Gravitational Redshift of Galaxies in Clusters from the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey

The gravitational redshift effect allows one to directly probe the gravitational potential in clusters of galaxies. Following up on Wojtak et al. [Nature (London) 477, 567 (2011)], we present a new measurement. We take advantage of new data from the tenth data release of the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey. We compare the spectroscopic redshift of the brightest cluster galaxies (BCGs) with that of galaxies at the outskirts of clusters, using a sample with an average cluster mass of ${10}^{14}{M}_{\odot }$. We find that these galaxies have an average relative redshift of $-11\mathrm{km}/\mathrm{s}$ compared with that of BCGs, with a standard deviation of $+7$ and $-5\mathrm{km}/\mathrm{s}$. Our measurement is consistent with that of Wojtak et al. [Nature (London) 477, 567 (2011)]. However, our derived standard deviation is larger, as we take into account various systematic effects, beyond the size of the data set. The result is in good agreement with the predictions from general relativity.

Figure 1

(a) Dependence of the number of galaxies $n_{\text{gal}}$, of the number of associated clusters $n_{\text{clst}}$, and of the ratio $n_{\text{gal}}/n_{\text{clst}}$ on the separation between BCGs and associated galaxies $r_{\mathrm{gc}}$. Bins of $r_{\mathrm{gc}}$ are defined by a sliding window with a width of $0.5r_{200}$, where each data point is placed in the center position of the corresponding bin. (b) Dependence of the signal of the GRS, $\mathrm{\Delta }{v}_{\mathrm{gc}}$, on $r_{\mathrm{gc}}$, where the width of the sliding window is denoted by $w_{\mathrm{sw}}$. The shaded areas around the two nominal results (circles and squares) correspond to the variations in the signal due to the systematic tests described in the text, combined with the uncertainty on the model fit. On average, $\mathrm{\Delta }{v}_{\mathrm{gc}}=-{11}_{-5}^{+7}\mathrm{km}/\mathrm{s}$ for $1<r_{\mathrm{gc}}/r_{200}<2.5$. The third data set (triangles) includes configurations in which SDSS and BOSS redshifts are mixed together. The bold lines represent the GR predictions of Kaiser [11], with and without his added kinematic effects, as indicated; finally, the crosses represent the measurement of WHH. The top axis specifies the median value and the width of the distribution of $r_{\mathrm{gc}}$ (in Mpc) for four bins of width $0.5r_{200}$, centered at (0.5, 1, 1.5, and 2) $r_{200}$.