We generalize Planck's law for black-bodies, classically described by Maxwell-Boltzmann distributions, to include space and astrophysical plasmas described by kappa distributions. This provides the spectral intensity of electromagnetic radiation emitted by black bodies in thermal equilibrium with the surrounding and interacting plasmas. According to the generalized concept of thermal equilibrium, systems with correlations among their particles' velocities/energies reside in stationary states described by kappa distributions associated with the thermodynamic parameters of temperature and kappa index. Using these distributions, we derive the generalized expressions of the i) mean energy of photon ensemble, ii) spectral intensity with respect to frequency and wavelength, and iii) Stefan-Boltzmann law, characterized by the well-known fourth power of temperature, but now multiplied by a new kappa-dependent factor. Finally, we discuss the implications of these new developments for space and astrophysical plasmas.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)