We present a new technique for the statistical evaluation of the Tully-Fisher relation (TFR) using spectral line stacking. This technique has the potential to extend TFR observations to lower masses and higher redshifts than possible through a galaxy-by-galaxy analysis. It further avoids the need for individual galaxy inclination measurements. To quantify the properties of stacked HI emission lines, we consider a simplistic model of galactic disks with analytically expressible line profiles. Using this model, we compare the widths of stacked profiles with those of individual galaxies. We then follow the same procedure using more realistic mock galaxies drawn from the S3-SAX model (a derivative of the Millennium simulation). Remarkably, when stacking the apparent HI lines of galaxies with similar absolute magnitude and random inclinations, the width of the stack is very similar to the width of the deprojected (= corrected for inclination) and dedispersed (= after removal of velocity dispersion) input lines. Therefore, the ratio between the widths of the stack and the deprojected/dedispersed input lines is approximately constant - about 0.93 - with very little dependence on the gas dispersion, galaxy mass, galaxy morphology, and shape of the rotation curve. Finally, we apply our technique to construct a stacked TFR using HIPASS data which already has a well defined TFR based on individual detections. We obtain a B-band TFR with a slope of $-8.5pm0.4$ and a K-band relation with a slope of $-11.7pm0.6$ for the HIPASS data set which is consistent with the existing results.
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