A Hydro-based MCMC Analysis of SNR 0509-67.5: Revealing the Explosion Properties from Fluid Discontinuities Alone

Using Hubble Space Telescope/ACS H alpha images of SNR 0509-67.5 taken similar to 10 yr apart, we measure the forward shock (FS) proper motions (PMs) at 231 rim locations. The average shock radius and velocity are 3.66 +/- 0.036 pc and 6315 +/- 310 km s(-1). Hydrodynamic simulations, recast as similarity solutions, provide models for the supernova remnant's expansion into a uniform ambient medium. These are coupled to a Markov chain Monte Carlo (MCMC) analysis to determine explosion parameters, constrained by the FS measurements. For our baseline model, the MCMC posteriors yield an age of 315.5 +/- 1.8 yr, a dynamical explosion center at 5(h)09(m)31.(s);16, -67 degrees 31 ' 17.'' 1 and ambient medium densities at each azimuth ranging over 3.7-8.0 x 10(-25) g cm(-3). The age uncertainty can be an order of magnitude larger when considering other models, or subsets of the data. We detect stellar PMs corresponding to speeds in the Large Magellanic Cloud >= 770 km s(-1). Five stars in the remnant show measurable PMs but none are moving radially from the dynamical center. There are four stars 1.'' 4 from the center, including three faint, previously unidentified ones. Using coronal [Fe XIV] lambda 5303 emission as a proxy for the reverse shock location, we constrain the explosion energy (for a compression factor of 4) to a value of E = (1.30 +/- 0.41) x 10(51) erg for the first time from shock kinematics alone. Higher compression factors (7 or more) are strongly disfavored based on multiple criteria, arguing for inefficient particle acceleration in the Balmer shocks of SNR 0509-67.5.