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Understanding the thermodynamic state of the hot intracluster medium (ICM) in a galaxy cluster requires a knowledge of the plasma transport processes, especially thermal conduction. The basic physics of thermal conduction in plasmas with ICM-like conditions

has yet to be elucidated, however. We use particle-in-cell simulations and analytic models to explore the dynamics of an ICM-like plasma (with small gyroradius, large mean-free-path, and strongly sub-dominant magnetic pressure) induced by the diffusive

heat flux associated with thermal conduction. Linear theory reveals that whistler waves are driven unstable by electron heat flux, even when the heat flux is weak. The resonant interaction of electrons with these waves then plays a critical role in scattering electrons

and suppressing the heat flux. In a 1D model where only whistler modes that propagate parallel to the magnetic field are captured, the only resonant electrons are moving in the opposite direction to the heat flux and the electron heat flux suppression is small. In 2D or more, oblique whistler modes also resonate with electrons moving in the direction of theheat flux. The overlap of resonances leads to effective symmetrization of the electron distribution function and a strong suppression of heat flux. The results suggest that thermal conduction in the ICM might be strongly suppressed.

In a numerical model with continually supplied heat flux in the system, two thermal reservoirs at different temperatures drive an electron heat flux that destabilizes off-angle whistler-type modes. The whistlers grow to large amplitude, 𝛿B=B0, and resonantly scatter the electrons. A surprise is that the resulting steady state heat flux is largely independent of the thermal gradient. The rate of thermal conduction is instead controlled by the finite propagation speed of the whistlers, which act as mobile scattering centers

that convect the thermal energy of the hot reservoir. The results are relevant to thermal transport in high β astrophysical plasmas such as hot accretion flows and the intracluster medium of galaxy clusters.

When the plasma β is reduced in the numerical model, we find that a transition takes place between whistler-dominated (high-β) and double-layer-dominated (low-β) heat flux suppression. Whistlers saturate at small amplitude in the low β limit and are

unable to effectively suppress the heat flux. Electrostatic double layers suppress the heat flux to a mostly constant factor of the free streaming value once this transition happens. The double layer physics is an example of ion-electron coupling and occurs on a scale of roughly the electron Debye length. The scaling of ion heating associated with the various heat flux driven instabilities is explored over the full range of β explored. The range of plasma-βs studied in this work makes it relevant to the dynamics of a large variety of astrophysical plasmas, including not just the intracluster medium but hot accretion flows, stellar and accretion disk coronae, and the solar wind.