Context. The CARMENES exoplanet survey of M dwarfs has obtained more than 18 000 spectra of 329 nearby M dwarfs over the past five years as part of its guaranteed time observations (GTO) program. Aims. We determine planet occurrence rates with the 71 stars from the GTO program for which we have more than 50 observations. Methods. We use injection-and-retrieval experiments on the radial-velocity time series to measure detection probabilities. We include 27 planets in 21 planetary systems in our analysis. Results. We find 0.06−0.03+0.04 giant planets (100 M⊕ < Mpl sin i < 1000 M⊕) per star in periods of up to 1000 d, but due to a selection bias this number could be up to a factor of five lower in the whole 329-star sample. The upper limit for hot Jupiters (orbital period of less than 10 d) is 0.03 planets per star, while the occurrence rate of planets with intermediate masses (10 M⊕ < Mpl sin i < 100 M⊕) is 0.18−0.05+0.07 planets per star. Less massive planets with 1 M⊕ < Mpl sin i < 10 M⊕ are very abundant, with an estimated rate of 1.32−0.31+0.33 planets per star for periods of up to 100 d. When considering only late M dwarfs with masses M⋆ < 0.34 M⊙, planets more massive than 10 M⊕ become rare. Instead, low-mass planets with periods shorter than 10 d are significantly overabundant. Conclusions. For orbital periods shorter than 100 d, our results confirm the known stellar mass dependences from the Kepler survey: M dwarfs host fewer giant planets and at least two times more planets with Mpl  sin i < 10 M⊕ than G-type stars. In contrast to previous results, planets around our sample of very low-mass stars have a higher occurrence rate in short-period orbits of less than 10 d. Our results demonstrate the need to take into account host star masses in planet formation models.

Stellar dynamos generate magnetic fields that are of fundamental importance to the variability and evolution of Sun-like and low-mass stars, and for the development of their planetary systems. As a key to understanding stellar dynamos, empirical relations between stellar parameters and magnetic fields are required for comparison to ab initio predictions from dynamo models. We report measurements of surface-average magnetic fields in 292 M dwarfs from a comparison with radiative transfer calculations; for 260 of them, this is the first measurement of this kind. Our data were obtained from more than 15 000 high-resolution spectra taken during the CARMENES project. They reveal a relation between average field strength, ⟨B⟩, and Rossby number, Ro, resembling the well-studied rotation–activity relation. Among the slowly rotating stars, we find that magnetic flux, ΦB, is proportional to rotation period, P, and among the rapidly rotating stars that average surface fields do not grow significantly beyond the level set by the available kinetic energy. Furthermore, we find close relations between nonthermal coronal X-ray emission, chromospheric Hα and Ca H&K emission, and magnetic flux. Taken together, these relations demonstrate empirically that the rotation–activity relation can be traced back to a dependence of the magnetic dynamo on rotation. We advocate the picture that the magnetic dynamo generates magnetic flux on the stellar surface proportional to rotation rate with a saturation limit set by the available kinetic energy, and we provide relations for average field strengths and nonthermal emission that are independent of the choice of the convective turnover time. We also find that Ca H&K emission saturates at average field strengths of ⟨B⟩≈800 G while Hα and X-ray emission grow further with stronger fields in the more rapidly rotating stars. This is in conflict with the coronal stripping scenario predicting that in the most rapidly rotating stars coronal plasma would be cooled to chromospheric temperatures.

We determined effective temperatures, surface gravities, and metallicities for a sample of 343 M dwarfs observed with CARMENES, the double-channel, high-resolution spectrograph installed at the 3.5 m telescope at Calar Alto Observatory. We employed STEPARSYN, a Bayesian spectral synthesis implementation particularly designed to infer the stellar atmospheric parameters of late-type stars following a Markov chain Monte Carlo approach. We made use of the BT-Settl model atmospheres and the radiative transfer code turbospectrum to compute a grid of synthetic spectra around 75 magnetically insensitive Fe I and Ti I lines plus the TiO γ and ϵ bands. To avoid any potential degeneracy in the parameter space, we imposed Bayesian priors on Teff and logg based on the comprehensive, multi-band photometric data available for the sample. We find that this methodology is suitable down to M7.0 V, where refractory metals such as Ti are expected to condense in the stellar photospheres. The derived Teff, logg, and [Fe/H] range from 3000 to 4200 K, 4.5 to 5.3 dex, and −0.7 to 0.2 dex, respectively. Although our Teff scale is in good agreement with the literature, we report large discrepancies in the [Fe/H] scales, which might arise from the different methodologies and sets of lines considered. However, our [Fe/H] is in agreement with the metallicity distribution of FGK-type stars in the solar neighbourhood and correlates well with the kinematic membership of the targets in the Galactic populations. Lastly, excellent agreement in Teff is found for M dwarfs with interferometric angular diameter measurements, as well as in the [Fe/H] between the components in the wide physical FGK+M and M+M systems included in our sample.

Obliquity variability could play an important role in the climate and habitability of a planet. Orbital modulations caused by planetary companions and the planet's spin axis precession due to the torque from the host star may lead to resonant interactions and cause large-amplitude obliquity variability.Here we consider the spin axis dynamics of Kepler-62f and Kepler-186f, both of which reside in the habitable zone around their host stars. Using N -body simulations and secular numerical integrations, we describe their obliquity evolution for particular realizations of the planetary systems. We then use a generalized analytic framework to characterize regions in parameter space where the obliquity is variable with large amplitude. We find that the locations of variability are fine-tuned over the planetary properties and system architecture in the lower-obliquity regimes ( 40 • ). As an example, assuming a rotation period of 24 hr, the obliquities of both Kepler-62f and Kepler-186f are stable below ∼ 40 • , whereas the high-obliquity regions (60 • − 90 • ) allow moderate variabilities. However, for some other rotation periods of Kepler-62f or Kepler-186f, the lower-obliquity regions could become more variable owing to resonant interactions. Even small deviations from coplanarity (e.g. mutual inclinations ∼ 3 • ) could stir peak-to-peak obliquity variations up to ∼ 20 • . Undetected planetary companions and/or the existence of a satellite could also destabilize the low-obliquity regions. In all cases, the high-obliquity region allows for moderate variations, and all obliquities corresponding to retrograde motion (i.e. > 90 • ) are stable.