Clustering environment of BL Lacertae object RGB 1745+398

Aims: The BL Lac object RGB 1745+398 lies in an environment that makes it possible to study the cluster around it more deeply than the environments of other BL Lac objects. The cluster centered on the BL Lac works as a strong gravitational lens, forming a large arc around itself. The aim of this paper is to study the environment and characteristics of this object more accurately than the environments of other BL Lac objects have been before.
Methods: We measured the redshifts of galaxies in the cluster from the absorption lines in their spectra. The velocity dispersion was then obtained from the redshifts. The gravitational lensing was used for measuring the mass at the center of the cluster. The mass of the whole cluster could then be estimated using the softened isothermal sphere mass distribution. Finally, the richness of the cluster was determined by counting the number of galaxies near the BL Lac object and obtaining the galaxy-BL Lac spatial covariance function, B_gb.
Results: The redshifts of nine galaxies in the field were measured to be near the redshift of the BL Lac object, confirming the presence of a cluster. The average redshift of the cluster is 0.268, and the velocity dispersion (470^+190_-110) km s^-1. The mass of the cluster is M₅₀₀ = (4^+3_-2)×10¹⁴ M_⊙, which implies a rather massive cluster. The richness measurement also suggests that this is a rich cluster: the result for covariance function is B_gb = (600±200) Mpc^1.77, which corresponds to Abell richness class 1 and which is consistent with the mass and velocity dispersion of the cluster.