Spatial Integration Grids in Line Profile Modelling of Nonradially Pulsating Magnetic Stars

Extract

For an optimum grid we postulate a fractional change of the emergent Stokes parameters between two adjacent surface points not to exceed some fixed value (say 20 %) at any frequency point. The contribution from a local Stokes IQUV profile to the observed integrated profile is a complicated non-linear function of rotational and pulsational Doppler shifts respectively, of Zeeman splitting, magnetic field direction relative to the line-of-sight, of the magnetic field azimuth in the observer’s frame and of limb darkening. The run of IQUV with visible disk coordinates (x, y) can be represented by curved surfaces f(x,y); these are different for each Stokes parameter and frequency point. The optimum integration grid then has to ensure that the maximum change δf(x,y) over all frequencies and Stokes parameters does not exceed the above-mentioned limit.