Cyclotron-synchrotron: Harmonic fitting functions in the non-relativistic and trans-relativistic regimes

The present work investigates the calculation of absorption and emission cyclotron line profiles in the non-relativistic and trans-relativistic regimes. We provide fits for the ten first harmonics with synthetic functions down to 10(-4) of the maximum flux with an accuracy of 20% at worst. The lines at a given particle energy are calculated from the integration of the Schott formula over the photon and the particle solid angles relative to the magnetic field direction. The method can easily be extended to a larger number of harmonics. We also derive spectral fits of thermal emission line plasmas at non-relativistic and trans-relativistic temperatures extending previous parameterisations.