Planetesimal disk evolution driven by embryo-planetesimal gravitational scattering

The process of gravitational scattering of planetesimals by a massive protoplanetary embryo is explored theoretically. We propose a method to describe the evolution of the disk surface density, eccentricity, and inclination caused by the embryo-planetesimal interaction. It relies on the analytical treatment of the scattering in two extreme regimes of the planetesimal epicyclic velocities: shear-dominated (dynamically ``cold'') and dispersion-dominated (dynamically ``hot''). In the former, planetesimal scattering can be treated as a deterministic process. In the latter, scattering is mostly weak because of the large relative velocities of interacting bodies. This allows one to use the Fokker-Planck approximation and the two-body approximation to explore the disk evolution. We compare the results obtained by this method with the outcomes of the direct numerical integrations of planetesimal orbits and they agree quite well. In the intermediate velocity regime an approximate treatment of the disk evolution is proposed based on interpolation between the two extreme regimes. We also calculate the rate of embryo's mass growth in an inhomogeneous planetesimal disk and demonstrate that it is in agreement with both the simulations and earlier calculations. Finally we discuss the question of the direction of the embryo-planetesimal interaction in the dispersion-dominated regime and demonstrate that it is repulsive. This means that the embryo always forms a gap in the disk around it, which is in contrast with the results of other authors. The machinery developed here will be applied to realistic protoplanetary systems in future papers.Comment: 40 pages, 9 figures, submitted to A

The evolution of surface magnetic fields in young solar-type stars

The surface rotation rates of young solar-type stars decrease rapidly with age from the end of the pre-main sequence though the early main sequence. This suggests that there is also an important change in the dynamos operating in these stars, which should be observable in their surface magnetic fields. Here we present early results in a study aimed at observing the evolution of these magnetic fields through this critical time period. We are observing stars in open clusters and stellar associations to provide precise ages, and using Zeeman Doppler Imaging to characterize the complex magnetic fields. Presented here are results for six stars, three in the in the beta Pic association (~10 Myr old) and three in the AB Dor association (~100 Myr old).Comment: To appear in the proceedings of IAU symposium 302: Magnetic fields throughout stellar evolution. 2 pages, 3 figure

Generalized Miller Formulae

We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding generalizes the Miller formula to any order of non-linearity. In the frequency-degenerate case, it yields the spectral dependence of non-linear refractive indices of arbitrary order.Comment: 12 pages, 1 figure (4 panels

Temporal fluctuations in the differential rotation of cool active stars

This paper reports positive detections of surface differential rotation on two rapidly rotating cool stars at several epochs, by using stellar surface features (both cool spots and magnetic regions) as tracers of the large scale latitudinal shear that distorts the convective envelope in this type of stars. We also report definite evidence that this differential rotation is different when estimated from cool spots or magnetic regions, and that it undergoes temporal fluctuations of potentially large amplitude on a time scale of a few years. We consider these results as further evidence that the dynamo processes operating in these stars are distributed throughout the convective zone rather than being confined at its base as in the Sun. By comparing our observations with two very simple models of the differential rotation within the convective zone, we obtain evidence that the internal rotation velocity field of the stars we investigated is not like that of the Sun, and may resemble that we expect for rapid rotators. We speculate that the changes in differential rotation result from the dynamo processes (and from the underlying magnetic cycle) that periodically converts magnetic energy into kinetic energy and vice versa. We emphasise that the technique outlined in this paper corresponds to the first practical method for investigating the large scale rotation velocity field within convective zones of cool active stars, and offers several advantages over asteroseismology for this particular purpose and this specific stellar class.Comment: 14 pages, 4 figure

A polarity reversal in the large-scale magnetic field of the rapidly rotating Sun HD 190771

Aims. We investigate the long-term evolution of the large-scale photospheric magnetic field geometry of the solar-type star HD 190771. With fundamental parameters very close to those of the Sun except for a shorter rotation period of 8.8 d, HD 190771 provides us with a first insight into the specific impact of the rotation rate in the dynamo generation of magnetic fields in 1 $M_\odot$ stars. Methods. We use circularly polarized, high-resolution spectra obtained with the NARVAL spectropolarimeter (Observatoire du Pic du Midi, France) and compute cross-correlation line profiles with high signal-to-noise ratio to detect polarized Zeeman signatures. From three phase-resolved data sets collected during the summers of 2007, 2008, and 2009, we model the large-scale photospheric magnetic field of the star by means of Zeeman-Doppler imaging and follow its temporal evolution. Results. The comparison of the magnetic maps shows that a polarity reversal of the axisymmetric component of the large-scale magnetic field occurred between 2007 and 2008, this evolution being observed in both the poloidal and toroidal magnetic components. Between 2008 and 2009, another type of global evolution occured, characterized by a sharp decrease of the fraction of magnetic energy stored in the toroidal component. These changes were not accompanied by significant evolution in the total photospheric magnetic energy. Using our spectra to perform radial velocity measurements, we also detect a very low-mass stellar companion to HD 190771.Comment: Accepted by Astronomy and Astrophysics (Letter to the Editor