On the upper limit for surface temperature of a static and spherical body

An upper limit for surface temperature of a static and spherical body in st eady state is determined by considering the gravitational temperature drop (GTD). For this aim, a body consisting of black body radiation (BBR) only i s considered. Thus, it is assumed that body has minimum mass and minimum GT D. By solving the Oppenheimer-Volkoff equation, density distribution of sel f-gravitating thermal photon sphere with infinite radius is obtained. Surfa ce temperature is defined as the temperature at distance of R from centre o f this photon sphere. By means of the density-temperature relation of BBR, surface temperature is expressed as a function of central temperature and r adius R. Variation of surface temperature with central temperature is exami ned. It is shown that surface temperature has a maximum for a finite Value of central temperature. For this maximum, an analytical expression dependin g on only the radius is obtained. Since a real static and stable body with finite radius has much more mass and much more GTD than their values consid ered here, obtained maximum constitutes an upper limit for surface temperat ure of a real body. This limitation on surface temperature also limits the radiative energy lose from a body. It is shown that this limit for radiativ e energy lose is a constant independently from body radius and central temp erature. Variation of the minimum mass with central temperature is also exa mined. It is seen that the surface temperature and minimum mass approach so me limit values, which are less than their maximums, by making damping osci llations when central temperature goes to infinity.