Self-consistent 2D models of fast rotating early-type star

This work aims at presenting the first two-dimensional models of an isolated rapidly rotating star that include the derivation of the differential rotation and meridional circulation in a self-consistent way.We use spectral methods in multidomains, together with a Newton algorithm to determine the steady state solutions including differential rotation and meridional circulation for an isolated non-magnetic, rapidly rotating early-type star. In particular we devise an asymptotic method for small Ekman numbers (small viscosities) that removes the Ekman boundary layer and lifts the degeneracy of the inviscid baroclinic solutions.For the first time, realistic two-dimensional models of fast-rotating stars are computed with the actual baroclinic flows that predict the differential rotation and the meridional circulation for intermediate-mass and massive stars. These models nicely compare with available data of some nearby fast-rotating early-type stars like Ras Alhague ($\alpha$ Oph), Regulus ($\alpha$ Leo), and Vega ($\alpha$ Lyr). It is shown that baroclinicity drives a differential rotation with a slow pole, a fast equator, a fast core, and a slow envelope. The differential rotation is found to increase with mass, with evolution (here measured by the hydrogen mass fraction in the core), and with metallicity. The core-envelope interface is found to be a place of strong shear where mixing will be efficient.Two-dimensional models offer a new view of fast-rotating stars, especially of their differential rotation, which turns out to be strong at the core-envelope interface. They also offer more accurate models for interpreting the interferometric and spectroscopic data of early-type stars.Comment: 16 pages, 17 figures, to appear in Astronomy and Astrophysic

MHD simulations of the solar photosphere

We briefly review the observations of the solar photosphere and pinpoint some open questions related to the magnetohydrodynamics of this layer of the Sun. We then discuss the current modelling efforts, addressing among other problems, that of the origin of supergranulation.Comment: 10 pages, 6 figures; 4th French-Chinese Meeting on Solar Physics Understanding Solar Activity: Advances and Challenges, 4th French-Chinese, Nice, Franc

An algorithm for computing the 2D structure of fast rotating stars

Stars may be understood as self-gravitating masses of a compressible fluid whose radiative cooling is compensated by nuclear reactions or gravitational contraction. The understanding of their time evolution requires the use of detailed models that account for a complex microphysics including that of opacities, equation of state and nuclear reactions. The present stellar models are essentially one-dimensional, namely spherically symmetric. However, the interpretation of recent data like the surface abundances of elements or the distribution of internal rotation have reached the limits of validity of one-dimensional models because of their very simplified representation of large-scale fluid flows. In this article, we describe the ESTER code, which is the first code able to compute in a consistent way a two-dimensional model of a fast rotating star including its large-scale flows. Compared to classical 1D stellar evolution codes, many numerical innovations have been introduced to deal with this complex problem. First, the spectral discretization based on spherical harmonics and Chebyshev polynomials is used to represent the 2D axisymmetric fields. A nonlinear mapping maps the spheroidal star and allows a smooth spectral representation of the fields. The properties of Picard and Newton iterations for solving the nonlinear partial differential equations of the problem are discussed. It turns out that the Picard scheme is efficient on the computation of the simple polytropic stars, but Newton algorithm is unsurpassed when stellar models include complex microphysics. Finally, we discuss the numerical efficiency of our solver of Newton iterations. This linear solver combines the iterative Conjugate Gradient Squared algorithm together with an LU-factorization serving as a preconditionner of the Jacobian matrix.Comment: 40 pages, 12 figures, accepted in J. Comput. Physic

Acoustic oscillations of rapidly rotating polytropic stars. II. Effects of the Coriolis and centrifugal accelerations

Context: With the launch of space missions devoted to asteroseismology (like COROT), the scientific community will soon have accurate measurements of pulsation frequencies in many rapidly rotating stars. Aims: The present work focuses on the effects of rotation on pulsations of rapidly rotating stars when both the Coriolis and centrifugal accelerations require a non-perturbative treatment. Method: We develop a 2-dimensional spectral numerical approach which allows us to compute acoustic modes in centrifugally distorted polytropes including the full influence of the Coriolis force. This method is validated through comparisons with previous studies, and the results are shown to be highly accurate. Results: In the frequency range considered and with COROT's accuracy, we establish a domain of validity for perturbative methods, thus showing the need for complete calculations beyond v.sin i = 50 km/s for a R = 2.3 R_\odot, M = 1.9 M_\odot polytropic star. Furthermore, it is shown that the main differences between complete and perturbative calculations come essentially from the centrifugal distortion.Comment: published in A&A, corrected minor mistakes and updated some reference

Solar supergranulation revealed by granule tracking

Context: Supergranulation is a pattern of the velocity field at the surface of the Sun, which has been known about for more than fifty years, however, no satisfactory explanation of its origin has been proposed. Aims: New observational constraints are therefore needed to guide theoretical approaches which hesitate between scenarios that either invoke a large-scale instability of the surface turbulent convection or a direct forcing by buoyancy. Method: Using the 14-Mpixel CALAS camera at the Pic-du-Midi observatory, we obtained a 7.5h-long sequence of high resolution images with unprecedented field size. Tracking granules, we have determined the velocity field at the Sun's surface in great detail from a scale of 2.5Mm up to 250Mm. Results: The kinetic energy density spectrum shows that supergranulation peaks at 36Mm and spans on scales ranging between 20Mm and 75Mm. The decrease of supergranular flows in the small scales is close to a $k^{-2}$-power law, steeper than the equipartition Kolmogorov one. The probability distribution function of the divergence field shows the signature of intermittency of the supergranulation and thus its turbulent nature.Comment: 4 pages, accepted in Astronomy and Astrophysics (Letters