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

Abstract

We present an analysis of high latitude δ Scuti stars (|b| > 1○) in the Galactic bulge region (−8○.3 < l < 9○.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 ($\rm E_{1},\rm E_{2}$) 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 center (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○.006 ± 2○.078.

Probing the Milky Way Stellar and Brown Dwarf Initial Mass Function with Modern Microlensing Observations

“…The smaller the bar angle, the larger the mass along the line of sight and then the larger the optical depth and number of events. As seen from the values of τ and Γ (Table 1) and the timescale distribution, the agreement of our fiducial model and the recent model of Deka et al (2022;see Appendix C.5) with the data suggests a Galactic bar around our fiducial angle f ; 28°.…”

“…The stellar mass of the bulge is taken to be M bulge = 1.88 × 10 10 M e (including the presence of a "photometric" nonaxisymmetric long bar; Portail et al 2017), and the angle of the bar f = 28° (Wegg & Gerhard 2013;Wegg et al 2015). This bulge model is in good agreement with the one derived recently by using OGLE-IV δ Scuti stars (Deka et al 2022). A more thorough comparison between these two models is given in Appendix C.5.…”

“…The choice of the bulge and disk models affects the optical depth and event rate, a direct consequence of the different total mass for each model. Figure 6 and Table 1 compare the results obtained with our fiducial model and the ones of Stanek et al (1997), Zhao (1996), and Deka et al (2022 for the bulge and Zheng et al (2001) for the disk. For the latter case, the figure also highlights the contribution of the thick disk.…”

Probing the Milky Way stellar and brown dwarf initial mass function with modern microlensing observations

“…The smaller the bar angle, the larger the mass along the l.o.s and then the larger the optical depth and the number of events. As seen from the values of τ and Γ (Table 2) and the timescale distribution, the agreement of our fiducial model and of the recent model of Deka et al (2022) (see §C.5 below) with the data suggests a Galactic bar around our fiducial angle φ 28 o .…”

“…The stellar mass of the bulge is taken to be M bulge = 1.88 × 10 10 M (including the presence of a 'photometric' non-axisymmetric long bar (Portail et al 2017b)) and the angle of the bar φ = 28 0 (Wegg et al 2013(Wegg et al , 2015. This bulge model is in good agreement with the one derived recently by using OGLE-IV δ Scuti stars (Deka et al 2022). A more thorough comparison between these two models is given in App.…”