Annu. Rev. Astron. Astrophys. 1979. 17: 135-87 Copyright © 1979 by Annual Reviews. All rights reserved

2.2 Mass of the Milky Way

Historically the mass of the Milky Way has been determined from the rotation curve. This involves two distinct but interrelated observational problems: finding the shape of the rotation curve interior and exterior to the solar radius R₀, usually from 21-cm HI studies (Kerr & Westerhout 1965, Burton 1974), and setting the scale of the rotation curve by estimating the circular velocity at the sun, V₀. The latter measurement is difficult due to lack of a suitable inertial reference frame. One approach is to use extreme Pop II objects as a reference; this technique yields a lower limit, since the amount of rotation of the Pop II spheroid is unknown.

Using this method, Oort (1965) showed that V₀ 190±30 km sec^-1, in good agreement with Hartwick & Sargent's (1978) value of 220 km sec^-1 based on velocities of globular clusters and dwarf spheroidal galaxies. On the other hand, a best-fit solution of 300 km sec^-1 is obtained from the dynamics of the Local Group (see Section 6.4). Between these two extremes is the officially adopted I.A.U. value of 250 km sec^-1 for a solar radius of 10 kpc.

A fresh attack on the determination of V₀ has been made recently by Gunn et al. (1979). They combine observations of H I interior to the sun with the requirement that the rotation curve join smoothly to their suggested flat rotation curve exterior to the sun. Their reasoning is too complex to detail here, but their preferred value of V₀ is 220 km sec^-1. In our opinion the uncertainties are large, but the method does minimally require V₀ 260, in contrast to V₀ = 300 found from Local Group dynamics.

Figure 1. Mass of the Milky Way interior to radius R determined from observations of globular clusters and dwarf spheroidal galaxies: all data have been averaged in radial bins. The vertical bars are the standard error of the mean of each bin. Filled dots are mass measurements from globular cluster tidal radii, stars refer to dynamical mass determinations, and open circles are masses derived from tidal radii of dwarf spheroidal galaxies.

Once V₀ and R₀ are known, the mass in the Milky Way interior to the sun can be obtained by a variety of modelling techniques (see, e.g., Schmidt 1965). However, these results have lately diminished in significance in the face of mounting evidence for large amounts of nonluminous matter far beyond the sun's orbit. From stellar motions, Fitzgerald et al. (1978) found that the rotation curve stays flat outside the sun for several kiloparsecs. Hartwick & Sargent (1978) analyzed the distribution of radial velocities of globular clusters and nearby dwarf spheroidal galaxies, which they took to be bound to the Milky Way. The outermost sample tests the potential at an effective radius of about 60 kpc and gives an interior mass of 8 x 10¹¹ M for an isotropic distribution of velocity components.

Finally, using the globular cluster system as a probe of the galactic potential and tidal fields, Webbink (in preparation) has mapped the mass distribution out to a radius of ~ 100 kpc. Independent estimates of galactic mass were obtained from the tidal radii and radial velocities of 126 globular clusters and 7 dwarf spheroidal companions of the galaxy. The deduced mass distribution of the Milky Way based on radial bin averages is shown in Figure 1. The present tidally-limited radius of the galaxy due to M31 is ~ 200 kpc. Within this assumed radius, Webbink derives a total mass of 1.4±0.3 x 10¹² M from tidal effects on globular clusters and 1.4±0.8 x 10¹² M from globular cluster radial velocities. The consistency between Webbink's two completely independent determinations of the mass distribution is strong empirical evidence for the existence of a dark envelope around the Milky Way.

To obtain M / L_B for the galaxy, we use Sandage & Tammann's (1976) calibration of L_B versus rotation velocity to estimate the luminosity of the galaxy. The result is 2.0 x 10¹⁰ L. With Webbink's mass estimate, we obtain M / L_B 70±20 on our mass-to-light system. This value is an upper limit, since the mass may not extend as far as the assumed tidal cutoff of 200 kpc.