Spurious Velocities in Dynamically-Cold Systems Due to the Gravitational Redshifts of their Constituent Stars

The Doppler effect is commonly used to infer the velocity difference between stars based on the relative shifts in the rest-frame wavelengths of their spectral features. In dynamically-cold systems with a low velocity dispersion, such as wide binaries, loose star clusters, cold stellar streams or cosmological mini-halos, the scatter in the gravitational redshift from the surface of the constituent stars needs to be taken into account as well. Gravitational redshifts could be important for wide binaries composed of main sequence stars with separations >0.01 pc or in mini-halos with velocity dispersions <1 km/s. Variable redshift could also lead to a spurious “detection” of low-mass planets around a star with periodic photospheric radius variations.