A Bayesian Approach to the Vertical Structure of the Disk of the Milky Way

This work investigates the vertical profile of the stars in the disk of the Milky Way. The models investigated are of the form $sech^{2/n}(nz/(2H))$ where, setting $\alpha = 2/n$, the three functions of the sequence $\alpha = 0,1,2$ correspond to exponential, $sech$, $sech^2$ functions. We consider symmetric models and asymmetric models, above and below the plane. The study uses the large sample of K and M stars of Ferguson et al. (2017) and applies the methods of Bayesian model comparison to discriminate between the 6 models. Two inconsistencies in Ferguson et al. (2017), concerning the vertical height cut and the model continuity across the plane, are noted and addressed. We find that (1) in the Milky Way the symmetric disc models are decisively ruled out, with northern thin disc scale heights $\sim25\%$ larger than southern, (2) there is moderate evidence for the exponential and $sech$ models over the $sech^2$ model, though a sample extending further into the Galactic mid-plane is needed to strengthen this result, (3) the photometric distances used by Ferguson et al. underestimate the GAIA distances by a factor of roughly 1.16, and (4) the increase of scale height with Galactic latitude observed by Ferguson et al. is due to incorrect cuts to the data.