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The velocity function is a fundamental observable statistic of the galaxypopulation, similarly impor- tant as the luminosity function, but much moredifficult to measure. In this work we present the first directly measuredcircular velocity function that is representative between 60 < v_circ < 320km/s for galaxies of all morphological types at a given rotation velocity. Forthe low mass galaxy population (60 < v_circ < 170 km/s), we use the HIPASSvelocity function. For the massive galaxy population (170 < v_circ < 320 km/s),we use stellar circular velocities from the Calar Alto Legacy Integral FieldArea Survey (CALIFA). In earlier work we obtained the measurements of circularvelocity at the 80% light radius for 226 galaxies and demonstrated that theCALIFA sample can produce volume- corrected galaxy distribution functions. TheCALIFA velocity function includes homogeneous velocity measurements of bothlate and early-type rotation-supported galaxies and has the crucial advantageof not missing gas-poor massive ellipticals that HI surveys are blind to. Weshow that both velocity functions can be combined in a seamless manner, astheir ranges of validity overlap. The resulting observed velocity function iscompared to velocity functions derived from cosmological simulations of the z =0 galaxy population. We find that dark matter-only simulations show a strongmismatch with the observed VF. Hydrodynamic simulations fare better, but stilldo not fully reproduce observations.

The Califa and Hipass velocity function for all morphological galaxy types