The Surface Density Profile of the Galactic Disk from the Terminal Velocity Curve

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 $5<M_{\ast }<6\times 10^{10}$ M${}_{\odot }$, scale length $2.0\le R_d\le 2.9$ kpc, LSR circular velocity $222\le {\Theta }_0\le 233$ km s${}^{-1}$, and solar circle stellar surface density $34\le {\Sigma }_d(R_0)\le 61$ M${}_{\odot }$ pc${}^{-2}$. The present inter-arm 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 $\sim 50\%$ overdensity). The rotation curve switches between positive and negative over scales of hundreds of parsecs. The rms amplitude $⟨$$|$$dV/dR$${|}^2$$⟩$${}^{1/2}\approx 14$ km s${}^{-1}$ kpc${}^{-1}$, implying that commonly neglected terms in the Jeans equations may be non-negligible. The spherically averaged local dark matter density is ${\rho }_{0,DM}\approx 0.009$ M${}_{\odot }$ pc${}^{-3}$ (0.3 GeV cm${}^{-3}$). Adiabatic compression of the dark matter halo may help reconcile the Milky Way with the $c$-$V_{200}$ relation expected in $\Lambda$CDM 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.

Accepted for publication in the Astrophysical Journal. 20 pages, 14 figures. Model data available at http://astroweb.case.edu/ssm/models/ See http://astroweb.case.edu/ssm/models/MWaddenda2015.html for further discussion of fit statistics, etc

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