Radiative cooling and modeling the Crab Synchrotron Nebula

Models of the Crab synchrotron nebula include energy losses by radiative and adiabatic expansion, but neglect the effect of radiative losses on the flow itself. The standard approach of all such models to date is to calculate a post-shocked flow and modify only the energy equation while assuming steady state flow dynamics. Even the most recent efforts at simulating the synchrotron emission from the Crab continue to adopt this approach. Typically, these authors argue that since the radiated power is only about 10 percent of the pulsar's spin down luminosity, radiative losses should have only negligible effects on flow dynamics. This argument implicitly assumes a spherically symmetric nebula: the estimate can be as high as 20 to 30 percent for a more realistic wedge geometry, for example.

A new, time-independent model of the Crab synchrotron nebula that incorporates radiative cooling for the first time is presented. Specifically, the relativistic magnetohydrodynamic (MHD) flow equations is first derived and then solved with radiative energy losses fully coupled to these equations from the start. The results of model calculations give plausible agreement with observations of the Crab Nebula. It is demonstrated that, for the particle energy and magnetic field values typical of the Crab, synchrotron cooling has too significant an effect upon the flow structure to be ignored. The possibility that the dynamic “wisps" observed in the nebular flow of the Crab are due to synchrotron cooling instabilities is discussed.