How "cold" are superthin discs ? An "MCMC" approach

Superthin galaxies are a class of low surface brightness galaxies with strikingly high values of planar-to-vertical axes ratio $\rm(b/a> 10 - 20)$ with little or no bulge component, possibly indicating the presence of an ultra-cold stellar disc, the origin, and evolution of which is not well understood. Using the 2-component model of gravitationally-coupled stars and gas in the external force field of a dark matter halo and assumed to be in vertical hydrostatic equilibrium, we determine the vertical velocity dispersion of stars and gas as a function of galactocentric radius for a sample of five superthin galaxies (UGC 7321, IC 5249, FGC 1540, IC2233 and UGC711) using observed stellar and atomic hydrogen gas (HI) scaleheights as constraints, and employing the Markov Chain Monte Carlo (MCMC) method. The mass models for our sample galaxies, constructed using stellar photometry and HI 21cm radio-synthesis observations were already available in the literature. We find that the central vertical velocity dispersion for the stellar disc in the optical band varies between ${\sigma}_0$ $\sim$ $10.2 - 18.4 km/s$ and falls off with an exponential scale length of $2.6$ to $3.2 R_{D}$ where $R_{D}$ is the exponential stellar disc scale length. Interestingly, in the $3.6 \mu$m, the same, averaged over the two components of the stellar disc, varies between $5.9$ to $11.8 km/s$, mainly representative of the denser, thinner and smaller of the two-disc components. However, the dispersion of the more massive disc component varies between 15.9 - 24.7 with a scalelength of $\sim$ 2.2 $R_{D}$. Our calculated values of the N-component disc stability parameter $Q_{min}$ lies between 1.7 - 5.7, thus confirming the dynamic stability of our model. Further, our model results are consistent with AGAMA(Action-based Galaxy Modelling Architecture).