A Bayesian/MCMC Approach to Galaxy Modelling: NGC 6503

Abstract

We use Bayesian statistics and Markov chain Monte Carlo (MCMC) techniques to construct dynamical models for the spiral galaxy NGC 6503. The constraints include surface brightness profiles which display a Freeman Type II structure; HI and ionized gas rotation curves; the stellar rotation, which is nearly coincident with the ionized gas curve; and the line of sight stellar dispersion, which displays a $\sigma-$drop at the centre. The galaxy models consist of a S\'{e}rsic bulge, an exponential disc with an optional inner truncation and a cosmologically motivated dark halo. The Bayesian/MCMC technique yields the joint posterior probability distribution function for the input parameters, allowing constraints on model parameters such as the halo cusp strength, structural parameters for the disc and bulge, and mass-to-light ratios. We examine several interpretations of the data: the Type II surface brightness profile may be due to dust extinction, to an inner truncated disc or to a ring of bright stars; and we test separate fits to the gas and stellar rotation curves to determine if the gas traces the gravitational potential. We test each of these scenarios for bar stability, ruling out dust extinction. We also find that the gas cannot trace the gravitational potential, as the asymmetric drift is then too large to reproduce the stellar rotation. The disc is well fit by an inner-truncated profile, but the possibility of ring formation by a bar to reproduce the Type II profile is also a realistic model. We further find that the halo must have a cuspy profile with $\gamma \gtrsim 1$; the bulge has a lower $M/L$ than the disc, suggesting a star forming component in the centre of the galaxy; and the bulge, as expected for this late type galaxy, has a low S\'{e}rsic index with $n_b\sim1-2$, suggesting a formation history dominated by secular evolution.