| Author(s) and Co-Author(s) with Affiliation: Sutirtha Mukherjee(Indian Institute of Science Education and Research (IISER) , Mohali -140306,India), Amogh Srivastava(Indian Institute of Technology Bombay, Mumbai - 400076, India), Prof. Subhabrata Majumdar(Tata Institute of Fundamental Research (TIFR) , Mumbai-400005,India) |
| Abstract: We present a robust stellar-kinematic analysis of the Milky Way and construct a unified galactic rotation curve from $\sim5$~kpc to the virial radius ($\sim250$~kpc), including tracers reaching the splashback radius to estimate the post-GAIA virial size and mass and constrain local dark matter density. We compile a homogenized 6D phase-space catalogue of $\sim4.5$ million metal-poor disc and halo stars, combining \textit{Gaia}~DR3 astrometry with spectro-photometric distances and radial velocities from 18 surveys (DESI, SDSS-BOSS, LAMOST, etc.). By prioritizing high-purity tracers (Cepheids, RR Lyrae, blue horizontal-branch stars, and K-giants) across bright ($G<17$) and faint ($G>17$) regimes, we overcome \textit{Gaia}'s geometric parallax limitation beyond $\sim10$~kpc, achieving median uncertainties of $\sim6\%$ in distance and $\sim0.05\%$ in radial velocity. Cross-survey matching is performed using a KD-tree-based multi-dimensional scheme, with duplicate measurements combined via weighted averaging. Survey-specific systematics are mitigated using the Three-Cornered Hat method, and the catalogue is externally validated against globular clusters, dwarf galaxies, and the Sagittarius stream.
Using the resultant homogenized dataset, we implement cylindrical and spherical Jeans equations alongside the tangent-point method and demonstrate that the inferred local dark matter density $\rho_0$ is critically sensitive to methodology, tracer selection, binning schemes, visible matter assumptions, LSR normalization, and solar motion, naturally explaining the wide literature range ($\rho_0 \sim 0.1$--$0.9$~GeV\,cm$^{-3}$). We also explore the scope of dark matter and baryonic velocity anisotropy using the full 6D phase-space information. Rotation curves are modeled via Bayesian nested sampling over eight parameters, adopting different physically motivated dark matter profiles (NFW, Burkert, Einasto, DK14, Dehnen) with baryonic components (stellar disc, gas, bulge); for the NFW halo, we constrain the virial mass $M_{200}$ and concentration $c_{200}$. From posterior samples, we apply Eddington inversion to self-consistently reconstruct the local dark matter velocity distribution function at $R_\odot = 8.1$~kpc, providing data-driven phase-space inputs with full uncertainty propagation for WIMP direct-detection experiments. |
