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.