The mass distribution in the galactic disc - I. A technique to determine the integral surface mass density of the disc near the Sun

Abstract

We present a new technique for the determination of the integral surface mass density of the galactic disc at the solar galactocentric distance. The requisite observational data are an observed distribution function of velocities and distances for a sample of tracer stars extending ≳ 1 kpc from the galactic plane, and the spatial density distribution corresponding to that tracer population. The analysis involves comparison of the observed distribution function with a variety of model distribution functions, calculated for a wide range of assumed galactic potentials and corresponding force laws Kz(z), to determine the best description of the data. The model distributions are calculated in a sufficiently general way that one can include the quite large effects due to the likely change in the orientation of the stellar velocity ellipsoid as one moves further from the galactic plane. The derived best fit Kz-force law is constrained to be consistent dynamically, in that the local mass density of the extended dark halo generating a large part of the radial acceleration in the Galaxy is also determined, in such a way as to ensure consistency with the observed rotation curve. An important feature of the analysis technique is that it utilizes the full observed distribution function, and so avoids the need for binning data and the use of a few velocity moments to represent a large number of observations.