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 S ^ { 3 } -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 -8.5 \pm 0.4 and a K-band relation with a slope of -11.7 \pm 0.6 for the HIPASS data set which is consistent with the existing results .