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Fuelled by space photometry, asteroseismology is vastly benefitting the study of cool main-sequence stars, which exhibit convection-driven solar-like oscillations. Even so, the tiny oscillation amplitudes in K dwarfs continue to pose a challenge to space-based asteroseismology. A viable alternative is offered by the lower stellar noise over the oscillation timescales in Doppler observations. In this letter we present the definite detection of solar-like oscillations in the bright K5 dwarf $\epsilon$ Indi based on time-intensive observations collected with the ESPRESSO spectrograph at the VLT, thus making it the coolest seismic dwarf ever observed. We measured the frequencies of a total of 19 modes of degree $\ell=0$--2 along with $\nu_{\rm max}=5305\pm176\:{\rm \mu Hz}$ and $\Delta\nu=201.25\pm0.16\:{\rm \mu Hz}$. The peak amplitude of radial modes is $2.6\pm0.5\:{\rm cm\,s^{-1}}$, or a mere ${\sim} 14\%$ of the solar value. Measured mode amplitudes are ${\sim} 2$ times lower than predicted from a nominal $L/M$ scaling relation and favour a scaling closer to $(L/M)^{1.5}$ below ${\sim} 5500\:{\rm K}$, carrying important implications for our understanding of the coupling efficiency between pulsations and near-surface convection in K dwarfs. This detection conclusively shows that precise asteroseismology of cool dwarfs is possible down to at least the mid-K regime using next-generation spectrographs on large-aperture telescopes, effectively opening up a new domain in observational asteroseismology., Comment: Accepted for publication in Astronomy & Astrophysics Letters

The photometric time series of solar-like stars can exhibit rotational modulation due to active regions co-rotating with the stellar surface, allowing us to constrain stellar rotation and magnetic activity. In this work we investigate the behavior, particularly the variability, of the photometric magnetic activity of Kepler solar-like stars and compare it with that of the Sun. We adopted the photometric magnetic activity proxy Sph, which was computed with a cadence of 5 x the rotation period, Prot. The average Sph was taken as the mean activity level, and the standard deviation was taken as a measure of the temporal variation of the magnetic activity over the observations. We also analyzed Sun-as-a-star photometric data from VIRGO. Sun-like stars were selected from a very narrow parameter space around the solar properties. We also looked into KIC 8006161 (HD 173701), an active metal-rich G dwarf, and we compared its magnetic activity to that of stars with similar stellar parameters. We find that the amplitude of Sph variability is strongly correlated with its mean value, independent of spectral type. An equivalent relationship has been found for ground-based observations of chromospheric activity emission and magnetic field strength, but in this work we show that photometric Kepler data also present the same behavior. While, depending on the cycle phase, the Sun is among the less active stars, we find that the solar Sph properties are consistent with those observed in Kepler Sun-like stars. KIC 8006161 is, however, among the most active of its peers, which tend to be metal-rich. This results from an underlying relationship between Prot and metallicity and supports the following interpretation of the magnetic activity of KIC 8006161: its strong activity is a consequence of its high metallicity, which affects the depth of the convection zone and, consequently, the efficiency of the dynamo., Comment: Published in A&A; 12 pages including 11 figures and 3 tables (main text); 10 additional pages including 17 figures and 5 tables (appendix)