Knowing the unknowns: uncertainties in simple estimators of galactic
  dynamical masses
  The observed stellar kinematics of dispersion-supported galaxies are often
used to measure dynamical masses. Recently, several analytical relationships
between the stellar line-of-sight velocity dispersion, the projected (2D) or
deprojected (3D) half-light radius, and the total mass enclosed within the
half-light radius, relying on the spherical Jeans equation, have been proposed.
Here, we make use of the APOSTLE cosmological hydrodynamical simulations of the
Local Group to test the validity and accuracy of such mass estimators for both
dispersion and rotation-supported galaxies, for field and satellite galaxies,
and for galaxies of varying masses, shapes, and velocity dispersion
anisotropies. We find that the mass estimators of Walker et al. and Wolf et al.
are able to recover the masses of dispersion-dominated systems with little
systematic bias, but with a 1-sigma scatter of 25 and 23 percent, respectively.
The error on the estimated mass is dominated by the impact of the 3D shape of
the stellar mass distribution, which is difficult to constrain observationally.
This intrinsic scatter becomes the dominant source of uncertainty in the masses
estimated for galaxies like the dwarf spheroidal (dSph) satellites of the Milky
Way, where the observational errors in their sizes and velocity dispersions are
small. Such scatter may also affect the inner density slopes of dSphs derived
from multiple stellar populations, relaxing the significance with which
Navarro-Frenk-White profiles may be excluded, depending on the degree to which
the relevant properties of the different stellar populations are correlated.
Finally, we derive a new optimal mass estimator that removes the residual
biases and achieves a statistically significant reduction in the scatter to 20
percent overall for dispersion-dominated galaxies, allowing more precise and
accurate mass estimates.
