Comparison of HI and optical redshifts of galaxies - The impact of
  redshift uncertainties on spectral line stacking
  Accurate optical redshifts will be critical for spectral co-adding techniques
used to extract detections from below the noise level in ongoing and upcoming
surveys for HI, which will extend our current understanding of gas reservoirs
in galaxies to lower column densities and higher redshifts. We have used
existing, high quality optical and radio data from the SDSS and ALFALFA surveys
to investigate the relationship between redshifts derived from optical
spectroscopy and neutral hydrogen (HI) spectral line observations. We find that
the two redshift measurements agree well, with a negligible systematic offset
and a small distribution width. Employing simple simulations, we determine how
the width of an ideal stacked HI profile depends on these redshift offsets, as
well as larger redshift errors more appropriate for high redshift galaxy
surveys. The width of the stacked profile is dominated by the width
distribution of the input individual profiles when the redshift errors are less
than the median width of the input profiles, and only when the redshift errors
become large, ~150 km/s, do they significantly affect the width of the stacked
profile. This redshift accuracy can be achieved with moderate resolution
optical spectra. We provide guidelines for the number of spectra required for
stacking to reach a specified mass sensitivity, given telescope and survey
parameters, which will be useful for planning optical spectroscopy observing
campaigns to supplement the radio data.
