C. P. Johnstone

Stellar winds on the main-sequence - II. The evolution of rotation and winds

Aims. We study the evolution of stellar rotation and wind properties for low-mass main-sequence stars. Our aim is to use rotational evolution models to constrain the mass loss rates in stellar winds and to predict how their properties evolve with time on the mainsequence. Methods. We construct a rotational evolution model that is driven by observed rotational distributions of young stellar clusters. Fitting the free parameters in our model allows us to predict how wind mass loss rate depends on stellar mass, radius, and rotation. We couple the results to the wind model developed in Paper I of this series to predict how wind properties evolve on the main-sequence. Results. We estimate that wind mass loss rate scales with stellar parameters as u M� ∝ R 2 Ω 1.33 � M −3.36 � . We estimate that at young ages, the solar wind likely had a mass loss rate that is an order of magnitude higher than that of the current solar wind. This leads to the wind having a higher density at younger ages; however, the magnitude of this change depends strongly on how we scale wind temperature. Due to the spread in rotation rates, young stars show a large range of wind properties at a given age. This spread in wind properties disappears as the stars age. Conclusions. There is a large uncertainty in our knowledge of the evolution of stellar winds on the main-sequence, due both to our lack of knowledge of stellar winds and the large spread in rotation rates at young ages. Given the sensitivity of planetary atmospheres to stellar wind and radiation conditions, these uncertainties can be significant for our understanding of the evolution of planetary environments.

The extreme ultraviolet and X-ray Sun in Time: High-energy evolutionary tracks of a solar-like star

Aims. We aim to describe the pre-main sequence and main-sequence evolution of X-ray and extreme-ultaviolet radiation of a solar mass star based on its rotational evolution starting with a realistic range of initial rotation rates. Methods. We derive evolutionary tracks of X-ray radiation based on a rotational evolution model for solar mass stars and the rotation-activity relation. We compare these tracks to X-ray luminosity distributions of stars in clusters with different ages. Results. We find agreement between the evolutionary tracks derived from rotation and the X-ray luminosity distributions from observations. Depending on the initial rotation rate, a star might remain at the X-ray saturation level for very different time periods, approximately from 10 Myr to 300 Myr for slow and fast rotators, respectively. Conclusions. Rotational evolution with a spread of initial conditions leads to a particularly wide distribution of possible X-ray luminosities in the age range of 20 to 500 Myrs, before rotational convergence and therefore X-ray luminosity convergence sets in. This age range is crucial for the evolution of young planetary atmospheres and may thus lead to very different planetary evolution histories.

Classical T Tauri stars: magnetic fields, coronae and star–disc interactions

The magnetic fields of young stars set their coronal properties and control their spin evolution via the star–disc interaction and outflows. Using 14 magnetic maps of 10 classical T Tauri stars (CTTSs) we investigate their closed X-ray emitting coronae, their open wind-bearing magnetic fields and the geometry of magnetospheric accretion flows. The magnetic fields of all the CTTSs are multipolar. Stars with simpler (more dipolar) large-scale magnetic fields have stronger fields, are slower rotators and have larger X-ray emitting coronae compared to stars with more complex large-scale magnetic fields. The field complexity controls the distribution of open and closed field regions across the stellar surface, and strongly influences the location and shapes of accretion hot spots. However, the higher order field components are of secondary importance in determining the total unsigned open magnetic flux, which depends mainly on the strength of the dipole component and the stellar surface area. Likewise, the dipole component alone provides an adequate approximation of the disc truncation radius. For some stars, the pressure of the hot coronal plasma dominates the stellar magnetic pressure and forces open the closed field inside the disc truncation radius. This is significant as accretion models generally assume that the magnetic field has a closed geometry out to the inner disc edge.

Stellar winds on the main-sequence: I. Wind model

Aims: We develop a method for estimating the properties of stellar winds for low-mass main-sequence stars between masses of 0.4 and 1.1 solar masses at a range of distances from the star. Methods: We use 1D thermal pressure driven hydrodynamic wind models run using the Versatile Advection Code. Using in situ measurements of the solar wind, we produce models for the slow and fast components of the solar wind. We consider two radically different methods for scaling the base temperature of the wind to other stars: in Model A, we assume that wind temperatures are fundamentally linked to coronal temperatures, and in Model B, we assume that the sound speed at the base of the wind is a fixed fraction of the escape velocity. In Paper II of this series, we use observationally constrained rotational evolution models to derive wind mass loss rates. Results: Our model for the solar wind provides an excellent description of the real solar wind far from the solar surface, but is unrealistic within the solar corona. We run a grid of 1200 wind models to derive relations for the wind properties as a function of stellar mass, radius, and wind temperature. Using these results, we explore how wind properties depend on stellar mass and rotation. Conclusions: Based on our two assumptions about the scaling of the wind temperature, we argue that there is still significant uncertainty in how these properties should be determined. Resolution of this uncertainty will probably require both the application of solar wind physics to other stars and detailed observational constraints on the properties of stellar winds. In the final section of this paper, we give step by step instructions for how to apply our results to calculate the stellar wind conditions far from the stellar surface.

THE EVOLUTION OF STELLAR ROTATION AND THE HYDROGEN ATMOSPHERES OF HABITABLE-ZONE TERRESTRIAL PLANETS

Terrestrial planets formed within gaseous protoplanetary disks can accumulate significant hydrogen envelopes. The evolution of such an atmosphere due to XUV driven evaporation depends on the activity evolution of the host star, which itself depends sensitively on its rotational evolution, and therefore on its initial rotation rate. In this letter, we derive an easily applicable method for calculating planetary atmosphere evaporation that combines models for a hydrostatic lower atmosphere and a hydrodynamic upper atmosphere. We show that the initial rotation rate of the central star is of critical importance for the evolution of planetary atmospheres and can determine if a planet keeps or loses its primordial hydrogen envelope. Our results highlight the need for a detailed treatment of stellar activity evolution when studying the evolution of planetary atmospheres.

Modelling stellar coronae from surface magnetograms: the role of missing magnetic flux

Recent advances in spectropolarimetry have allowed the reconstruction of stellar coronal magnetic fields. This uses Zeeman–Doppler magnetograms (ZDI) of the surface magnetic field as a lower boundary condition. The ZDI maps, however, suffer from the absence of information about the magnetic field over regions of the surface due to the presence of dark starspots and portions of the surface out of view due to a tilt in the rotation axis. They also suffer from finite resolution which leads to small-scale field structures being neglected. This paper explores the effects of this loss of information on the extrapolated coronal fields. For this, we use simulated stellar surface magnetic maps for two hypothetical stars. Using the potential field approximation, the coronal fields and emission measures are calculated. This is repeated for the cases of missing information due to, (i) starspots, (ii) a large area of the stellar surface out of view and (iii) a finite resolution. The largest effect on the magnetic field structure arises when a significant portion of the stellar surface remains out of view. This changes the nature of the field lines that connect to this obscured hemisphere. None the less, the field structure in the visible hemisphere is reliably reproduced. Thus, the calculation of the locations and surface filling factors of accretion funnels is reasonably well reproduced for the observed hemisphere. The decrease with height of the magnetic pressure, which is important in calculating disc truncation radii for accreting stars, is also largely unaffected in the equatorial plane. The fraction of surface flux that is open and therefore able to supply angular momentum loss in a wind, however, is often overestimated in the presence of missing flux. The magnitude and rotational modulation of the calculated emission measures is consistently decreased by the loss of magnetic flux in dark starspots. For very inactive stars, this may make it impossible to recover a magnetic cycle in the coronal emission. Finite resolution has little effect on those quantities, such as the emission measure and the average coronal electron density, that can currently be observed.

EUV-driven mass-loss of protoplanetary cores with hydrogen-dominated atmospheres: the influences of ionization and orbital distance

We investigate the loss rates of the hydrogen atmospheres of terrestrial planets with a range of masses and orbital distances by assuming a stellar extreme ultraviolet (EUV) luminosity that is 100 times stronger than that of the current Sun. We apply a 1D upper atmosphere radiation absorption and hydrodynamic escape model that takes into account ionization, dissociation and recombination to calculate hydrogen mass loss rates. We study the effects of the ionization, dissociation and recombination on the thermal mass loss rates of hydrogen-dominated super-Earths and compare the results to those obtained by the energy-limited escape formula which is widely used for mass loss evolution studies. Our results indicate that the energy-limited formula can to a great extent over- or underestimate the hydrogen mass loss rates by amounts that depend on the stellar EUV flux and planetary parameters such as mass, size, effective temperature, and EUV absorption radius.

Identifying the “true” radius of the hot sub-Neptune CoRoT-24b by mass loss modelling

For the hot exoplanets CoRoT-24b and CoRoT-24c, observations have provided transit radii R-T of 3.7 +/- 0.4R(circle plus) and 4.9 +/- 0.5R(circle plus), and masses of = 5.7M(circle plus) and 28 +/- 11M(circle plus), respectively. We study their upper atmosphere structure and escape applying an hydrodynamic model. Assuming R-T +/- R-PL, where R-PL is the planetary radius at the pressure of 100 mbar, we obtained for CoRoT-24b unrealistically high thermally driven hydrodynamic escape rates. This is due to the planets high temperature and low gravity, independent of the stellar EUV flux. Such high escape rates could last only for< 100 Myr, while R-PL shrinks till the escape rate becomes less than or equal to the maximum possible EUV-driven escape rate. For CoRoT-24b, R-PL must be therefore located at approximate to 1.9-2.2R(circle plus) and high altitude hazes/clouds possibly extinct the light at R-T. Our analysis constraints also the planets mass to be 5-5.7M(circle plus). For CoRoT-24c, R-PL and R-T lie too close together to be distinguished in the same way. Similar differences between R-PL and R-T may be present also for other hot, low-density sub-Neptunes.

The contribution of star-spots to coronal structure

Significant progress has been made recently in our understanding of the structure of stellar magnetic fields, thanks to advances in detection methods such as Zeeman-Doppler Imaging. The extrapolation of this surface magnetic field into the corona has provided 3D models of the coronal magnetic field and plasma. This method is sensitive mainly to the magnetic field in the bright regions of the stellar surface. The dark (spotted) regions are censored because the Zeeman signature there is suppressed. By modelling the magnetic field that might have been contained in these spots, we have studied the effect that this loss of information might have on our understanding of the coronal structure. As examples, we have chosen two stars (V374 peg and AB Dor) that have very different magnetograms and patterns of spot coverage. We find that the effect of the spot field depends not only on the relative amount of flux in the spots, but also its distribution across the stellar surface. For a star such as AB Dor with a high spot coverage and a large polar spot, at its greatest effect the spot field may almost double the fraction of the flux that is open (hence decreasing the spindown time) while at the same time increasing the X-ray emission measure by two orders of magnitude and significantly affecting the X-ray rotational modulation.

The coronal temperatures of low-mass main-sequence stars

Aims. We study the X-ray emission of low-mass main-sequence stars to derive a reliable general scaling law between coronal temperature and the level of X-ray activity. Methods. We collect ROSAT measurements of hardness ratios and X-ray luminosities for a large sample of stars to derive which stellar X-ray emission parameter is most closely correlated with coronal temperature. We calculate average coronal temperatures for a sample of 24 low-mass main-sequence stars with measured emission measure distributions (EMDs) collected from the literature. These EMDs are based on high-resolution X-ray spectra measured by XMM-Newton and Chandra. Results. We confirm that there is one universal scaling relation between coronal average temperature and surface X-ray flux, Fx, that applies to all low-mass main-sequence stars. We find that coronal temperature is related to Fx by Tcor=0.11 Fx^0.26, where Tcor is in MK and Fx is in erg/s/cm^2.