A Direct Dynamical Measurement of the Milky Way's Disk Surface Density Profile, Disk Scale Length, and Dark Matter Profile at 4 kpc <~ R <~ 9 kpc

We present and apply rigorous dynamical modeling with which we infer unprecedented constraints on the stellar and dark matter mass distribution within our Milky Way (MW), based on large sets of phase-space data on individual stars. Specifically, we model the dynamics of 16,269 G-type dwarfs from SEGUE, which sample 5 kpc < R_GC < 12 kpc and 0.3 kpc <~ |Z| <~ 3 kpc. We independently fit a parameterized MW potential and a three-integral, action-based distribution function (DF) to the phase-space data of 43 separate abundance-selected sub-populations (MAPs), accounting for the complex selection effects affecting the data. We robustly measure the total surface density within 1.1 kpc of the mid-plane to 5% over 4.5 kpc < R_GC < 9 kpc. Using metal-poor MAPs with small radial scale lengths as dynamical tracers probes 4.5 kpc <~ R_GC <~ 7 kpc, while MAPs with longer radial scale lengths sample 7 kpc <~ R_GC <~ 9 kpc. We measure the mass-weighted Galactic disk scale length to be R_d = 2.15 ± 0.14 kpc, in agreement with the photometrically inferred spatial distribution of stellar mass. We thereby measure dynamically the mass of the Galactic stellar disk to unprecedented accuracy: M _* = 4.6 ± 0.3 + 3.0 (R ₀/ kpc - 8) × 10¹⁰ M _⊙ and a total local surface density of \Sigma _{R_0}(Z=1.1\,{kpc}) = 68\, {+/- }\, 4\,M_\odot \,{pc}^{-2} of which 38 ± 4 M _⊙ pc^-2 is contributed by stars and stellar remnants. By combining our surface density measurements with the terminal velocity curve, we find that the MW's disk is maximal in the sense that V _{c, disk}/V _{c, total} = 0.83 ± 0.04 at R = 2.2 R_d . We also constrain for the first time the radial profile of the dark halo at such small Galactocentric radii, finding that ρ_DM(r ≈R ₀)vprop1/r ^α with α < 1.53 at 95% confidence. Our results show that action-based DF modeling of complex stellar data sets is now a feasible approach that will be fruitful for interpreting Gaia data.