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 Γ + Q + H = R throughout a cluster, where Γ, 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 αr + l0, where α is a constant, r is distance from cluster center, and l0 = 0.5 kpc. For 0.05 α 1, we find velocities in the range 100 u 300 km s-1. The inclusion of dissipation substantially reduces the value of u needed to balance cooling when α 0.5, relative to models in which turbulent diffusion is the only form of turbulent heating. We find that Γ Q when α 0.5, and Γ Q when α 0.5, although there are exceptions to this rule. For some values of α, 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 α. 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 α = 0.5 and large for α 1.
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机译：大量研究表明，湍流加热在星系团等离子体的热平衡中起着重要作用。在本文中，我们构建了一个簇内等离子体模型，该模型中的辐射冷却是通过湍流运动的粘性耗散，高比熵等离子体向低比熵区域的湍流扩散以及热传导进行加热而达到平衡的。我们通过在整个群集中设置Γ+ Q + H = R来求解均方根湍流速度u，其中Γ，Q和H分别是湍流消散，湍流扩散和传导的加热速率，而R是速率辐射冷却。我们在表达涡流扩散性和忽略非热压力时考虑了浮力的影响。对于非磁化等离子体，我们将电导率设为Spitzer值的固定分数（通常为五分之一），并通过对公开数据的分析拟合得出密度和温度。我们将主导速度长度尺度l设置为等于αr+ l0，其中α为常数，r为距簇中心的距离，l0 = 0.5 kpc。对于0.05 <α<1，我们发现速度在100 u 300 km s-1范围内。相对于其中湍流扩散是湍流加热的唯一形式的模型，耗散的包含实质上降低了在α为0.5时平衡冷却所需的u值。我们发现，当α<0.5时，ΓQ;当α> 0.5时，ΓQ;尽管该规则有例外。对于某些α值，我们发现湍流扩散产生的热通量在某些位置具有正发散，因此湍流扩散会局部冷却等离子体。浮力将热量沿径向的湍流扩散抑制到一定程度，随着α的增加而增加。相对于忽略浮力的模型，这导致u的计算值增加; α= 0.5时增加幅度适中，而α> 1时增加幅度较大。
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