Limb darkening

Solar limb darkening is a phenomenon observed on the disc of the sun where regions at greater radial distances emit less total radiance than the peak radiance emitted at the centre[1]. This effect is caused by an observer's line of sight passing through deeper, hotter, regions of the Sun's photosphere near the observed centre and only shallower, cooler, regions nearer the limb before the optical depth in each case reaches unity and renders greater depths inaccessible to the observer.

The radial change in observed solar radiance is not uniform as a function of wavelength as a greater degree of darkening occurs for shorter wavelength (higher energy) photons, which are emitted in greater relative proportions from the hotter regions of the photosphere[2].

UVIS Observations

This work presents an analysis of spectral radiance scans across the solar disc, ranging from ultraviolet to visible wavelengths (200-650~nm), taken during multiple observing windows over a period of approximately 2 years by the NOMAD instrument's UVIS spectrometer[3] aboard ESA's Trace Gas Orbiter spacecraft, currently in orbit around Mars.

The individual measurements comprising one of these complete scans form a 2-dimensional grid over the solar surface with parallel lines of closely separated measurements, these grids have a spatial resolution of 2~minutes of arc. Interpolated surface maps over individual observational grids and combined averaged maps are constructed from the observed radiances at various wavelengths representing the normalised surface radiance relative to the central peak intensity.

Surface fits against multiple limb darkening models[4] are performed yielding corresponding sets of limb darkening coefficients which characterise the magnitude of the observed effect, the mean observed spectral surface intensity and the darkening wavelength sensitivity over the full spectral range of the UVIS instrument.

[1] Sanchez-Bajo et al. (2002)
[2] Solanki et al. (2001)
[3] Patel et al. (2017)
[4] Claret et al. (2013)