Galaxy clusters host a large reservoir of diffuse plasma with radially-varying temperature profiles. The efficiency of thermal conduction in the intracluster medium (ICM) is complicated by the existence of turbulence and magnetic fields, and has received a lot of attention in the literature. Previous studies suggest that the magnetothermal instability developed in outer regions of galaxy clusters would drive magnetic field lines preferentially radial, resulting in efficient conduction along the radial direction. Using a series of spherically-symmetric simulations, here we investigate the impact of thermal conduction on the observed temperature distributions in outer regions of three massive clusters, and find that thermal conduction substantially modifies the ICM temperature profile. Within 3 Gyr, the gas temperature at a representative radius of $0.3r_{500}$ typically decreases by ~10 - 20% and the average temperature slope between $0.3r_{500}$ and $r_{500}$ drops by ~ 30 - 40%, indicating that the observed ICM would not stay in a long-term equilibrium state in the presence of thermal conduction. However, X-ray observations show that the outer regions of massive clusters have remarkably similar radially-declining temperature profiles, suggesting that they should be quite stable. Our study thus suggests that the effective conductivity along the radial direction must be suppressed below the Spitzer value by a factor of 10 or more, unless additional heating sources offset conductive cooling and maintain the observed temperature distributions. Our study provides a smoking-gun evidence for the suppression of parallel conduction along magnetic field lines in low-collisionality plasmas by kinetic mirror or whistler instabilities.
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