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The Earth's magnetosphere extension is controlled by the solar activity level via solar wind properties. Understanding such a relation in the Solar system is important for predicting the condition of exoplanetary magnetospheres near Sun-like stars. We use measurements of a chromospheric proxy, the Ca  ii K index, and solar wind OMNI parameters to connect the solar activity variations, on decennial time-scales, to the solar wind properties. The data span the period 1965–2021, which almost entirely covers the last five solar cycles. Using both cross-correlation and mutual information analysis, we find a 3.2-yr lag of the solar wind speed with respect to the Ca  ii K index. Analogously, a 3.6-yr lag is found once we consider the dynamic pressure. A correlation between the solar wind dynamic pressure and the solar ultraviolet emission is found and used to derive the Earth's magnetopause standoff distance. Moreover, the advantage of using a chromospheric proxy, such as the Ca  ii K index, creates the possibility to extend the relation found for the Sun to Sun-like stars, by linking stellar variability to stellar wind properties. The model is applied to a sample of Sun-like stars as a case study, where we assume the presence of an Earth-like exoplanet at 1 au. Finally, we compare our results with previous estimates of the magnetosphere extension for the same set of Sun-like stars. [ABSTRACT FROM AUTHOR]

Solar radiation variability spans a wide range in time, ranging from seconds to decadal and longer. The nearly 40 years of measurements of solar irradiance from space established that the total solar irradiance varies by ≈ 0.1 % in phase with the Sun's magnetic cycle. Specific intervals of the solar spectrum, e.g., ultraviolet (UV), vary by orders of magnitude more. These variations can affect the Earth's climate in a complex non-linear way. Specifically, some of the processes of interaction between solar UV radiation and the Earth's atmosphere involve threshold processes and do not require a detailed reconstruction of the solar spectrum. For this reason a spectral UV index based on the (FUV-MUV) color has been recently introduced. This color is calculated using SORCE SOLSTICE integrated fluxes in the FUV and MUV bands. We present in this work the reconstructions of the solar (FUV-MUV) color and Ca ii K and Mg ii indices, from 1749–2015, using a semi-empirical approach based on the reconstruction of the area coverage of different solar magnetic features, i.e., sunspot, faculae and network. We remark that our results are in noteworthy agreement with latest solar UV proxy reconstructions that exploit more sophisticated techniques requiring historical full-disk observations. This makes us confident that our technique can represent an alternative approach which can complement classical solar reconstruction efforts. Moreover, this technique, based on broad-band observations, can be utilized to estimate the activity on Sun-like stars, that cannot be resolved spatially, hosting extra-solar planetary systems. [ABSTRACT FROM AUTHOR]