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Empirical relations between the intensities of Lyman lines of H and He$^+$

Empirical relations between major UV and extreme UV spectral lines are one of the inputs for models of chromospheric and coronal spectral radiances and irradiances. They are also needed for the interpretation of some of the observations of the Solar Orbiter mission. We aim to determine an empirical relation between the intensities of the HI 121.6 nm and HeII 30.4 nm Lyman $α$ lines. Images at 121.6 nm from the Chromospheric Lyman Alpha Spectro Polarimeter (CLASP) and Multiple XUV Imager (MXUVI) sounding rockets were co-registered with simultaneous images at 30.4 nm from the EIT and AIA orbital telescopes in order to derive a spatially resolved relationship between the intensities. We have obtained a relationship between the HI 121.6 nm and HeII 30.4 nm intensities that is valid for a wide range of solar features, intensities, and activity levels. Additional SUMER data have allowed the derivation of another relation between the HI 102.5 nm (Ly$β$) and HeII 30.4 nm lines for quiet-Sun regions. We combined these two relationships to obtain a Ly$α$/Ly$β$ intensity ratio that is comparable to the few previously published results. The relationship between the HI 121.6~nm and HeII 30.4 nm lines is consistent with the one previously obtained using irradiance data. We have also observed that this relation is stable in time but that its accuracy depends on the spatial resolution of the observations. The derived Ly$α$/Ly$β$ intensity ratio is also compatible with previous results.