The Mass of the Milky Way Galaxy

Abstract

We use the Jaffe model as a global mass distribution for the Galaxy and determine the circular velocity $v_c$ and the Jaffe radius $r_j$ using the satellites of the Galaxy, estimates of the local escape velocity of stars, the constraints imposed by the known rotation curve of the disk, and the Local Group timing model. The models include the systematic uncertainties in the isotropy of the satellite orbits, the form of the stellar distribution function near the escape velocity, and the ellipticity of the M31/Galaxy orbit. If we include the Local Group timing constraint, then Leo I is bound, $v_c=230\pm30\kms$, and $r_j=180$ kpc (110 kpc $\ltorder r_j \ltorder $ 300 kpc) at 90\% confidence. The satellite orbits are nearly isotropic with $\beta=1-\sigma_\theta^2/\sigma_r^2=0.07$ ($-0.7 \ltorder \beta \ltorder 0.6$) and the stellar distribution function near the escape velocity is $f(\epsilon)\propto \epsilon^k$ with $k_r=3.7$ ($0.8 \ltorder k_r \ltorder 7.6$) where $k_r=k+5/2$. While not an accurate measurement of $k$, it is consistent with models of violent relaxation ($k=3/2$). The mass inside 50 kpc is $(5.4\pm1.3)\times 10^{11} M_\odot$. Higher mass models require that M31 is on its second orbit and that the halo is larger than the classical tidal limit of the binary. Such models must have a significant fraction of the Local Group mass in an extended Local Group halo. Lower mass models require that both M31 and Leo I are unbound, but there is no plausible mechanism to produce the observed deviations of M31 and Leo I from their expected velocities in an unbound system. If we do not use the Local Group timing model, the median mass of the Galaxy {\it increases} significantly, and the error bars broaden. Using only the satellite, escape velocity, and disk rotation curve constraints, the