Dusty wind of W Hya. Multi-wavelength modelling of the present-day and recent mass-loss

Low- and intermediate-mass stars go through a period of intense mass-loss at the end of their lives in a phase known as the asymptotic giant branch (AGB). During the AGB a significant fraction of their initial mass is expelled in a stellar wind. This process controls the final stages of their evolution and contributes to the chemical evolution of galaxies. However, the wind-driving mechanism of AGB stars is not yet well understood, especially so for oxygen-rich sources. Characterizing both the present-day mass-loss and wind structure and the evolution of the mass-loss rate of such stars is paramount to advancing our understanding of this processes. We modelled the dust envelope of W Hya using an advanced radiative transfer code. The dust model was analysed in the light of a previously calculated gas-phase wind model and compared to measurements available in the literature, such as infrared spectra, infrared images, and optical scattered light fractions. We find that the dust spectrum of W Hya can partly be explained by a gravitationally bound dust shell that probably is responsible for most of the amorphous Al$_2$O$_3$ emission. The composition of the large ($sim$,0.3,$mu$m) grains needed to explain the scattered light cannot be constrained, but probably is dominated by silicates. Silicate emission in the thermal infrared was found to originate from beyond 40 AU from the star and we find that they need to have substantial near-infrared opacities to be visible at such large distances. The increase in near-infrared opacity of the dust at these distances roughly coincides with a sudden increase in expansion velocity as deduced from the gas-phase CO lines. Finally, the recent mass loss of W Hya is confirmed to be highly variable and we identify a strong peak in the mass-loss rate that occurred about 3500 years ago and lasted for a few hundred years.

The wind of W Hya as seen by Herschel. II. The molecular envelope of W Hya

The evolution of low- and intermediate-mass stars on the asymptotic giant branch (AGB) is mainly controlled by the rate at which these stars lose mass in a stellar wind. Understanding the driving mechanism and strength of the stellar winds of AGB stars and the processes enriching their surfaces with products of nucleosynthesis are paramount to constraining AGB evolution and predicting the chemical evolution of galaxies. In a previous paper we have constrained the structure of the outflowing envelope of W Hya using spectral lines of the $^{12}$CO molecule. Here we broaden this study by modelling an extensive set of H$_{2}$O and $^{28}$SiO lines observed by the three instruments on board Herschel using a state-of-the-art molecular excitation and radiative transfer code. The oxygen isotopic ratios and the $^{28}$SiO abundance profile can be connected to the initial stellar mass and to crucial aspects of dust formation at the base of the stellar wind, respectively. The modelling of H$_{2}$O and $^{28}$SiO confirms the properties of the envelope model of W Hya derived from $^{12}$CO lines. We find an H$_2$O ortho-to-para ratio of 2.5,$^{+2.5}_{-1.0}$, consistent with what is expected for an AGB wind. The O$^{16}$/O$^{17}$ ratio indicates that W Hya has an initial mass of about 1.5 M$_odot$. Although the ortho- and para-H$_{2}$O lines observed by HIFI appear to trace gas of slightly different physical properties, a turbulence velocity of $0.7pm0.1$ km s$^{-1}$ fits the HIFI lines of both spin isomers and those of $^{28}$SiO well. The ortho- and para-H$_2^{16}$O and $^{28}$SiO abundances relative to H$_{2}$ are $(6^{+3}_{-2}) times 10^{-4}$, $(3^{+2}_{-1}) times 10^{-4}$, and $(3.3pm 0.8)times 10^{-5}$, respectively. Assuming a solar silicon-to-carbon ratio, the $^{28}$SiO line emission model is consistent with about one-third of the silicon atoms being locked up in dust particles.

The wind of W Hya as seen by Herschel - I. The CO envelope

Asymptotic giant branch (AGB) stars lose their envelopes by means of a stellar wind whose driving mechanism is not understood well. Characterizing the composition and thermal and dynamical structure of the outflow provides constraints that are essential for understanding AGB evolution, including the rate of mass loss and isotopic ratios. We modeled the CO emission from the wind of the low mass-loss rate oxygen-rich AGB star W Hya using data obtained by the HIFI, PACS, and SPIRE instruments onboard the Herschel Space Observatory and ground-based telescopes. $^{12}$CO and $^{13}$CO lines are used to constrain the intrinsic $^{12}$C/$^{13}$C ratio from resolved HIFI lines. The acceleration of the outflow up to about 5.5 km/s is quite slow and can be represented by a beta-type velocity law with index 5. Beyond this point, acceleration up the terminal velocity of 7 km/s is faster. Using the J=10-9, 9-8, and 6-5 transitions, we find an intrinsic $^{12}$C/$^{13}$C ratio of $18pm10$ for W Hya, where the error bar is mostly due to uncertainties in the $^{12}$CO abundance and the stellar flux around 4.6 $mu$m. To match the low-excitation CO lines, these molecules need to be photo-dissociated at about 500 stellar radii. The radial dust emission intensity profile measured by PACS images at 70 $mu$m shows substantially stronger emission than our model predicts beyond 20 arcsec. The initial slow acceleration of the wind implies inefficient wind driving in the lower part of the envelope. The final injection of momentum in the wind might be the result of an increase in the opacity thanks to the late condensation of dust species. The derived intrinsic isotopologue ratio for W Hya is consistent with values set by the first dredge-up and suggestive of an initial mass of 2 M$_odot$ or more. However, the uncertainty in the main-sequence mass derived based on this isotopologic ratio is large.

Charge Kondo Effect in Thermoelectric Properties of Lead Telluride doped with Thallium Impurities

We investigate the thermoelectric properties of PbTe doped with a small concentration $x$ of Tl impurities acting as acceptors and described by Anderson impurities with negative on-site (effective) interaction. The resulting charge Kondo effect naturally accounts for a number of the low temperature anomalies in this system, including the unusual doping dependence of the carrier concentration, the Fermi level pinning and the self-compensation effect. The Kondo anomalies in the low temperature resistivity at temperatures $Tleq 10, {rm K}$ and the $x$-dependence of the residual resistivity are also in good agreement with experiment. Our model also captures the qualitative aspects of the thermopower at higher temperatures $T>300, {rm K}$ for high dopings ($x>0.6%$) where transport is expected to be largely dominated by carriers in the heavy hole band of PbTe.

Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model, we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat, $C_{rm imp}$, to be calculated accurately from local static correlation functions; specifically via $C_{rm imp}=frac{partial E_{rm ionic}}{partial T} + 1/2frac{partial E_{rm hyb}}{partial T}$, where $E_{rm ionic}$ and $E_{rm hyb}$ are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to $C_{rm imp}$. For the non-degenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The new approach could also be of interest within other impurity solvers, e.g., within quantum Monte Carlo techniques.

Transport Coefficients of the Anderson Model

The transport coefficients of the Anderson model require knowledge of both the temperature and frequency dependence of the single--particle spectral densities and consequently have proven difficult quantities to calculate. Here we show how these quantities can be calculated via an extension of Wilsons numerical renormalization group method. Accurate results are obtained in all parameter regimes and for the full range of temperatures of interest ranging from the high temperature perturbative regime $T>>T_{K}$, through the cross--over region $Tapprox T_{K}$, and into the low temperature strong coupling regime $T<<T_{K}$. The Fermi liquid relations for the $T^2$ coefficient of the resistivity and the linear coefficient of the thermopower are satisfied to a high degree of accuracy. The techniques used here provide a new highly accurate approach to strongly correlated electrons in high dimensions.

Mechanism for large thermoelectric power in negative-U molecular quantum dots

We investigate with the aid of numerical renormalization group techniques the thermoelectric properties of a molecular quantum dot described by the negative-U Anderson model. We show that the charge Kondo effect provides a mechanism for enhanced thermoelectric power via a correlation induced asymmetry in the spectral function close to the Fermi level. We show that this effect results in a dramatic enhancement of the Kondo induced peak in the thermopower of negative-U systems with Seebeck coefficients exceeding 50$mu V/K$ over a wide range of gate voltages.

Kondo decoherence: finding the right spin model for iron impurities in gold and silver

We exploit the decoherence of electrons due to magnetic impurities, studied via weak localization, to resolve a longstanding question concerning the classic Kondo systems of Fe impurities in the noble metals gold and silver: which Kondo-type model yields a realistic description of the relevant multiple bands, spin and orbital degrees of freedom? Previous studies suggest a fully screened spin $S$ Kondo model, but the value of $S$ remained ambiguous. We perform density functional theory calculations that suggest $S = 3/2$. We also compare previous and new measurements of both the resistivity and decoherence rate in quasi 1-dimensional wires to numerical renormalization group predictions for $S=1/2,1$ and 3/2, finding excellent agreement for $S=3/2$.