Galaxy clusters and a possible variation of fine structure constant. (arXiv:1901.10947v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Colaco_L/0/1/0/all/0/1">L. R. Colaço</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Holanda_R/0/1/0/all/0/1">R. F. L. Holanda</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Silva_R/0/1/0/all/0/1">R. Silva</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Alcaniz_J/0/1/0/all/0/1">J. S. Alcaniz</a>
Galaxy clusters have been used as a cosmic laboratory to verify a possible
time variation of fundamental constants. Particularly, it has been shown that
the ratio $Y_{SZ}D_{A}^{2}/C_{XZS}Y_X $, which is expected to be constant with
redshift, can be used to probe a variation of the fine structure constant,
$alpha$. In this ratio, $Y_{SZ}D_{A}^{2}$ is the integrated comptonization
parameter of a galaxy cluster obtained via Sunyaev-Zel’dovich (SZ) effect
observations multiplied by its angular diameter distance, $D_A$, $Y_X$ is the
X-ray counterpart and $C_{XSZ}$ is an arbitrary constant. Using a combination
of SZ and X-ray data, a recent analysis found $Y_{SZ}D_{A}^{2}/C_{XZS}Y_X =
{rm{C}} alpha(z)^{3.5}$, where ${rm{C}}$ is a constant. In this paper,
following previous results that suggest that a variation of $alpha$
necessarily leads to a violation of the cosmic distance duality relation,
$D_L/D_A(1+z)^2 = 1$, where $D_L$ is the luminosity distance of a given source,
we derive a new expression, $Y_{SZ}D_{A}^{2}/C_{XSZ}Y_X = {rm{C}} alpha^{3.5}
eta^{-1}(z)$, where $eta(z) = D_L/D_A(1+z)^2$. In particular, considering the
direct relation $eta(z) propto alpha(z)^{1/2}$, derived from a class of
dilaton runaway models, %class of modified gravity theories, and 61
measurements of the ratio $Y_{SZ}D_{A}^{2}/C_{XSZ}Y_X$ provided by the Planck
collaboration, we discuss bounds on a possible variation of $alpha$. We also
estimate the value of the constant $ {rm{C}}$, which is compatible with the
unity at $2sigma$ level, indicating that the assumption of isothermality for
the temperature profile of the galaxy clusters used in the analysis holds.
Galaxy clusters have been used as a cosmic laboratory to verify a possible
time variation of fundamental constants. Particularly, it has been shown that
the ratio $Y_{SZ}D_{A}^{2}/C_{XZS}Y_X $, which is expected to be constant with
redshift, can be used to probe a variation of the fine structure constant,
$alpha$. In this ratio, $Y_{SZ}D_{A}^{2}$ is the integrated comptonization
parameter of a galaxy cluster obtained via Sunyaev-Zel’dovich (SZ) effect
observations multiplied by its angular diameter distance, $D_A$, $Y_X$ is the
X-ray counterpart and $C_{XSZ}$ is an arbitrary constant. Using a combination
of SZ and X-ray data, a recent analysis found $Y_{SZ}D_{A}^{2}/C_{XZS}Y_X =
{rm{C}} alpha(z)^{3.5}$, where ${rm{C}}$ is a constant. In this paper,
following previous results that suggest that a variation of $alpha$
necessarily leads to a violation of the cosmic distance duality relation,
$D_L/D_A(1+z)^2 = 1$, where $D_L$ is the luminosity distance of a given source,
we derive a new expression, $Y_{SZ}D_{A}^{2}/C_{XSZ}Y_X = {rm{C}} alpha^{3.5}
eta^{-1}(z)$, where $eta(z) = D_L/D_A(1+z)^2$. In particular, considering the
direct relation $eta(z) propto alpha(z)^{1/2}$, derived from a class of
dilaton runaway models, %class of modified gravity theories, and 61
measurements of the ratio $Y_{SZ}D_{A}^{2}/C_{XSZ}Y_X$ provided by the Planck
collaboration, we discuss bounds on a possible variation of $alpha$. We also
estimate the value of the constant $ {rm{C}}$, which is compatible with the
unity at $2sigma$ level, indicating that the assumption of isothermality for
the temperature profile of the galaxy clusters used in the analysis holds.
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