The Tully-Fisher Relation for 25,000 SDSS Galaxies as Function of
  Environment
  We construct Tully-Fisher relationships (TFRs) in the $u$, $g$, $r$, $i$ and
$z$ bands and stellar mass TFRs (smTFRs) for a sample of $25,698$ late spiral
type galaxies (with $0.045<z<0.085$) from the Sloan Digital Sky Survey (SDSS)
and study the effects of environment on the relation. We use SDSS-measured
Balmer emission line widths, $v_{\rm FWHM}$, as a proxy for disc circular
velocity, $v_{\rm circ}$. A priori it is not clear whether we can construct
accurate TFRs given the small $3"$ diameter of the fibres used for SDSS
spectroscopic measurements. However, we show by modelling the H$\alpha$
emission profile as observed through a $3"$ aperture that for galaxies at
appropriate redshifts ($z>0.045$) the fibres sample enough of the disc to
obtain a linear relationship between $v_{\rm FWHM}$ and $v_{\rm circ}$,
allowing us to obtain a TFR and to investigate dependence on other variables.
We also develop a methodology for distinguishing between astrophysical and
sample bias in the fibre TFR trends. We observe the well-known steepening of
the TFR in redder bands in our sample. We divide the sample of galaxies into
four equal groups using projected neighbour density ($\Sigma$) quartiles and
find no significant dependence on environment, extending previous work to a
wider range of environments and a much larger sample. Having demonstrated that
we can construct SDSS-based TFRs is very useful for future applications because
of the large sample size available.
