On the Sun's distance from the center and the shape of the inner halo in the Galaxy: Gaia EDR3, HST and literature globular clusters

A statistical method is used to derive both the Sun's distance r₀ from the Galactic Center (GC) and the 3D geometry of the inner (< 25 kpc) halo. The spatial distribution of the 138 Gaia EDR3 globular clusters (GCs) with distances established on a combination of HST and literature data of Baumgardt and Vasiliev (2021) is explored. An estimate by using these ancient objects of the pressure-supported subsystem of the Galaxy with newly derived distances leads to the mean r₀=7.81±0.14 kpc. The distribution of GCs within 25 kpc is almost spherically symmetric, and has the shape of an ellipsoid with a major axis of its symmetry slightly elongated toward the Sun and two minor axes of almost the same length. The obtained scale-length ratio of the major axis to the minor axis in the plane and to the vertical axis of the ellipsoid is ≈ 1:0.8:0.7. Based on the papers of a series, for practical use we argue to employ the following Sun's distances from the GC and the plane: r₀=8.15±0.15 kpc and z₀=15±5 pc.