Testing pre-main sequence models: the power of a Bayesian approach

Pre-main sequence (PMS) models provide invaluable tools for the study of star forming regions as they allow to assign masses and ages to young stars. Thus it is of primary importance to test the models against observations of PMS stars with dynamically determined mass. We developed a Bayesian method for testing the present generation of PMS models which allows for a quantitative comparison with observations, largely superseding the widely used isochrones and tracks qualitative superposition. Using the available PMS data we tested the newest PISA PMS models establishing their good agreement with the observations. The data cover a mass range from ~0.3 to ~3.1 Msun, temperatures from ~3x10^3 to ~1.2x10^4 K and luminosities from ~3x10^-2 to ~60 Lsun. Masses are correctly predicted within 20% of the observed values in most of the cases and for some of them the difference is as small as 5%. Nevertheless some discrepancies are also observed and critically discussed. By means of simulations, using typical observational errors, we evaluated the spread of log \tau_sim - log \tau_rec, i.e. simulated minus recovered ages distribution of the single objects. We also found that stars in binary systems simulated as coeval might be recovered as non coeval, due to observational errors. The actual fraction of fake non coevality is a complex function of the simulated ages, masses and mass ratios. We demonstrated that it is possible to recover the systems' ages with better precision than for single stars using the composite age-probability distribution, i.e. the product of the components' age distributions. Using this valuable tool we estimated the ages of the presently observed PMS binary systems.Comment: Accepted for publication in MNRAS. Fig.2 presented in low-resolution in this versio

The Pisa pre-main sequence stellar evolutionary models: results for non-accreting and accreting models

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

Single stars in the Hyades open cluster. Fiducial sequence for testing stellar and atmospheric models

Age and mass determinations for isolated stellar objects remain model-dependent. While stellar interior and atmospheric theoretical models are rapidly evolving, we need a powerful tool to test them. Open clusters are good candidates for this role. We complement previous studies on the Hyades multiplicity by Lucky Imaging observations with the AstraLux Norte camera. This allows us to exclude possible binary and multiple systems with companions outside 2--7 AU separation and to create a "single-star sequence" for the Hyades. The sequence encompasses 250 main-sequence stars ranging from A5V to M6V. Using the "Tool for Astrophysical Data Analysis" (TA-DA), we create various theoretical isochrones applying different combinations of interior and atmospheric models. We compare the isochrones with the observed Hyades single-star sequence on J vs. J - K_s, J vs. J - H and K_s vs. H - K_s color-magnitude diagrams. As a reference we also compute absolute fluxes and magnitudes for all stars from X-ray to mid-infrared based on photometric measurements available in the literature(ROSAT X-ray, GALEX UV, APASS gri, 2MASS JHK_s, and WISE W1 to W).We find that combinations of both PISA and DARTMOUTH stellar interior models with BT-Settl 2010 atmospheric models describe the observed sequence well. The full sequence covers the mass range 0.13 to 2.3 Msun, and effective temperatures between 3060 K and 8200 K. Within the measurement uncertainties, the current generation of models agree well with the single-star sequence. The primary limitations are the uncertainties in the measurement of the distance to individual Hyades members, and uncertainties in the photometry. Additionally, a small (~0.05 mag) systematic offset can be noted on J vs. J - K and K vs. H - K diagrams - the observed sequence is shifted to redder colors from the theoretical predictions.Comment: 6 pages, 2 figures, 1 table. The extended version of the table will be available online soon. Accepted for publication in Astronomy & Astrophysic

ÆSOPUS 2.0: Low-temperature Opacities with Solid Grains

In this study we compute the equation of state and Rosseland mean opacity from temperatures of T similar or equal to 30,000 K down to T similar or equal to 400 K, pushing the capabilities of the ae SOPUS code into the regime where solid grains can form. The GGchem code is used to solve the chemistry for temperatures less than similar or equal to 3000 K. Atoms, molecules, and dust grains in thermodynamic equilibrium are all included in the equation of state. To incorporate monochromatic atomic and molecular cross sections, an optimized opacity sampling technique is used. The Mie theory is employed to calculate the opacity of 43 grain species. Tables of Rosseland mean opacities for scaled-solar compositions are provided. Based on our computing resources, opacities for other chemical patterns, as well as various grain sizes, porosities, and shapes, can be easily computed upon user request to the corresponding author

When the tale comes true: multiple populations and wide binaries in the Orion Nebula Cluster

The high-quality OmegaCAM photometry of the 3x3 deg around the Orion Nebula Cluster (ONC) in r, and i filters by Beccari et al.(2017) revealed three well-separated pre-main sequences in the color-magnitude diagram (CMD). The objects belonging to the individual sequences are concentrated towards the center of the ONC. The authors concluded that there are two competitive scenarios: a population of unresolved binaries and triples with an exotic mass ratio distribution, or three stellar populations with different ages. We use Gaia DR2 in combination with the photometric OmegaCAM catalog to test and confirm the presence of the putative three stellar populations. We also study multiple stellar systems in the ONC for the first time using Gaia DR2. We confirm that the second and third sequence members are more centrally concentrated towards the center of the ONC. In addition we find an indication that the parallax and proper motion distributions are different among the members of the stellar sequences. The age difference among stellar populations is estimated to be 1-2 Myr. We use Gaia measurements to identify and remove as many unresolved multiple system candidates as possible. Nevertheless we are still able to recover two well-separated sequences with evidence for the third one, supporting the existence of the three stellar populations. We were able to identify a substantial number of wide binary objects (separation between 1000-3000 au). This challenges previously inferred values that suggested no wide binary stars exist in the ONC. Our inferred wide-binary fraction is approx 5%. We confirm the three populations correspond to three separated episodes of star formation. Based on this result, we conclude that star formation is not happening in a single burst in this region. (abridged)Comment: Astronomy and Astrophysics (A&A) accepted. 12 pages, 9 figures + appendix. New version with language corrections and new ID values in Tab.A.

ASTROPHYSICAL IMPACT of the UPDATED 9Be(p,)6Li and 10B(p,)7Be REACTION RATES AS DEDUCED by THM

The complete understanding of the stellar abundances of lithium, beryllium, and boron represents one of the most interesting open problems in astrophysics. These elements are largely used to probe stellar structure and mixing phenomena in different astrophysical scenarios, such as pre-main-sequence or main-sequence stars. Their different fragility against (p,) burning reactions allows one to investigate different depths of the stellar interior. Such fusion mechanisms are triggered at temperatures between T ≈ (2-5) × K, thus defining a corresponding Gamow energy between ≈ 3-10 keV, where S(E)-factor measurements need to be performed to get reliable reaction rate evaluations. The Trojan Horse Method is a well defined procedure to measure cross sections at Gamow energies overcoming the uncertainties due to low-energy S(E)-factor extrapolation as well as electron screening effects. Taking advantage of the measure of the 9Be(p,)6Li and 10B(p,)7Be cross sections, the corresponding reaction rates have been calculated and compared with the evaluations by the NACRE collaboration, widely used in the literature. The impact on surface abundances of the updated 9Be and 10B (p,) burning rates is discussed for pre-MS stars

Lithium evolution in young open clusters from the Gaia-ESO Survey

The Gaia-ESO Survey provides the largest database of homogeneously-determined lithium abundances and stellar parameters for open star clusters of different age and metallicity. It is therefore well suited to investigate young stellar evolution and to provide independent age estimates in young clusters. We present the lithium results for a sample of young clusters of ages between 10 and 100 Myr, and compare the observed lithium depletion patterns with models of lithium depletion in pre-main sequence stars

Lithium and age of pre-main sequence stars: The case of Parenago 1802

With the aim to test the present capability of the stellar surface lithium abundance in providing an estimation for the age of PMS stars, we analyze the case of the detached, double-lined, eclipsing binary system PAR 1802. For this system, the lithium age has been compared with the theoretical one, as estimated by applying a Bayesian analysis method on a large grid of stellar evolutionary models. The models have been computed for several values of chemical composition and mixing length, by means of the code FRANEC updated with the Trojan Horse reaction rates involving lithium burning

The clustered nature of star formation. Pre--main-sequence clusters in the star-forming region NGC 602/N90 in the Small Magellanic Cloud

Located at the tip of the wing of the Small Magellanic Cloud (SMC), the star-forming region NGC602/N90 is characterized by the HII nebular ring N90 and the young cluster of pre--main-sequence (PMS) and early-type main sequence stars NGC602. We present a thorough cluster analysis of the stellar sample identified with HST/ACS camera in the region. We show that apart from the central cluster, low-mass PMS stars are congregated in thirteen additional small compact sub-clusters at the periphery of NGC602. We find that the spatial distribution of the PMS stars is bimodal, with an unusually large fraction (~60%) of the total population being clustered, while the remaining is diffusely distributed in the inter-cluster area. From the corresponding color-magnitude diagrams we disentangle an age-difference of ~2.5Myr between NGC602 and the compact sub-clusters which appear younger. The diffuse PMS population appears to host stars as old as those in NGC602. Almost all detected PMS sub-clusters appear to be centrally concentrated. When the complete PMS stellar sample, including both clustered and diffused stars, is considered in our cluster analysis, it appears as a single centrally concentrated stellar agglomeration, covering the whole central area of the region. Considering also the hot massive stars of the system, we find evidence that this agglomeration is hierarchically structured. Based on our findings we propose a scenario, according to which the region NGC602/N90 experiences an active clustered star formation for the last ~5Myr. The central cluster NGC602 was formed first and rapidly started dissolving into its immediate ambient environment, possibly ejecting also massive stars found away from its center. Star formation continued in sub-clusters of a larger stellar agglomeration, introducing an age-spread of the order of 2.5Myr among the PMS populations.Comment: Accepted for publication by The Astrophysical Journal. 14 pages, 11 figures, 1 table, 2-columns forma

On a New Theoretical Framework for RR Lyrae Stars. II. Mid-infrared Period-Luminosity-Metallicity Relations

We present new theoretical period-luminosity-metallicity (PLZ) relations for RR Lyrae stars (RRL) at Spitzer and WISE wavelengths. The PLZ relations were derived using nonlinear, time-dependent convective hydrodynamical models for a broad range in metal abundances (Z=0.0001 to 0.0198). In deriving the light curves, we tested two sets of atmospheric models (Brott & Hauschildt 2005, Castelli & Kurucz 2003) and found no significant difference between the resulting mean magnitudes. We also compare our theoretical relations to empirical relations derived from RRL in both the field and in the globular cluster M4. Our theoretical PLZ relations were combined with multi-wavelength observations to simultaneously fit the distance modulus, mu_0, and extinction, Av, of both the individual Galactic RRL and of the cluster M4. The results for the Galactic RRL are consistent with trigonometric parallax measurements from Gaia's first data release. For M4, we find a distance modulus of $\mu_0=11.257 \pm 0.035$ mag with $A_V = 1.45 \pm 0.12$ mag, which is consistent with measurements from other distance indicators. This analysis has shown that when considering a sample covering a range of iron abundances, the metallicity spread introduces a dispersion in the PL relation on the order of 0.13 mag. However, if this metallicity component is accounted for in a PLZ relation, the dispersion is reduced to ~0.02 mag at MIR wavelengths