THE SURFACE DENSITY PROFILE OF THE GALACTIC DISK FROM THE TERMINAL VELOCITY CURVE

Abstract

ABSTRACT The mass distribution of the Galactic disk is constructed from the terminal velocity curve and the mass discrepancy–acceleration relation. Mass models numerically quantifying the detailed surface density profiles are tabulated. For R 0 = 8 kpc, the models have stellar mass 5 < M * < 6 × 1010 M ⊙ ?> , scale length 2.0 ≤ R d ≤ 2.9 kpc, LSR circular velocity 222 ≤ Θ0 ≤ 233 km s - 1 ?> , and solar circle stellar surface density 34 ≤ Σ d (R 0) ≤ 61 M ⊙ pc - 2 ?> . The present interarm location of the solar neighborhood may have a somewhat lower stellar surface density than average for the solar circle. The Milky Way appears to be a normal spiral galaxy that obeys scaling relations like the Tully–Fisher relation, the size–mass relation, and the disk maximality–surface brightness relation. The stellar disk is maximal, and the spiral arms are massive. The bumps and wiggles in the terminal velocity curve correspond to known spiral features (e.g., the Centaurus arm is a ∼50% overdensity). The rotation curve switches between positive and negative over scales of hundreds of parsecs. The rms amplitude ⟨ ∣ dV / dR ∣ 2 ⟩ 1 / 2 ≈ 14 km s - 1 kpc - 1 ?> , implying that commonly neglected terms in the Jeans equations may be nonnegligible. The spherically averaged local dark matter density is ρ 0,DM ≈ 0.009 M ⊙ pc - 3 ?> (0.34 GeV cm - 3 ?> ). Adiabatic compression of the dark matter halo may help reconcile the Milky Way with the c–V 200 relation expected in ΛCDM while also helping to mitigate the too-big-to-fail problem, but it remains difficult to reconcile the inner bulge/bar-dominated region with a cuspy halo. We note that NGC 3521 is a near twin to the Milky Way, having a similar luminosity, scale length, and rotation curve.