2,912 research outputs found
A remark on homogeneous affine varieties and related matters
In this note we give an example of affine quotient where is an
affine algebraic group over an algebraically closed field of characteristic 0
and is a unipotent subgroup not contained in the unipotent radical of .
Some remarks about symmetric algebras of centralizers of nilpotent elements in
simple Lie algebras, in particular cases, are added.Comment: 23 pages - from page 15 to 22 are presented programs for calculatio
Nucleosynthesis of light element isotopes in evolved stars experiencing extended mixing
We present computations of nucleosynthesis in red giants and asymptotic giant
branch stars of Population I experiencing extended mixing. The assumed physical
cause for mass transport is the buoyancy of magnetized structures, according to
recent suggestions. The peculiar property of such a mechanism is to allow for
both fast and slow mixing phenomena, as required for reproducing the spread in
Li abundances displayed by red giants and as discussed in an accompanying
paper. We explore here the effects of this kind of mass transport on CNO and
intermediatemass nuclei and compare the results with the available evidence
from evolved red giants and from the isotopic composition of presolar grains of
AGB origin. It is found that a good general accord exists between predictions
and measurements; in this framework we also show which type of observational
data best constrains the various parameters. We conclude that magnetic
buoyancy, allowing for mixing at rather different speeds, can be an interesting
scenario to explore for explaining together the abundances of CNO nuclei and of
Li.Comment: 8 pages, 7 figures, proceeding of 'The Origin of the Elements Heavier
than Fe' September 24-28, 2008, Torino, Italy. PASA (accepted for
publication
On a variety related to the commuting variety of a reductive Lie algebra
For a reductive Lie algbera over an algbraically closed field of
charasteristic zero,we consider a borel subgroup of its adjoint group, a
Cartan subalgebra contained inthe Lie algebra of and the closure of its
orbit under in the Grassmannian.The variety plays an important role in
the study of the commuting variety. In thisnote, we prove that is
Gorenstein with rational singularities
On the Need for Deep Mixing in AGB Stars of Low Mass
The photospheres of low-mass red giants show CNO isotopic abundances that are
not satisfactorily accounted for by canonical stellar models. The same is true
for the measurements of these isotopes and of the Al/Al ratio in
presolar grains of circumstellar origin. Non-convective mixing, occurring
during both Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stages is
the explanation commonly invoked to account for the above evidence. Recently,
the need for such mixing phenomena on the AGB was questioned, and chemical
anomalies usually attributed to them were suggested to be formed in earlier
phases. We have therefore re-calculated extra-mixing effects in low mass stars
for both the RGB and AGB stages, in order to verify the above claims. Our
results contradict them; we actually confirm that slow transport below the
convective envelope occurs also on the AGB. This is required primarily by the
oxygen isotopic mix and the Al content of presolar oxide grains. Other
pieces of evidence exist, in particular from the isotopic ratios of carbon
stars of type N, or C(N), in the Galaxy and in the LMC, as well as of SiC
grains of AGB origin. We further show that, when extra-mixing occurs in the RGB
phases of population I stars above about 1.2 , this consumes He
in the envelope, probably preventing the occurrence of thermohaline diffusion
on the AGB. Therefore, we argue that other extra-mixing mechanisms should be
active in those final evolutionary phases.Comment: Accepted for publication on "The Astrophysical Journal Letters
From Canonical to Enhanced Extra Mixing in Low-Mass Red Giants: Tidally Locked Binaries
Stellar models which incorporate simple diffusion or shear induced mixing are
used to describe canonical extra mixing in low mass red giants of low and solar
metallicity. These models are able to simultaneously explain the observed Li
and CN abundance changes along upper red giant branch (RGB) in field
low-metallicity stars and match photometry, rotation and carbon isotopic ratios
for stars in the old open cluster M67. The shear mixing model requires that
main sequence (MS) progenitors of upper RGB stars possessed rapidly rotating
radiative cores and that specific angular momentum was conserved in each of
their mass shells during their evolution. We surmise that solar-type stars will
not experience canonical extra mixing on the RGB because their more efficient
MS spin-down resulted in solid-body rotation, as revealed by helioseismological
data for the Sun. Thus, RGB stars in the old, high metallicity cluster NGC 6791
should show no evidence for mixing in their carbon isotopic ratios.
We develop the idea that canonical extra mixing in a giant component of a
binary system may be switched to its enhanced mode with much faster and
somewhat deeper mixing as a result of the giant's tidal spin-up. This scenario
can explain photometric and composition peculiarities of RS CVn binaries. The
tidally enforced enhanced extra mixing might contribute to the star-to-star
abundance variations of O, Na and Al in globular clusters. This idea may be
tested with observations of carbon isotopic ratios and CN abundances in RS CVn
binaries.Comment: 47 pages, 19 figures, accepted for publication in Ap
Hydrodynamical stellar models including rotation, internal gravity waves and atomic diffusion. I. Formalism and tests on Pop I dwarfs
In this paper, we develop a formalism in order to incorporate the
contribution of internal gravity waves to the transport of angular momentum and
chemicals over long time-scales in stars. We show that the development of a
double peaked shear layer acts as a filter for waves, and how the asymmetry of
this filter produces momentum extraction from the core when it is rotating
faster than the surface. Using only this filtered flux, it is possible to
follow the contribution of internal waves over long (evolutionary) time-scales.
We then present the evolution of the internal rotation profile using this
formalism for stars which are spun down via magnetic torquing. We show that
waves tend to slow down the core, creating a "slow" front that may then
propagate from the core to the surface. Further spin down of the surface leads
to the formation of a new front. Finally we show how this momentum transport
reduces rotational mixing in a 1.2Msun, Z=0.02 model, leading to a surface
lithium abundance in agreement with observations in the Hyades.Comment: 14 pages, accepted for publication in A&
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