We investigate how the observed large-scale surface magnetic fields of low-mass stars (∼0.1 -2 M ), reconstructed through Zeeman-Doppler imaging (ZDI), vary with age t, rotation and X-ray emission. Our sample consists of 104 magnetic maps of 73 stars, from accreting pre-main sequence to main-sequence objects (1 Myr t 10 Gyr). For non-accreting dwarfs we empirically find that the unsigned average large-scale surface field |B V | is related to age as t −0.655±0.045 . This relation has a similar dependence to that identified by Skumanich (1972), used as the basis for gyrochronology. Likewise, our relation could be used as an age-dating method ("magnetochronology"). The trends with rotation we find for the large-scale stellar magnetism are consistent with the trends found from Zeeman broadening measurements (sensitive to large-and small-scale fields). These similarities indicate that the fields recovered from both techniques are coupled to each other, suggesting that small-and large-scale fields could share the same dynamo field generation processes. For the accreting objects, fewer statistically significant relations are found, with one being a correlation between the unsigned magnetic flux Φ V and P rot . We attribute this to a signature of star-disc interaction, rather than being driven by the dynamo.

Recently, Fossati et al. observed that the UV transit of WASP-12b showed an early ingress compared to the optical transit. We suggest that the resulting early ingress is caused by a bow shock ahead of the planetary orbital motion. In this Letter we investigate the conditions that might lead to the formation of such a bow shock. We consider two scenarios: (1) the stellar magnetic field is strong enough to confine the hot coronal plasma out to the planetary orbit and (2) the stellar magnetic field is unable to confine the plasma, which escapes in a wind. In both cases, a shock capable of compressing plasma to the observed densities will form around the planet for plasma temperatures T (4 − 5) × 10 6 K. In the confined case, the shock always forms directly ahead of the planet, but in the wind case the shock orientation depends on the wind speed and hence on the plasma temperature. For higher wind temperatures, the shock forms closer to the line of centers between the planet and the star. We conclude that shock formation leading to an observable early UV ingress is likely to be a common feature of transiting systems and may prove to be a useful tool in setting limits on planetary magnetic field strengths B p . In the case of WASP-12b, we derive an upper limit of about B p = 24 G. Subject headings: planet-star interactions -planets and satellites: individual (WASP-12b) -planets and satellites: magnetic fields -stars: coronae -stars: individual (WASP-12)stars: winds, outflows

Observations of the warm Neptune GJ 436 b were performed with HST/STIS at three different epochs (2012, 2013, 2014) in the stellar Lyman-α line. They showed deep, repeated transits that were attributed to a giant exosphere of neutral hydrogen. The low radiation pressure from the M-dwarf host star was shown to play a major role in the dynamics of the escaping gas and its dispersion within a large volume around the planet. Yet by itself it cannot explain the specific time-variable spectral features detected in each transit. Here we investigate the combined role of radiative braking and stellar wind interactions using numerical simulations with the EVaporating Exoplanet code (EVE) and we derive atmospheric and stellar properties through the direct comparison of simulated and observed spectra. The first epoch of observations is difficult to interpret because of the lack of out-of-transit data. In contrast, the results of our simulations match the observations obtained in 2013 and 2014 well. The sharp early ingresses observed in these epochs come from the abrasion of the planetary coma by the stellar wind. Spectra observed at later times during the transit can be produced by a dual exosphere of planetary neutrals (escaped from the upper atmosphere of the planet) and neutralized protons (created by charge-exchange with the stellar wind). We find similar properties at both epochs for the planetary escape rate (∼2.5 × 10 8 g s −1 ), the stellar photoionization rate (∼2 × 10 −5 s −1 ), the stellar wind bulk velocity (∼85 km s −1 ), and its kinetic dispersion velocity (∼10 km s −1 , corresponding to a kinetic temperature of 12 000 K). We also find high velocities for the escaping gas (∼50−60 km s −1 ) that may indicate magnetohydrodynamic (MHD) waves that dissipate in the upper atmosphere and drive the planetary outflow. In 2014 the high density of the stellar wind (∼3 × 10 3 cm −3 ) led to the formation of an exospheric tail that was mainly composed of neutralized protons and produced a stable absorption signature during and after the transit. The observations of GJ 436 b allow for the first time to clearly separate the contributions of radiation pressure and stellar wind and to probe the regions of the exosphere shaped by each mechanism. The overall shape of the cloud, which is constant over time, is caused by the stability of the stellar emission and the planetary mass loss, while the local changes in the cloud structure can be interpreted as variations in the density of the stellar wind.