Statistical determination of the distance to the Galactic Centre and the outset of the Milky Way old bulge: astrophysical conclusions

In this concluding work of the series, a sample of selected ∼ 20 , 000 type-ab RR Lyrae stars from a total of 39,617 sources of the old bulge at distances r< 3.5 kpc from the Galactic Centre (GC) identified in the Vista Variables in the Vía Láctea survey (VVV) via the latest sample of the VIrac VAriable Classification Ensemble (VIVACE) pipeline is leveraged. As a model of the bulge, an oblate spheroid of stars with two major perpendicular axes a and b situated in the Galactic plane and a minor axis c perpendicular to this plane is adopted. The spatial distribution of stars is approximated by a standard power law with constant flattening and truncations at the lower and upper limits while allowing for the Sun’s distance from the GC r , the power-law index α , and the oblateness q= c/ a to be free parameters. Our estimate of the distance is r= 8.15 ± 0.04 kpc. The implied r is almost the same for 1.5 < r_max< 3.5 kpc, while the | α| and q values are varying systematically with increasing truncation radius r_max in the ranges 1.56 − 2.66 and 1.0 − 0.76 . A weighted average and weighted uncertainty associated with all our measurements of r in the series is also taken, r= 8.2 ± 0.1 kpc. We argue that the ensuing result may be among the most robust indirect estimates that exist, as certain of the findings are tied to passbands of the Optical Gravitational Lensing Experiment (OGLE) RR Lyraes and globular clusters, and to near-infrared passbands of the VVV Type II Cepheids and VIVACE-VVV RR Lyraes. The distribution of stars within ≈ 3 kpc from the GC is spherical-like, q≈ 1 . The average power-law indexes derived from the distribution of bulge RRab and inner halo globular clusters are nearly identical. This pertinent result demonstrates that the old bulge and inner halo form a continuous subsystem, and the bulk of the bulge objects represents the inner extension of a centrally concentrated, almost axisymmetric halo in the Galaxy.