An MCMC approach to the three-dimensional structure of the Milky Way bulge using OGLE-IV δ Scuti stars

Abstract

ABSTRACT We present an analysis of high-latitude δ Scuti stars (|b| > 1°) in the Galactic bulge region (−8${_{.}^{\circ}}$3 < l < 9${_{.}^{\circ}}$4) using a clean sample of the photometric data of 7440 stars recently released by the OGLE-IV project. The geometrical parameters of the bulge are determined based on Maximum Likelihood (ML) analysis in five-dimensional parameter space. More refined values of these parameters as well as their uncertainties are obtained from a fully Bayesian Markov chain Monte Carlo (MCMC) analysis. Approximating the bulge as an ellipsoid, the distribution of the number density of stars as a function of Galacto-centric distance has been modelled using three distribution functions: two Exponential ($\rm E_{1},\rm E_{2}$) types and one Gaussian ($\rm G$) type. Based on the AIC and BIC values, the exponential model $\rm E_{1}$ 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 Centre (GC) is found to be R0 = 8.034 ± 0.012stat ± 0.586sys kpc; the bulge δ Scuti distribution has a triaxial shape with normalized (a ≡ 1) axes ratios (a: b: c) as 1.000 ± 0.005: 0.348 ± 0.002: 0.421 ± 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 ≥ 2.0 kpc indicate the presence of a bar-like structure of the bulge with a bar angle of 22${_{.}^{\circ}}$006 ± 2${_{.}^{\circ}}$078.