Reformulation of the M1 model of radiative transfer

- We reformulate the M1 model of the radiative transfer.
- It is equivalent to the hydrodynamic equations of ultra relativistic particles.
- We find the bulk velocity of radiation subject to the Lorentz transform.
- The bulk velocity is the ratio of flux to the enthalpy density.

We reformulate the M1 model of the radiative transfer, i.e. the moment equations up to the first order, for clarifying the physical and mathematical properties. The M1 model is proved to be equivalent to the hydrodynamic equations of ultra relativistic particles. We show two forms: one expressed with the classical Newtonian velocity and the other expressed with the relativistic four velocity. We use the enthalpy density, i.e. the sum of the energy density and the isotropic component of the pressure, instead of the energy density in both forms. The former serves to show us that the ratio of the flux to the enthalpy density denotes the bulk velocity of the radiation in the M1 model. The latter serves us to propose a Lorentz invariant form useful for taking account of the Doppler shift.