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(Abridged) Understanding stellar activity in M dwarfs is crucial for thephysics of stellar atmospheres as well as for ongoing radial velocity exoplanetprogrammes. Despite the increasing interest in M dwarfs, our knowledge of thechromospheres of these stars is far from being complete. We aim to test whetherthe relations between activity, rotation, and stellar parameters and flux-fluxrelationships also hold for early-M dwarfs on the main-sequence. We analyse inan homogeneous and coherent way a well defined sample of 71 late-K/early-Mdwarfs that are currently being observed in the framework of the HArps-n redDwarf Exoplanet Survey (HADES). Rotational velocities are derived using thecross-correlation technique while emission flux excesses in the Ca II H & K andBalmer lines from Halpha up to Hepsilon are obtained by using the spectralsubtraction technique. The relationships between the emission excesses and thestellar parameters are studied. Relations between pairs of fluxes of differentchromospheric lines are also studied. We find that the strength of thechromospheric emission in the Ca II H & K and Balmer lines is roughly constantfor stars in the M0-M3 spectral range. Our data suggest that a moderate butsignificant correlation between activity and rotation might be present as wellas a hint of kinematically selected young stars showing higher levels ofemission. We find our sample of M dwarfs to be complementary in terms ofchromospheric and X-ray fluxes with those of the literature, extending theanalysis of the flux-flux relationships to the very low flux domain. Ourresults agree with previous works suggesting that the activity-rotation-agerelationship known to hold for solar-type stars also applies to early-M dwarfs.We also confirm previous findings that the field stars which deviate from thebulk of the empirical flux-flux relationships show evidence of youth.

The HADES RV Programme with HARPS-N@TNG. III. Flux-flux and activity-rotation relationships of early-M dwarfs