A new mass model describing motion in axially symmetric galaxies with dark matter

• Published in: Monthly notices of the Royal Astronomical Society 2012-07, Vol.423 (3), p.2668-2679
• Main Author: Caranicolas, N. D.
• Format: Article
• Language: English
• Subjects: Astrophysics; Dark matter; Density; Discs; Disks; Elliptical galaxies; Galaxies; galaxies: kinematics and dynamics; Mathematical analysis; Mathematical models; Stars & galaxies
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2012.21073.x

We present a new analytical model in order to describe motion in axially symmetric galaxies containing dark matter. The model has a finite mass and can describe motion in disc as well as in elliptical galaxies. The advantage of this new model is an additional parameter that characterizes the percentage of dark matter in the system. This fractional portion of dark matter affects some basic physical quantities of the galaxy, such as the rotational velocity, the mass density and the vertical force. Adding to this model a dense spherical nucleus, we obtain a composite mass model, which can be used to describe motion in galaxies with central mass concentrations, where, for low values of the star's z-component of angular momentum, regular motion together with large chaotic regions in the r-p r phase plane is observed. We find that the presence of the dark matter causes an increase in the rotational velocity, the mass density and the vertical force, both in the discussed disc model and in the oblate elliptical galaxy model. The significant difference is that the increase in the elliptical galaxy model is larger than that observed in the disc model. On the contrary, the fraction A per cent in the r-p r phase plane covered by chaotic orbits, which is measured empirically, for the same fractional portion of dark matter, is much larger in the disc model than that found in the elliptical model. This result may depend on the particular way the dark matter is built-in into the model. The numerical experiments indicate that the distribution of dark matter in our model is such that the amount of dark matter increases as the distance from the centre increases, which seems to be in agreement with the observational data.