The Mass of the Milky Way
Abstract
We use the Jaffe model as a global mass distribution for the Galaxy and determine the circular velocity υ_{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, υ_{c} = 220±30km s^{1}, and r_{j} = 200 kpc (115 kpc ≲ r_{j} ≲ 360 kpc) at 90% confidence. The satellite orbits are nearly isotropic with β = 1 σ^{2}/_{θ}/σ^{2}_{r} = 0.2 (0.5 ≲ β ≲ 0.6), and the stellar distribution function near the escape velocity is f(ɛ) ∝ ɛ_{k} with k_{r} = 4.4 (1.6 ≲ k_{r} ≲ 8.5), 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 (4.9±1.1) × 10^{11} M_{sun}. Higher mass models require that M31 is on its second orbit and that the halo is larger than the classical tidal limit of the Galaxy/M31 binary system. 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 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 increases significantly, and the error bars broaden. Using only the satellite, escape velocity, and disk rotation curve constraints, the median mass interior to 50 kpc is 3.9 (5.1), and the 90% confidence interval is 3.25.5 (4.06.4) without (with) Leo I in units of 10^{11} M_{sun}. The lower bound without Leo I is 65% of the mass expected for a continuation of a flat rotation curve.
 Publication:

The Astrophysical Journal
 Pub Date:
 January 1996
 DOI:
 10.1086/176724
 arXiv:
 arXiv:astroph/9505068
 Bibcode:
 1996ApJ...457..228K
 Keywords:

 CELESTIAL MECHANICS;
 STELLAR DYNAMICS;
 GALAXY: FUNDAMENTAL PARAMETERS;
 GALAXIES: LOCAL GROUP;
 GALAXY: KINEMATICS AND DYNAMICS;
 Astrophysics
 EPrint:
 31 pages, uuencoded compressed postscript without figures, complete file including figures available at ftp://cfa0.harvard.edu/outgoing/kochanek/milkyway.ps.Z (0.5 MByte, compressed), submitted to ApJ