The impact of the gas distribution on the determination of dynamical masses of galaxies using unresolved observations

Abstract

Dynamical mass (M dyn) is a key property of any galaxy, yet a determination of M dyn is not straightforward if spatially resolved measurements are not available. This situation occurs in single-dish H I 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 in most cases the CO line width can 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 (e.g., H I tracing extended, "flat," emission versus CO tracing more compact, "exponential," emission) significantly affects the shape of the global profiles. In particular, in the case of high (∼50 km s-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. This leads to significantly different determinations of M dyn if different distributions of the tracer material ("flat" versus "exponential") are considered. 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: H I 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. © 2014. The American Astronomical Society. All rights reserved..