303 research outputs found
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.
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 when the dimensionless diffusivity factors 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.
Differential rotation of main sequence F stars
The differential rotation of a 1.2 zero age MS star (spectral type
F8) is computed and the results are compared with those from a similar model of
the Sun. The rotation pattern is determined by solving the Reynolds equation
including the convective energy transport. The latter is anisotropic due to the
Coriolis force causing a horizontal temperature gradient of ~ 7 K between the
poles and the equator. Comparison of the transport mechanisms of angular
momentum (the eddy viscosity, the -effect and the meridional flow)
shows that for the F star the -effect is the most powerful transporter
for rotation periods of 7 d or less. In the limit of very fast rotation the
-effect is balanced by the meridional flow alone and the rotation is
nearly rigid. The rotation pattern found for the F star is very similar to the
solar rotation law, but the horizontal shear is about twice the solar value. As
a function of the rotation period, the total equator-pole difference of the
angular velocity has a (slight) maximum at a period of 7 d and (slowly)
vanishes in both the limiting cases of very fast and very slow rotation. A
comparison of the solar models with those for the F-type star shows a much
stronger dependence of the differential surface rotation on the stellar
luminosity rather than on the rotation rate.Comment: 7 pages, 10 figure
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
Cycle period, differential rotation and meridional flow for early M dwarf stars
Recent observations suggest the existence of two characteristic cycle times
for early-type M stars dependent on the rotation period. They are of order one
year for the fast rotators ( day) and of order 4 years for the
slower rotators. Additionally, the equator-to-pole differences of the rotation
rates with up to 0.03 rad d are known from Kepler data
for the fast-rotating stars. These values are well-reproduced by the theory of
large-scale flows in rotating convection zones on the basis of the
effect. The resulting amplitudes of the bottom value of the
meridional circulation allows the calculation of the travel time from pole to
equator at the base of the convection zone of early-type M stars. These travel
times strongly increase with rotation period and they always exceed the
observed cycle periods. Therefore, the operation of an advection-dominated
dynamo in early M dwarfs, where the travel time must always be shorter than the
cycle period, is not confirmed by our model nor the data
Seismic inference of differential rotation in Procyon A
The differential rotation of the F5V-IV star Procyon A is computed for a
class of models which are consistent with recent astrometric and asteroseismic
data. The rotation pattern is determined by solving the Reynolds equation for
motion, including the convective energy transport, where the latter is
anisotropic owing to the Coriolis force action which produces a horizontal
temperature gradient between the poles and the equator. All the models show a
decrease of the rotation rate with increasing radius and solar-type isorotation
surfaces with the equator rotating faster than the poles, the horizontal
rotational shear being much smaller for models with a less extended convective
envelope. The meridional flow circulation can be either clockwise or
counter-clockwise, and in some cases a double latitudinal cell appears. The
rotational splittings are calculated for low degree -modes with
and , and it is shown that, for modes with , the stronger is
the horizontal differential rotation shear the weaker the effect on the average
rotational splitting expected, whilst the opposite happens for the mode with
. On the basis of the present study, a resolution of in
individual oscillation frequencies seems to be necessary to test the different
dynamical behaviour of the proposed models, that appears barely achievable even
in the forthcoming space missions. However, the average over several observed
splittings could produce the required accuracy.Comment: 9 pages, 7 figures, A&A to appea
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