On the proper use of the Schwarzschild and Ledoux criteria in stellar evolution computations

The era of detailed asteroseismic analyses opened by space missions such as CoRoT and $\textit{Kepler}$ has highlighted the need for stellar models devoid of numerical inaccuracies, in order to be able to diagnose which physical aspects are being ignored or poorly treated in standard stellar modeling. We tackle here the important problem of fixing convective zones boundaries in the frame of the local mixing length theory. First we show that the only correct way to locate a convective zone boundary is to find, at each iteration step, through interpolations or extrapolations from points $\textit{within the convective zone}$, the mass where the radiative luminosity is equal to the total one. We then discuss two misuses of the boundary condition and the way they affect stellar modeling and stellar evolution. The first one consists in applying the neutrality condition for convective instability on the $\textit{radiative}$ side of the convective boundary. The second way of misusing the boundary condition comes from the process of fixing the convective boundary through the search for a change of sign of a possibly \textit{discontinuous} function. We show that these misuses can lead to completely wrong estimates of convective core sizes with important consequences for the following evolutionary phases. We point out the advantages of using a double mesh point at each convective zone boundaries. The specific problem of a convective shell is discussed and some remarks concerning overshooting are given.Comment: 14 pages, 10 figures, to appear in A&

Ab initio Study of Luminescence in Ce-doped Lu2_2SiO5_5: The Role of Oxygen Vacancies on Emission Color and Thermal Quenching Behavior

We study from first principles the luminescence of Lu$_2$SiO$_5$:Ce$^{3+}$ (LSO:Ce), a scintillator widely used in medical imaging applications, and establish the crucial role of oxygen vacancies (V$_O$) in the generated spectrum. The excitation energy, emission energy and Stokes shift of its luminescent centers are simulated through a constrained density-functional theory method coupled with a ${\Delta}$SCF analysis of total energies, and compared with experimental spectra. We show that the high-energy emission band comes from a single Ce-based luminescent center, while the large experimental spread of the low-energy emission band originates from a whole set of different Ce-V$_O$ complexes together with the other Ce-based luminescent center. Further, the luminescence thermal quenching behavior is analyzed. The $4f-5d$ crossover mechanism is found to be very unlikely, with a large crossing energy barrier (E$_{fd}$) in the one-dimensional model. The alternative mechanism usually considered, namely the electron auto-ionization, is also shown to be unlikely. In this respect, we introduce a new methodology in which the time-consuming accurate computation of the band gap for such models is bypassed. We emphasize the usually overlooked role of the differing geometry relaxation in the excited neutral electronic state Ce$^{3+,*}$ and in the ionized electronic state Ce$^{4+}$. The results indicate that such electron auto-ionization cannot explain the thermal stability difference between the high- and low-energy emission bands. Finally, a hole auto-ionization process is proposed as a plausible alternative. With the already well-established excited state characterization methodology, the approach to color center identification and thermal quenching analysis proposed here can be applied to other luminescent materials in the presence of intrinsic defects.Comment: 13 pages, 8 figures, accepted by Phys. Rev. Material

Discriminating between overshooting and rotational mixing in massive stars: any help from asteroseismology?

Chemical turbulent mixing induced by rotation can affect the internal distribution of mu near the energy-generating core of main-sequence stars, having an effect on the evolutionary tracks similar to that of overshooting. However, this mixing also leads to a smoother chemical composition profile near the edge of the convective core, which is reflected in the behaviour of the buoyancy frequency and, therefore, in the frequencies of gravity modes. We show that for rotational velocities typical of main-sequence B-type pulsating stars, the signature of a rotationally induced mixing significantly perturbs the spectrum of gravity modes and mixed modes, and can be distinguished from that of overshooting. The cases of high-order gravity modes in Slowly Pulsating B stars and of low-order g modes and mixed modes in beta Cephei stars are discussed.Comment: 6 pages, 4 figures, Comm. in Asteroseismology, Contribution to the Proceedings of the 38th LIAC, HELAS-ESTA, BAG, 200

L'Infant romà

Català: La política d'Alexandre VI de crear un estat familiar propi amb territoris assignats als seus fills, és exemplificada amb el cas de Joan de Borja, duc de Nepi i Camerino, conegut com a Infant romà (1498-1547). English: Alexander VI's policy to create a state controlled by the family by assigning land territories to his sons and daughter, is exemplified by the case of one of them, Juan Borgia, Duke of Camerino and Nepi, known as Infans romanus (1498-1547). Italiano: La politica di Alessandro VI finalizzata a creare uno stato familiare proprio con territori assegnati ai suoi figli, è esemplificata dal caso di Giovanni Borgia, duca di Nepi e Camerino, conosciuto come l'infante romano (1498-1547)