The CARMENES search for exoplanets around M dwarfs. The He I triplet at 10830 $\mathrm{\AA}\,$ across the M dwarf sequence
The He I infrared (IR) triplet at 10830 AA is an important activity indicator for the Sun and in solar-type stars, however, it has rarely been studied in relation to M dwarfs to date. In this study, we use the time-averaged spectra of 319 single stars with spectral types ranging from M0.0 V to M9.0 V obtained with the CARMENES high resolution optical and near-infrared spectrograph at Calar Alto to study the properties of the He I IR triplet lines. In quiescence, we find the triplet in absorption with a decrease of the measured pseudo equivalent width (pEW) towards later sub-types. For stars later than M5.0 V, the He I triplet becomes undetectable in our study. This dependence on effective temperature may be related to a change in chromospheric conditions along the M dwarf sequence. When an emission in the triplet is observed, we attribute it to flaring. The absence of emission during quiescence is consistent with line formation by photo-ionisation and recombination, while flare emission may be caused by collisions within dense material. The He I triplet tends to increase in depth according to increasing activity levels, ultimately becoming filled in; however, we do not find a correlation between the pEW(He IR) and X-ray properties. This behaviour may be attributed to the absence of very inactive stars ($L_{\rm X}/L_{\rm bol}$ < -5.5) in our sample or to the complex behaviour with regard to increasing depth and filling in.