The circular velocity and halo mass functions of galaxies in the nearby Universe

The circular velocity function (CVF) of galaxies is a fundamental test of the $\Lambda$ Cold Dark Matter (CDM) paradigm as it traces the variation of galaxy number densities with circular velocity ($v_{\rm{circ}}$), a proxy for dynamical mass. Previous observational studies of the CVF have either been based on \ion{H}{I}-rich galaxies, or encompassed low-number statistics and probed narrow ranges in $v_{\rm{circ}}$. We present a benchmark computation of the CVF between $100-350\ \rm{km\ s^{-1}}$ using a sample of 3527 nearby-Universe galaxies, representative for stellar masses between $10^{9.2}-10^{11.9} \rm{M_{\odot}}$. We find significantly larger number densities above 150 $\rm{km\ s^{-1}}$ compared to results from \ion{H}{I} surveys, pertaining to the morphological diversity of our sample. Leveraging the fact that circular velocities are tracing the gravitational potential of halos, we compute the halo mass function (HMF), covering $\sim$1 dex of previously unprobed halo masses ($10^{11.7}-10^{12.7} \rm{M_{\odot}}$). The HMF for our sample, representative of the galaxy population with $M_{200}\geqslant10^{11.35} \rm{M_{\odot}}$, shows that spiral morphologies contribute 67 per cent of the matter density in the nearby Universe, while early types account for the rest. We combine our HMF data with literature measurements based on \ion{H}{I} kinematics and group/cluster velocity dispersions. We constrain the functional form of the HMF between $10^{10.5}-10^{15.5} \rm{M_{\odot}}$, finding a good agreement with $\Lambda$CDM predictions. The halo mass range probed encompasses 72$\substack{+5 \\ -6}$ per cent ($\Omega_{\rm{M,10.5-15.5}} = 0.227 \pm 0.018$) of the matter density in the nearby Universe; 31$\substack{+5 \\ -6}$ per cent is accounted for by halos below $10^{12.7}\rm{M_{\odot}}$ occupied by a single galaxy.