The gravitational heat conduction and the hierarchical structure in   solar interior
  With the assumption of local Tsallis equilibrium, the newly defined gravitational temperature is calculated in the solar interior, whose distribution curve can be divided into three parts, the solar core region, radiation region and convection region, in excellent agreement with the solar hierarchical structure. By generalizing the Fourier law, one new mechanism of heat conduction, based on the gradient of the gravitational temperature, is introduced into the astrophysical system. This mechanism is related to the self-gravity of such self-gravitating system whose characteristic scale is large enough. It perhaps plays an important role in the astrophysical system which, in the solar interior, leads to the heat accumulation at the bottom of the convection layer and then motivates the convection motion. 
Yahui Zheng, Jiulin Du
physics.gen-ph astro-ph.SR