The mass of the Milky Way Galaxy

We present a method for determining the Galactic mass and mass distribution based on maximum likelihood parameter estimation. We show that the number density of the Galaxy’s outer satellites can be modelled by a power-law function. Assuming that the total distribution of matter (visible and dark) can be modelled in a similar way, we construct a self-consistent, self-similar model of the outer Galaxy. From this we derive a probability distribution for two quantities; the radial velocity and galactocentric distance. Considering the velocity distribution in the outer Galaxy to be isotropic, this probability distribution contains two free parameters; the Galactic mass and the power-law index for the total matter density profile which we subsequently determine by way of maximum likelihood estimation. We obtain a mass of around $$1.3\times {10}^{12} {M}_{\odot}$$ out to a distance of 230 kpc from the Galactic Centre with a corresponding power-law index of 2.4. Confidence regions are derived for these estimates from which a ‘low-mass’ galaxy, $$(\text{i.e.}\,M\lt6\times {10}^{11}{M}_{\odot})$$, can be ruled out with 98 per cent confidence. Our result suggests a high mass for the Milky Way out to a large distance and relies on the inclusion of the dwarf spheroidal galaxy Leo I in the sample. The most recent velocity and distance data we could find for all globular clusters and dwarf spheroidal galaxies, beyond R₀, including the newly discovered dwarf spheroidal galaxy in Sextans were used in the analysis. We also briefly discuss a self-similar galactic model where the velocity distribution is anisotropic.