Anisotropic nonlinear elasticity in a spherical bead pack: influence of the fabric anisotropy

Stress-strain measurements and ultrasound propagation experiments in glass bead packs have been simultaneously conducted to characterize the stress-induced anisotropy under uniaxial loading. These measurements, realized respectively with finite and incremental deformations of the granular assembly, are analyzed within the framework of the effective medium theory based on the Hertz-Mindlin contact theory. Our work shows that both compressional and shear wave velocities and consequently the incremental elastic moduli agree fairly well with the effective medium model by Johnson et al. [J. Appl. Mech. 65, 380 (1998)], but the anisotropic stress ratio resulting from finite deformation does not at all. As indicated by numerical simulations, the discrepancy may arise from the fact that the model doesn't properly allow the grains to relax from the affine motion approximation. Here we find that the interaction nature at the grain contact could also play a crucial role for the relevant prediction by the model; indeed, such discrepancy can be significantly reduced if the frictional resistance between grains is removed. Another main experimental finding is the influence of the inherent anisotropy of granular packs, realized by different protocols of the sample preparation. Our results reveal that compressional waves are more sensitive to the stress-induced anisotropy, whereas the shear waves are more sensitive to the fabric anisotropy, not being accounted in analytical effective medium models.Comment: 9 pages, 8 figure

Abundances of lithium, oxygen, and sodium in the turn-off stars of Galactic globular cluster 47 Tuc

We aim to determine abundances of Li, O and Na in a sample of of 110 turn-off (TO) stars, in order to study the evolution of light elements in this cluster and to put our results in perspective with observations of other globular and open clusters, as well as with field stars. We use medium resolution spectra obtained with the GIRAFFE spectrograph at the ESO 8.2m Kueyen VLT telescope and use state of the art 1D model atmospheres and NLTE line transfer to determine the abundances. We also employ CO5BOLD hydrodynamical simulations to assess the impact of stellar granulation on the line formation and inferred abundances. Our results confirm the existence of Na-O abundance anti-correlation and hint towards a possible Li-O anti-correlation in the TO stars of 47 Tuc. We find no convincing evidence supporting the existence of Li-Na correlation. The obtained 3D NLTE mean lithium abundance in a sample of 94 TO stars where Li lines were detected reliably, $\langle A({\rm Li})_{\rm 3D~NLTE}\rangle = 1.78 \pm 0.18$ dex, appears to be significantly lower than what is observed in other globular clusters. At the same time, star-to-star spread in Li abundance is also larger than seen in other clusters. The highest Li abundance observed in 47 Tuc is about 0.1 dex lower than the lowest Li abundance observed among the un-depleted stars of the metal-poor open cluster NGC 2243. The lithium abundances in 47 Tuc, when put into context with observations in other clusters and field stars, suggest that stars that are more metal-rich than [FeH] \sim -1.0 experience significant lithium depletion during their lifetime on the main sequence, while the more metal-poor stars do not. Rather strikingly, our results suggest that initial lithium abundance with which the star was created may only depend on its age (the younger the star, the higher its Li content) and not on its metallicity.Comment: 24 pages, 13 figures; discussion and conclusions expanded. Accepted for publication in A&

Critical study of the distribution of rotational velocities of Be stars; II: Differential rotation and some hidden effects interfering with the interpretation of the Vsin i parameter

We assume that stars may undergo surface differential rotation to study its impact on the interpretation of $V\!\sin i$ and on the observed distribution $\Phi(u)$ of ratios of true rotational velocities u=V/V_\rm c (V_\rm c is the equatorial critical velocity). We discuss some phenomena affecting the formation of spectral lines and their broadening, which can obliterate the information carried by $V\!\sin i$ concerning the actual stellar rotation. We studied the line broadening produced by several differential rotational laws, but adopted Maunder's expression $\Omega(\theta)=\Omega_o(1+\alpha\cos^2\theta)$ as an attempt to account for all of these laws with the lowest possible number of free parameters. We studied the effect of the differential rotation parameter $\alpha$ on the measured $V\!\sin i$ parameter and on the distribution $\Phi(u)$ of ratios u=V/V_\rm c. We conclude that the inferred $V\!\sin i$ is smaller than implied by the actual equatorial linear rotation velocity V_\rm eq if the stars rotate with $\alpha0$. For a given $|\alpha|$ the deviations of $V\!\sin i$ are larger when $\alpha<0$. If the studied Be stars have on average $\alpha<0$, the number of rotators with V_\rm eq\simeq0.9V_\rm c is larger than expected from the observed distribution $\Phi(u)$; if these stars have on average $\alpha>0$, this number is lower than expected. We discuss seven phenomena that contribute either to narrow or broaden spectral lines, which blur the information on the rotation carried by $V\!\sin i$ and, in particular, to decide whether the Be phenomenon mostly rely on the critical rotation. We show that two-dimensional radiation transfer calculations are needed in rapid rotators to diagnose the stellar rotation more reliably.Comment: To appear in A&

Properties and nature of Be stars 30. Reliable physical properties of a semi-detached B9.5e+G8III binary BR CMi = HD 61273 compared to those of other well studied semi-detached emission-line binaries

Reliable determination of the basic physical properties of hot emission-line binaries with Roche-lobe filling secondaries is important for developing the theory of mass exchange in binaries. It is a very hard task, however, which is complicated by the presence of circumstellar matter in these systems. So far, only a small number of systems with accurate values of component masses, radii, and other properties are known. Here, we report the first detailed study of a new representative of this class of binaries, BR CMi, based on the analysis of radial velocities and multichannel photometry from several observatories, and compare its physical properties with those for other well-studied systems. BR CMi is an ellipsoidal variable seen under an intermediate orbital inclination of ~51 degrees, and it has an orbital period of 12.919059(15) d and a circular orbit. We used the disentangled component spectra to estimate the effective temperatures 9500(200) K and 4655(50) K by comparing them with model spectra. They correspond to spectral types B9.5e and G8III. We also used the disentangled spectra of both binary components as templates for the 2-D cross-correlation to obtain accurate RVs and a reliable orbital solution. Some evidence of a secular period increase at a rate of 1.1+/-0.5 s per year was found. This, together with a very low mass ratio of 0.06 and a normal mass and radius of the mass gaining component, indicates that BR CMi is in a slow phase of the mass exchange after the mass-ratio reversal. It thus belongs to a still poorly populated subgroup of Be stars for which the origin of Balmer emission lines is safely explained as a consequence of mass transfer between the binary components.Comment: 17 pages, 5 figures, accepted for publication in Astronomy and Astrophysics. appears in Astronomy and Astrophysics 201

Constraints on the H2O formation mechanism in the wind of carbon-rich AGB stars

Context. The recent detection of warm H$_2$O vapor emission from the outflows of carbon-rich asymptotic giant branch (AGB) stars challenges the current understanding of circumstellar chemistry. Two mechanisms have been invoked to explain warm H$_2$O vapor formation. In the first, periodic shocks passing through the medium immediately above the stellar surface lead to H$_2$O formation. In the second, penetration of ultraviolet interstellar radiation through a clumpy circumstellar medium leads to the formation of H$_2$O molecules in the intermediate wind. Aims. We aim to determine the properties of H$_2$O emission for a sample of 18 carbon-rich AGB stars and subsequently constrain which of the above mechanisms provides the most likely warm H$_2$O formation pathway. Methods, Results, and Conclusions. See paper

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 $0.7\pm0.1$ 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 $(3.3\pm 0.8)\times 10^{-5}$, 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

Herschel spectral-mapping of the Helix Nebula (NGC 7293): Extended CO photodissociation and OH+ emission

The Helix Nebula (NGC 7293) is the closest planetary nebulae. Therefore, it is an ideal template for photochemical studies at small spatial scales in planetary nebulae. We aim to study the spatial distribution of the atomic and the molecular gas, and the structure of the photodissociation region along the western rims of the Helix Nebula as seen in the submillimeter range with Herschel. We use 5 SPIRE FTS pointing observations to make atomic and molecular spectral maps. We analyze the molecular gas by modeling the CO rotational lines using a non-local thermodynamic equilibrium (non-LTE) radiative transfer model. For the first time, we have detected extended OH+ emission in a planetary nebula. The spectra towards the Helix Nebula also show CO emission lines (from J= 4 to 8), [NII] at 1461 GHz from ionized gas, and [CI] (2-1), which together with the OH+ lines, trace extended CO photodissociation regions along the rims. The estimated OH+ column density is (1-10)x1e12 cm-2. The CH+ (1-0) line was not detected at the sensitivity of our observations. Non-LTE models of the CO excitation were used to constrain the average gas density (n(H2)=(1-5)x1e5 cm-3) and the gas temperature (Tk= 20-40 K). The SPIRE spectral-maps suggest that CO arises from dense and shielded clumps in the western rims of the Helix Nebula whereas OH+ and [CI] lines trace the diffuse gas and the UV and X-ray illuminated clumps surface where molecules reform after CO photodissociation. [NII] traces a more diffuse ionized gas component in the interclump medium.Comment: Accepted for publication in Astronomy and Astrophysic