Kinematics and Mass Distributions for Non-Spherical Deprojected S\'ersic Density Profiles and Applications to Multi-Component Galactic Systems

Using kinematics to decompose galaxies' mass profiles, including the dark matter contribution, often requires parameterization of the baryonic mass distribution based on ancillary information. One such model choice is a deprojected S\'ersic profile with an assumed intrinsic geometry. The case of flattened, deprojected S\'ersic models has previously been applied to flattened bulges in local star-forming galaxies (SFGs), but can also be used to describe the thick, turbulent disks in distant SFGs. Here we extend this previous work that derived density ($\rho$) and circular velocity ($v_{\rm circ}$) curves by additionally calculating the spherically-enclosed 3D mass profiles ($M_{\rm sph}$). Using these profiles, we compare the projected and 3D mass distributions, quantify the differences between the projected and 3D half-mass radii ($R_{\rm e}; r_{\rm 1/2,mass,3D}$), and present virial coefficients relating $v_{\rm circ}(R)$ and $M_{\rm sph}(<r=R)$ or $M_{\rm tot}$. We then quantify differences between mass fraction estimators for multi-component systems, particularly for dark matter fractions, and consider the compound effects of measuring dark matter fractions at the projected versus 3D half-mass radii. While the fraction estimators produce only minor differences, using different aperture radius definitions can strongly impact the inferred dark matter fraction. As pressure support is important in analysis of gas kinematics (particularly at high redshifts), we also calculate the self-consistent pressure support correction profiles, which generally predict less pressure support than for the self-gravitating disk case. These results have implications for comparisons between simulation and observational measurements, and for the interpretation of SFG kinematics at high redshifts. A set of precomputed tables and the code to calculate the profiles are made publicly available. [Abridged]