Bayesian analysis of resolved stellar spectra: Application to MMT/Hectochelle observations of the Draco dwarf spheroidal

We introduce a Bayesian method for fitting faint, resolved stellar spectra in order to obtain simultaneous estimates of redshift and stellar-atmospheric parameters. We apply the method to thousands of spectra - covering 5160-5280 Å at resolution R ~ 20 000 - that we have acquired with the MMT/Hectochelle fibre spectrograph for red giant and horizontal branch candidates along the line of sight to the Milky Way's dwarf spheroidal satellite in Draco. The observed stars subtend an area of ~4 deg², extending ~3 times beyond Draco's nominal 'tidal' radius. For each spectrum, we tabulate the first four moments - central value, variance, skewness and kurtosis - of posterior probability distribution functions representing estimates of the following physical parameters: line-of-sight velocity (v_los), effective temperature (T_eff), surface gravity (log g) and metallicity ([Fe/H]). After rejecting low-quality measurements, we retain a new sample consisting of 2813 independent observations of 1565 unique stars, including 1879 observations for 631 stars with (as many as 13) repeat observations. Parameter estimates have median random errors of σ_{v los} = 0.88 km s^-1, σ_{T eff} = 162 K, σ_{log g} = 0.37 dex and σ_[Fe/H] = 0.20 dex. Our estimates of physical parameters distinguish ~470 likely Draco members from interlopers in the Galactic foreground.