• Bayesian method
• binary stars
• elements abundances
• HR-diagram
• pre-main sequence
• stellar evolution

Through the years the understanding of stellar physics has been continuously refined thanks to the progress in the determination of the input physics for the stellar models and in new observational capabilities. Now the general scenario is well defined and confirmed by a vast amount of observational data for the Sun and for field and cluster stars in our Galaxy. Several problems however are still not completely solved (e.g. the accurate treatment of external convection, the overshooting and diffusion efficiency...) and the input physics adopted in the calculations are often affected by not negligible uncertainties. However more and more precise available observational data requires theoretical models the most reliable and accurate as possible.

I emphasize that the computation of a stellar model is a quite challenging task which involves different fields of physics due to the very wide range of physical conditions (i.e. temperatures and density) covered by a star during its evolution. Calculations require many and accurate ingredients related to the microphysics by which I mean the study of the plasma properties in stellar conditions ( i.e. equations of state for the matter, opacity coefficients, cross sections for nuclear burning etc...), and to the macrophysics, that is the modelling of several processes present in a stars such as the energy transport along the whole structure or the element diffusion. All these quantities are obviously given within a specific uncertainty due to, for example, the adopted physical approximations.

In this PhD thesis work I focused my attention to the pre-main sequence phase (pre-MS), which is the early evolution of a star starting from a cold gravitational contracting fully convective structure where no nuclear burning is active (Hayashi track), to the first model sustained by the totally efficient central hydrogen burning (the Zero Age Main Sequence model or simply ZAMS).

Pre-MS tracks and isochrones represent the indispensable theoretical tool to infer the star formation history and the initial mass function of young stellar system. In recent years new observations of pre-MS stars in young open clusters or in stars forming regions with metallicity also lower than solar one have been made available. To take fully advantage of the continuously growing amount of data in different environments, updated pre-MS models in a wide range of metallicity are needed to assign ages and masses to the observed stars.

Although the pre-MS evolution of a star can be treated as a quasi-static gravitational contraction, therefore it should be, at least in principle, not too much complex from the computational point of view, however the calculations are particularly challenging especially in the case of cold and dense matter, because they require an accurate treatment. This is the case of low (0.4 < M/Msun < 1.0 ) and very-low mass stars (M < 0.4 Msun). As already shown by several authors (D'Antona et al. 1993, D'Antona et al. 1997, Baraffe et al. 1998, Siess et al. 2000, Baraffe et al. 2002, Montalban et al. 2004}, the theoretical predictions of pre-MS stars sensitively depend on the adopted EOS, radiative opacity (mainly molecular opacity), outer boundary conditions, and convection treatment. The uncertainties due to these quantities progressively increase as the stellar mass decreases.

In this PhD thesis I analysed in detail the main uncertainty sources in the input physics that affects the pre-MS evolution and, when possible, I upgraded the current version the Pisa stellar evolutionary code (PROSECCO code, developed from the FRANEC, Degl'Innocenti 2008, Tognelli et al. 2011, Dell'Omodarme et al. 2012) to the current state-of-art of the input physics available (Chapter 1).

The theoretical models obtained by means of the PROSECCO code have been compared to the results obtained by largely used evolutionary codes (Chapter 2), to test both the reliability of the present computations and to show and discuss the entity of the differences present among the current generation of stellar evolutionary models, differences that translate into uncertainties on the main parameters inferred when comparing models to observational data for stars in different environments (i.e. isolated, clusters, star forming regions, or in binary systems).

In order to supply a powerful tool to analyse and investigate the large amount of pre-MS data collected, I made available a large pre-MS tracks and isochrones database, which cover a wide range of masses (0.2 - 7.0 Msun), ages (1 - 100 Myr), chemical compositions, and convection efficiency (Pisa pre-MS database).

The models have also been tested against a sample of pre-MS stars in binary systems, which are ideal environments to check the validity of stellar computations. Indeed, contrarily to isolated stars, binaries allow a direct measurement of the masses of the two stellar components. Moreover, there is a particular class of binaries (the double-lined detached eclipsing binaries) for which also the radius and the effective temperature ratio of the two components are measurable. It is clear that such objects put strong constraint on the stellar models and in particular allow, at least in principle, to better constrain the parameters adopted for theoretical stellar computations (i.e. convection efficiency). The comparison have been performed by generalising/applying a robust statistical method (Jorgensen & Lindegren 2005) to the case of binaries. Such method allows not only to quantify the agreement level between predictions and data, but it also allows to unambiguously discriminate the most probable model among a large ensemble of theoretical models spanning a very large parameters space. Given such a situation, the method has been applied to the Pisa pre-MS database using the whole available set of parameters.

The comparison with observation has been conducted also for few young and well studied open clusters, in particular for what concerns the temporal evolution of lithium surface abundance (Chapter 3). Lithium is a fragile element that is destroyed into stars via proton capture at relatively low temperatures (2.5 x 10^6 K). Such temperatures can be easily reached even during the early pre-MS evolution along the Hayashi track. In these phases the stars are fully (or almost fully) convective, thus the continuous mixing of the surface matter with the central one, where the nuclear burning occurs, produces an observable depletion of lithium. The temporal evolution of surface Li abundance strongly depends on the star characteristics, mainly on its mass, on the temperature stratification inside the stellar structure, and on the mixing mechanisms.

Despite of this simple picture, the difficulty of reproducing surface lithium abundances even in young stars is a long-standing problem and an intriguing issue; thus, it is worth to re-analyse the old lithium problem, in the light of the recent updates in the input physics.

Given the large effort in collecting surface lithium abundances in isolated stars, binary systems, and open clusters, from pre-MS to the late-MS phase, it has become possible to have a quite clear view of Li depletion, which is a strong function of both stellar mass and age.

I will discuss the comparison between theoretical predictions and data available for $^7$Li by analysing in detail the theoretical uncertainties on the predicted surface lithium abundances due to the errors on the adopted input physics. This is an essential step to define in a consistent way (for the first time) quantitative error bars for model predictions, and thus to give a more quantitative estimation of the agreement/disagreement level between models and data. I will also show how the comparison can give precious information about the convection efficiency during the pre-MS phase.

The last topic that I will discuss in this PhD thesis concerns how the predictions of theoretical models change if accretion processes are taken into account (Chapter 4). Indeed, stars form from the fragmentation of molecular clouds, which originate the seeds (protostars) on which accretion processes occur. It is commonly accepted that at some stage of the fragmentation an accretion disk forms. The presence of circumstellar accretion disks has been largely demonstrated by the huge amount of observations collected for young star-forming regions. Such observations suggest that disks are quite common around young objects.

The detailed treatment of how the cloud fragmentation and the following accretion process occur is still largely debated and uncertain, however, in the recent year, thanks to the development of hydrodynamical code, simulations of fragmenting molecular cloud, disk formation and accretion processes have became partially accessible.

Currently the accretion scenario can be divided into two geometries: 1) disk and 2) spherical accretion. In the first case, the matter is supposed to fall onto a central object from an accretion disk; depending on the structure of the disk, the accretion can interest a small portion of the central object (i.e. polar accretion caused by magnetic fields), or a large part of the stellar surface.

In the case of the spherical accretion, the matter falls (almost) radially on the star, and the assumption that only a small fraction of the stellar surface is interested by the accretion drops.

Concerning stellar evolutionary code, a formalism to tread the spherical accretion scenario has been proposed in the pioneering work by Stahler et al. 1980, while the disk accretion model formalism has been proposed by Hartmann et al. 1997 and Siess et al. 1997. More recently, such work have been adopted as basis to develop accretion evolution models by Hosokawa et al. 2009 (spherical accretion) and Baraffe et al. 2009 (disk accretion).

I will focus on the thin-disk accretion, similarly to what done by Hartmann et al. 1997, Siess et al. 1997, and Baraffe et al. 2009. In this case the fraction of the stellar surface where matter is accreted is very small compared to the total surface, thus allowing the star to radiate almost freely. This approximation has been confirmed to be valid by the observations conducted by Hartigan et al. 1991 on a large sample of young accreting objects (T Tauri).

As a first step I will present the formalism adopted in the PROSECCO code to treat the accretion process, and then I will discuss in detail the evolution of accreting models. I will analyse the dependency of such models on the adoption of several (poorly constrained) parameters (accretion rates, accretion history, accretion energy parameter), to try to clarify the main parameters that strongly affects the predictions. A qualitative comparison with few observational data will be also shown.