding equilibrium distribution functions (DFs). The resulting models are characterized by a well-behaved surface density, as in the case of generalized Kalnajs discs. Then, we present a study of the kinematical behaviour which reveals, in some particular cases, a very satisfactory behaviour of the rotational curves (without the assumption of a dark matter halo). We also analyse the equatorial orbit's stability, and Poincaré surfaces of section are performed for the three-dimensional orbits. Finally, we obtain the corresponding equilibrium DFs, using the approaches introduced by Kalnajs and Dejonghe.

Integrability of motion around galactic razor-thin disks

“…The last issue was partially encompassed in Ramos-Caro et al (2011), for instance, where a linear stability study of the monopole-ring system was performed by using superpositions of Morgan & Morgan disks. Similar studies were conducted by the authors in the Newtonian realm of galactic dynamics Pedraza et al 2008).…”

“…We remarked in the Introduction that motion is integrable near a stable circular orbit, a well-known result in the case of smooth density distributions. There are many evidences of this general behavior for razor-thin disks in the literature (Saa and Venegeroles 1999;Hunter 2003Hunter , 2005Pedraza et al 2008;Ramos-Caro et al 2008;González et al 2010;Ramos-Caro et al 2011), where it is found numerically, by means of Poincaré sections, that motion is integrable around what appears to be a stable point of the effective potential -corresponding to a stable circular orbit in the equatorial plane. These evidences also show that the integrable domain goes well beyond the neighborhood of the stable circular orbit, reaching regions where the approximation of a separable potential is not valid anymore.…”

Distribution functions for a family of axially symmetric galaxy models.

“…Such kind of DFs describes stellar systems with a preferred rotational state, characterized by the parameter α. This paper can be considered as a natural complement of the work previously presented by González and Reina (2006) and Ramos-Caro, López-Suspez and González (2008), where the PDP formulation and the kinematics, respectively, of the disks were analyzed. Now, by the construction of the corresponding two-integral DFs, the first four members of this family can be considered as a set of self-consistent stellar models for axially symmetric galaxies.…”

“…In González and Reina (2006), we use the Hunter method in order to obtain an infinite family of axially symmetric finite thin disks, characterized by a well-behaved surface density, whose first member is precisely the well-known Kalnajs disk. Also, the motion of test particles in the gravitational fields generated by the first four members of this family was studied in Ramos-Caro, López-Suspez and González (2008), and a new infinite family of self-consistent models was obtained in Pedraza, Ramos-Caro and González (2008) as a superposition of members belonging to the family.…”

Analytical potentials for flat galaxies with spheroidal halos

“…This family of disc models was derived by requiring that the surface density behaves as a monotonously decreasing function of the radius, with a maximum at the center of the disc and vanishing at the edge. Furthermore, the motion of test particles in the gravitational fields generated by the first four members of this family was studied in Ramos-Caro, López-Suspez and González (2008). So, although the mass distribution of this family of discs presents a satisfactory behaviour in such a way that they could be considered adequate as flat galaxy models, their corresponding rotation curves do not present a so good behavior, as they do not reproduce the flat region of the observed rotation curve.…”