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.