The information on halo properties contained in spectroscopic observations of late-type galaxies

Abstract

ABSTRACT Rotation curves are the key observational manifestation of the dark matter distribution around late-type galaxies. In a halo model context, the precision of constraints on halo parameters is a complex function of properties of the measurements as well as properties of the galaxy itself. Forthcoming surveys will resolve rotation curves to varying degrees of precision, or measure their integrated effect in the $\mathrm{H}\, \small {\rm I}$ linewidth. To ascertain the relative significance of the relevant quantities for constraining halo properties, we study the information on halo mass and concentration as quantified by the Kullback–Leibler divergence of the kinematics-informed posterior from the uninformative prior. We calculate this divergence as a function of the different types of spectroscopic observation, properties of the measurement, galaxy properties, and auxiliary observational data on the baryonic components. Using the SPARC (Spitzer Photometry & Accurate Rotation Curves) sample, we find that fits to the full rotation curve exhibit a large variation in information gain between galaxies, ranging from ~1 to ~11 bits. The variation is predominantly caused by the vast differences in the number of data points and the size of velocity uncertainties between the SPARC galaxies. We also study the relative importance of the minimum $\mathrm{H}\, \small {\rm I}$ surface density probed and the size of velocity uncertainties on the constraining power on the inner halo density slope, finding the latter to be significantly more important. We spell out the implications of these results for the optimization of galaxy surveys aiming to constrain galaxies’ dark matter distributions, highlighting the need for precise velocity measurements.