Measuring Gravitational Redshifts in Galaxy Clusters

Understand

Wojtak {\it et al} have stacked 7,800 clusters from the SDSS survey in redshift space.

• They find a small net blue-shift for the cluster galaxies relative to the brightest cluster galaxies, which agrees quite well with the gravitational redshift from GR.
• Zhao {\it et al.} have pointed out that, in addition to the gravitational redshift, one would expect to see transverse Doppler (TD) redshifts, and that these two effects are generally of the same order.
• Here we show that there are other corrections that are also of the same order of magnitude.