Stellar systems following the $R^{1/m}$ luminosity law. III. Photometric, intrinsic and dynamical properties for all S’ersic indices. (arXiv:1905.10359v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Baes_M/0/1/0/all/0/1">Maarten Baes</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ciotti_L/0/1/0/all/0/1">Luca Ciotti</a>
The S’ersic or $R^{1/m}$ model has become the de facto standard model to The S’ersic or $R^{1/m}$ model has become the de facto standard model to http://arxiv.org/icons/sfx.gif
describe the surface brightness profiles of early-type galaxies and the bulges
of spiral galaxies. The photometric, intrinsic and dynamical properties of this
model have been investigated, but mainly for fairly large S’ersic indices $m$.
For small values of $m$, appropriate for low-mass and dwarf ellipticals, a
detailed investigation of these properties is still lacking. In this study, we
use a combination of numerical and analytical techniques to investigate the
S’ersic model over the entire range of S’ersic parameters, focusing on the
small $m$ regime, where a number of interesting and surprising properties are
found. For all values $m<1$, the model is characterised by a finite central
luminosity density, and for $m
describe the surface brightness profiles of early-type galaxies and the bulges
of spiral galaxies. The photometric, intrinsic and dynamical properties of this
model have been investigated, but mainly for fairly large S’ersic indices $m$.
For small values of $m$, appropriate for low-mass and dwarf ellipticals, a
detailed investigation of these properties is still lacking. In this study, we
use a combination of numerical and analytical techniques to investigate the
S’ersic model over the entire range of S’ersic parameters, focusing on the
small $m$ regime, where a number of interesting and surprising properties are
found. For all values $m<1$, the model is characterised by a finite central
luminosity density, and for $m<tfrac12$, even a central depression in the
luminosity density profile. This behaviour translates to the dynamical
properties: we show that all S’ersic models with $m geqslanttfrac12$ can be
supported by an isotropic velocity dispersion tensor, and that these isotropic
models are stable to both radial and non-radial perturbations. The models with
$m < tfrac12$, on the other hand, cannot be supported by an isotropic velocity
dispersion tensor.
