Relativistic Effects on Galaxy Redshift Samples due to Target Selection

In a galaxy redshift survey the objects to be targeted for spectra are selected from a photometrically observed sample. The observed magnitudes and colours of galaxies in this parent sample will be affected by their peculiar velocities, through relativistic Doppler and relativistic beaming effects. In this paper we compute the resulting expected changes in galaxy photometry. The magnitudes of the relativistic effects are a function of redshift, stellar mass, galaxy velocity and velocity direction. We focus on the CMASS sample from the Sloan Digital Sky Survey (SDSS), Baryon Oscillation Spectroscopic Survey (BOSS), which is selected on the basis of colour and magnitude. We find that 0.10\% of the sample ($\sim 585$ galaxies) has been scattered into the targeted region of colour-magnitude space by relativistic effects, and conversely 0.09\% of the sample ($\sim 532$ galaxies) has been scattered out. Observational consequences of these effects include an asymmetry in clustering statistics, which we explore in a companion paper. Here we compute a set of weights which can be used to remove the effect of modulations introduced into the density field inferred from a galaxy sample. We conclude by investigating the possible effects of these relativistic modulation on large scale clustering of the galaxy sample.