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Stellar activity is ubiquitously encountered in M dwarfs and oftencharacterised by the H$\alpha$ line. In the most active M dwarfs, H$\alpha$ isfound in emission, sometimes with a complex line profile. Previous studies havereported extended wings and asymmetries in the H$\alpha$ line during flares. Weused a total of 473 high-resolution spectra of 28 active M dwarfs obtained bythe CARMENES (Calar Alto high-Resolution search for M dwarfs with Exo-earthswith Near-infrared and optical Echelle Spectrographs) spectrograph to study theoccurrence of broadened and asymmetric H$\alpha$ line profiles and theirassociation with flares, and examine possible physical explanations. Wedetected a total of 41 flares and 67 broad, potentially asymmetric, wings inH$\alpha$. The broadened H$\alpha$ lines display a variety of profiles withsymmetric cases and both red and blue asymmetries. Although some of these lineprofiles are found during flares, the majority are at least not obviouslyassociated with flaring. We propose a mechanism similar to coronal rain orchromospheric downward condensations as a cause for the observed redasymmetries; the symmetric cases may also be caused by Stark broadening. Wesuggest that blue asymmetries are associated with rising material, and ourresults are consistent with a prevalence of blue asymmetries during the flareonset. Besides the H$\alpha$ asymmetries, we find some cases of additional lineasymmetries in \ion{He}{i} D$_{3}$, \ion{Na}{i}~D lines, and the \ion{He}{i}line at 10830\,\AA\, taken all simultaneously thanks to the large wavelengthcoverage of CARMENES. Our study shows that asymmetric H$\alpha$ lines are arather common phenomenon in M~dwarfs and need to be studied in more detail toobtain a better understanding of the atmospheric dynamics in these objects.

The CARMENES search for exoplanets around M dwarfs: Wing asymmetries of H$\alpha$, Na I D, and He I lines