We present an analysis of the small–to–intermediate scale clustering of samples of Luminous Red Galaxies ( LRGs ) from the Sloan Digital Sky Survey ( SDSS ) and the 2dF-SDSS LRG and QSO ( 2SLAQ ) survey carefully matched to have the same rest-frame colours and luminosity .
We study the spatial two–point auto-correlation function in both redshift-space ( \xi ( s ) ) and real–space ( \xi ( r ) ) of a combined sample of over 10,000 LRGs , which represent the most massive galaxies in the universe with stellar masses > 10 ^ { 11 } h ^ { -1 } M _ { \odot } and space densities \simeq 10 ^ { -4 } h ^ { 3 } Mpc ^ { -3 } .
We find no significant evolution in the amplitude ( r _ { 0 } ) of the correlation function with redshift , but do see a slight decrease in the slope ( \gamma ) with increasing redshift over 0.19 < z < 0.55 and scales of 0.32 < r < 32 h ^ { -1 } Mpc .
We compare our measurements with the predicted evolution of dark matter clustering and use the halo model to interpret our results .
We find that our clustering measurements are inconsistent ( > 99.9 \% significance ) with a passive model whereby the LRGs do not merge with one another ; a model with a merger rate of 7.5 \pm 2.3 % from z = 0.55 to z = 0.19 ( i.e .
an average rate of 2.4 % Gyr ^ { -1 } ) provides a better fit to our observations .
Our clustering and number density measurements are consistent with the hypothesis that the merged LRGs were originally central galaxies in different haloes which , following the merger of these haloes , merged to create a single Brightest Cluster Galaxy ( BCG ) .
In addition , we show that the small scale clustering signal constrains the scatter in halo merger histories .
When combined with measurements of the luminosity function , our results suggest that this scatter is sub-Poisson .
While this is a generic prediction of hierarchical models , it has not been tested before .