Density-potential pairs for spherical stellar systems with Sérsic light profiles and (optional) power-law cores

Abstract

Popular models for describing the luminosity‐density profiles of dynamically hot stellar systems (e.g. Jaffe, Hernquist, Dehnen) were constructed with the desire to match the deprojected form of an R1/4 light profile. Real galaxies, however, are now known to have a range of different light‐profile shapes that scale with mass. Consequently, although highly useful, the above models have implicit limitations, and this is illustrated here through their application to a number of real galaxy density profiles. On the other hand, the analytical density profile given by Prugniel & Simien closely matches the deprojected form of Sérsic R1/n light profiles – including deprojected exponential light profiles. It is thus applicable for describing bulges in spiral galaxies, dwarf elliptical galaxies, and both ordinary and giant elliptical galaxies. Moreover, the observed Sérsic quantities define the parameters of the density model. Here we provide simple equations, in terms of elementary and special functions, for the gravitational potential and force associated with this density profile. Furthermore, to match galaxies with partially depleted cores, and better explore the supermassive black hole/galaxy connection, we have added a power‐law core to this density profile and derived similar expressions for the potential and force of this hybrid profile. Expressions for the mass and velocity dispersion, assuming isotropy, are also given. These spherical models may also prove appropriate for describing the dark matter distribution in haloes formed from ΛCDM cosmological simulations.

The effect of bars on the M•-σe relation: offset, scatter and residuals correlations

“…which yields, on projection, the Sérsic law with p = 1 − 0.6097/n + 0.055 63/n 2 (Prugniel & Simien 1997;Terzić & Graham 2005), where n is the Sérsic index and ρ b is the central surface density. The constant b is adjusted so that R eff contains half of the total projected mass of the bulge.…”

Total mass distributions of Sersic galaxies from photometry and central velocity dispersion

“…The corresponding deprojected spherical luminosity density distribution is discussed in Terzić & Graham (2005); Mazure & Capelato (2002). In Terzić & Sprague (2007), the spherical models of Terzić & Graham (2005) were generalised to include triaxiality. The luminosity density profile in the triaxial case is approximately given as:…”

Testing the tidal stripping origin of ultra-compact dwarf galaxies

“…In the analytic method, a profile is used for the main body of each galaxy (where the mass profile is of the form given by Terzić & Graham 2005) and a Plummer (1911) In Fig. 6.2 we compare f r J with the ratio of pericentre-to-apocentre distance for each simulation.…”

“…The constant b is chosen such that R e contains half the projected light and we use the relation between b and n found by Prugniel & Simien (1997). For the simulations the Sérsic surface brightness profile is converted into a potential using the method of Terzić & Graham (2005). We adopt for the stellar component a Sérsic index n = 11.84, an effective radius R e = 16.22 kpc and a central intensity I 0 = 2.732 × 10 17 L kpc −2 , consistent with , and a mass-to-light ratio ϒ = 9.1 (M/L) consistent with .…”

“…(i) The fitted surface density profiles of the simulated UCDs in Section 3.3 were converted to three-dimensional profiles (where we use the deprojected form of the Sérsic profile as given by Terzić & Graham 2005). …”