Radiative Heat Conduction and the Magnetorotational Instability

A photon or neutrino gas--semi-contained by a baryonic species through scattering--comprises a rather peculiar MHD fluid where the magnetic field is truly frozen only to the co-moving volume associated with the mass density. Although radiative diffusion precludes an adiabatic treatment of compressive perturbations, we show that the energy equation may be cast in "quasi-adiabatic" form for exponentially growing non-propagating wave modes. Defining a generalized quasi-adiabatic index leads to a relatively straightforward dispersion relation for non-axisymmetric magnetorotational modes in the horizontal regime when an accretion disk has comparable stress contributions from diffusive and non-diffusive particle species. This analysis is generally applicable to optically thick, neutrino-cooled disks since the pressure contributions from photons, pairs and neutrinos, all have the same temperature dependence whereas only the neutrino component has radiative heat conduction properties on the time and length scales of the instability. We discuss the energy deposition process and the temporal and spatial properties of the ensuing turbulent disk structure on the basis of the derived dispersion relation.