An MCMC Approach to the Three-dimensional Structure of the Milky Way Bulge using OGLE-IV $\delta$ Scuti Stars

Abstract

We present an analysis of high latitude $\delta$ Scuti stars ($\left|b\right|>1^{\circ }$) in the Galactic bulge region ($-8^{\circ }.3<l<9^{\circ }.4$) using a clean sample of the photometric data of $7,440$ stars recently released by the OGLE-IV project. The geometrical parameters of the bulge are determined based on Maximum Likelihood (ML) analysis in five-dimensional parameter space. More refined values of these parameters as well as their uncertainties are obtained from a fully Bayesian Markov Chain Monte Carlo (MCMC) analysis. Approximating the bulge as an ellipsoid, the distribution of the number density of stars as a function of Galacto-centric distance has been modelled using three distribution functions: two Exponential (${\mathrm{E}}_1,{\mathrm{E}}_2$) types and one Gaussian ($\mathrm{G}$) type. Based on the AIC and BIC values, the exponential model ${\mathrm{E}}_1$ is chosen as the best statistical model for the parameter values obtained from the MCMC analysis. The MCMC analysis yields the following results: the mean distance to the Galactic center (GC) is found to be $R_0=8.034\pm 0.012_{\mathrm{stat}}\pm 0.586_{\mathrm{sys}}$ kpc; the bulge $\delta$ Scuti distribution has a triaxial shape with normalized ($a\equiv 1$) axes ratios ($a:b:c$) as $1.000\pm 0.005:0.348\pm 0.002:0.421\pm 0.002$. Here $a$ is the semi-major axis lying in the Galactic plane and pointing towards us; $b$ and $c$ are the two semi-minor axes, the former lying in the Galactic plane and the later perpendicular to it. Smaller values of $b$ as compared to $a$ obtained for Galacto-centric distances $R\ge 2.0$~kpc indicate the presence of a bar-like structure of the bulge with a bar angle of $22^{\circ }.006\pm 2^{\circ }.078$.

11 pages, 5 figures, accepted for publication in MNRAS

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