Self-consistent, axisymmetric two-integral models of elliptical galaxies with embedded nuclear discs

Abstract

Ionized gas discs in the nuclei of ellipticals have proven to be excellent tools for the determination of the central mass density in these galaxies. The recent discovery with the Hubble Space Telescope of small stellar discs embedded in the nuclei of a number of ellipticals and S0s might be of similar importance. We construct two-integral axisymmetric models for such systems. The models consist of a spheroidal bulge with a central density cusp, and a disc described by a strongly flattened exponential spheroid. We use the Hunter & Qian (1993) method to calculate the even part of the phase-space distribution function (DF), and specify the odd part by means of a simple parameterization. We consider both local stability against axisymmetric perturbations, as well as global stability against bar forming modes, and find that our models are stable as long as the discs are not too flat and/or compact. The margin of stability is derived as a function of disc scalelength and central surface density. Its location agrees well with the observed values of these disc parameters. This suggests that discs build up their mass until they become marginally stable.We investigate the photometric as well as the kinematic signatures of nuclear discs, including their velocity profiles (VPs), and study the influence of seeing convolution. In particular, we study to what extent these kinematic signatures can be used to determine the central density of the galaxy, and to test for the presence of massive black holes. We consider nuclear discs that are either dynamically coupled to or decoupled from the host elliptical, including counter-rotating discs. The latter are models for the counter-rotating cores observed in a number of galaxies, which are often found to exhibit discy isophotes in the central region. The counter-rotation is only detectable when the disc light contributes significantly to the central velocity profiles. We find that in this case the observed velocity dispersion will show a central decrease.The rotation curve of a nuclear disc gives an excellent measure of the central massto-light ratio whenever the VPs clearly reveal the narrow, rapidly rotating component associated with the nuclear disc. Steep cusps and seeing convolution both result in central VPs that are dominated by the bulge light, and these VPs barely show the presence of the nuclear disc, impeding measurements of the central rotation velocities of the disc stars. However, if a massive BH is present, the disc component of the VP can be seen in the wing of the bulge part, and measurements of its mean rotation provide a clear signature of the presence of the BH. This signature is insensitive to the uncertainties in the velocity anisotropy, which often lead to ambiguity in the interpretation of a central rise in velocity dispersion as due to a central BH.

Dark halo response and the stellar initial mass function in early-type and late-type galaxies

“…In this case the 3D density profile is given by (e.g. van den Bosch & de Zeeuw 1996) where , and K 0 is a modified Bessel function. We then obtain the circular velocity by integrating .…”

A census of nuclear stellar discs in early-type galaxies

“…Despite the relatively high frequency of NSDs, only a few studies were aimed at deriving their fundamental properties (Scorza & van den Bosch 1998; Pizzella et al 2002; Morelli et al 2004; Balcells et al 2007), whereas the interest in NSD revolved mainly around their dynamically cold character, which facilitates the mass measurement of central supermassive black holes (SMBHs) (e.g. van den Bosch & de Zeeuw 1996).…”

Two-integral Schwarzschild models

“…Various methods have been developed, many of which circumvent knowledge of the DF by solving the Jeans equations directly (van der Marel et al 1994; Magorrian 1995), while others assume that the DF can be represented by a superposition of basis functions (Dehnen & Gerhard 1994; Kuijken 1995). Accurate estimates of the mass‐to‐light ratio M / L can be obtained in both ways (van der Marel 1991; Shaw et al 1993; van den Bosch & de Zeeuw 1996). The predicted central black hole masses that are obtained with two‐integral models (Magorrian et al 1998) seem to overestimate the true values, but are still very useful to narrow down the parameter range for more sophisticated modelling (van der Marel et al 1998, hereafter vdM98; Gebhardt et al 2000; Bower et al 2001).…”