Small-Scale Magnetic Fields of Hyades M Dwarfs: Evolution with Age from the Pleiades to Field Stars

Small-scale magnetic fields are derived for 18 M-dwarf stars in the Hyades open cluster through an analysis of Zeeman broadening in magnetically sensitive lines from the APOGEE spectra, resulting in mean magnetic fields ranging from 0.7 to 4.3 kG. Comparison with results for field stars hosting exoplanets and stars in the Pleiades open cluster from our previous works reveals distinct distributions of mean magnetic fields, reflecting differences in stellar age. Pleiades stars exhibit stronger fields ($2965\pm632$ G) and are predominantly in the saturated regime, while the roughly 500 million years older Hyades sample has weaker fields ($1925\pm1028$ G) with a larger dispersion, spanning both saturated and unsaturated regimes. Field stars show substantially weaker fields ($573\pm272$ G) and consistently occupy the unsaturated regime. Using the three samples, we derive the relationship between small-scale magnetic field strength and Rossby number, identifying saturation limits for the Rossby number ($\mathrm{Ro_{SAT}}=0.145$) and mean magnetic field ($\langle\mathrm{B}\rangle_{\rm SAT}=2452$ G). Within the Hyades sample, we find that, at a given age, cooler stars tend to have stronger magnetic fields. This trend is less apparent in the other samples, due to the broader age distribution of the field stars and magnetic saturation among the Pleiades stars. Comparisons with isochrones indicate positive correlations between mean magnetic field strength and both stellar radius inflation and photospheric spot coverage. We also find positive correlations between magnetic field strength and chromospheric and coronal activity, with stronger fields associated with larger H$α$ equivalent width excess and higher X-ray-to-bolometric luminosity ratios.