648 research outputs found
Bohr-Sommerfeld conditions for several commuting Hamiltonians
The goal of this paper is to find the quantization conditions of
Bohr-Sommerfeld of k quantum Hamiltonians acting on the euclidian space of
dimension n, depending on a small parameter h, and which commute to each other.
That is we determine, around a regular energy level E of the euclidian space of
dimension k the principal term of the asymptotics in h of the eigenvalues of
the operators that are associated to a common eigenfunction. Thus we localize
the so-called joint spectrum of the operators.
Under the assumption that the classical Hamiltonian flow of the joint
principal symbol is periodic with constant periods on the energy level of E(a
submanifold of codimension k) we prove that the part of the joint spectrum
lying in a small neighbourhood of E is localized near a lattice of size h
determined in terms of actions and Maslov indices. The multiplicity of the
spectrum is also determined.Comment: 18 pages, LaTe
Calibration of the CH and CN Variations Among Main Sequence Stars in M71 and in M13
An analysis of the CN and CH band strengths measured in a large sample of M71
and M13 main sequence stars by Cohen (1999a,b) is undertaken using synthetic
spectra to quantify the underlying C and N abundances. In the case of M71 it is
found that the observed CN and CH band strengths are best matched by the
{\it{identical}} C/N/O abundances which fit the bright giants, implying: 1)
little if any mixing is taking place during red giant branch ascent in M71, and
2) a substantial component of the C and N abundance inhomogeneities is in place
before the main sequence turn-off. The unlikelihood of mixing while on the main
sequence requires an explanation for the abundance variations which lies
outside the present stars (primordial inhomogeneities or intra-cluster self
enrichment). For M13 it is shown that the 3883\AA CN bands are too weak to be
measured in the spectra for any reasonable set of expected compositions. A
similar situation exists for CH as well. However, two of the more luminous
program stars do appear to have C abundances considerably greater than those
found among the bright giants thereby suggesting deep mixing has taken place on
the M13 red giant branch.Comment: 14 pages, 4 figures, accepted for publication by A
The different origins of magnetic fields and activity in the Hertzsprung gap stars, OU Andromedae and 31 Comae
Context: When crossing the Hertzsprung gap, intermediate-mass stars develop a
convective envelope. Fast rotators on the main sequence, or Ap star
descendants, are expected to become magnetic active subgiants during this
evolutionary phase. Aims: We compare the surface magnetic fields and activity
indicators of two active, fast rotating red giants with similar masses and
spectral class but diferent rotation rates - OU And (Prot=24.2 d) and 31 Com
(Prot=6.8 d) - to address the question of the origin of their magnetism and
high activity.
Methods: Observations were carried out with the Narval spectropolarimeter in
2008 and 2013.We used the least squares deconvolution technique to extract
Stokes V and I profiles to detect Zeeman signatures of the magnetic field of
the stars. We provide Zeeman-Doppler imaging, activity indicator monitoring,
and a precise estimation of stellar parameters. We use stellar evolutionary
models to infer the evolutionary status and the initial rotation velocity on
the main sequence.
Results: The detected magnetic field of OU And is a strong one. Its
longitudinal component Bl reaches 40 G and presents an about sinusoidal
variation with reversal of the polarity. The magnetic topology of OU And is
dominated by large scale elements and is mainly poloidal with an important
dipole component, and a significant toroidal component. The detected magnetic
field of 31 Com is weaker, with a magnetic map showing a more complex field
geometry, and poloidal and toroidal components of equal contributions. The
evolutionary models show that the progenitors of OU And and 31 Com must have
been rotat
Conclusions: OU And appears to be the probable descendant of a magnetic Ap
star, and 31 Com the descendant of a relatively fast rotator on the main
sequence.Comment: 16 pages, 12 figure
The Lithium Flash - Thermal instabilities generated by lithium burning in RGB stars
We present a scenario to explain the lithium-rich phase which occurs on the red giant branch at the so-called bump in the luminosity function. The high transport coefficients required to enhance the surface lithium abundance are obtained in the framework of rotation-induced mixing thanks to the impulse of the important nuclear energy released in a lithium burning shell. Under certain conditions a lithium flash is triggered off. The enhanced mass loss rate due to the temporary increase of the stellar luminosity naturally accounts for a dust shell formation
3He-Driven Mixing in Low-Mass Red Giants: Convective Instability in Radiative and Adiabatic Limits
We examine the stability and observational consequences of mixing induced by
3He burning in the envelopes of first ascent red giants. We demonstrate that
there are two unstable modes: a rapid, nearly adiabatic mode that we cannot
identify with an underlying physical mechanism, and a slow, nearly radiative
mode that can be identified with thermohaline convection. We present
observational constraints that make the operation of the rapid mode unlikely to
occur in real stars. Thermohaline convection turns out to be fast enough only
if fluid elements have finger-like structures with a length to diameter ratio
l/d > 10. We identify some potentially serious obstacles for thermohaline
convection as the predominant mixing mechanism for giants. We show that
rotation-induced horizontal turbulent diffusion may suppress the 3He-driven
thermohaline convection. Another potentially serious problem for it is to
explain observational evidence of enhanced extra mixing. The 3He exhaustion in
stars approaching the red giant branch (RGB) tip should make the 3He mixing
inefficient on the asymptotic giant branch (AGB). In spite of this, there are
observational data indicating the presence of extra mixing in low-mass AGB
stars similar to that operating on the RGB. Overmixing may also occur in
carbon-enhanced metal-poor stars.Comment: 25 pages, 6 figures, modified version, accepted by Ap
Magnetic field structure in single late-type giants: Beta Ceti in 2010 - 2012
The data were obtained using two spectropolarimeters - Narval at the Bernard
Lyot Telescope, Pic du Midi, France, and ESPaDOnS at CFHT, Hawaii. Thirty-eight
circularly-polarized spectra have been collected in the period June 2010 -
January 2012. The Least Square Deconvolution method was applied for extracting
high signal-to-noise ratio line profiles, from which we measure the
surface-averaged longitudinal magnetic field Bl. Chromospheric activity
indicators CaII K, H_alpha, CaII IR (854.2 nm) and radial velocity were
simultaneously measured and their variability was analysed together with the
behavior of Bl. The Zeeman Doppler Imaging (ZDI) inversion technique was
employed for reconstruction of the large-scale magnetic field and two magnetic
maps of Beta Ceti are presented for two periods (June 2010 - December 2010 and
June 2011 - January 2012). Bl remains of positive polarity for the whole
observational period. The behavior of the line activity indicators is in good
agreement with the Bl variations. The two ZDI maps show a mainly axisymmetric
and poloidal magnetic topology and a simple surface magnetic field
configuration dominated by a dipole. Little evolution is observed between the
two maps, in spite of a 1 yr interval between both subsets. We also use
state-of-the-art stellar evolution models to constrain the evolutionary status
of Beta Ceti. We derive a mass of 3.5 M_sun and propose that this star is
already in the central-helium burning phase. Taking into account all our
results and the evolutionary status of the star, we suggest that dynamo action
alone may not be eficient enough to account for the high magnetic activity of
Beta Ceti. As an alternate option, we propose that it may be an Ap star
descendant presently undergoing central helium-burning and still exhibiting a
remnant of the Ap star magnetic field.Comment: 10 pages; 5 figures; 3 table
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