2,065 research outputs found
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 ( Oph), Regulus
( Leo), and Vega ( 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
Two-dimensional models of early-type fast rotating stars: new challenges in stellar physics
Two-dimensional models of rapidly rotating stars are already unavoidable for
the interpretation of interferometric or asteroseismic data of this kind of
stars. When combined with time evolution, they will allow the including of a
more accurate physics for the computation of element transport and the
determination of surface abundances. In addition, modeling the evolution of
rotation will improve gyrochronology.
Presently, two-dimensional ESTER models predict the structure and the
large-scale flows (differential rotation and meridional circulation) of stars
with mass larger than 1.7Msun at any rotation rate. Main sequence evolution can
be mimicked by varying the hydrogen content of the convective core. Models have
been successfully tested on half a dozen of nearby fast rotating stars observed
with optical or infra-red interferometers. They are now the right tool to
investigate the oscillation spectrum of early-type fast rotators.Comment: 10 pages, to appear in the proceedings of the conference "New
advances in stellar physics: from microscopic to macroscopic processes",
Roscoff, May 201
Gravity Darkening in Binary Stars
Context.Interpretation of light curves of many types of binary stars requires
the inclusion of the (cor)relation between surface brightness and local
effective gravity. Until recently, this correlation has always been modeled by
a power law relating the flux or the effective temperature and the effective
gravity, namely T_eff {\alpha} g_eff^{\beta}.
Aims. We look for a simple model that can describe the variations of the flux
at the surface of stars belonging to a binary system.
Methods. This model assumes that the energy flux is a divergence-free vector
anti-parallel to the effective gravity. The effective gravity is computed from
the Roche model.
Results. After explaining in a simple manner the old result of Lucy (1967),
which says that {\beta}=0.08 for solar type stars, we first argue that
one-dimensional models should no longer be used to evaluate gravity darkening
laws. We compute the correlation between log T_eff and log g_eff using a new
approach that is valid for synchronous, weakly magnetized, weakly irradiated
binaries. We show that this correlation is approximately linear, validating the
use of a power law relation between effective temperature and effective gravity
as a first approximation. We further show that the exponent {\beta} of this
power law is a slowly varying function, which we tabulate, of the mass ratio of
the binary star and the Roche lobe filling factor of the stars of the system.
The exponent {\beta} remains mostly in the interval (0.20, 0.25) if extreme
mass ratios are eliminated.
Conclusions. For binary stars that are synchronous, weakly magnetized and
weakly irradiated, the gravity darkening exponent is well constrained and may
be removed from the free parameters of the models
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
Physical processes leading to surface inhomogeneities: the case of rotation
In this lecture I discuss the bulk surface heterogeneity of rotating stars,
namely gravity darkening. I especially detail the derivation of the omega-model
of Espinosa Lara & Rieutord (2011), which gives the gravity darkening in
early-type stars. I also discuss the problem of deriving gravity darkening in
stars owning a convective envelope and in those that are members of a binary
system.Comment: 23 pages, 11 figure, Lecture given to the school on the cartography
of the Sun and the stars (May 2014 in Besan\c{c}on), to appear in LNP, Neiner
and Rozelot edts V2: typos correcte
The effect of domain and framing on elicited risk aversion
Experimental literature has found that risk attitudes are not robust to different elicitation techniques. However, most comparisons across elicitation methods involve different rewards and framings simultaneously. Our experimental design helps to disentangle the effect of these two factors. We consider two different personal rewards (money domain and grade domain) and two different scenarios while keeping the reward constant (lottery framing and exam framing). We find no differences in elicited risk aversion between the two domains. However, framing matters: elicited risk aversion is lower in the exam framing.Gobierno Vasco (IT1336-19), MINECO/ FEDER (PID2019-108718GB-I00) and Fundacion Ramon Areces (XVII concurso Nacional para la Adjudicacion de Ayudas a la Investigacion en Ciencias Sociales). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
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