A method for comparing discrete kinematic data and N-body simulations

Abstract

This paper describes a method for quantitatively comparing an N-body model with a sample of discrete kinematic data. The comparison has two stages: (i) finding the optimum scaling and orientation of the model relative to the data; and (ii) calculating a goodness of fit, and hence assessing the plausibility of the model in vew of the data. The method derives from considering the data and model both as samples from some underlying binned distribution function, and applying probability theory arguments. As an example, I consider a published N-body model for the Galactic bulge and disc, and fictitious l,b,v measurements, and recover (with error estimates) the spatial and velocity scales of the model and the orientation of the bar. The fictitious data are actually derived from the model by assuming the mass scale and the solar position, but their size and extent mimics a recent survey of OH/IR stars. The results indicate that mass of the bulge and our viewing angle of the bar are usefully estimable from current surveys.