The distance duality relation and the temperature profile of Galaxy
  Clusters
  The validity of distance duality relation, $\eta=D_L(z)(1+z)^{-2}/D_A(z)=1$,
an exact result required by the Etherington reciprocity theorem, where $D_A(z)$
and $D_L(z)$ are the angular and luminosity distances, plays an essential part
in cosmological observations and model constraints. In this paper, we
investigate some consequences of such a relation by assuming $\eta$ a constant
or a function of the redshift. In order to constrain the parameters concerning
$\eta$, we consider two groups of cluster gas mass fraction data including 52
X-ray luminous galaxy clusters observed by Chandra in the redshift range
$0.3\sim 1.273$ and temperature range $T_{\rm gas}> 4$ keV, under the
assumptions of two different temperature profiles [1]. We find that the
constant temperature profile is in relatively good agreement with no violation
of the distance duality relation for both parameterizations of $\eta$, while
the one with temperature gradient (the Vikhlinin et al. temperature profile)
seems to be incompatible even at 99% CL.
