Relative entropy in diffusive relaxation

We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy. The relative entropy method is also employed to establish convergence from entropic weak solutions of viscoelasticity with memory to the system of viscoelasticity of the rate-type

Partial mixing and the formation of 13C pockets in AGB stars: effects on the s-process elements

The production of the elements heavier than iron via slow neutron captures (the s process) is a main feature of the contribution of asymptotic giant branch (AGB) stars of low mass (< 5 Msun) to the chemistry of the cosmos. However, our understanding of the main neutron source, the 13C(alpha,n)16O reaction, is still incomplete. It is commonly assumed that in AGB stars mixing beyond convective borders drives the formation of 13C pockets. However, there is no agreement on the nature of such mixing and free parameters are present. By means of a parametric model we investigate the impact of different mixing functions on the final s-process abundances in low-mass AGB models. Typically, changing the shape of the mixing function or the mass extent of the region affected by the mixing produce the same results. Variations in the relative abundance distribution of the three s-process peaks (Sr, Ba, and Pb) are generally within +/-0.2 dex, similar to the observational error bars. We conclude that other stellar uncertainties - the effect of rotation and of overshoot into the C-O core - play a more important role than the details of the mixing function. The exception is at low metallicity, where the Pb abundance is significantly affected. In relation to the composition observed in stardust SiC grains from AGB stars, the models are relatively close to the data only when assuming the most extreme variation in the mixing profile.Comment: 17 pages, 8 figures, 6 tables, accepted for publications on Monthly Notices of the Royal Astronomical Societ

Magnetohydrodynamics of Cloud Collisions in a Multi-phase Interstellar Medium

We extend previous studies of the physics of interstellar cloud collisions by beginning investigation of the role of magnetic fields through 2D magnetohydrodynamic (MHD) numerical simulations. We study head-on collisions between equal mass, mildly supersonic diffuse clouds. We include a moderate magnetic field and two limiting field geometries, with the field lines parallel (aligned) and perpendicular (transverse) to the colliding cloud motion. We explore both adiabatic and radiative cases, as well as symmetric and asymmetric ones. We also compute collisions between clouds evolved through prior motion in the intercloud medium and compare with unevolved cases. We find that: In the (i) aligned case, adiabatic collisions, like their HD counterparts, are very disruptive, independent of the cloud symmetry. However, when radiative processes are taken into account, partial coalescence takes place even in the asymmetric case, unlike the HD calculations. In the (ii) transverse case, collisions between initially adjacent unevolved clouds are almost unaffected by magnetic fields. However, the interaction with the magnetized intercloud gas during the pre-collision evolution produces a region of very high magnetic energy in front of the cloud. In collisions between evolved clouds with transverse field geometry, this region acts like a ``bumper'', preventing direct contact between the clouds, and eventually reverses their motion. The ``elasticity'', defined as the ratio of the final to the initial kinetic energy of each cloud, is about 0.5-0.6 in the cases we considered. This behavior is found both in adiabatic and radiative cases.Comment: 40 pages in AAS LaTeX v4.0, 13 figures (in degraded jpeg format). Full resolution images as well as mpeg animations are available at http://www.msi.umn.edu:80/Projects/twj/mhd-cc/ . Accepted for publication in The Astrophysical Journa

A Sr-Rich Star on the Main Sequence of Omega Centauri

Abundance ratios relative to iron for carbon, nitrogen, strontium and barium are presented for a metal-rich main sequence star ([Fe/H]=--0.74) in the globular cluster omega Centauri. This star, designated 2015448, shows depleted carbon and solar nitrogen, but more interestingly, shows an enhanced abundance ratio of strontium [Sr/Fe] ~ 1.6 dex, while the barium abundance ratio is [Ba/Fe]<0.6 dex. At this metallicity one usually sees strontium and barium abundance ratios that are roughly equal. Possible formation scenarios of this peculiar object are considered.Comment: 13 pages, 3 figures. Accepted to ApJ

An extreme paucity of second population AGB stars in the normal globular cluster M4

Galactic Globular clusters (GCs) are now known to harbour multiple stellar populations, which are chemically distinct in many light element abundances. It is becoming increasingly clear that asymptotic giant branch (AGB) stars in GCs show different abundance distributions in light elements compared to those in the red giant branch (RGB) and other phases, skewing toward more primordial, field-star-like abundances, which we refer to as subpopulation one (SP1). As part of a larger program targeting giants in GCs, we obtained high-resolution spectra for a sample of 106 RGB and 15 AGB stars in Messier 4 (NGC 6121) using the 2dF+HERMES facility on the Anglo-Australian Telescope. In this Letter we report an extreme paucity of AGB stars with [Na/O] > -0.17 in M4, which contrasts with the RGB that has abundances up to [Na/O] =0.55. The AGB abundance distribution is consistent with all AGB stars being from SP1. This result appears to imply that all subpopulation two stars (SP2; Na-rich, O-poor) avoid the AGB phase. This is an unexpected result given M4's horizontal branch morphology -- it does not have an extended blue horizontal branch. This is the first abundance study to be performed utilising the HERMES spectrograph.Comment: 5 pages, 2 figures, 4 tables (full Table 1 online). Accepted for publication in MNRAS Letter