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Description
We measure the distribution in absolute magnitude-circular velocity space for a well-defined sample of 199 rotating Calar Alto Legacy Integral Field Area Survey (CALIFA) galaxies using their stellar kinematics. Our aim in this analysis is to avoid subjective selection criteria and to take volume and large-scale structure factors into account. Using stellar velocity fields instead of gas emission line kinematics allows including rapidly rotating early type galaxies. Our initial sample contains 277 galaxies with available stellar velocity fields and growth curve r-band photometry. After rejecting 51 velocity fields that could not be modelled due to the low number of bins, foreground contamination or significant interaction we perform Markov Chain Monte Carlo (MCMC) modelling of the velocity fields, obtaining the rotation curve and kinematic parameters and their realistic uncertainties. We perform an extinction correction and calculate the circular velocity v_circ_ accounting for pressure support a given galaxy has. The resulting galaxy distribution on the M_r_-v_circ_ plane is then modelled as a mixture of two distinct populations, allowing robust a nd reproducible rejection of outliers, a significant fraction of which are slow rotators. The selection effects are understood well enough that the incompleteness of thesample can be corrected for and the 199 galaxies can be weighted by volume and large-scale structure factors enabling us to fit a volume-corrected Tully-Fisher relation (TFR). More importantly, we also provide the volume-corrected distribution of galaxies in the M_r_-v_circ_ plane, which can be compared with cosmological simulations. The joint distribution of the luminosity and circular velocity space densities, representative over the range of -20>M_r_>-22mag, can place more stringent constraints on the galaxy formation and evolution scenarios than linear TFR fit parameters or the luminosity function alone.
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