Low-mass stars are known to have magnetic fields that are believed to be of dynamo origin. Two complementary techniques are principally used to characterise them. Zeeman-Doppler imaging (ZDI) can determine the geometry of the large-scale magnetic field while Zeeman broadening can assess the total unsigned flux including that associated with small-scale structures such as spots. In this work, we study a sample of stars that have been previously mapped with ZDI. We show that the average unsigned magnetic flux follows an activity-rotation relation separating into saturated and unsaturated regimes. We also compare the average photospheric magnetic flux recovered by ZDI, B V , with that recovered by Zeeman broadening studies, B I . In line with previous studies, B V ranges from a few % to ∼20% of B I . We show that a power law relationship between B V and B I exists and that ZDI recovers a larger fraction of the magnetic flux in more active stars. Using this relation, we improve on previous attempts to estimate filling factors, i.e. the fraction of the stellar surface covered with magnetic field, for stars mapped only with ZDI. Our estimated filling factors follow the well-known activity-rotation relation which is in agreement with filling factors obtained directly from Zeeman broadening studies. We discuss the possible implications of these results for flux tube expansion above the stellar surface and stellar wind models.

Context. The principle definition of habitability for exoplanets is whether they can sustain liquid water on their surfaces, i.e. that they orbit within the habitable zone. However, the planet's magnetosphere should also be considered, since without it, an exoplanet's atmosphere may be eroded away by stellar winds. Aims. The aim of this paper is to investigate magnetospheric protection of a planet from the effects of stellar winds from solar-mass stars. Methods. We study hypothetical Earth-like exoplanets orbiting in the host star's habitable zone for a sample of 124 solar-mass stars. These are targets that have been observed by the Bcool Collaboration. Using two wind models, we calculate the magnetospheric extent of each exoplanet. These wind models are computationally inexpensive and allow the community to quickly estimate the magnetospheric size of magnetised Earth-analogues orbiting cool stars. Results. Most of the simulated planets in our sample can maintain a magnetosphere of ∼5 Earth radii or larger. This suggests that magnetised Earth analogues in the habitable zones of solar analogues are able to protect their atmospheres and is in contrast to planets around young active M dwarfs. In general, we find that Earth-analogues around solar-type stars, of age 1.5 Gyr or older, can maintain at least a Paleoarchean Earth sized magnetosphere. Our results indicate that planets around 0.6-0.8 solar-mass stars on the low activity side of the Vaughan-Preston gap are the optimum observing targets for habitable Earth analogues.

Spectropolarimetric observations have been used to map stellar magnetic fields, many of which display strong bands of azimuthal fields that are toroidal. A number of explanations have been proposed to explain how such fields might be generated though none are definitive. In this paper, we examine the toroidal fields of a sample of 55 stars with magnetic maps, with masses in the range 0.1-1.5 M . We find that the energy contained in toroidal fields has a power law dependence on the energy contained in poloidal fields. However the power index is not constant across our sample, with stars less and more massive than 0.5 M having power indices of 0.72±0.08 and 1.25±0.06 respectively. There is some evidence that these two power laws correspond to stars in the saturated and unsaturated regimes of the rotationactivity relation. Additionally, our sample shows that strong toroidal fields must be generated axisymmetrically. The latitudes at which these bands appear depend on the stellar rotation period with fast rotators displaying higher latitude bands than slow rotators. The results in this paper present new constraints for future dynamo studies.

Main sequence low-mass stars are known to spin-down as a consequence of their magnetised stellar winds. However, estimating the precise rate of this spin-down is an open problem. The mass-loss rate, angular momentum-loss rate and the magnetic field properties of low-mass stars are fundamentally linked making this a challenging task. Of particular interest is the stellar magnetic field geometry. In this work, we consider whether non-dipolar field modes contribute significantly to the spin-down of low-mass stars. We do this using a sample of stars that have all been previously mapped with Zeeman-Doppler imaging. For a given star, as long as its mass-loss rate is below some critical mass-loss rate, only the dipolar fields contribute to its spin-down torque. However, if it has a larger mass-loss rate, higher order modes need to be considered. For each star, we calculate this critical mass-loss rate, which is a simple function of the field geometry. Additionally, we use two methods of estimating mass-loss rates for our sample of stars. In the majority of cases, we find that the estimated mass-loss rates do not exceed the critical mass-loss rate and hence, the dipolar magnetic field alone is sufficient to determine the spin-down torque. However, we find some evidence that, at large Rossby numbers, non-dipolar modes may start to contribute.

Magnetic activity and rotation are known to be intimately linked for low-mass stars. Understanding rotation evolution over the stellar lifetime is therefore an important goal within stellar astrophysics. In recent years, there has been increased focus on how the complexity of the stellar magnetic field affects the rate of angular momentum-loss from a star. This is a topic that Zeeman-Doppler imaging (ZDI), a technique that is capable of reconstructing the large-scale magnetic field topology of a star, can uniquely address.Using a potential field source surface model, we estimate the open flux, mass loss-rate and angular momentum-loss rates for a sample of 66 stars that have been mapped with ZDI. We show that the open flux of a star is predominantly determined by the dipolar component of its magnetic field for our choice of source surface radius. We also show that, on the main sequence, the open flux, mass-and angular momentum-loss rates increase with decreasing Rossby number. The exception to this rule is stars less massive than 0.3 M . Previous work suggests that low mass M dwarfs may possess either strong, ordered and dipolar fields or weak and complex fields. This range of field strengths results in a large spread of angular momentum-loss rates for these stars and has important consequences for their spin down behaviour. Additionally, our models do not predict a transition in the mass-loss rates at the so called wind dividing line noted from Lyα studies.