Restoration of the Tully-Fisher Relation by Statistical Rectification

I employ the Lucy rectification algorithm to recover the inclination-corrected distribution of local disk galaxies in the plane of absolute magnitude (M-i) and HI velocity width (W-20). By considering the inclination angle as a random variable with a known probability distribution, the novel approach eliminates one major source of uncertainty in studies of the Tully-Fisher relation: inclination angle estimation from axial ratio. Leveraging the statistical strength derived from the entire sample of 28,264 HI-selected disk galaxies at z<0.06 from the Arecibo Legacy Fast ALFA (ALFALFA) survey, I show that the restored distribution follows a sharp correlation that is approximately a power law between -16>M-i>-22: M-i=M-0-2.5 beta [log(W-20/250km/s)], with M-0=-19.77 +/- 0.04 and beta=4.39 +/- 0.06. At the brighter end (M-i<-22), the slope of the correlation decreases to beta approximate to 3.3, confirming previous results. Because the method accounts for measurement errors, the intrinsic dispersion of the correlation is directly measured: sigma(logW(20))approximate to 0.06 dex between -17>M-i>-23, while sigma(M-i) decreases from similar to 0.8 in slow rotators to similar to 0.4 in fast rotators. The statistical rectification method holds significant potential, especially in the studies of intermediate-to-high-redshift samples, where limited spatial resolution hinders precise measurements of inclination angles.