The morpho-kinematics of the circumstellar envelope around the AGB star EP Aqr

ALMA observations of CO(1-0) and CO(2-1) emissions of the circumstellar envelope of EP Aqr, an oxygen-rich AGB star, are reported. A thorough analysis of their properties is presented using an original method based on the separation of the data-cube into a low velocity component associated with an equatorial outflow and a faster component associated with a bipolar outflow. A number of important and new results are obtained concerning the distribution in space of the effective emissivity, the temperature, the density and the flux of matter. A mass loss rate of (1.6$\pm$0.4)10$^{-7}$ solar masses per year is measured. The main parameters defining the morphology and kinematics of the envelope are evaluated and uncertainties inherent to de-projection are critically discussed. Detailed properties of the equatorial region of the envelope are presented including a measurement of the line width and a precise description of the observed inhomogeneity of both morphology and kinematics. In particular, in addition to the presence of a previously observed spiral enhancement of the morphology at very small Doppler velocities, a similarly significant but uncorrelated circular enhancement of the expansion velocity is revealed, both close to the limit of sensitivity. The results of the analysis place significant constraints on the parameters of models proposing descriptions of the mass loss mechanism, but cannot choose among them with confidence.Comment: 26 pages, 31 figures, accepted for publication in MNRA

Observation of narrow polar jets in the nascent wind of oxygen-rich AGB star EP Aqr

Using ALMA observations of $^{12}$CO(2-1), $^{28}$SiO(5-4) and $^{32}$SO$_2$(16$_{6,10}$-17$_{5,13}$) emissions of the circumstellar envelope of AGB star EP Aqr, we describe the morpho-kinematics governing the nascent wind. Main results are: 1) Two narrow polar structures, referred to as jets, launched from less than 25 au away from the star, build up between $\sim$ 20 au and $\sim$ 100 au to a velocity of $\sim$ 20 \kms. They fade away at larger distances and are barely visible in CO data. 2) SO$_2$, SiO and CO emissions explore radial ranges reaching respectively $\sim$30 au, 250 au and 1000 au from the star, preventing the jets to be detected in SO$_2$ data. 3) Close to the star photosphere, rotation (undetected in SiO and CO data) and isotropic radial expansion combine with probable turbulence to produce a broad SO$_2$ line profile ($\sim$ 7.5 \kms\ FWHM). 4) A same axis serves as axis of rotation close to the star, as jet axis and as axi-symmetry axis at large distances. 5) A radial wind builds up at distances up to $\sim$ 300 au from the star, with larger velocity near polar than equatorial latitudes. 6) A sharp depletion of SiO and CO emissions, starting near the star, rapidly broadens to cover the whole blue-western quadrant, introducing important asymmetry in the CO and particularly SiO observations. 7) The $^{12}$C/$^{13}$C abundance ratio is measured as 9$\pm$2. 8) Plausible interpretations are discussed, in particular assuming the presence of a companion.Comment: 18 pages, 16 figures, MNRAS accepte

Static behaviour of functionally graded sandwich beams using a quasi-3D theory

This paper presents static behaviour of functionally graded (FG) sandwich beams by using a quasi-3D theory, which includes both shear deformation and thickness stretching effects. Various symmetric and non-symmetric sandwich beams with FG material in the core or skins under the uniformly distributed load are considered. Finite element model (FEM) and Navier solutions are developed to determine the displacement and stresses of FG sandwich beams for various power-law index, skin-core-skin thickness ratios and boundary conditions. Numerical results are compared with those predicted by other theories to show the effects of shear deformation and thickness stretching on displacement and stresses

Time-varying Learning and Content Analytics via Sparse Factor Analysis

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education

Contributions of rotation, expansion and line broadening to the morpho-kinematics of the inner CSE of oxygen-rich AGB star R Hya

We use archival ALMA observations of the CO(2-1) and SiO(5-4) molecular line emissions of AGB star R Hya to illustrate the relative contributions of rotation, expansion and line broadening to the morpho-kinematics of the circumstellar envelope (CSE) within some ~0.5 arcsec from the centre of the star. We give evidence for rotation and important line broadening to dominate the inner region, within ~100 mas from the centre of the star. The former is about an axis that projects a few degrees west of north and has a projected rotation velocity of a few km/s. The latter occurs within some 50-100 mas from the centre of the star, the line width reaching two to three times its value outside this region. We suggest that it is caused by shocks induced by stellar pulsations and convective cell ejections. We show the importance of properly accounting for the observed line broadening when discussing rotation and evaluating the radial dependence of the rotation velocity.Comment: 8 pages, 8 figure