Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering environment of BL Lac object RGB 1745+398   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.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, $B_{gb}$. 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 $M_{500}=(4^{+3}_{-2})\times10^{14}
M_{\sun}$ which implies a rather massive cluster. The richness measurement also
suggests that this is a rich cluster: the result for covariance function is
$B_{gb}=(600\pm200)$ Mpc$^{1.77}$, which corresponds to Abell richness class 1
and which is consistent with the mass and velocity dispersion of the cluster.

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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
1
The categories of this paper are: cs