QUIP: A time-dependent standard model

A time-dependent solution representing the monotonic expansion o contraction of a self-gravitating gas sphere with polytropic index QUIP (quasi-invariant polytrope) is obtained from group theory. Radiation is introduced into the model through a dynamic diffusion description. Compatibility between the equations of hydrodynamics and radiation leads to the definition of a (time-dependent) standard QUIP generalizing Eddington's standard (static) model. The second-order dimensionless ordinary differential equation depending on a characteristic time scale a, used to describe the model, is solved numerically. Integral theorems by Ritter, Milne, Eddington, and Chandrasekhar, valid for a static configuration, are generalized to the case of the standard QUIP provided that two quantities are introduced: a Q-factor and a normalized moment of inertia. These two functions are calculated for different values of a. The solution of the standard QUIP is proved to depend on only three initial conditions related to experimental values. All quantities such as the ratio of the mean to the central density, the central density, pressure and temperature, etc., are calculated. A mass--radius--hydrodynamical time scale relation is given, together with a luminosity formula. Families of standard QUIPS can be characterized by a constant Q-factor and an effective temperature