47 research outputs found
Latitudinal Propagation of Thermal Rossby Waves in Stellar Convection Zones
Using an analytic model, we derive the eigenfrequencies for thermal Rossby
waves that are trapped radially and latitudinally in an isentropically
stratified atmosphere. We ignore the star's curvature and work in an equatorial
f-plane geometry. The propagation of inertial waves is found to be sensitive to
the relative direction of the wave vector to the zonal direction. Prograde
propagating thermal Rossby waves are naturally trapped in the radial direction
for frequencies above a critical threshold, which depends on the angle of
propagation. Below the threshold frequency, there exists a continuous spectrum
of prograde and retrograde inertial waves that are untrapped in an isentropic
atmosphere, but can be trapped by gradients in the specific entropy density
such as occurs in a stellar convection zone. Finally, we discuss the
implications of these waves on recent observations of inertial oscillations in
the Sun, as well as in numerical simulations.Comment: 14 pages, 5 figures, accepted by Ap
Dwindling Surface Cooling of a Rotating Jovian Planet Leads to a Convection Zone that Grows to a Finite Depth
Recent measurements of Jupiter's gravitational field (by Juno) and seismology
of Saturn's rings (by Cassini) strongly suggest that both planets have a
stably-stratified core that still possesses a primordial gradient in the
concentration of heavy elements. The existence of such a "diffusely" stratified
core has been a surprise as it was long expected that the Jovian planets should
be fully convective and hence fully mixed. A vigorous zone of convection,
driven by surface cooling, forms at the surface and deepens through entrainment
of fluid from underneath. In fact, it was believed that this convection zone
should grow so rapidly that the entire planet would be consumed in less than a
million years. Here we suggest that two processes, acting in concert, present a
solution to this puzzle. All of the giant planets are rapidly rotating and have
a cooling rate that declines with time. Both of these effects reduce the rate
of fluid entrainment into the convection zone. Through the use of an analytic
prescription of entrainment in giant planets, we demonstrate that these two
effects, rotation and dwindling surface cooling, result in a convection zone
which initially grows but eventually stalls. The depth to which the convective
interface asymptotes depends on the rotation rate and on the stratification of
the stable interior. Conversely, in a nonrotating planet, or in a planet that
maintains a higher level of cooling than current models suggest, the convection
zone deepens forever, eventually spanning the entire planet.Comment: 7 pages, 2 figures, accepted for publication by Astrophysical Journal
Letter
Exploring the Influence of Density Contrast on Solar Near-Surface Shear
The advent of helioseismology has determined in detail the average rotation rate of the Sun as a function of radius and latitude. These data immediately reveal two striking boundary layers of shear in the solar convection zone (CZ): a tachocline at the base, where the differential rotation of the CZ transitions to solid-body rotation in the radiative zone, and a 35-Mm-thick near-surface shear layer (NSSL) at the top, where the rotation rate slows by about 5% with increasing radius. Though asteroseismology cannot probe the differential rotation of distant stars to the same level of detail that helioseismology can achieve for the Sun, it is possible that many cool stars with outer convective envelopes possess similar differential rotation characteristics, including both a tachocline and a NSSL. Here we present the results of 3D global hydrodynamic simulations of spherical-shell convection for a Sun-like star at different levels of density contrast across the shell. The simulations with high stratification possess characteristics of near-surface shear, especially at low latitudes. We discuss in detail the dynamical balance of torques giving rise to the NSSL in our models and interpret what these balances imply for the real Sun. We further discuss the dynamical causes that may serve to wipe out near-surface shear at high latitudes, and conclude by offering some theories as to how this problem might be tackled in future work
Rotation reduces convective mixing in Jupiter and other gas giants
Recent measurements of Jupiter's gravitational moments by the Juno spacecraft
and seismology of Saturn's rings suggest that the primordial composition
gradients in the deep interior of these planets have persisted since their
formation. One possible explanation is the presence of a double-diffusive
staircase below the planet's outer convection zone, which inhibits mixing
across the deeper layers. However, hydrodynamic simulations have shown that
these staircases are not long-lasting and can be disrupted by overshooting
convection. In this paper we suggests that planetary rotation could be another
factor for the longevity of primordial composition gradients. Using rotational
mixing-length theory and 3D hydrodynamic simulations, we demonstrate that
rotation significantly reduces both the convective velocity and the mixing of
primordial composition gradients. In particular, for Jovian conditions at
after formation, rotation reduces the convective
velocity by a factor of 6, and in turn, the kinetic energy flux available for
mixing gets reduced by a factor of . This leads to an entrainment
timescale that is more than two orders of magnitude longer than without
rotation. We encourage future hydrodynamic models of Jupiter and other gas
giants to include rapid rotation, because the decrease in the mixing efficiency
could explain why Jupiter and Saturn are not fully mixed.Comment: Accepted for publication in the Astrophysical Journal Letter