Supplementary file 1_Formation-height diagnostics across a sunspot: a comparison of Lightweaver radiative transfer and NICOLE inversions using the Ca ii 8542Å line.pdf

However, interpreting observations in this line requires a characterisation of the effective height ranges sampled by each spectral tuning, particularly when geometric height is obtained from inversion atmospheres that assume hydrostatic equilibrium. Using high resolution observations of a sunspot, we present a direct comparison between formation-height diagnostics derived from non-LTE radiative-transfer calculations and the geometric heights returned by NICOLE inversions, covering atmospheres corresponding to the umbra, umbral–penumbral boundary, penumbra, and the penumbral–quiet sun boundary.

Formation-height probability distributions are computed from Lightweaver contribution functions evaluated in the inversion atmospheres, and convolved with the SST/CRISP transmission profile. We then identify the optical-depth layers whose associated geometric-height distributions from the inversions best match these formation-height probability distributions. We find that the optical-depth range sampled by the line remains broadly stable across the sunspot, whilst the corresponding geometric heights vary systematically in the radial direction.