Transport in ultradilute solutions of 3^3He in superfluid 4^4He

We calculate the effect of a heat current on transporting $^3$He dissolved in superfluid $^4$He at ultralow concentration, as will be utilized in a proposed experimental search for the electric dipole moment of the neutron (nEDM). In this experiment, a phonon wind will generated to drive (partly depolarized) $^3$He down a long pipe. In the regime of $^3$He concentrations $\tilde < 10^{-9}$ and temperatures $\sim 0.5$ K, the phonons comprising the heat current are kept in a flowing local equilibrium by small angle phonon-phonon scattering, while they transfer momentum to the walls via the $^4$He first viscosity. On the other hand, the phonon wind drives the $^3$He out of local equilibrium via phonon-$^3$He scattering. For temperatures below $0.5$ K, both the phonon and $^3$He mean free paths can reach the centimeter scale, and we calculate the effects on the transport coefficients. We derive the relevant transport coefficients, the phonon thermal conductivity and the $^3$He diffusion constants from the Boltzmann equation. We calculate the effect of scattering from the walls of the pipe and show that it may be characterized by the average distance from points inside the pipe to the walls. The temporal evolution of the spatial distribution of the $^3$He atoms is determined by the time dependent $^3$He diffusion equation, which describes the competition between advection by the phonon wind and $^3$He diffusion. As a consequence of the thermal diffusivity being small compared with the $^3$He diffusivity, the scale height of the final $^3$He distribution is much smaller than that of the temperature gradient. We present exact solutions of the time dependent temperature and $^3$He distributions in terms of a complete set of normal modes.Comment: NORDITA PREPRINT 2015-37, 9 pages, 6 figure

Transport in very dilute solutions of 3^3He in superfluid 4^4 He

Motivated by a proposed experimental search for the electric dipole moment of the neutron (nEDM) utilizing neutron-$^3$He capture in a dilute solution of $^3$He in superfluid $^4$He, we derive the transport properties of dilute solutions in the regime where the $^3$He are classically distributed and rapid $^3$He-$^3$He scatterings keep the $^3$He in equilibrium. Our microscopic framework takes into account phonon-phonon, phonon-$^3$He, and $^3$He-$^3$He scatterings. We then apply these calculations to measurements by Rosenbaum et al. [J.Low Temp.Phys. {\bf 16}, 131 (1974)] and by Lamoreaux et al. [Europhys.Lett. {\bf 58}, 718 (2002)] of dilute solutions in the presence of a heat flow. We find satisfactory agreement of theory with the data, serving to confirm our understanding of the microscopics of the helium in the future nEDM experiment.Comment: 10 pages, 5 figures, v

Low Temperature Transport Properties of Very Dilute Classical Solutions of 3^3He in Superfluid 4^4He

We report microscopic calculations of the thermal conductivity, diffusion constant and thermal diffusion constant for classical solutions of $^3$He in superfluid $^4$He at temperatures T \la 0.6~K, where phonons are the dominant excitations of the $^4$He. We focus on solutions with $^3$He concentrations \la \,10^{-3}, for which the main scattering mechanisms are phonon-phonon scattering via 3-phonon Landau and Beliaev processes, which maintain the phonons in a drifting equilibrium distribution, and the slower process of $^3$He-phonon scattering, which is crucial for determining the $^3$He distribution function in transport. We use the fact that the relative changes in the energy and momentum of a $^3$He atom in a collision with a phonon are small to derive a Fokker-Planck equation for the $^3$He distribution function, which we show has an analytical solution in terms of Sonine polynomials. We also calculate the corrections to the Fokker-Planck results for the transport coefficients.Comment: 29 pages, 2 figure

The Infrared Nucleus of the Wolf-Rayet Galaxy Henize 2-10

We have obtained near-infrared images and mid-infrared spectra of the starburst core of the dwarf Wolf-Rayet galaxy He 2-10. We find that the infrared continuum and emission lines are concentrated in a flattened ellipse 3-4'' or 150 pc across which may show where a recent accretion event has triggered intense star formation. The ionizing radiation from this cluster has an effective temperature of 40,000 K, corresponding to $30M_\odot$ stars, and the starburst is $0.5-1.5 \times 10^7$ years old.Comment: 17 pages Latex, 7 postscript figures, 1 postscript table, accepted to A

Magnetic loop emergence within a granule

We investigate the temporal evolution of magnetic flux emerging within a granule in the quiet-Sun internetwork at disk center. We combined IR spectropolarimetry performed in two Fe I lines at 1565 nm with speckle-reconstructed G-band imaging. We determined the magnetic field parameters by a LTE inversion of the full Stokes vector using the SIR code, and followed their evolution in time. To interpret the observations, we created a geometrical model of a rising loop in 3D. The relevant parameters of the loop were matched to the observations where possible. We then synthesized spectra from the 3D model for a comparison to the observations. We found signatures of magnetic flux emergence within a growing granule. In the early phases, a horizontal magnetic field with a distinct linear polarization signal dominated the emerging flux. Later on, two patches of opposite circular polarization signal appeared symmetrically on either side of the linear polarization patch, indicating a small loop-like structure. The mean magnetic flux density of this loop was roughly 450 G, with a total magnetic flux of around 3x10^17 Mx. During the ~12 min episode of loop occurrence, the spatial extent of the loop increased from about 1 to 2 arcsec. The middle part of the appearing feature was blueshifted during its occurrence, supporting the scenario of an emerging loop. The temporal evolution of the observed spectra is reproduced to first order by the spectra derived from the geometrical model. The observed event can be explained as a case of flux emergence in the shape of a small-scale loop.Comment: 10 pages, 13 figures; accepted for Astronomy and Astrophysics; ps and eps figures in full resolution are available at http://www.astro.sk/~koza/figures/aa2009_loop

Sulphur molecules in the circumstellar envelopes of M-type AGB stars

The sulphur compounds SO and SO$_2$ have not been widely studied in the circumstellar envelopes of asymptotic giant branch (AGB) stars. By presenting and modelling a large number of SO and SO$_2$ lines in the low mass-loss rate M-type AGB star R Dor, and modelling the available lines of those molecules in a further four M-type AGB stars, we aim to determine their circumstellar abundances and distributions. We use a detailed radiative transfer analysis based on the accelerated lambda iteration method to model circumstellar SO and SO$_2$ line emission and molecular data files for both SO and SO$_2$ that are more extensive than those previously available. Using 17 SO lines and 98 SO2 lines to constrain our models for R Dor, we find an SO abundance of 6.7x10$^{-6}$ and an SO$_2$ abundance of 5x10$^{-6}$ with both species having high abundances close to the star. We also modelled $^{34}$SO and found an abundance of 3.1x10$^{-7}$, giving an $^{32}$SO/$^{34}$SO ratio of 21.6. We derive similar results for the circumstellar SO and SO$_2$ abundances and their distributions for the low mass-loss rate object W Hya. For these stars, the circumstellar SO and SO$_2$ abundances are much higher than predicted by chemical models and these two species may account for all available sulphur. For the higher mass-loss rate stars, we find shell-like SO distributions with peak abundances that decrease and peak abundance radii that increase with increasing mass-loss rate. The positions of the peak SO abundance agree very well with the photodissociation radii of H$_2$O. We find evidence that SO is most likely through the photodissociation of H$_2$O and the subsequent reaction between S and OH. The S-bearing parent molecule appears not to be H$_2$S. The SO$_2$ models suggest an origin close to the star for this species, also disagreeing with current chemical models.Comment: 25 page

Phase II of the ASCE Benchmark Study on SHM

The task group on structural health monitoring of the Dynamic Committee of ASCE was formed in 1999 at the 12 th Engineering Mechanics Conference. The task group has designed a number of analytical studies on a benchmark structure and there are plans to follow these with an experimental program. The first phase of the analytical studies was completed in 2001. The second phase, initiated in the summer of 2001, was formulated in the light of the experience gained on phase I and focuses on increasing realism in the simulation of the discrepancies between the actual structure and the mathematical model used in the analysis. This paper describes the rational that lead the SHM task group to the definition of phase II and presents the details of the cases that are being considered

Simulations of the Galaxy Cluster CIZA J2242.8+5301 I: Thermal Model and Shock Properties

The giant radio relic in CIZA J2242.8+5301 is likely evidence of a Mpc sized shock in a massive merging galaxy cluster. However, the exact shock properties are still not clearly determined. In particular, the Mach number derived from the integrated radio spectrum exceeds the Mach number derived from the X-ray temperature jump by a factor of two. We present here a numerical study, aiming for a model that is consistent with the majority of observations of this galaxy cluster. We first show that in the northern shock upstream X-ray temperature and radio data are consistent with each other. We then derive progenitor masses for the system using standard density profiles, X-ray properties and the assumption of hydrostatic equilibrium. We find a class of models that is roughly consistent with weak lensing data, radio data and some of the X-ray data. Assuming a cool-core versus non-cool-core merger, we find a fiducial model with a total mass of $1.6 \times 10^{15}\,M_\odot$, a mass ratio of 1.76 and a Mach number that is consistent with estimates from the radio spectrum. We are not able to match X-ray derived Mach numbers, because even low mass models over-predict the X-ray derived shock speeds. We argue that deep X-ray observations of CIZA J2242.8+5301 will be able to test our model and potentially reconcile X-ray and radio derived Mach numbers in relics.Comment: 19 pages, 19 figure

Onion-shell model for cosmic ray electrons and radio synchrotron emission in supernova remnants

The spectrum of cosmic ray electrons, accelerated in the shock front of a supernova remnant (SNR), is calculated in the test-particle approximation using an onion-shell model. Particle diffusion within the evolving remnant is explicity taken into account. The particle spectrum becomes steeper with increasing radius as well as SNR age. Simple models of the magnetic field distribution allow a prediction of the intensity and spectrum of radio synchrotron emission and their radial variation. The agreement with existing observations is satisfactory in several SNR's but fails in other cases. Radiative cooling may be an important effect, especially in SNR's exploding in a dense interstellar medium