A two-dimensional mixing length theory of convective transport

The helioseismic observations of the internal rotation profile of the Sun raise questions about the two-dimensional (2D) nature of the transport of angular momentum in stars. Here we derive a convective prescription for axisymmetric (2D) stellar evolution models. We describe the small scale motions by a spectrum of unstable linear modes in a Boussinesq fluid. Our saturation prescription makes use of the angular dependence of the linear dispersion relation to estimate the anisotropy of convective velocities. We are then able to provide closed form expressions for the thermal and angular momentum fluxes with only one free parameter, the mixing length. We illustrate our prescription for slow rotation, to first order in the rotation rate. In this limit, the thermodynamical variables are spherically symetric, while the angular momentum depends both on radius and latitude. We obtain a closed set of equations for stellar evolution, with a self-consistent description for the transport of angular momentum in convective regions. We derive the linear coefficients which link the angular momentum flux to the rotation rate ($\Lambda$- effect) and its gradient ($\alpha$-effect). We compare our results to former relevant numerical work.Comment: MNRAS accepted, 10 pages, 1 figure, version prior to language editio

Seismic tests for solar models with tachocline mixing

We have computed accurate 1-D solar models including both a macroscopic mixing process in the solar tachocline as well as up-to-date microscopic physical ingredients. Using sound speed and density profiles inferred through primary inversion of the solar oscillation frequencies coupled with the equation of thermal equilibrium, we have extracted the temperature and hydrogen abundance profiles. These inferred quantities place strong constraints on our theoretical models in terms of the extent and strength of our macroscopic mixing, on the photospheric heavy elements abundance, on the nuclear reaction rates such as $S_{11}$ and $S_{34}$ and on the efficiency of the microscopic diffusion. We find a good overall agreement between the seismic Sun and our models if we introduce a macroscopic mixing in the tachocline and allow for variation within their uncertainties of the main physical ingredients. From our study we deduce that the solar hydrogen abundance at the solar age is $X_{\rm inv}=0.732\pm 0.001$ and that based on the $^9$Be photospheric depletion, the maximum extent of mixing in the tachocline is 5% of the solar radius. The nuclear reaction rate for the fundamental $pp$ reaction is found to be $S_{11}(0)=4.06\pm 0.07$ $10^{-25}$ MeV barns, i.e., 1.5% higher than the present theoretical determination. The predicted solar neutrino fluxes are discussed in the light of the new SNO/SuperKamiokande results.Comment: 16 pages, 12 figures, A&A in press (1) JILA, University of Colorado, Boulder, CO 80309-0440, USA, (2) LUTH, Observatoire de Paris-Meudon, 92195 Meudon, France, (3) Tata Institute of Fundamental Research, Homi Bhabha road, Mumbai 400005, India, (4) Department of Physics, University of Mumbai, Mumbai 400098, Indi

Solar rotation rate and its gradients during cycle 23

Available helioseismic data now span almost the entire solar activity cycle 23 making it possible to study solar-cycle related changes of the solar rotation rate in detail. In this paper we study how the solar rotation rate, in particular, the zonal flows change with time. In addition to the zonal flows that show a well known pattern in the solar convection zone, we also study changes in the radial and latitudinal gradients of the rotation rate, particularly in the shear layer that is present in the immediate sub-surface layers of the Sun. In the case of the zonal-flow pattern, we find that the band indicating fast rotating region close to the equator seems to have bifurcated around 2005. Our investigation of the rotation-rate gradients show that the relative variation in the rotation-rate gradients is about 20% or more of their average values, which is much larger than the relative variation in the rotation rate itself. These results can be used to test predictions of various solar dynamo models.Comment: To appear in ApJ. Fig 5 has been corrected in this versio

Genome-wide association study in two cohorts from a multi-generational mouse advanced intercross line highlights the difficulty of replication due to study-specific heterogeneity

There has been extensive discussion of the Replication Crisis in many fields, including genome-wide association studies

Is the solar convection zone in strict thermal wind balance?

Context: The solar rotation profile is conical rather than cylindrical as one could expect from classical rotating fluid dynamics (e.g. Taylor-Proudman theorem). Thermal coupling to the tachocline, baroclinic effects and latitudinal transport of heat have been advocated to explain this peculiar state of rotation. Aims: To test the validity of thermal wind balance in the solar convection zone using helioseismic inversions for both the angular velocity and fluctuations in entropy and temperature. Methods: Entropy and temperature fluctuations obtained from 3-D hydrodynamical numerical simulations of the solar convection zone are compared with solar profiles obtained from helioseismic inversions. Results: The temperature and entropy fluctuations in 3-D numerical simulations have smaller amplitude in the bulk of the solar convection zone than those found from seismic inversions. Seismic inversion find variations of temperature from about 1 K at the surface up to 100 K at the base of the convection zone while in 3-D simulations they are of order 10 K throughout the convection zone up to 0.96 $R_{\odot}$. In 3-D simulations, baroclinic effects are found to be important to tilt the isocontours of $\Omega$ away from a cylindrical profile in most of the convection zone helped by Reynolds and viscous stresses at some locations. By contrast the baroclinic effect inverted by helioseismology are much larger than what is required to yield the observed angular velocity profile. Conclusion: The solar convection does not appear to be in strict thermal wind balance, Reynolds stresses must play a dominant role in setting not only the equatorial acceleration but also the observed conical angular velocity profile.Comment: 8 pages, 6 figures (low resolution), Accepted by Astronomy and Astrophysics - Affiliation: (1) AIM, CEA/DSM-CNRS-Univ. Paris Diderot, IRFU/SAp, France & (2) LUTH, Observatoire de Paris, CNRS-Univ. Paris Diderot, France ; (3) Tata Institute of Fundamental Research, India; (4) Centre for Basic Sciences, University of Mumbai, Indi