On the Determination of Rotation Velocity and Dynamical Mass of Galaxies
  Based on Integrated H I Spectra
  The integrated 21 cm H I emission profile of a galaxy encodes valuable
information on the kinematics, spatial distribution, and dynamical state of its
cold interstellar medium. The line width, in particular, reflects the rotation
velocity of the galaxy, which, in combination with a size scale, can be used to
constrain the dynamical mass of the system. We introduce a new method based on
the concept of the curve of growth to derive a set of robust parameters to
characterize the line width, asymmetry, and concentration of the integrated H I
spectra. We use mock spectra to evaluate the performance of our method, to
estimate realistic systematic uncertainties for the proposed parameters, and to
correct the line widths for the effects of instrumental resolution and
turbulence broadening. Using a large sample of nearby galaxies with available
spatially resolved kinematics, we demonstrate that the newly defined line
widths can predict the rotational velocities of galaxies to within an accuracy
of $\lesssim 30$ km s$^{-1}$. We use the calibrated line widths, in conjunction
with the empirical relation between the size and mass of H I disks, to
formulate a prescription for estimating the dynamical mass within the H
I-emitting region of gas-rich galaxies. Our formalism yields dynamical masses
accurate to $\sim 0.3$ dex based solely on quantities that can be derived
efficiently and robustly from current and future extragalactic H I surveys. We
further extend the dynamical mass calibration to the scale of the dark matter
halo.
