Mass Modeling of Disk Galaxies: Degeneracies, Constraints, and Adiabatic Contraction

This paper addresses available constraints on mass models fitted to rotation curves. Mass models of disk galaxies have well-known degeneracies that prevent a unique mass decomposition. The most notable is due to the unknown value of the stellar mass-to-light ratio (the disk-halo degeneracy); even with this known, degeneracies between the halo parameters themselves may prevent an unambiguous determination of the shape of the dark halo profile, which includes the inner density slope of the dark matter halo. The latter is often referred to as the ``cusp-core degeneracy.'' We explore constraints on the disk and halo parameters and apply these to four mock and six observed disk galaxies with high resolution and extended rotation curves. Our full set of constraints consists of mass-to-light (M/L) ratios from stellar population synthesis models based on B-R colors, constraints on halo parameters from N-body simulations, and constraining the halo virial velocity to be less than the maximum observed velocity. These constraints are only partially successful in lifting the cusp-core degeneracy. The effect of adiabatic contraction of the halo by the disk is to steepen cores into cusps and reduce the best-fit halo concentration and M/L values (often significantly). We also discuss the effect of disk thickness, halo flattening, distance errors, and rotation curve error values on mass modeling. Increasing the imposed minimum rotation curve error from typically low, underestimated values to more realistic estimates decreases the χ² substantially and makes distinguishing between a cuspy or cored halo profile even more difficult. In spite of the degeneracies and uncertainties present, our constrained mass modeling favors submaximal disks (i.e., a dominant halo) at 2.2 disk scale lengths, with V_disk/V_tot<~0.6. This result holds for both the unbarred and weakly barred galaxies in our sample.