Pitch Angle Distributions of Solar Energetic Particles and the Local Scattering Properties of the Interplanetary Magnetic Field

An approximate solution of the Fokker-Planck equation containing pitch angle scattering and adiabatic focusing is discussed. For modest focusing effects the omnidirectional density obeys an ordinary diffusion equation with a modified diffusion coefficient. The anisotropic part of the distribution function is properly normalized and split into an even and an odd part. The even part is determined by the ratio between the scattering mean free path and the focusing length and by the degree of polarization of the magnetic field fluctuations. The odd part is determined by the deviation of the pitch angle scattering from isotropic scattering. The method supplies a powerful tool to obtain the local characteristics of pitch angle scattering. It is insensitive to long lasting solar injections and to moderate radial variations of the mean free path. The method is applied to solar particle events observed on Helio-1 and -2

Three-dimensional simulations of near-surface convection in main-sequence stars. IV. Effect of small-scale magnetic flux concentrations on centre-to-limb variation and spectral lines

Magnetic fields affect the local structure of the photosphere of stars. They can considerably influence the radiative properties near the optical surface, flow velocities, and the temperature and pressure profiles. We aim at understanding qualitatively the influence of small magnetic flux concentrations in unipolar plage regions on the centre-to-limb variation of the intensity and its contrast and on the shape of spectral line profiles in cool main-sequence stars. We analyse the bolometric and continuum intensity and its angular dependence of 24 radiative magnetohydrodynamic simulations of the near-surface layers of main-sequence stars with six different sets of stellar parameters (spectral types F to early M) and four different average magnetic field strengths (including the non-magnetic case). We also calculated disc-integrated profiles of three spectral lines. The small magnetic flux concentrations formed in the magnetic runs of simulations have a considerable impact on the intensity and its centre-to-limb variation. Spectral lines are not only broadened owing to the Zeeman effect, but are also strongly affected by the modified thermodynamical structure and flow patterns. This indirect magnetic impact on the line profiles is often bigger than that of the Zeeman effect. The effects of the magnetic field on the radiation leaving the star can be considerable and is not restricted to spectral line broadening and polarisation by the Zeeman effect. The inhomogeneous structure of the magnetic field on small length scales and its impact on (and spatial correlation with) the local thermodynamical structure and the flow field near the surface influence the measurement of the global field properties and stellar parameters. These effects need to be taken into account in the interpretation of observations.Comment: 16 pages, 13+3 figures, 1 appendix, accepted for publication in A&

Three-dimensional simulations of near-surface convection in main-sequence stars - I. Overall structure

The near-surface layers of cool main-sequence stars are structured by convective flows, which are overshooting into the atmosphere. The flows and the associated spatio-temporal variations of density and temperature affect spectral line profiles and thus have an impact on estimates of stellar properties such as effective temperature, gravitational acceleration, and abundances. We aim at identifying distinctive properties of the thermodynamic structure of the atmospheres of different stars and understand their causes. We ran comprehensive 3D radiation hydrodynamics simulations of the near-surface layers of six simulated stars of spectral type F3V to M2V with the MURaM code. We carry out a systematic parameter study of the mean stratifications, flow structures, and the energy flux in these stars.\par Results: We find monotonic trends along the lower main sequence in granule size, flow velocity, and intensity contrast. The convection in the M-star models differs substantially from that of the hotter stars, mainly owing to the more gradual transition from convective to radiative energy transport. While the basic mechanisms driving surface convection in cool stars are the same, the properties of the convection vary along the main sequence. Apart from monotonic trends in rms velocity, intensity contrast, granule size, etc., there is a transition between "naked" and "hidden" granulation around spectral type K5V caused by the (highly non-linear) temperature dependence of the opacity. These variations have to be taken into account when stellar parameters are derived from spectra.Comment: 14 pages, 1 appendix, 15+2 figures, 2 tables; accepted for publication in A&

Three-dimensional simulations of near-surface convection in main-sequence stars - II. Properties of granulation and spectral lines

The atmospheres of cool main-sequence stars are structured by convective flows from the convective envelope that penetrate the optically thin layers and lead to structuring of the stellar atmospheres analogous to solar granulation. The flows have considerable influence on the 3D structure of temperature and pressure and affect the profiles of spectral lines formed in the photosphere. For the set of six 3D radiative (M)HD simulations of cool main-sequence stars described in the first paper of this series, we analyse the near-surface layers. We aim at describing the properties of granulation of different stars and at quantifying the effects on spectral lines of the thermodynamic structure and flows of 3D convective atmospheres. We detected and tracked granules in brightness images from the simulations to analyse their statistical properties, as well as their evolution and lifetime. We calculated spatially resolved spectral line profiles using the line synthesis code SPINOR. To enable a comparison to stellar observations, we implemented a numerical disc-integration, which includes (differential) rotation. Although the stellar parameters change considerably along the model sequence, the properties of the granules are very similar. The impact of the 3D structure of the atmospheres on line profiles is measurable in disc-integrated spectra. Line asymmetries caused by convection are modulated by stellar rotation. The 3D structure of cool stellar atmospheres as shaped by convective flows has to be taken into account when using photospheric lines to determine stellar parameters.Comment: 18 pages, 22 figures, 3 tables; accepted for publication in A&

Three-dimensional simulations of near-surface convection in main-sequence stars. III. The structure of small-scale magnetic flux concentrations

The convective envelopes of cool main-sequence stars harbour magnetic fields with a complex global and local structure. These fields affect the near-surface convection and the outer stellar atmospheres in many ways and are responsible for the observable magnetic activity of stars. Our aim is to understand the local structure in unipolar regions with moderate average magnetic flux density. These correspond to plage regions covering a substantial fraction of the surface of the Sun (and likely also the surface of other Sun-like stars) during periods of high magnetic activity. We analyse the results of 18 local-box magnetohydrodynamics simulations covering the upper layers of the convection zones and the photospheres of cool main-sequence stars of spectral types F to early M. The average vertical field in these simulations ranges from 20 to 500G. We find a substantial variation of the properties of the surface magnetoconvection between main-sequence stars of different spectral types. As a consequence of a reduced efficiency of the convective collapse of flux tubes, M dwarfs lack bright magnetic structures in unipolar regions of moderate field strength. The spatial correlation between velocity and the magnetic field as well as the lifetime of magnetic structures and their sizes relative to the granules vary significantly along the model sequence of stellar types.Comment: 15 pages, 12 figures, accepted for publication in A&