1,649 research outputs found
Inhibition of thermohaline mixing by a magnetic field in Ap star descendants: Implications for the Galactic evolution of 3He
To reconcile the measurements of 3He/H in Galactic HII regions with high
values of 3He in a couple of planetary nebulae, we propose that thermohaline
mixing is inhibited by a fossil magnetic field in red giant stars that are
descendants of Ap stars. We examine the effect of a magnetic field on the
salt-finger instability, using a local analysis. We obtain a threshold for the
magnetic field of 10^4 - 10^5 Gauss, above which it inhibits thermohaline
mixing in red giant stars located at or above the bump. Fields of that order
are expected in the descendants of the Ap stars, taking into account the
contraction of their core. We conclude that in a large fraction of the
descendants of Ap stars thermohaline mixing does not occur. As a consequence
these objects must produce 3He as predicted by the standard theory of stellar
evolution and as observed in the planetary nebulae NGC3242 and J320. The
relative number of such stars with respect to non-magnetic objects that undergo
thermohaline mixing is consistent with the statistical constraint coming from
observations of the carbon isotopic ratio in red giant stars. It also satisfies
the Galactic requirements for the evolution of the 3He abundance.Comment: Accepted for publication in A&A Letters (Vol.476
Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables
We investigate Gevrey order and 1-summability properties of the formal
solution of a general heat equation in two variables. In particular, we give
necessary and sufficient conditions for the 1-summability of the solution in a
given direction. When restricted to the case of constants coefficients, these
conditions coincide with those given by D.A. Lutz, M. Miyake, R. Schaefke in a
1999 article, and we thus provide a new proof of their result.Comment: 16 page
On optimal truncation of divergent series solutions of nonlinear differential systems; Berry smoothing
We prove that for divergent series solutions of nonlinear (or linear)
differential systems near a generic irregular singularity, the common
prescription of summation to the least term is, if properly interpreted,
meaningful and correct, and we extend this method to transseries solutions. In
every direction in the complex plane at the singularity (Stokes directions {\em
not} excepted) there exists a nonempty set of solutions whose difference from
the ``optimally'' (i.e., near the least term) truncated asymptotic series is of
the same (exponentially small) order of magnitude as the least term of the
series. There is a family of generalized Borel summation formulas
which commute with the usual algebraic and analytic operations (addition,
multiplication, differentiation, etc). We show that there is exactly one of
them, , such that for any formal series solution ,
differs from the optimal truncation of
by at most the order of the least term of . We show in addition that
the Berry (1989) smoothing phenomenon is universal within this class of
differential systems. Whenever the terms ``beyond all orders'' {\em change} in
crossing a Stokes line, these terms vary smoothly on the Berry scale
and the transition is always given by the error
function; under the same conditions we show that Dingle's rule of signs for
Stokes transitions holds
The Arecibo HII Region Discovery Survey
We report the detection of radio recombination line emission (RRL) using the
Arecibo Observatory at X-band (9GHz, 3cm) from 37 previously unknown HII
regions in the Galactic zone 66 deg. > l > 31 deg. and |b| < 1 deg. This
Arecibo HII Region Discovery Survey (Arecibo HRDS) is a continuation of the
Green Bank Telescope (GBT) HRDS. The targets for the Arecibo HRDS have
spatially coincident 24 micron and 20 cm emission of a similar angular
morphology and extent. To take advantage of Arecibo's sensitivity and small
beam size, sources in this sample are fainter, smaller in angle, or in more
crowded fields compared to those of the GBT HRDS. These Arecibo nebulae are
some of the faintest HII regions ever detected in RRL emission. Our detection
rate is 58%, which is low compared to the 95% detection rate for GBT HRDS
targets. We derive kinematic distances to 23 of the Arecibo HRDS detections.
Four nebulae have negative LSR velocities and are thus unambiguously in the
outer Galaxy. The remaining sources are at the tangent point distance or
farther. We identify a large, diffuse HII region complex that has an associated
HI and 13CO shell. The ~90 pc diameter of the G52L nebula in this complex may
be the largest Galactic HII region known, and yet it has escaped previous
detection.Comment: Accepted to ApJ Data can be found here: http://go.nrao.edu/hrd
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