Classical broad-band photometry can provide direct comparisons of star clusters both with each other and with theoretical models of stellar evolution. The confidence with which conclusions can be drawn is often limited by the accuracy of the measurements. The present work is part of a long-term attempt to improve photometric calibrations.

Horizontal branch (HB) stars play a particularly important role in the “age debate,” since they are at the very center of the long-standing “second parameter” problem. In this review, I discuss some recent progress in our understanding of the nature and origin of HB stars.

We present a review of the latest work concerned with the relative and absolute ages of the Galactic globular clusters (GCs). Relative age-dating techniques generally divide into two types - those that measure a magnitude difference between two features in the color-magnitude diagram (i.e. Vertical Methods) and those that rely on color differences in the color-magnitude diagram (i.e. Horizontal Methods). Both types of diagnostics have been successfully applied and generally reach the same conclusions. Galactic GCs exhibit a mean age range of ~3 Gyr, smaller (or nonexistent) for metal-poor clusters and larger (as much as 6 Gyr) for metal-rich ones. Generally speaking, the inner-halo GCs are older and more uniform in age as compared with those outside of the solar circle. Furthermore, the tendency of GCs with predominantly red horizontal branches (HBs) located in the outer halo to be preferentially younger than those with bluer HBs closer to the Galactic center suggests that age is the second parameter which, in addition to metal abundance, controls the HB morphology. In particular, we present additional compelling evidence supporting this assertion using a detailed examination of new photometry for the classic second-parameter cluster pair NGC 288 and NGC 362. Moving on to the absolute ages, we note that the absolute ages of the most metal-poor Galactic GCs sets a lower limit on the age of the Universe. The preferred age indicator for absolute ages is the luminosity of the main-sequence turnoff because most theoretical models agree on the onset of hydrogen exhaustion in the cores of low-mass stars. Based on the technique of main-sequence fitting to field subdwarfs with Hipparcos parallaxes, we find an age of 11.6+1.4−1.1 Gyr for four metal-poor GCs with deep color-magnitude diagrams on a consistent photometric scale; this age is consistent with the results of a number of previous investigations.

An increasing number of photometric observations of multiple stellar populations in Galactic globular clusters is seriously challenging the paradigm of GCs hosting single, simple stellar populations. These multiple populations manifest themselves in a split of different evolutionary sequences as observed in the cluster color-magnitude diagrams. Multiple stellar populations have been identified in Galactic and Magellanic Cloud clusters. In this paper we will summarize the observational scenario.

We present a new method to solve for the star-formation history (SFH) of a complex stellar population system from the analysis of the color-magnitude diagram (CMD). The SFH is obtained in four steps: i) computing a synthetic CMD, ii) simulating observational effects, iii) parameterization and sampling of the synthetic and observed CMDs, and iv) solving and averaging the solutions. The consistency and stability of the method have been tested using a mock stellar population.

The method has been used to solve the SFH of a set of six isolated Local Group dwarf galaxies observed with HST. The main goal is to probe the effects of cosmological processes, such as reionization in the early star formation, or the ability of SNe feedback to remove gas in small halos, in dwarf galaxies free from environmental effects due to the strong interaction with the host galaxy.

The spreads in chemical abundances inferred by recent precision observations suggest that some or possibly all globular clusters can no longer be considered as simple stellar populations. The most striking case is ω Cen in the sense that its bluest main-sequence, despite its high metallicity, demands an extreme helium abundance of Y ≈ 0.4. I focus on this issue of “the extreme helium population problem” in this review.

A significant fraction of stars in globular clusters (about 70%-85%) exhibit peculiar chemical patterns, with strong abundance variations in light elements along with constant abundances in heavy elements. These abundance anomalies can be created in the H-burning core of a first generation of fast-rotating massive stars, and the corresponding elements are conveyed to the stellar surface thanks to rotational induced mixing. If the rotation of the stars is fast enough, this material is ejected at low velocity through a mechanical wind at the equator. It then pollutes the interstellar medium (ISM) from which a second generation of chemically anomalous stars can be formed. The proportion of anomalous stars to normal stars observed today depends on at least two quantities: (1) the number of polluter stars; (2) the dynamical history of the cluster, which may lose different proportions of first- and second-generation stars during its lifetime. Here we estimate these proportions, based on dynamical models for globular clusters. When internal dynamical evolution and dissolution due to tidal forces are accounted for, starting from an initial fraction of anomalous stars of 10% produces a present-day fraction of about 25%, still too small with respect to the observed 70-85%. In the case of gas expulsion by supernovae, a much higher fraction is expected to be produced. In this paper we also address the question of the evolution of the second-generation stars that are He-rich, and deduce consequences for the age determination of globular clusters.

The Magellanic Clouds possess extensive systems of rich star clusters. These objects span a wide range in age and metal abundance, and are close enough to be fully resolved into individual stars. They represent the most accessible examples of such clusters and are therefore key to a wide variety of astronomical research. In this contribution I describe recent results from work on several problems in Magellanic Cloud cluster astronomy of relevance to The Ages of Stars. These include testing and constraining stellar evolution and simple stellar population models, investigating the formation and evolution of the Clouds themselves, and the discovery of several intermediate-age clusters which apparently possess more than one stellar population.

White dwarfs represent the endpoint of the evolution of the large majority of stars formed in the Galaxy. In the last two decades observations and theory have improved to a level that makes possible to employ white dwarfs for determining ages of the stellar populations in the solar neighborhood, and in the nearest star clusters. This review is centered on the theory behind the methods for white dwarf age-dating, and the related uncertainties, with particular attention paid to the problem of the CO stratification, envelope thickness and chemical composition, and the white dwarf initial-final-mass relationship.

Much of our knowledge regarding the ages of stars derives from our understanding of the Hertzsprung-Russell Diagram. The diagram is typically dominated by hydrogen burning main-sequence stars, which historically, have been used to establish our most fundamental knowledge of stellar ages and evolution. In this brief article, I highlight how deep ground and space based imaging can uncover the stellar remnants of these hydrogen burning stars, white dwarfs. We have followed up our initial discovery of several large white dwarf populations in nearby star clusters with multiobject spectrographs. The spectroscopy allows us to characterize the properties of the remnant stars (e.g., mass, temperature, and age), which are in turn used to shed new light on fundamental astrophysical problems. Specifically, we estimate the ages of the Milky Way disk and halo, provide the inputs needed to calculate the chemical evolution of galaxies, and re-iterate the important role of HB stars in producing the UV-upturn seen in elliptical galaxies.

White dwarfs are the evolutionary end product of stars with low and intermediate masses. The evolution of white dwarfs can be understood as a cooling process, which is relatively well known at the moment. For this reason, wide binaries containing white dwarfs are a powerful tool to constrain stellar ages. We have studied several wide binaries containing white dwarfs with two different purposes: when the age of the companion of the white dwarf can be determined with accuracy, we use the binary to improve the knowledge about the white dwarf member. On the contrary, if the companion is a low-mass star with no age indicator available, the white dwarf member itself is used to calibrate the age of the system. In this contribution we present some results using both methodologies to constrain the ages of wide binaries.

The white dwarf cooling age of a globular star cluster provides a potentially precise method of determining the ages of these ancient systems. This age-dating technique should be viewed as one distinct from that of turn-off ages, with a largely different set of input physics and problems. As such the ages produced by these two methods are complimentary and we seek convergent to the same value. In addition to deep photometry and astrometry of cluster stars, precise distances to the clusters and their reddenings are required. Theoretical models of both main sequence stars and cooling white dwarfs are also needed as well as the masses of the white dwarfs and an initial-final mass relationship. In this contribution I discuss a potentially precise approach to cluster distances via a geometric technique (comparing the internal proper motion dispersion of cluster stars with their radial velocity dispersion) and spectroscopically determined masses of M4 white dwarfs at the top of the cooling sequence. These latter data extend the initial-final mass relationship down to the lowest mass stars that are currently forming white dwarfs.

Brown dwarfs are natural clocks, cooling and dimming over time due to insufficient core fusion. They are also numerous and present in nearly all Galactic environments, making them potentially useful chronometers for a variety of Galactic studies. For this potential to be realized, however, precise and accurate ages for individual sources are required, a prospect made difficult by the complex atmospheres and spectra of low-temperature brown dwarfs; degeneracy between mass, age and luminosity; and the lack of useful age trends in magnetic activity and rotation. In this contribution, I review five ways in which ages for brown dwarfs are uniquely determined, discuss their applicability and limitations, and give current empirical precisions.

We present a study of the dynamics and magnetic activity of M dwarfs using the largest spectroscopic sample of low-mass stars ever assembled. The age at which strong surface magnetic activity (as traced by Hα) ceases in M dwarfs has been inferred to have a strong dependence on mass (spectral type, surface temperature) and explains previous results showing a large increase in the fraction of active stars at later spectral types. Using spectral observations of more than 40000 M dwarfs from the Sloan Digital Sky Survey, we show that the fraction of active stars decreases as a function of vertical distance from the Galactic plane (a statistical proxy for age), and that the magnitude of this decrease changes significantly for different M spectral types. Adopting a simple dynamical model for thin disk vertical heating, we assign an age for the activity decline at each spectral type, and thus determine the activity lifetimes for M dwarfs. In addition, we derive a statistical age-activity relation for each spectral type using the dynamical model, the vertical distance from the Plane and the Hα emission line luminosity of each star (the latter of which also decreases with vertical height above the Galactic plane).

By definition, brown dwarfs never reach the main-sequence, cooling and dimming over their entire lifetime, thus making substellar models challenging to test because of the strong dependence on age. Currently, most brown dwarfs with independently determined ages are companions to nearby stars, so stellar ages are at the heart of the effort to test substellar models. However, these models are only fully constrained if both the mass and age are known. We have used the Keck adaptive optics system to monitor the orbit of HD 130948BC, a brown dwarf binary that is a companion to the young solar analog HD 130948A. The total dynamical mass of 0.109 ± 0.003 M⊙ is the most precise mass measurement (3%) for any brown dwarf binary to date and shows that both components are substellar for any plausible mass ratio. The ensemble of available age indicators from the primary star suggests an age comparable to the Hyades, with the most precise age being 0.79+0.22−0.15 Gyr based on gyrochronology. Therefore, HD 130948BC is unique among field L and T dwarfs as it possesses a well-determined mass, luminosity, and age. Our results indicate that substellar evolutionary models may underpredict the luminosity of brown dwarfs by as much as a factor of ≈2–3×. The implications of such a systematic error in evolutionary models would be far-reaching, for example, affecting determinations of the initial mass function and predictions of the radii of extrasolar gas-giant planets. This result is largely based on the reliability of stellar age estimates, and the case study of HD 130948A highlights the difficulties in determining the age of an arbitrary field star, even with the most up-to-date chromospheric activity and gyrochronology relations. In order to better assess the potential systematic errors present in substellar models, more refined age estimates for HD 130948A and other stars with binary brown dwarf companions (e.g., ϵ Ind Bab) are critically needed.

The construction of all age indicators consists of certain basic steps which lead to the identification of the properties desirable for stellar age indicators. Prior age indicators for main sequence field stars possess only some of these properties. The measured rotation periods of cool stars are particularly useful in this respect because they have well-defined dependencies that allow stellar ages to be determined with ~20% errors. This method, called gyrochronology, is explained informally in this talk, shown to have the desired properties, compared to prior methods, and used to derive ages for samples of main sequence field stars.

Our ability to determine stellar ages from measurements of stellar rotation, hinges on how well we can measure the dependence of rotation on age for stars of different masses. Rotation periods for stars in open clusters are essential to determine the relations between stellar age, rotation, and mass. Until recently, ambiguities in vsini data and lack of cluster membership information, prevented a clear empirical definition of the dependence of rotation on color. Direct measurements of stellar rotation periods for members in young clusters have now revealed a well-defined period-color relation. We show new results for the open clusters M35 and M34. However, rotation periods based on ground-based observations are limited to young clusters. The Hyades represent the oldest coeval population of stars with measured rotation periods. Measurements of rotation periods for older stars are needed to properly constrain the dependence of stellar rotation on age. We present our plans to use the Kepler space telescope to measure rotation periods in clusters as old as and older than the Sun.

We summarise recent progress in the understanding of the rotational evolution of low-mass stars (here defined as solar mass down to the hydrogen burning limit) both in terms of observations and modelling. Wide-field imaging surveys on moderate-size telescopes can now efficiently derive rotation periods for hundreds to thousands of open cluster members, providing unprecedented sample sizes which are ripe for exploration. We summarise the available measurements, and provide simple phenomenological and model-based interpretations of the presently-available data, while highlighting regions of parameter space where more observations are required, particularly at the lowest masses and ages ≳500 Myr.

It is well established that activity and rotation diminishes during the life of sun-like main sequence (~F7-K2V) stars. Indeed, the evolution of rotation and activity among these stars appears to be so deterministic that their rotation/activity diagnostics are often utilized as estimators of stellar age. A primary motivation for the recent interest in improving the ages of solar-type field dwarfs is in understanding the evolution of debris disks and planetary systems. Reliable isochronal age-dating for field, solar-type main sequence stars is very difficult given the observational uncertainties and multi-Gyr timescales for significant structural evolution. Observationally, significant databases of activity/rotation diagnostics exist for field solar-type field dwarfs (mainly from chromospheric and X-ray activity surveys). But how well can we empirically age-date solar-type field stars using activity/rotation diagnostics? Here I summarize some recent results for F7-K2 dwarfs from an analysis by Mamajek & Hillenbrand (2008), including an improved “gyrochronology” [Period(color, age)] calibration, improved chromospheric (R′HK) and X-ray (log(LX/Lbol)) activity vs. rotation (via Rossby number) relations, and a chromospheric vs. X-ray activity relation that spans four orders of magnitude in log(LX/Lbol). Combining these relations, one can produce predicted chromospheric and X-ray activity isochrones as a function of color and age for solar type dwarfs.

A brief summary of the history of stellar evolution theory and the use of isochrones is given. The present state of the subject is summarized. The major uncertainties in isochrone construction are considered: chemical abundances and color calibrations, and the treatment of turbulent convection in stellar interior and atmosphere models. The treatment of convection affects the modeling of stellar interiors principally in two ways: convective core overshoot which increases evolutionary lifetimes, and the depth of convection zones which determines theoretical radii. Turbulence also modifies atmospheric structure and dynamics, and the derivation of stellar abundances. The symbiosis of seismic techniques with increasingly more realistic three-dimensional radiation hydrodynamics simulations is transforming the study of late-type stars. The important case of very low mass stars, which are fully convective, is briefly visited.