Characterisation of the HD 219134 multi-planet system I. Observations of stellar magnetism, wind, and high-energy flux

HD 219134 hosts several planets, with seven candidates reported, and the two shortest period planets are rocky (4-5 \(M_{\oplus}\)) and transit the star. Here we present contemporaneous multi-wavelength observations of the star HD 219134. We observed HD 219134 with the Narval spectropolarimeter at the Observatoire du Pic du Midi, and used Zeeman Doppler Imaging to characterise its large-scale stellar magnetic field. We found a weak poloidal magnetic field with an average unsigned strength of 2.5 G. From these data we confidently confirm the rotation period of 42 days, measure a stellar inclination of 77\(\pm\)8 degrees, and find evidence for differential rotation. The projected obliquity of the two transiting super-Earths is therefore between 0 and 20 degrees. We employed HST STIS observations of the Ly\(\alpha\) line to derive a stellar wind mass-loss rate of half the solar value (\(10^{-14} M_{\odot} {\rm yr}^{-1}\)). We further collected photometric transit observations of the closest planet at near-UV wavelengths centred on the Mg II h&k lines with AstroSat. We found no detectable absorption, setting an upper limit on the transit depth of about 3%, which rules out the presence of a giant magnesium cloud larger than 9 planet radii. Finally, we estimated the high-energy flux distribution of HD 219134 as seen by planets b and c. These results present a detailed contemporaneous characterisation of HD 219134, and provide the ingredients necessary for accurately modelling the high-energy stellar flux, the stellar wind, and their impact on the two shortest-period planets, which will be presented in the second paper of this series.