A New Mass Modelling Trick

The extraction of the three dimensional mass profiles of early type systems is anything but trivial. Even when kinematic data is available, as for only a few of the nearby systems, its implementation is mired in problems such as the mass-anisotropy degeneracy. A formalism is proposed, which utilises the underlying smoothness in the velocity dispersion profiles of elliptical galaxies between about 0.5 to 2 times the effective radius, to estimate the mass models of these systems. The proposed scheme does not consider mass to follow light in these galaxies and typically works by scaling the luminosity density profile by a mass-to-light (M/L) ratio profile that resembles a step-function over a radial range that corresponds to 2 to 3 times the effective radius of the system. This step-like profile is characterised by a constant value of M/L within the very inner parts of the galaxy and a different, higher M/L value in general for the outer part. The resultant mass density profile is then smoothed, using the same smoothing filter size over the whole radial range. The M/L value in the inner part is determined in terms of the central velocity dispersion while that in the outer part is set to a numerical value from the range of 50to 200. A similarly large range is allowed for the location of the break; between 1 and 3 times the effective X[e][, ] where X[e ][ ]is given as -3.33/m, and m is the slope of the straight line that is fit to the plot of log(I) against x^1/4. Here I is the surface brightness and x is the coordinate along the photometric major axis. The luminosity profile can be obtained by deprojecting the observed brightness using a sophisticated deprojection code such as DOPING (Chakrabarty & Ferrarese, submitted to AJ). Tests have been carried out successfully with toy galaxies that were considered to be embedded in NFW type dark halo profiles, with different surface brightness profiles and varying halo fractions; the results of the analysis are displayed. The proposed formalism has also been used with the ACS photometry of M87 and the results are shown to compare favourably with already published mass models of M87, (modelling performed with kinematic data). The aim of this work is to advance this new mass modelling technique that uses nothing but photometry and the central velocity dispersion.