The high energy spectrum of Proxima Centauri simultaneously observed at X-ray and FUV wavelengths

The M dwarf Proxima~Centauri is known to be magnetically active and it hosts a likely Earth-like planet in its habitable zone. Understanding the characteristics of stellar radiation by understanding the properties of the emitting plasma is of paramount importance for a proper assessment of the conditions on Proxima~Centauri~b and exoplanets around M dwarfs in general. We determine the temperature structure of the coronal and transition region plasma of Proxima Centauri from simultaneous X-ray and far-ultraviolet (FUV) observations. The differential emission measure distribution (DEM) was constructed for flaring and quiescent periods by analysing optically thin X-ray and FUV emission lines. Four X-ray observations of Proxima Centauri were conducted by the LETGS instrument on board of the Chandra X-ray Observatory and four FUV observations were carried out using the Hubble STIS spectrograph. From the X-ray light curves, we determined a variation of the quiescent count rate by a factor of two within 20\% of the stellar rotation period. To obtain the DEM, 18 optically thin emission lines were analysed (12 X-ray and six FUV). The flare fluxes differ from the quiescence fluxes by factors of 4-20 (FUV) and 1-30 (X-ray). The temperature structure of the stellar corona and transition region was determined for both the quiescence and flaring state by fitting the DEM(T) with Chebyshev polynomials for a temperature range $\log$T = 4.25 - 8. Compared to quiescence, the emission measure increases during flares for temperatures below 0.3\,MK (FUV dominated region) and beyond 3.6\,MK (X-ray dominated region). The reconstructed DEM shape provides acceptable line flux predictions compared to the measured values. We provide synthetic spectra at 1-1700 \AA, which may be considered as representative for the high-energy irradiation of Proxima~Cen~b during quiescent and flare periods.