Mapping the circumstellar SiO maser emission in R Leo

The study of the innermost circumstellar layers around AGB stars is crucial to understand how these envelopes are formed and evolve. The SiO maser emission occurs at a few stellar radii from the central star, providing direct information on the stellar pulsation and on the chemical and physical properties of these regions. Our data also shed light on several aspects of the SiO maser pumping theory that are not well understood yet. We aim to determine} the relative spatial distribution of the 43 GHz and 86 GHz SiO maser lines in the oxygen-rich evolved star R Leo. We have imaged with milliarcsecond resolution, by means of Very Long Baseline Interferometry, the 43 GHz (28SiO v=1, 2 J=1-0 and 29SiO v=0 J=1-0) and 86 GHz (28SiO v=1 J=2-1 and 29SiO v=0 J=2-1) masing regions. We confirm previous results obtained in other oxygen-rich envelopes. In particular, when comparing the 43 GHz emitting regions, the 28SiO v=2 transition is produced in an inner layer, closer to the central star. On the other hand, the 86 GHz line arises in a clearly farther shell. We have also mapped for the first time the 29SiO v=0 J=1-0 emission in R Leo. The already reported discrepancy between the observed distributions of the different maser lines and the theoretical predictions is also found in R Leo.Comment: accepted for publication in A&

The molecular envelope of CRL 618: A new model based on Herschel/HIFI observations

We study the physical properties and molecular excitation of the different warm gas components found in the protoplanetary nebula CRL 618. We revise our previous Herschel/HIFI observations, which consist of several 12CO and 13CO lines in the far-infrared/sub-mm band. These data have been re-analyzed in detail by improving calibration, the signal-to-noise-ratio, and baseline substraction. We identify the contributions of the different nebular components to the line profiles. We have used a spatio-kinematical model to better constrain the temperature, density, and kinematics of the molecular components probed by the improved CO observations. The 12CO and 13CO J=16-15, J=10-9, and J=6-5 transitions are detected in this source. The line profiles present a composite structure showing spectacular wings in some cases, which become dominant as the energy level increases. Our analysis of the high-energy CO emission with the already known low-energy J=2-1 and J=1-0 lines confirms that the high-velocity component, or fast bipolar outflow, is hotter than previously estimated with a typical temperature of ~300 K. This component may then be an example of a very recent acceleration of the gas by shocks that has not yet cooled down. We also find that the dense central core is characterized by a very low expansion velocity, ~5 km/s, and a strong velocity gradient. We conclude that this component is very likely to be the unaltered circumstellar layers that are lost in the last AGB phase, where the ejection velocity is particularly low. The physical properties of the other two nebular components, the diffuse halo and the double empty shell, more or less agrees with the estimations derived in previous models.Comment: Accepted for publication in Astronomy & Astrophysics. 8 pages, 3 figure

Rubio de Francia's extrapolation theory: estimates for the distribution function

Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution function of $Tf$ with respect to any weight $u$ can be essentially majorized by the distribution function of $Mf$ with respect to $u$ (plus an integral term easy to control). As a consequence, well-known extrapolation results, including results in a multilinear setting, can be obtained with very simple proofs. New applications in extrapolation for two-weight problems and estimates on rearrangement invariant spaces are established too.Comment: 29 page

Studying complex fluid dynamics - from direct numerical simulations to tomographic digital holographic particle image velocimetry

Fluid Mechanics is an example of a complex dynamical system with uncountable applications in industry, transportation, manufacturing, medicine, atmospheric sciences, oceanography, hydrology, ionised gases or plasma, the earth’s interior and space plasma turbulence. The scales of the fluid flows in these applications vary widely in the range from microns, as seen in the blood flow of living organisms, micro electro-mechanical system and micro-reactors to thousands of km in atmospheric, oceanographic and astrophysical flows. There are basically two approaches to the study of the three-dimensional spatiotemporal dynamics of complex fluid flows: experimental and numerical with both relying heavily on theory to interpret and explain the results. Complex flows such a turbulence, interaction between shear flows and fluidic actuators (flow control) are examples of flows which exhibit a wide range of coherent structures interacting in a complex fashion. The identification of the coherent structures is important in order to extract knowledge regarding the scales, kinematics and dynamics of these structures. The use of invariant quantities and topological methodology is a useful approach in this endeavor. In the topological approach introduced by [6], which has its roots in critical point theory [10], the structure and evolution of the velocity gradient tensor, the rate-of-strain tensor and the rate-of-rotation tensor are carried out by not studying these tensors directly but by studying their invariants. Examples of studies that have used this methodology to gain physical insight into the structure of various complex flows include the study of: transitional mixing layer and wakes [4, 11, 13, 12, 9]; the structure of homogeneous and homogeneous isotropic turbulence [14, 2, 3, 5, 8]; and wall-bounded turbulent flows [1, 7]. Topological methodology will be reviewed and how topological methodology can be used to visualize spatial and temporal structures using data from direct numerical simulations and some novel experimental measurement techniques will be illustrated. The main and more recent techniques in numerical and experimental techniques are also reviewed and by drawing on examples from research in our laboratory and that of others the specific and complementary nature of these two approaches is presented