The He I infrared (IR) line at a vacuum wavelength of 10833 A is a diagnostic for the investigation of atmospheres of stars and planets orbiting them. For the first time, we study the behavior of the He I IR line in a set of chromospheric models for M-dwarf stars, whose much denser chromospheres may favor collisions for the level population over photoionization and recombination, which are believed to be dominant in solar-type stars. For this purpose, we use published PHOENIX models for stars of spectral types M2 V and M3 V and also compute new series of models with different levels of activity following an ansatz developed for the case of the Sun. We perform a detailed analysis of the behavior of the He I IR line within these models. We evaluate the line in relation to other chromospheric lines and also the influence of the extreme ultraviolet (EUV) radiation field. The analysis of the He I IR line strengths as a function of the respective EUV radiation field strengths suggests that the mechanism of photoionization and recombination is necessary to form the line for inactive models, while collisions start to play a role in our most active models. Moreover, the published model set, which is optimized in the ranges of the Na I D2, H$alpha$, and the bluest Ca II IR triplet line, gives an adequate prediction of the He I IR line for most stars of the stellar sample. Because especially the most inactive stars with weak He I IR lines are fit worst by our models, it seems that our assumption of a 100% filling factor of a single inactive component no longer holds for these stars.
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