Mass Modelling with Minimum Kinematic Information

Abstract

Mass modelling of early-type systems is a thorny issue. In this paper, we present a new mass modelling formalism for ellipticals that invokes no observations other than the central velocity dispersion ($σ_0$) and photometry. The essence of the method lies in choosing a local mass-to-light ratio ($M/L$) profile for a galaxy, with which the deprojected luminosity density distribution (along the major axis coordinate $x$) is scaled. The resulting discontinuous mass density profile is then smoothed, according to a laid out prescription; the local $M/L$ profile that stems from this smoothed mass density, is found to be significantly different from the raw $M/L$ distribution. A suite of model galaxies (both Sersic and cored in nature) is used for extensive experimentation in order to characterise this raw $M/L$ profile and in each case, the mass density recovered from this mass modelling technique is compared to the known mass distribution. We opt to work with a raw $M/L$ profile that is a simple two-stepped function of $x$, with a low inner and higher outer value of $M/L-Υ_{in}$ and $Υ_{out}$, respectively. The only constraint that we have on this profile is in the centre of the galaxy, via $σ_0$. This value of $σ_0$ is implemented in the virial theorem to obtain an estimate of the central $M/L$ ratio of the galaxy. The fallibility of the virial mass estimate is taken care of, by allowing for a range in the values of $Υ_{in}$ that can be used for a given galaxy model. Moreover, our experiments indicate that $Υ_{out}$ is uniquely known, for a given $Υ_{in}$; for cored galaxies, this functional form is found uniquely dependant on the core radius. The jump radius of the raw $M/L$ profile is chosen to be thrice the effective radius of the galaxy.