The impact of the gas distribution on the determination of dynamical
  masses of galaxies using unresolved observations
  The dynamical mass (M_dyn) is a key property of any galaxy, yet a
determination of M_dyn is not straight-forward if spatially resolved
measurements are not available. This situation occurs in single-dish HI
observations of the local universe, but also frequently in high-redshift
observations. M_dyn-measurements in high-redshift galaxies are commonly
obtained through observations of the CO line, the most abundant tracer of the
molecular medium. Even though the CO linewidth can in most cases be determined
with reasonable accuracy, a measurement of the size of the emitting region is
typically challenging given current facilities. We show how the integrated
spectra (`global profiles') of a variety of galaxy models depend on the spatial
distribution of the tracer gas as well as its velocity dispersion. We
demonstrate that the choice of tracer emission line significantly affects the
shape of the global profiles. In particular, in the case of high (~50 kms-1)
velocity dispersions, compact tracers (such as CO) result in Gaussian-like
(non-double-horned) profiles, as is indeed frequently seen in high-redshift
observations. We determine at which radii the rotation curve reaches the
rotation velocity corresponding to the velocity width, and find that for each
tracer this happens at a well-defined radius: HI velocity widths typically
originate at ~5 optical scale lengths, while CO velocity widths trace the
rotation velocity at ~2 scale lengths. We additionally explore other
distributions to take into account that CO distributions at high redshift
likely differ from those at low redshift. Our models, while not trying to
reproduce individual galaxies, define characteristic radii that can be used in
conjunction with the measured velocity widths in order to define dynamical
masses consistent with the assumed gas distribution.
