There have recently been detections of radio emission from low-mass stars, some of which are indicative of star-planet interactions. Motivated by these exciting new results, in this paper we present Alfvén wave-driven stellar wind models of the two active planet-hosting M dwarfs Prox Cen and AU Mic. Our models incorporate large-scale photospheric magnetic field maps reconstructed using the Zeeman-Doppler Imaging method. We obtain a mass-loss rate of $0.25~\dot{M}_{\odot }$ for the wind of Prox Cen. For the young dwarf AU Mic, we explore two cases: a low and high mass-loss rate. Depending on the properties of the Alfvén waves which heat the corona in our wind models, we obtain mass-loss rates of 27 and $590~\dot{M}_{\odot }$ for AU Mic. We use our stellar wind models to assess the generation of electron cyclotron maser instability emission in both systems, through a mechanism analogous to the sub-Alfvénic Jupiter-Io interaction. For Prox Cen we do not find any feasible scenario where the planet can induce radio emission in the star’s corona, as the planet orbits too far from the star in the super-Alfvénic regime. However, in the case that AU Mic has a stellar wind mass-loss rate of $27~\dot{M}_{\odot }$, we find that both planets b and c in the system can induce radio emission from ∼10 MHz – 3 GHz in the corona of the host star for the majority of their orbits, with peak flux densities of ∼10 mJy. Detection of such radio emission would allow us to place an upper limit on the mass-loss rate of the star.

We present stellar wind modelling of the hot Jupiter host HD189733, and predict radio emission from the stellar wind and the planet, the latter arising from the interaction of the stellar wind with the planetary magnetosphere. Our stellar wind models incorporate surface stellar magnetic field maps at the epochs as boundary conditions. We find that the mass-loss rate, angular momentumloss rate, and open magnetic flux of HD189733 vary by 9%, 40%, and 19% over these three epochs. Solving the equations of radiative transfer, we find that from 10 MHz-100 GHz the stellar wind emits fluxes in the range of 10 −3 -5 µJy, and becomes optically thin above 10 GHz. Our planetary radio emission model uses the radiometric Bode's law, and neglects the presence of a planetary atmosphere. For assumed planetary magnetic fields of 1-10 G, we estimate that the planet emits at frequencies of 2-25 MHz, with peak flux densities of ∼ 10 2 mJy. We find that the planet orbits through regions of the stellar wind that are optically thick to the emitted frequency from the planet. As a result, unattenuated planetary radio emission can only propagate out of the system and reach the observer for 67% of the orbit for a 10 G planetary field, corresponding to when the planet is approaching and leaving primary transit. We also find that the plasma frequency of the stellar wind is too high to allow propagation of the planetary radio emission below 21 MHz. This means a planetary field of at least 8 G is required to produce detectable radio emission.

In the present paper, we model the wind of solar analogues at different ages to investigate the evolution of the solar wind. Recently, it has been suggested that winds of solar type stars might undergo a change in properties at old ages, whereby stars older than the Sun would be less efficient in carrying away angular momentum than what was traditionally believed. Adding to this, recent observations suggest that old solar-type stars show a break in coronal properties, with a steeper decay in X-ray luminosities and temperatures at older ages. We use these X-ray observations to constrain the thermal acceleration of winds of solar analogues. Our sample is based on the stars from the 'Sun in time' project with ages between 120-7000 Myr. The break in X-ray properties leads to a break in wind mass-loss rates ( M) at roughly 2 Gyr, with M (t < 2 Gyr) ∝ t −0.74 and M (t > 2 Gyr) ∝ t −3.9 . This steep decay in M at older ages could be the reason why older stars are less efficient at carrying away angular momentum, which would explain the anomalously rapid rotation observed in older stars. We also show that none of the stars in our sample would have winds dense enough to produce thermal emission above 1-2 GHz, explaining why their radio emissions have not yet been detected. Combining our models with dynamo evolution models for the magnetic field of the Earth we find that, at early ages (≈100 Myr) our Earth had a magnetosphere that was 3 or more times smaller than its current size.1 Ro represents Rossby number, which is the ratio between stellar rotation and convective turnover time. Ro = P rot /τ conv

In this work, we simulate the evolution of the solar wind along its main sequence lifetime and compute its thermal radio emission. To study the evolution of the solar wind, we use a sample of solar mass stars at different ages. All these stars have observationally-reconstructed magnetic maps, which are incorporated in our 3D magnetohydrodynamic simulations of their winds. We show that angular-momentum loss and mass-loss rates decrease steadily on evolutionary timescales, although they can vary in a magnetic cycle timescale. Stellar winds are known to emit radiation in the form of thermal bremsstrahlung in the radio spectrum. To calculate the expected radio fluxes from these winds, we solve the radiative transfer equation numerically from first principles. We compute continuum spectra across the frequency range 100 MHz -100 GHz and find maximum radio flux densities ranging from 0.05 -8.3 µJy. At a frequency of 1 GHz and a normalised distance of d = 10 pc, the radio flux density follows 0.24 (Ω/Ω ) 0.9 (d/[10pc]) 2 µJy, where Ω is the rotation rate. This means that the best candidates for stellar wind observations in the radio regime are faster rotators within distances of 10 pc, such as κ 1 Ceti (2.83 µJy) and χ 1 Ori (8.3 µJy). These flux predictions provide a guide to observing solar-type stars across the frequency range 0.1 -100 GHz in the future using the next generation of radio telescopes, such as ngVLA and SKA.

Context. 55 Cancri hosts five known exoplanets, most notably the hot super-Earth 55 Cnc e, which is one of the hottest known transiting super-Earths. Aims. Because of the short orbital separation and host star brightness, 55 Cnc e provides one of the best opportunities for studying star-planet interactions (SPIs). We aim to understand possible SPIs in this system, which requires a detailed understanding of the stellar magnetic field and wind impinging on the planet. Methods. Using spectropolarimetric observations and Zeeman Doppler Imaging, we derived a map of the large-scale stellar magnetic field. We then simulated the stellar wind starting from the magnetic field map, using a 3D magneto-hydrodynamic model. Results. The map of the large-scale stellar magnetic field we derive has an average strength of 3.4 G. The field has a mostly dipolar geometry; the dipole is tilted by 90° with respect to the rotation axis and the dipolar strength is 5.8 G at the magnetic pole. The wind simulations based on this magnetic geometry lead us to conclude that 55 Cnc e orbits inside the Alfvén surface of the stellar wind, implying that effects from the planet on the wind can propagate back to the stellar surface and result in SPI.