Differential rotation and meridional flow in the solar supergranulation layer: Measuring the eddy viscosity

We measure the eddy viscosity in the outermost layers of the solar convection zone by comparing the rotation law computed with the Reynolds stress resulting from f-plane simulations of the angular momentum transport in rotating convection with the observed differential rotation pattern. The simulations lead to a negative vertical and a positive horizontal angular momentum transport. The consequence is a subrotation of the outermost layers, as it is indeed indicated both by helioseismology and the observed rotation rates of sunspots. In order to reproduce the observed gradient of the rotation rate a value of about 1.5 x 10^{13} cm/s for the eddy viscosity is necessary. Comparison with the magnetic eddy diffusivity derived from the sunspot decay yields a surprisingly large magnetic Prandtl number of 150 for the supergranulation layer. The negative gradient of the rotation rate also drives a surface meridional flow towards the poles, in agreement with the results from Doppler measurements. The successful reproduction of the abnormally positive horizontal cross correlation (on the northern hemisphere) observed for bipolar groups then provides an independent test for the resulting eddy viscosity.Comment: 6 pages, 8 figures, Astronomy and Astrophysics (subm.

Local models of stellar convection: Reynolds stresses and turbulent heat transport

We study stellar convection using a local three-dimensional MHD model, with which we investigate the influence of rotation and large-scale magnetic fields on the turbulent momentum and heat transport. The former is studied by computing the Reynolds stresses, the latter by calculating the correlation of velocity and temperature fluctuations, both as functions of rotation and latitude. We find that the horisontal correlation, Q_(theta phi), capable of generating horisontal differential rotation, is mostly negative in the southern hemisphere for Coriolis numbers exceeding unity, corresponding to equatorward flux of angular momentum in accordance with solar observations. The radial component Q_(r phi) is negative for slow and intermediate rotation indicating inward transport of angular momentum, while for rapid rotation, the transport occurs outwards. Parametrisation in terms of the mean-field Lambda-effect shows qualitative agreement with the turbulence model of Kichatinov & R\"udiger (1993) for the horisontal part H \propto Q_(theta phi)/cos(theta), whereas for the vertical part, V \propto Q_(r phi)/sin(theta), agreement only for intermediate rotation exists. The Lambda-coefficients become suppressed in the limit of rapid rotation, this rotational quenching being stronger for the V component than for H. We find that the stresses are enhanced by the presence of the magnetic field for field strengths up to and above the equipartition value, without significant quenching. Concerning the turbulent heat transport, our calculations show that the transport in the radial direction is most efficient at the equatorial regions, obtains a minimum at midlatitudes, and shows a slight increase towards the poles. The latitudinal heat transport does not show a systematic trend as function of latitude or rotation.Comment: 26 pages, 20 figures, final published version. For a version with higher resolution figures, see http://cc.oulu.fi/~pkapyla/publ.htm

Meridional flow and differential rotation by gravity darkening in fast rotating solar-type stars

An explanation is presented for the rather strong total surface differential rotation of the observed very young solar-type stars like AB Dor and PZ Tel. Due to its rapid rotation a nonuniform energy flux leaves the stellar core so that the outer convection zone is nonuniformly heated from below. Due to this `gravity darkening' of the equator a meridional flow is created flowing equatorwards at the surface and thus accelerating the equatorial rotation. The effect linearly grows with the normalized pole-equator difference, \epsilon, of the heat-flux at the bottom of the convection zone. A rotation rate of about 9 h leads to \epsilon=0.1 for a solar-type star. In this case the resulting equator-pole differences of the angular velocity at the stellar surface, \delta\Omega, varies from unobservable 0.005/day to the (desired) value of 0.03 day$^{-1}$ when the dimensionless diffusivity factors $c_\nu$ and c_\chi vary between 1 and 0.1 (standard value c_\nu \simeq c_\chi \simeq 0.3, see Table 1.) In all cases the related temperature differences between pole and equator at the surface are unobservably small. The (clockwise) meridional circulation which we obtain flows opposite to the (counterclockwise) circulation appearing as a byproduct in the \Lambda-theory of the nonuniform rotation in outer convection zones. The consequences of this situation for those dynamo theories of stellar activity are discussed which work with the meridional circulation as the dominant magnetic-advection effect in latitude to produce the solar-like form of the butterfly diagram. Key words: Hydrodynamics, Star: rotation, Stars: pre-main sequence, Stellar activityComment: 4 pages, 3 figures, Astronomy and Astrophysics (subm.

The cross helicity at the solar surface by simulations and observations

The quasilinear mean-field theory for driven MHD turbulence leads to the result that the observed cross helicity may directly yield the magnetic eddy diffusivity \eta_{T} of the quiet Sun. In order to model the cross helicity at the solar surface, magnetoconvection under the presence of a vertical large-scale magnetic field is simulated with the nonlinear MHD code NIRVANA. The very robust result of the calculations is that \simeq 2 independent of the applied magnetic field amplitude. The correlation coefficient for the cross helicity is about 10%. Of similar robustness is the finding that the rms value of the magnetic perturbations exceeds the mean-field amplitude (only) by a factor of five. The characteristic helicity speed u_{\eta} as the ratio of the eddy diffusivity and the density scale height for an isothermal sound velocity of 6.6 km/s proves to be 1 km/s for weak fields. This value well coincides with empirical results obtained from the data of the HINODE satellite and the Swedish 1-m Solar Telescope (SST) providing the cross helicity component . Both simulations and observations thus lead to a numerical value of \eta_{T} \simeq 10^12 cm^2 /s as characteristic for the surface of the quiet Sun.Comment: 6 pages, 6 figure

Meridional Circulation and Global Solar Oscillations

We investigate the influence of large-scale meridional circulation on solar p-modes by quasi-degenerate perturbation theory, as proposed by \cite{lavely92}. As an input flow we use various models of stationary meridional circulation obeying the continuity equation. This flow perturbs the eigenmodes of an equilibrium model of the Sun. We derive the signatures of the meridional circulation in the frequency multiplets of solar p-modes. In most cases the meridional circulation leads to negative average frequency shifts of the multiplets. Further possible observable effects are briefly discussed.Comment: 14 pages, 5 figures, submittted to Solar Physics Topical Issue "HELAS

Magnetic Field Topology in Low-Mass Stars: Spectropolarimetric Observations of M Dwarfs

(ABRIDGED) We report here our mapping of the magnetic field topology of the M4 dwarf G 164-31 (or Gl 490B), which is expected to be fully convective, based on time series data collected from 20 hours of observations spread over 3 successive nights with the ESPaDOnS spectropolarimeter. Our tomographic imaging technique applied to time series of rotationally modulated circularly polarized profiles reveals an axisymmetric large-scale poloidal magnetic field on the M4 dwarf. We then apply a synthetic spectrum fitting technique for measuring the average magnetic flux on the star. The flux measured in G 164-31 is Bf = 3.2+-0.4 kG, which is significantly greater than the average value of 0.68 kG determined from the imaging technique. The difference indicates that a significant fraction of the stellar magnetic energy is stored in small-scale structures at the surface of G 164-31. Our H_alpha emission light curve shows evidence for rotational modulation suggesting the presence of localized structure in the chromosphere of this M dwarf. The radius of the M4 dwarf derived from the rotational period and the projected equatorial velocity is at least 30% larger than that predicted from theoretical models. We argue that this discrepancy is likely primarily due to the young nature of G 164-31 rather than primarily due to magnetic field effects, indicating that age is an important factor which should be considered in the interpretation of this observational result. We also report here our polarimetric observations of five other M dwarfs with spectral types from M0 to M4.5, three of them showing strong Zeeman signatures.Comment: 16 pages, 6 figures, accepted by Ap

Doppler images and the underlying dynamo. The case of AF Leporis

The (Zeeman-)Doppler imaging studies of solar-type stars very often reveal large high-latitude spots. This also includes F stars that possess relatively shallow convection zones, indicating that the dynamo operating in these stars differs from the solar dynamo. We aim to determine whether mean-field dynamo models of late-F type dwarf stars can reproduce the surface features recovered in Doppler maps. In particular, we wish to test whether the models can reproduce the high-latitude spots observed on some F dwarfs. The photometric inversions and the surface temperature maps of AF Lep were obtained using the Occamian-approach inversion technique. Low signal-to-noise spectroscopic data were improved by applying the least-squares deconvolution method. The locations of strong magnetic flux in the stellar tachocline as well as the surface fields obtained from mean-field dynamo solutions were compared with the observed surface temperature maps. The photometric record of AF Lep reveals both long- and short-term variability. However, the current data set is too short for cycle-length estimates. From the photometry, we have determined the rotation period of the star to be 0.9660+-0.0023 days. The surface temperature maps show a dominant, but evolving, high-latitude (around +65 degrees) spot. Detailed study of the photometry reveals that sometimes the spot coverage varies only marginally over a long time, and at other times it varies rapidly. Of a suite of dynamo models, the model with a radiative interior rotating as fast as the convection zone at the equator delivered the highest compatibility with the obtained Doppler images.Comment: accepted for publication in Astronomy & Astrophysic

Temperature distribution in magnetized neutron star crusts

We investigate the influence of different magnetic field configurations on the temperature distribution in neutron star crusts. We consider axisymmetric dipolar fields which are either restricted to the stellar crust, ``crustal fields'', or allowed to penetrate the core, ``core fields''. By integrating the two-dimensional heat transport equation in the crust, taking into account the classical (Larmor) anisotropy of the heat conductivity, we obtain the crustal temperature distribution, assuming an isothermal core. Including quantum magnetic field effects in the envelope as a boundary condition, we deduce the corresponding surface temperature distributions. We find that core fields result in practically isothermal crusts unless the surface field strength is well above $10^{15}$ G while for crustal fields with surface strength above a few times $10^{12}$ G significant deviations from isothermality occur at core temperatures inferior or equal to $10^8$ K. At the stellar surface, the cold equatorial region produced by the quantum suppression of heat transport perpendicular to the field in the envelope, present for both core and crustal fields, is significantly extended by the classical suppression at higher densities in the case of crustal fields. This can result, for crustal fields, in two small warm polar regions which will have observational consequences: the neutron star has a small effective thermally emitting area and the X-ray pulse profiles are expected to have a distinctively different shape compared to the case of a neutron star with a core field. These features, when compared with X-ray data on thermal emission of young cooling neutron stars, will open a way to provide observational evidence in favor, or against, the two radically different configurations of crustal or core magnetic fields.Comment: 10 pages, 10 figures, submitted to A&

Magnetospheric Accretion and Ejection of Matter in Resistive Magnetohydrodynamic Simulations

The ejection of matter in the close vicinity of a young stellar object is investigated, treating the accretion disk as a gravitationally bound reservoir of matter. By solving the resistive MHD equations in 2D axisymmetry using our version of the Zeus-3D code with newly implemented resistivity, we study the effect of magnetic diffusivity in the magnetospheric accretion-ejection mechanism. Physical resistivity was included in the whole computational domain so that reconnection is enabled by the physical as well as the numerical resistivity. We show, for the first time, that quasi-stationary fast ejecta of matter, which we call {\em micro-ejections}, of small mass and angular momentum fluxes, can be launched from a purely resistive magnetosphere. They are produced by a combination of pressure gradient and magnetic forces, in presence of ongoing magnetic reconnection along the boundary layer between the star and the disk, where a current sheet is formed. Mass flux of micro-ejection increases with increasing magnetic field strength and stellar rotation rate, and is not dependent on the disk to corona density ratio and amount of resistivity.Comment: 18 pages, many revisions from previous version, accepted in Ap