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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - THOT (Comprehensive code for stellar dating, and analysis of exoplanetary systems observed by direct imaging)

Teaser

Summary

Knowledge of how stars are born, evolve and die underpins much of our understanding of the Universe. In this effort, stellar dating is critical. It helps to interpret observational data and to understand the underlying physics of very different astrophysical issues. Although there are a number of techniques in the literature for estimating stellar ages, none is suitable for all-stars, and the uncertainties are very large in general.

As a consequence, there are no research groups in the world dating stars using all the techniques available. What we find is that a number of research groups dating stars using a subset of these techniques, for which they are specialized. Therefore, there is a lack of a general tool for automated stellar dating. It is critical and timely to develop this tool as current and future space missions such as Kepler/K2 and TESS (NASA), Gaia and Plato (ESA), JWST (NASA-ESA-CSA), etc., will provide a large amount of very accurate observational data. Gaia will observe 1 billion stars, for example. The automated analysis of these data will be a must, and stellar dating is far from being automated nowadays.

The overarching aims of THOT are: 1) to gather all the techniques available for stellar dating, updating those having huge potential for application to data from new and upcoming missions (gyrochronology, isochrones, asteroseismology, and kinematics), and 2) to develop software to automate this dating with a double purpose: a) to offer a user-friendly code for stellar dating, and b) to evaluate the age of exoplanetary systems observed by direct imaging. It is the first time, up to our knowledge, that such a global project for stellar dating has been tackled.

Stellar-mass (M) and radius (R) are key variables for estimating stellar ages. Unfortunately, they cannot be directly observed for most of the stars. In these cases, one of the most used options is to estimate these quantities as a function of other observables (such as effective temperature, metallicity, luminosity, etc.) thanks to data-driven relations. For facing the first objective of THOT, we must include a goal 0: update the empirical relations for estimating stellar masses and radii using observational data coming from eclipsing binaries and asteroseismology.

During this MSCA we have combined an exceptional database and machine learning techniques for providing, for the first time in some of the stellar characterization fields, an important step beyond the state-of-the-art in empirical estimations of stellar masses, radii, and ages, this last using chemical clocks and gyrochronology. We have reached a stellar-mass estimation with an uncertainty of around 5%, a radius estimation with an uncertainty of around 3%, and age estimations with an error of the order of 1 Gyr for isolated stars. This last value is beyond our expectations. Finally, we have gathered the most recent results and codes for stellar dating using stellar activity, isochrones Bayesian fitting, and asteroseismology.

Work performed

The project started gathering the most complete database up to date for obtaining empirical relations for estimating stellar masses and radii. More than 700 Main Sequence stars with very accurate stellar masses, radii, effective temperatures, luminosities, surface gravities, and mean densities (in some cases) were put together. Using classical statistical methods, we selected a total of 52 relations coming from data. We have also used machine learning techniques (in particular Random Forest) for non-parametric estimation of the stellar mass and radius when any group of observables is provided. We have also developed a computational application for the general use of these relations and models. This work has been published in the Astrophysical Journal Supplement Series. We have presented these results in three international meetings, three seminars, and some of these relations have been selected for estimating the stellar mass of the stars at the Plato2.0 Input Catalogue.

With this result, we moved to the next step of THOT: the gathering of stellar dating methods and updating the most important ones. First, in collaboration with the first secondment (IA, Porto), we revised the method called â€œChemical clocksâ€. We obtained a database with more than 1000 stars with planets with accurate effective temperatures, metallicities, surface gravities, masses and radii coming from our empirical relations, ages using isochrones fitting, and the abundance of more than 20 chemical elements. With this database, we added eight new chemical clocks to the already two known at that time and presented different multidimensional linear regressions for estimating stellar ages. This work was published in Astronomy & Astrophysics, presented in two international meetings and three seminars.

We have also faced the improvement of the method called gyrochronology. We have gathered a total of more than 600 Main Sequence stars with accurate effective temperatures, luminosities, metallicities, masses, radii, rotational periods, and ages, all coming from clusters (thanks to our new empirical relations) and asteroseismology. With this exceptional database, we have trained a Hierarchical Bayesian model for the estimation of the stellar age. The results are really encouraging, and they have been presented in an international meeting.

We have studied and developed a code for the stellar age estimation using proper motions. We have found that this technique is, by far, the less reliable and inconsistent of all. We aborted this subline.

Finally, we have gathered the most recent results and codes for stellar dating using stellar activity, isochrones Bayesian fitting, and asteroseismology. Now we have all the pieces planned for the computational code THOT.

As side products of this main research line, we have published a paper analyzing the erosion provoked on exoplanetary atmospheres by stellar winds and we have collaborated in the age estimation of the exoplanetary system GJ 3512, where the exoplanets formation and evolution theories are threated (published in Science). In addition, we have also collaborated in the analysis of the naked-eye star nu Indi, currently under review in Nature.
The dissemination plan was completed: 5 publications, two more under preparation, one under review, and 4 external collaborations. 8 international meetings. 3 seminars. Open days of the University of Birmingham. Dedicated Facebook page, and the THOT project webpage.

Final results

The combination of an exceptional database and machine learning techniques have provided, for the first time in some of these fields, an important step beyond the state-of-the-art in empirical estimations of stellar masses, radii, and ages, this last using chemical clocks and gyrochronology. This is the main contribution of this project. All the results have been already obtained, and in the near future, we plan to finish the publication and dissemination plan. These results are really impressive and encouraging. We have reached a stellar-mass estimation with an uncertainty of around 5%, a radius estimation with an uncertainty of around 3%, and age estimations with an error of the order of 1 Gyr for isolated stars. This last value is beyond our expectations.