We investigate the gas density, temperature, and pressure profiles in a dark matter halo under the influence of the chameleon force. We solve the hydrostatic equilibrium equation for the gas coupled with the chameleon field in an analytic manner, using an approximate solution for the chameleon field equation with the source term, with a generalized Navarro-Frenk-White universal density profile. We find that the gas distribution becomes compact because a larger pressure gradient is necessary due to the additional chameleon force. By confronting the theoretical prediction with the data of the temperature profile of the Hydra A cluster according to Suzaku x-ray observations out to the virial radius, we demonstrate that a useful constraint on a model parameter can be obtained depending on the value of the coupling constant. For example, the upper bound of the background value of chameleon field, ${\varphi }_{\infty }<{10}^{-4}{M}_{\mathrm{Pl}}$, is obtained in the case $\beta =1$, where $\beta$ is the coupling constant between the chameleon field and the matter, and $M_{\mathrm{Pl}}$ is the Planck mass. However, the error of the present data is not so small that we obtain a useful constraint in the case $\beta =1/\sqrt{6}$, which corresponds to an $f(R)$ model.

• Received 30 March 2012

DOI:https://doi.org/10.1103/PhysRevD.86.103503