Induced semi-convection in helium-burning horizontal-branch stars

In the evolutionary phase of central helium burning, models of horizontal-branch stars reach a stage at which an intermediate region is unstable against convection. This feature is due to the progressive increase of the core mass by overshooting during the previous evolutionary stages and to the behaviour of the radiative temperature gradient at the core boundary. By consideration of the typical time scales of propagation of convection and nuclear burning, a partial mixing (semi-convection) can be induced in a region around the convective core.

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Riassunto Come conseguenza del progressivo aumento in massa per overshooting del nucleo convettivo nella fase iniziale di combustione centrale dell'elio in stelle di ramo orizzontale e per l'andamento del gradiente radiativo della temperatura al bordo del nucleo, viene raggiunto uno stadio nel quale una zona intermedia è instabile rispetto alla convezione. Dalla considerazione dei tempi caratteristici di propagazione della convezione e di combustione nucleare, si conclude che l'instabilità può indurre un mescolamento parziale (semiconvezione) in una regione esterna al nucleo.

     

An extension of Szebehely's problem to holonomic systems

We study the problem of the determination of the potential function of forces generating a given family of orbits in the n-dimensional configuration space of the representative point of a holonomic system. We obtain first-order partial differential equations to solve the problem and we discuss some particular examples.

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Sunto Si studia il problema della determinazione del potenziale delle forze atte a far descrivere al punto rappresentativo di un sistema olonomo ad n gradi di libertà una traiettoria appartenente ad una assegnata famiglia di curve. Si scrivono le equazioni differenziali alle derivate parziali del primo ordine che reggono il problema e si considerano alcuni esempi particolari.

     

Self-accretion of matter,red subluminous stars and early evolution of low-mass stars

Low-mass stars during their pre-main sequence contraction phase are expected to be surrounded by a certain amount of the primordial gas. At low luminosities, accretion of this gas can make the stars to follow a peculiar evolutionary course which can account for certain types of red subluminous stars. The efficiency of the accretion mechanism can also account for some peculiarities in the spectra of the stars of low mass.

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Sommario Stelle di bassa massa in fase di contrazione pre-sequenza sono con ogni probabilità circondate da abbondante gas. In queste condizioni al diminuire della luminosità può divenire efficiente il meccanismo di accrescimento, cosi da condurre la stella su una linea evolutiva del tutto peculiare. Una simile evoluzione può rendere conto di oggetti sottoluminosi e a bassa temperatura, come pure di alcune peculiarità negli spettri di stelle di bassa massa.

     

On the models of core-helium-burning stars

Summary Some aspects concerning the core-mass increase and the appearance and development of an intermediate semiconvective zone in helium-burning stars are discussed. An iterative method of computation of core increase and semiconvection is also presented. Details of this procedure are given with regard to the horizontal-branch stars of globular clusters.

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Riassunto Sono presi in esame alcuni aspetti relativi all'aumento in massa del nucleo ed alla comparsa e sviluppo di una zona semiconvettiva intermedia in modelli di stelle con combustione centrale dell'elio. E'inoltre schematizzato il metodo iterativo di calcolo con particolare riferimento alle stelle di ramo orizzontale degli ammassi globulari.

     

Stellar atmospheres models of K-giant stars: the influence of opacity sources

Four different models for a K-giant atmosphere (T _e=4500K, logg=2) have been computed. Each model is characterized by the inclusion of different opacity sources (H, H^–, (H), metals, blanketing effect, He^–) in order to obtain an evaluation of the model sensitivity concerning the atmospheric structure and the emergent flux. The results show that hydrogen, metals and blanketing effect must be taken into account to achieve self-consistent and reliable models.A picture of the influence of the frequency distribution of the absorption coefficient on the model features is also shown.

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Sommario Sono stati calcolati quattro differenti modelli di una stella gigante K(T _e=4500K, logg=2). Ogni modello è caratterizzato dalla inclusione di differenti sorgenti di opacità (H, H^–, (H), metalli, effetto blanketing, He^–) per ottenere una valutazione della sensibilità del modello per quel che riguarda la struttura atmosferica ed il flusso emergente. I risultati ottenuti mostrano che per costruire modelli auto-consistenti e con un buon grado di affidabilità occorre tener conto almeno delle seguenti sorgenti di opacità: H, metalli, effetto blanketing.Si mostra inoltre come sia possibile una descrizione schematica dell'influenza del coefficiente di assorbimento sulle varie caratteristiche del modello.

     

Smooth models of overshooting at the base of the solar convective zone

A set of smoothed temperature gradient profiles around overshooting layers at the solar convective zone bottom is considered. In classical local theories of convection the one point defined according to the Schwarzschild criterion is enough to describe a convective boundary. To get a sophisticated picture of the overshooting we use four points to compute the transition overshooting functions. Analyzing the transition gradient profiles we found that the overshooting convective flux may be either positive or negative. A negative overshooting flux appears in nonlocal convective theories and causes a steep temperature gradient profile. But we propose an evenly smoothed gradient which corresponds to a convective flux positive everywhere. To outline the effect of the temperature gradient on the solar oscillations the squared Brunt–Väisälä frequency N ² is calculated. In local convective theories the N ² profile shows the discontinuity of the first derivative at the convective boundary, while all smoothed profiles eliminate the break.     

Physical conditions in the convective envelope of stars

Summary The mechanical flux originating in the convective envelope of stars is shown to depend critically by the treatment of convection. In particular, in the framework of the mixing-length theory, in passing from a mixing lengthl=H _P to a mixing lengthl=H the presence of mechanical fluxes shifts from being a marginal phenomenon to a dominant one.Possible implications concerning atmospheric microturbulence in Main Sequence stars, as so asA _p andA _m stars, several types of variables and mass loss are briefly discussed.

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Sommario Si mostra come il flusso cinetico originato negli inviluppi convettivi di una stella dipenda criticamente dalle assunzioni fatte nel trattamento della convezione superadiabatica. In particolare, sulla base della teoria della lunghezza di rimescolamento, a seconda che si assumal=H _P o l=H i flussi cinetici passano dall'essere un fenomeno marginale a contributi determinanti.E' discussa una serie di possibili implicazioni riguardanti la microturbolenza atmosferica in stelle di sequenza principale, le stelleA _p eA _m, diversi tipi di variabili e la perdita di massa in fase di gigante.

     

Physical conditions in the convective envelopes of stars

The physical conditions in the convective envelopes of Pop. II main-sequence stars are described with some detail. A particular care has been devoted to the effects due to the formation of hydrogen molecules and to the pressure ionization.

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Riassunto Vengono descritte in dettaglio le condizioni fisiche nelle zone convettive esterne delle stelle di sequenza principale di Popolazione II. In particolare vengono studiati gli effetti dovuti alla formazione della molecola dell'idrogeno ed alla ionizzazione per pressione.

     

An observation on the inverse extended problem of Szebehely

Through the use of Jacobi's formulation of the least action principle, differential equations for Szebehely's problem extended to a holonomic system with n degrees of freedom are obtained.

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Sunto Si riottengono le equazioni differenziali relative al problema di Szebehely esteso ad un sistema olonomo ad n gradi di libertà utilizzando il principio di minima azione nella formulazione di Jacobi.

     

On the evolutionary stage of stars in the Draco dwarf Galaxy

An analysis of the colour-magnitude diagram of stars in Draco dwarf Galaxy is performed on the basis of Baade and Swope observational results. Some evidence is found for the occurrence of a clump in the luminosity distribution of Red Giants stars. By combining this characteristic with the morphology of Horizontal Branch one obtains — in the frame of present knowledge of star-evolution —a suggestion for accepting high helium content (Y-0.30) with a relatively small age (1–2×10⁹ yr) for the evolving stars.Some correlations among lifetimes of evolutionaries stages are derived.

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Sommario Sulla base dei risultati osservativi di Baade e Swope viene eseguita un'analisi del diagramma colore-magnitudine delle stelle della Galassia Nana in Draco. Viene così evidenziata la possibile esistenza di un picco nella distribuzione in luminosità delle Giganti Rosse. Combinando questa caratteristica con l'osservato andamento del Ramo Orizzontale si mostra come — nell'ambito delle attuali conoscenze sull'evoluzione stellare — un simile comportamento conduca a postulare un alto contenuto di elio (Y-0.30) e una età relativamente bassa (1–2×10⁹ anni) per le stelle del sistema.Sono infine ricavate alcune correlazioni, tra le vite medie delle principali fasi evolutive.

     

Variation of the gradient and balmer discontinuity during the eclipse of the variable RW Tauri: Comparison between observations and theory

For the first time after Barbier and Chalonge's (1938, 1941) pioneering works, the variations of b andD during the eclipse of a variable (RT Tau), have been observed. The observations have been performed at the Observatories of Jungfraujoch and Haute Provence with the photoelectric system in seven colors of Geneva (Golay, 1964; Hauck, 1968). The comparison between the observed curves ofD and the theoretical ones, provides the limb darkening coefficients; the same comparison between the observed b (reddened) and theoretical ones (not reddened) together with that ofD, points out some anomalies of the variable RW Tau.

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Sommario Per la prima volta, dopo i primi lavori di Barbier e Chalonge (1938, 1941), sono state osservate le variazioni di b eD durante l'eclisse di una variabile (RW Tau). Le osservazioni sono state fatte agli Osservatori della Jungfraujoch e di Haute Provence col sistema fotoelettrico in sette colori di Ginevra (Golay, 1964; Hauck, 1968). Il confronto fra le curve osservate e teoriche diD, fornisce i coefficienti di oscuramento al bordo; lo stesso confronto fra i b osservati (arrossati) e quelli teorici (non arrossati) unitamente a quello delleD mette in evidenza alcune anomalie della variabile RW Tau.

     

On the role of the collisionally broadened wings of strong lines in the blanketing problem

The importance in the blanketing effect of the wings of strong lines broadened by collisions is evaluated. It is found that in stars of spectral types F5-K5 the cumulative absorption by a group of lines is due half to the center of the lines and half to the wings.For the same stars it is evaluated the influence of the collisional broadening on the computed color indices (U-B), (B-V).

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Sommario Viene valutata l'importanza nell'effetto blanketing delle ali delle righe forti allargate per collisioni. Si trova che per stelle dei tipi spettrali F5-K5 l'assorbimento complessivo di un gruppo di righe è all'incirca dovuto per metà all'assorbimento al centro delle righe e per metà alle ali.Per le stesse stelle viene anche data una stima dell'influenza dell'allargamento collisionale sugli indici di colore calcolati.

     

Current problems on asymptotic branch stars

An effort is made to select, from the available observational data, information concerning the asymptotic branch stars. Particular care is devoted to derive luminosity functions for these stars in clusters representative of selected classes. Some theoretical predictions are briefly made. It is stressed that, from a theoretical point of view, the comparison between the one-shell H-burning evolutionary characteristics and the corresponding ones for the A.B. phase could be expected to provide a powerful means of investigation.

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Sommario Sulla base dei dati osservativi disponibili sono raccolte ed esaminate le possibili informazioni riguardanti la fase di braccio asintotico. In particolare vengono investigate le funzioni di luminosità relative a questa fase evolutiva, e ne viene tentato un inquadramento nella classificazione multidimensionale degli ammassi globulari recentemente proposta. Sono fornite alcune valutazioni teoriche, ed è messo in evidenza come il confronto delle caratteristiche evolutive delle fasi di bruciamento ad una (H) e due (H, He) shell potrebbe rivelarsi come un potente mezzo di investigazione.

     

The effect of turbulent mixing on the g‐mode spectrum of MS stars

Understanding transport processes inside stars is one of the main goals of asteroseismology. Chemical turbulent mixing can affect the internal distribution of μ near the energy generating core, having an effect on the evolutionary tracks similar to that of overshooting. This mixing leads to a smoother chemical composition profile near the edge of the convective core, which is reflected in the behavior of the buoyancy frequency and, therefore, in the frequencies of gravity modes. We describe the effects of convective overshooting and turbulent mixing on the frequencies of gravity modes in B‐type main sequence stars. In particular, the cases of p‐g mixed modes in β Cep stars and high‐order modes in SPBs are considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Luminosity and mass functions for low main-sequence stars

The luminosity function derived for main sequence stars in the neighbourhood of the Sun shows evidence for a flattening in the interval 5≲M _v ≲8. An interpretation of this feature by means of theoretical models enables us to deduce the mass function for stars belonging to the main sequence.

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Sommario Viene ricavata la funzione di luminosità per stelle di sequenza principale vicine al Sole. Si evidenzia un pianerottolo per 5≲M _v ≲8. II confronto con i modelli teorici consente di desumere la funzione di massa della sequenza principale.

     

The accretion of interstellar matter by white dwarfs

The problem of the energy released by interstellar matter in its accretion by low-luminosity stars is examined. It is found that nearly all the gravitational energy is available as the energy source for the accreting star. When this source of energy becomes predominant, a luminosity-temperature relation can be derived.Evolutionary consequences for the white dwarfs are discussed.The behaviour of selected classes of white dwarfs is recognized in the theoretical H.R. diagram.The evidence for a separation between field white dwarfs and Hyades cluster's white dwarfs is shortly discussed. For the Hyades white dwarfs a well defined sequence in good agreement with a constant accretion locus is found.A critical discussion is finally given on the efficiency of the accretion mechanism in the Hyades dwarfs.

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Sommario Viene discusso il problema dell'energia ceduta dalla materia interstellare nei processi di cattura gravitazionale da parte di oggetti stellari di bassa luminosità. Si mostra come le maggior parte di questa energia sia effettivamente ceduta alla struttura stellare.Nei casi in cui l'energia di accrescimento predomini sulle altre sorgenti di energia è possibile ricavare una relazione luminosità-temperatura. Sono discusse possibili conseguenze sull'evoluzione delle nane bianche.E'esaminato il comportamento di alcune classi di nane bianche nel diagramma H.R. teorico, e viene brevemente discussa l'evidenza per una reale separazione delle nane bianche di campo da quelle nell'ammasso delle Iadi. Per queste ultime in particolare si trova una sequenza molto ben definita, in ottimo accordo con un luogo di costante accrescimento.Un esame critico è infine compiuto riguardo la possibile efficienza dell'accrescimento nelle nane delle Iadi.

     

Cooling sequence of a pure helium white dwarf of 0.15 solar masses

A new method of integration has been performed and applied to the computation of the cooling sequence of a 0.15M white dwarf consisting of helium. The results are discussed and compared with the previous ones obtained by other authors.

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Riassunto E' stato elaborato un nuovo metodo di integrazione numerica, ed applicato al calcolo della sequenza evolutiva di raffreddamento di una nana bianca di puro elio di 0.15M . I risultati vengono discussi e confrontati con i precedenti modelli ottenuti da altri autori.

     

On the effect of overshooting as predicted by the modelling of the pre-main-sequence evolution of a 2 M⊙ star

We discuss the effects of convective overshooting in the pre-main-sequence (PMS) evolution of intermediate-mass stars, by analysing in detail the early evolution towards the main sequence of a  2 M_⊙  stellar model. These effects can be extremely important in the end of the PMS, when the abundances in CNO elements approach the equilibrium in the centre. We provide a possible physical explanation on why a moderate amount of overshooting produces, as the star approaches the zero-age main-sequence, an extra loop in the evolutionary tracks on the Hertzsprung–Russell diagram.
An interesting feature is that there is a very well defined amount of overshooting (for a given stellar mass and chemical composition) beyond which a loop is produced. For smaller amounts of overshooting such a loop does not take place and the evolutionary tracks are similar to those found in the literature. The amount of overshooting needed to produce the loop decreases with stellar mass.
We discuss the underlining physical reasons for the behaviour predicted by the evolution models and argue that it provides a crucial observational test for convective overshooting in the core of intermediate-mass stars.     

Present problems of the solar interior

The standard model of solar evolution is reviewed and a number of problems highlighted. A fundamental question is whether there is any mixing of matter in the central regions, since such mixing could radically alter the model of the present Sun and modify our understanding of the evolution of other stars. Standard models of solar evolution become unstable to ³He driven global oscillations at an age of 3 × 10⁸ years and this may drive some mixing, even if this is not the case the finite amptitude limit of these oscillations is likely to produce modifications in the standard model. Convective overshooting at the bottom of the outer convective zone leads to an increased depth of this zone and small changes in the interior. It is pointed out that the young Sun had a ¹²C driven convective core whose extent and duration depends on the extent of overshooting. Such a core is likely to produce a magnetic field which will affect the internal dynamics. The internal rotation of the Sun remains an enigma and absence of knowledge of any internal magnetic field makes it difficult to study the problem. Rotationally driven instabilities are ineffective in the central chemically inhomogenous regions but may contribute to the inward diffusion of lithium from the convective zone. These and other problems are considered, but few solutions are proposed.     

Can mass loss and overshooting prevent the excitation of g-modes in blue supergiants?

Thanks to their past history on the main-sequence phase, supergiant massive stars develop a convective shell around the helium core. This intermediate convective zone (ICZ) plays an essential role in governing which g-modes are excited. Indeed, a strong radiative damping occurs in the high-density radiative core but the ICZ acts as a barrier preventing the propagation of some g-modes into the core. These g-modes can thus be excited in supergiant stars by the κ-mechanism in the superficial layers due to the opacity bump of iron, at  log  T = 5.2  . However, massive stars are submitted to various complex phenomena such as rotation, magnetic fields, semiconvection, mass loss, overshooting. Each of these phenomena exerts a significant effect on the evolution and some of them could prevent the onset of the convective zone. We develop a numerical method which allows us to select the reflected, thus the potentially excited, modes only. We study different cases in order to show that mass loss and overshooting, in a large enough amount, reduce the extent of the ICZ and are unfavourable to the excitation of g-modes.