The rotation rate, level of magnetic activity and surface lithium abundance are age-dependent quantities in stars of about a solar mass and below. The physical reasons for the evolution of these ...phenomena are qualitatively understood, but accurate quantitative models remain dependent on empirical calibration using the Sun and stars of known age, chiefly in clusters. In this work I review the status of these “empirical age indicators”, outlining the astrophysics of their time dependence, describing the measurements, assessing the precision (and accuracy) of age estimates when applied to individual stars, and identifying their principle limitations in terms of the mass and age ranges over which they are useful. Finally, I discuss the “lithium depletion boundary” technique which, in contrast to the empirical methods, appears to provide robust, almost model-independent ages that are both precise and accurate, but which is only applicable to coeval groups of stars.
This chapter deals with the multiple linear regression. That is we investigate the situation where the mean of a variable depends linearly on a set of covariables. The noise is supposed to be ...gaussian. We develop the least squared method to get the parameter estimators and estimates of their precisions. This leads to design confidence intervals, prediction intervals, global tests, individual tests and more generally tests of submodels defined by linear constraints. Methods for model's choice and variables selection, measures of the quality of the fit, residuals study, diagnostic methods are presented. Finally identification of departures from the model's assumptions and the way to deal with these problems are addressed. A real data set is used to illustrate the methodology with software R. Note that this chapter is intended to serve as a guide for other regression methods, like logistic regression or AFT models and Cox regression.
We present calculations illustrating the potential of gravitational microlensing to discriminate between classical models of stellar surface brightness profiles and the recently computed “Next ...Generation” models of Hauschildt et al. These spherically-symmetric models include a much improved treatment of molecular lines in the outer atmospheres of cool giants – stars which are very typical sources in Galactic bulge microlensing events. We show that the microlensing signatures of intensively monitored point and fold caustic crossing events are readily able to distinguish between NextGen and the classical models, provided a photometric accuracy of 0.01 mag is reached. This accuracy is now routinely achieved by alert networks, and hence current observations can discriminate between such model atmospheres, providing a unique insight on stellar photospheres.
We use data from the Hipparcos catalogue to construct colour-magnitude diagrams for the solar neighbourhood, which are then treated using advanced Bayesian analysis techniques to derive the star ...formation rate history, SFR(t), of this region over the last 3 Gyr. The method we use allows the recovery of the underlying SFR(t) without the need of assuming any a priori structure or condition on SFR(t), and hence yields a highly objective result. The remarkable accuracy of the data permits the reconstruction of the local SFR(t) with an unprecedented time resolution of ≈50 Myr. An SFR(t) that has an oscillatory component of period ≈0.5 Gyr is found, superimposed on a small level of constant star formation activity. Problems arising from the non-uniform selection function of the Hipparcos satellite are discussed and treated. Detailed statistical tests are then performed on the results, which confirm the inferred SFR(t) to be compatible with the observed distribution of stars.
Among the various methods used to age-date stars, methods based on stellar model predictions are widely used, for nearly all kind of stars in large ranges of masses, chemical compositions and ...evolutionary stages. The precision and accuracy on the age determination depend on both the precision and number of observational constraints, and on our ability to correctly describe the stellar interior and evolution. The imperfect input physics of stellar models as well as the uncertainties on the initial chemical composition of stars are responsible for uncertainties in the age determination. We present an overview of the calculation of stellar models and discuss the impact on age of their numerous inputs.
Accurate and precise stellar ages are best determined for stars which are strongly observationally constrained, that is which are intrinsically oscillating. We review here the seismic diagnostics ...which are sensitive to stellar ages and provide some illustrating examples of seismically age-dated stars.
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