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 \mathrm { kpc } < R _ { GC } < 12 \mathrm { kpc } and 0.3 \mathrm { kpc } \lesssim|Z| \lesssim 3 \mathrm { 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 \mathrm { kpc } of the mid-plane to 5 \% over 4.5 < R _ { GC } < 9 \mathrm { kpc } .
Using metal-poor MAPs with small radial scale lengths as dynamical tracers probes 4.5 \lesssim R _ { GC } \lesssim 7 \mathrm { kpc } , while MAPs with longer radial scale lengths sample 7 \lesssim R _ { GC } \lesssim 9 \mathrm { kpc } .
We measure the mass-weighted Galactic disk scale length to be R _ { d } = 2.15 \pm 0.14 \mathrm { 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 \pm 0.3 + 3.0 ( R _ { 0 } / \mathrm { kpc } -8 ) \times 10 ^ { 10 } M _ { \odot } and a total local surface density of \Sigma _ { R _ { 0 } } ( Z = 1.1 \mathrm { kpc } ) = 68 \pm 4 M _ { \odot } \mathrm { pc } ^ { -2 } of which 38 \pm 4 M _ { \odot } \mathrm { 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, \mathrm { disk } } / V _ { c, \mathrm { total } } = 0.83 \pm 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 \rho _ { \mathrm { DM } } ( r; \approx R _ { 0 } ) \propto 1 / r ^ { \alpha } with \alpha < 1.53 at 95 % confidence .
Our results show that action-based distribution-function modeling of complex stellar data sets is now a feasible approach that will be fruitful for interpreting Gaia data .