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Early-type galaxy velocity dispersions and luminosities are correlated. Thecorrelation estimated in local samples (< 100 Mpc) differs from that measuredmore recently in the SDSS. This is true even when systematics in the SDSSphotometric and spectroscopic parameters have been accounted-for. We show thatthis is also true for the ENEAR sample if galaxy luminosities are estimatedusing distances which have been corrected for peculiar motions. We then showthat, because the estimate of the `true' distance is derived from a correlationwith velocity dispersion, in this case the D_n-sigma relation, using it in thesigma-L relation leads to an artificially tight relation with a biased slope.Making no correction for peculiar velocities results in a sigma-L relationwhich is very similar to that of the SDSS, although with larger scatter. Wealso measure the sigma-L correlation in a mock ENEAR catalog, in which theunderlying galaxy sample has the same sigma-L correlation as seen in the SDSS.The mock catalog produces the same D_n-sigma relation as the data, the samebiased slope when D_n-sigma distances are used to estimate luminosities, andgood agreement with the input sigma-L relation when redshift is used as thedistance indicator. This provides further evidence that the true sigma-Lrelation of ENEAR galaxies is indeed very similar to that of SDSS early-types.Our results suggest that local sigma-L relations which are based on FundamentalPlane distances should also be re-evaluated. Our findings also have importantimplications for black hole demographics; the best direct estimates of themasses of supermassive black holes come from local galaxies, so estimates ofthe black hole mass function are more safely made by working with the Mbh-sigmacorrelation than with Mbh-L.Comment: 9 pages, 9 figures. Accepted by AJ. A new appendix describes  systematics effects we found in the SDSS velocity dispersion measurements  (sigmas < 150 km/s are biased towards larger values; this bias was not  present in the Bernardi et al. 2003 sample) and luminosity measurement

The σ-LCorrelation in Nearby Early-Type Galaxies