# HADES RV Programme with HARPS-N at TNG. X. The non-saturated regime of the stellar activity-rotation relationship for M-Dwarfs

## TL;DR

This study investigates the relationship between stellar activity and rotation in early-M dwarfs, confirming that the activity-rotation relation observed in more massive stars also applies to these low-mass stars in the non-saturated regime.

## Contribution

It extends the known activity-rotation relationship to early-M dwarfs and accurately determines the saturation rotation period for these stars.

## Key findings

- The activity-rotation relation for FGK stars also applies to early-M dwarfs.
- The saturation rotation period (P_sat) for M dwarfs is identified.
- The relation holds in the non-saturated regime for slow rotators.

## Abstract

Aims. We aim to extend the relationship between X-ray luminosity (Lx) and rotation period (Prot) found for main-sequence FGK stars and test whether it also holds for early-M dwarfs, especially in the non-saturated regime (Lx {\alpha} P_{rot}^{-2}) which corresponds to slow rotators. Methods. We use the luminosity coronal activity indicator (Lx) of a sample of 78 early-M dwarfs with masses in the range from 0.3 to 0.75 Msun from the HArps-N red Dwarf Exoplanet Survey (HADES) radial velocity (RV) programme collected from ROSAT and XMM-Newton. The determination of the rotation periods (P_{rot}) was done by analysing time-series of high-resolution spectroscopy of the Ca ii H & K and H{\alpha} activity indicators. Our sample principally covers the slow rotation regime with rotation periods from 15 to 60 days. Results. Our work extends to the low mass regime the observed trend for more massive stars showing a continuous shift of the Lx/Lbol vs. Prot power-law towards longer rotation period values and includes the determination, in a more accurate way, of the value of the rotation period at which the saturation occurs (P_{sat}) for M dwarf stars. Conclusions. We conclude that the relations between coronal activity and stellar rotation for FGK stars also hold for early-M dwarfs in the non-saturated regime, indicating that the rotation period is sufficient to determine the ratio Lx/Lbol.