Turbulent heating of galaxy-cluster plasmas

A number of studies suggest that turbulent heating plays an important role in the thermal balance of galaxy-cluster plasmas. In this paper, we construct a model of intracluster plasmas in which radiative cooling is balanced by heating from viscous dissipation of turbulent motions, turbulent diffusion of high-specific-entropy plasma into low-specific-entropy regions, and thermal conduction. We solve for the rms turbulent velocity u by setting Gamma + Q + H = R throughout a cluster, where Gamma, Q, and H are the heating rates from dissipation of turbulence, turbulent diffusion, and conduction, respectively, and R is the rate of radiative cooling. We account for the effects of buoyancy in our expression for the eddy diffusivity and neglect nonthermal pressure. We take the conductivity to be a fixed fraction (typically one-fifth) of the Spitzer value for a nonmagnetized plasma and the density and temperature to be given by analytical fits to published data. We set the dominant velocity length scale l equal to alpha r + l(0), where alpha is a constant, r is distance from cluster center, and l(0) = 0.5 kpc. For 0.05 < alpha < 1, we find velocities in the range 100 less than or similar to u less than or similar to 300 km s(-1). The inclusion of dissipation substantially reduces the value of u needed to balance cooling when alpha 0: 5, relative to models in which turbulent diffusion is the only form of turbulent heating. We find that Gamma greater than or similar to Q when alpha < 0.5, and Gamma less than or similar to Q when alpha > 0.5, although there are exceptions to this rule. For some values of alpha, we find that at some locations the heat flux from turbulent diffusion has positive divergence, so that turbulent diffusion locally cools the plasma. Buoyancy inhibits turbulent diffusion of heat in the radial direction to a degree that increases with increasing alpha. This leads to an increase in the computed value of u relative to models that neglect buoyancy; the magnitude of the increase is moderate for alpha = 0.5 and large for alpha > 1.