Tachyonic Cherenkov radiation from supernova remnants

The subexponential decay observed in the γ-ray spectral maps of supernova remnants is explained in terms of tachyonic Cherenkov emission from a relativistic electron population. The tachyonic radiation densities of an electronic spinor current are derived, the total density as well as the transversal and longitudinal polarization components, taking account of electron recoil. Tachyonic flux quantization subject to dispersive and dissipative permeabilities is discussed, the matrix elements of the transversal and longitudinal Poynting vectors of the Maxwell-Proca field are obtained, Cherenkov emission angles and radiation conditions are derived. The spectral energy flux of an ultra-relativistic electron plasma is calculated, a tachyonic Cherenkov fit to the high-energy (1 GeV to 30 TeV) γ-ray spectrum of the Crab Nebula is performed, and estimates of the linear polarization degree are given. The spectral tail shows subexponential Weibull decay, which can be modeled with a frequency-dependent tachyon mass in the dispersion relations. Tachyonic flux densities interpolate between exponential and power-law spectral decay, which is further illustrated by Cherenkov fits to the γ-ray spectra of the supernova remnants IC 443 and W44. Subexponential spectral decay is manifested in double-logarithmic spectral maps as curved Weibull or straight power-law slope.