Dynamical Models for NGC 6503 using a Markov Chain Monte Carlo Technique David Puglielli $^{1}$, Lawrence M. Widrow2 and St´ ephane Courteau 3 Department of Physics, Engineering Physics, and Astronomy, Queen’s University, Kingston, ON, K7L 3N6, Canada We use Bayesian statistics and Markov chain Monte Carlo (MCMC) tech- niques to construct dynamical models for the spiral galaxy NGC 6503. The constraints include surface brightness profiles which display a Freeman Type II structure; H I 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 σ − drop at the centre. The galaxy models consist of a S´ ersic 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 gravi- tational potential. We test each of these scenarios for bar stability, ruling out dust extinction. We also find that the gas likely does not trace the gravitational potential, since the predicted stellar rotation curve, which includes asymmetric drift, is then inconsistent with the observed stellar rotation curve. 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 γ ≳ 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´ ersic index with n$_{b}$ ∼ 1 − 2, suggesting a formation history dominated by secular evolution. $^{1}$dpuglielli@astro.queensu.ca $^{2}$widrow@astro.queensu.ca $^{3}$courteau@astro.queensu.ca arXiv:1002.0819v3 [astro-ph.CO] 8 Apr 2010 ABSTRACT