Grand Rotation Curve and Dark-Matter Halo in the Milky Way Galaxy

A grand rotation curve of the Milky Way Galaxy was constructed, which covers a wide range of radius from the Galactic Center to ~ 1 Mpc, and was deconvolved into bulge, disk, and halo components by least-squares fittings. We determined the masses and scale radii of the bulge and disk to be Mb =$ (1.652 $ ±$ 0.083) $ ×$ 10$ ¹⁰{\ M_}$ , $ {ab}$$ =$ 0.522 ± 0.037 kpc, Md =$ (3.41 $ ±$ 0.41) $ ×$ 10$ ¹⁰{\ M_}$ , and $ {ad}$$ =$ 3.19 ± 0.35 kpc. The dark halo was fitted by the Navaro–Frenk–White (NFW) density profile, ρ =ρ₀/ [($ R/h$ )(1 $ +$$ R/h$ )$ ^2$ ], and the fit yielded $ h$$ =$ 12.5 ± 0.9 kpc and ρ₀ =$ (1.06 $ ±$ 0.14) $ ×$ 10$ ⁻²\ M_{}$ pc$ ⁻³$ . The local dark-matter density near the Sun at $ R_0$$ =$ 8 kpc was estimated to be ρ₀^ =$ (6.12 $ ±$ 0.80) $ ×$ 10$ ⁻³\ M_{}$ pc$ ⁻³$$ =$ 0.235 ± 0.030 GeV cm⁻³ . The total mass inside the gravitational boundary of the Galaxy at R ~$ 385 kpc, a half distance to M 31, was estimated to be $ {Mb+d+h}$$ =$ (7.03 ± 1.01) × 10¹¹\ M_ . This leads to a stellar baryon fraction of Mb+d/Mb+d+h =$ 0.072 $ ±$ 0.018. Considering the expected baryon fraction in the Local Group, we suggest that baryons in the form of hot gas are filling the dark halo with a temperature of $ ~$ 10$ ⁶$ K and an emission measure of $ ~$ 10$ ⁻⁵$ pc cm$ ²$ . Such hot halo gas may share a small fraction of the observed X-ray background emission.