Eulerian digraphs and Dyck words, a bijection

The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in both directions. The connection between Dyck words and Eulerian digraphs exploits a novel combinatorial structure: a binary matrix, we call Dyck matrix, representing the cycles of an Eulerian digraph

Magnesium isotopes: a tool to understand self-enrichment in Globular Clusters

A critical issue in the asymptotic giant branch (AGB) self-enrichment scenario for the formation of multiple populations in Globular Clusters (GCs) is the inability to reproduce the magnesium isotopic ratios, despite the model in principle can account for the depletion of magnesium. In this work we analyze how the uncertainties on the various p-capture cross sections affect the results related to the magnesium content of the ejecta of AGB stars. The observed distribution of the magnesium isotopes and of the overall Mg-Al trend in M13 and NGC 6752 are successfully reproduced when the proton-capture rate by 25Mg at the temperatures 100 MK, in particular the 25Mg(p, gamma)26Alm channel, is enhanced by a factor 3 with respect to the most recent experimental determinations. This assumption also allows to reproduce the full extent of the Mg spread and the Mg-Si anticorrelation observed in NGC 2419. The uncertainties in the rate of the 25Mg(p,gamma)26Alm reaction at the temperatures of interest here leave space for our assumption and we suggest that new experimental measurements are needed to settle this problem. We also discuss the competitive model based on the super massive star nucleosynthesis.Comment: accepted for publication on MNRA

Stars caught in the braking stage in young Magellanic Clouds clusters

The color-magnitude diagrams of many Magellanic Cloud clusters (with ages up to 2 billion years) display extended turnoff regions where the stars leave the main sequence, suggesting the presence of multiple stellar populations with ages which may differ even by hundreds million years (Mackey et al. 2008, Milone et al. 2009, Girardi et al. 2011). A strongly debated question is whether such an extended turnoff is instead due to populations with different stellar rotations (Girardi et al. 2011, Goudfrooij et al. 2011, Rubele et al. 2013, Li et al. 2014). The recent discovery of a `split' main sequence in some younger clusters (about 80--400Myr) added another piece to this puzzle. The blue (red) side of the main sequence is consistent with slowly (rapidly) rotating stellar models (D'Antona et al. 2015, Milone et al. 2016, Correnti et al. 2017, Milone et al 2016), but a complete theoretical characterization of the observed color-magnitude diagram appeared to require also an age spread (Correnti et al. 2017). We show here that, in three clusters so far analyzed, if the blue main sequence stars are interpreted with models that have been always slowly rotating, they must be about 30% younger than the rest of the cluster. If they are instead interpreted as stars initially rapidly rotating, but that have later slowed down, the age difference disappears, and "braking" also helps to explain the apparent age differences of the extended turnoff. The age spreads in Magellanic Cloud clusters are a manifestation of rotational stellar evolution. Observational tests are suggested.Comment: Accepted for publication and in state of Advance Online Publication (from 24 July 2017) on Nature Astronom

Identification of muscle innervation zones using linear electrode arrays: a fundamental step to measure fibers conduction velocity

Fiber conduction velocity (CV) is a parameter correlated to the physiological membrane properties of the skeletal muscle fibers. Changes in muscle fiber CV are correlated to the gradation of force and fatigue, and can be measured by means of surface electromyography EMG (sEMG). sEMG measurement of CV during muscle contractions requires the correct identification of the skeletal muscle innervation zone (IZ). In superficial muscles, IZ location can be detected using linear electrode arrays and visually identified as the point of inversion of the detected motor unit action potential (MUAP) propagation. In the present work, we present a method for the effective and fast detection of the IZ location, through the following procedures: (1) identification of the target superficial muscle considering the muscle fiber architecture; (2) electrode array selection based on interelectrode distance and number of electrodes; (3) subject training to perform submaximal isometric contractions of the target muscle/s; (4) electrode array positioning along the muscle surface to investigate the IZ position during the contractions by visual identification of MUAP patterns

Self-enrichment in Globular Clusters: the extreme He-rich population of NGC 2808

Almost several decades after the discovery of the first multiple populations in galactic globular clusters (GC) the debate on their formation is still extremely current and NGC2808 remains one of the best benchmark to test any scenario for their origin and the evolution. In this work we focus on the chemical composition of stars belonging to the extreme He-rich population populated by stars with the most extreme abundance of Mg, Al, Na, O and Si. We checked whether the most recent measures are consistent with the AGB yields of stars of $6.5-8~M_{\odot}$. These stars evolve on time scales of the order of 40-60 Myr and eject matter strongly enriched in helium, owing to a deep penetration of the surface convective zone down to regions touched by CNO nucleosynthesis occurring after the core He-burning phase. Since the big unknown of the AGB phase of massive stars is the mass loss, we propose a new approch that takes into account the effects of the radiation pressure on dust particles. We show that this more realistic description is able to reproduce the observed abundances of Mg, Al, Na and Si in these extreme stars. The large spread in the oxygen abundances is explained by invoking deep mixing during the RGB phase. It will be possible to check this work hypothesis as soon as the oxygen measurements of the main sequence stars of NGC2808 will be available.Comment: 12 pages, 5 figures, accepted 2018 June 29 by MNRA

An HST/WFC3 view of stellar populations on the horizontal branch of NGC 2419

We use images acquired with the Hubble Space Telescope Wide Field Camera 3 and new models to probe the horizontal branch (HB) population of the Galactic globular cluster (GC) NGC 2419. A detailed analysis of the composite HB highlights three populations: (1) the blue luminous HB, hosting standard helium stars (Y = 0.25) with a very small spread of mass; (2) a small population of stars with intermediate helium content (0.26 < Y ≲ 0.29); and (3) the well-populated extreme HB. We can fit the last group with models having high helium abundance (Y ∼ 0.36), half of which (the hottest part, ‘blue hook’ stars) are identified as possible ‘late flash mixed stars’. The initial helium abundance of this extreme population is in nice agreement with the predicted helium abundance in the ejecta of massive asymptotic giant branch (AGB) stars of the same metallicity as NGC 2419. This result further supports the hypothesis that second-generation stars in GCs formed from the ashes of intermediate-mass AGB stars. We find that the distribution in magnitude of the blue hook stars is larger than that predicted by theoretical models. We discuss the possible uncertainties in the magnitude scales and different attempts to model this group of stars. Finally, we suggest that consistency can be better achieved if we assume core masses larger than predicted by our models. This may be possible if the progenitors were fast rotators on the main sequence. If further study confirms this interpretation, a fast initial rotation would be a strong signature of the peculiarity of extreme second-generation stars in GCs

The Lithium test for multiple populations in Globular Clusters: Lithium in NGC 2808

In the globular cluster NGC2808, a quasi-standard initial lithium abundance is derived for a red giant belonging to the `extreme' population, characterized by a large helium overabundance, and by abundances of proton capture elements typical of nuclear processing in gas at very high temperatures, where the initial lithium has been fully destroyed. The observations of lithium in such extreme cluster stars are important to test different models for the formation of multiple populations in old Globular Clusters. In the asymptotic giant branch (AGB) scenario, fresh lithium is synthetized during the initial phases of hot bottom burning which, afterwards, synthetize the other p-capture elements. We model the abundance of lithium in the ejecta of superAGB models, finding values consistent or larger than observed in the `extreme' giant; these same models describe correctly the magnesium depletion and silicon enrichment of the extreme population of NGC 2808, so the overall agreement provides further support to the AGB scenario. In the models involving massive or supermassive stars, the Lithium observed requires a mixture of the lithium-free ejecta of the polluting population with more than 40% of standard-lithium pristine gas. The extended chemical anomalies of NGC 2808 stars are then to be all explained within at most 60% of the possible dilution range, the initial helium mass fraction in the ejecta should be Y >= 0.5, to account for the Ye 0.38-0.40 of the extreme population, and further observations of p-process elements are needed to check the model.Comment: accepted for publication in The Astrophysical Journal Letter