The age of an individual star cannot be measured, only estimated through mostly model-dependent or empirical methods, and no single method works well for a broad range of stellar types or for a full range in age. This review presents a summary of the available techniques for age-dating stars and ensembles of stars, their realms of applicability, and their strengths and weaknesses. My emphasis is on low-mass stars because they are present from all epochs of star formation in the Galaxy and because they present both special opportunities and problems. The ages of open clusters are important for understanding the limitations of stellar models and for calibrating empirical age indicators. For individual stars, a hierarchy of quality for the available age-dating methods is described. Although our present ability to determine the ages of even the nearest stars is mediocre, the next few years hold great promise as asteroseismology probes beyond stellar surfaces and starts to provide precise interior properties of stars and as models continue to improve when stressed by better observations.
We present estimates of distances, ages and masses for over 3.5 million stars. These estimates are derived from the combination of spectrophotometric data and Gaia DR2 parallaxes. For that, we used the previously published Unified tool to estimate Distances, Ages, and Masses (UniDAM).
In the era of large-scale surveys of stars in the Milky Way, stellar ages are crucial for studying the evolution of the Galaxy. But determining ages of field stars is notoriously difficult; therefore, we attempt to determine benchmark ages for the extensively studied Gaia benchmark stars which can be used for validation purposes. By searching the literature for age estimates from different methods and deriving new ages based on Bayesian isochrone fitting, we are able to put reliable limits on the ages of 16 out of the 33 benchmark stars. The giants with well-defined ages are all young, and an …
Detailed modelling of stellar oscillations is able to give precise estimates for stellar ages, but the inferred results typically depend on the adopted model parameters used for the age inference. High-quality asteroseismic data with precise measurements of mixed modes are available for 36 Kepler subgiants. To obtain a handle on the robustness of the ages for these stars, we first study the dependencies of seismic ages on three model input parameters. We find that inferred ages do not change systematically with the helium fraction (Y) or the mixing-length parameter but depend strongly on the m…
I review progress towards understanding the time-scales of star and cluster formation and of the absolute ages of young stars. I focus in particular on the areas in which Francesco Palla made highly significant contributions - interpretation of the Hertzsprung-Russell diagrams of young clusters and the role of photospheric lithium as an age diagnostic.
Estimating stellar ages is important for advancing our understanding of stellar and exoplanet evolution and investigating the history of the Milky Way. However, ages for low-mass stars are hard to infer as they evolve slowly on the main sequence. In addition, empirical dating methods are difficult to calibrate for low-mass stars as they are faint. In this work, we calculate ages for Kepler F, G, and crucially K and M dwarfs, using their rotation and kinematic properties. We apply the simple assumption that the velocity dispersion of stars increases over time and adopt an age--velocity--dispers…
We analyze 4\,050 wide binary star systems involving a white dwarf (WD) and usually a main sequence (MS) star, drawn from the large sample assembled by \citet[][hereafter, T20]{Tian_2020}. Using the modeling code BASE-9, we determine the system's ages, the WD progenitors' ZAMS masses, the extinction values ($A_V$), and the distance moduli. Discarding the cases with poor age convergences, we obtain ages for 3\,551 WDs, with a median age precision of $σ_τ/τ= 20$\%, and system ages typically in the range of 1-6 Gyr. We validated these ages against the very few known clusters and through cross-val…
Main sequence turnoff ages in young open clusters are complicated by turnoffs that are sparse, have high binarity fractions, can be affected by differential reddening, and typically include a number of peculiar stars. Furthermore, stellar rotation can have a significant effect on a star's photometry and evolutionary timescale. In this paper we analyze in 12 nearby open clusters, ranging from ages of 50 Myr to 350 Myr, how broadband UBV color-color relations can be used to identify turnoff stars that are Be stars, blue stragglers, certain types of binaries, or those affected by differential red…
Much progress has been achieved in the age-dating of old stellar systems, and even of individual stars in the field, in the more than sixty years since the evolution of low-mass stars was first correctly described. In this paper, I provide an overview of some of the main methods that have been used in this context, and discuss some of the issues that still affect the determination of accurate ages for the oldest stars.
The impact of the white dwarf initial-final mass relation on star clusters' ages inferred from their cooling sequence
INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所博洛尼亚天文物理与空间科学观测站）；Astrophysics Research Institute, Liverpool John Moores University（利物浦约翰摩尔斯大学天体物理研究所）；INAF – Osservatorio Astronomico di Abruzzo（意大利国家天体物理研究所阿布鲁佐天文台）；INFN – Sezione di Pisa（意大利国家核物理研究所比萨分部）；INAF – Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）
The Ages of Early-Type Stars: Strömgren Photometric Methods Calibrated, Validated, Tested, and Applied to Hosts and Prospective Hosts of Directly Imaged Exoplanets
Stellar magnetic activity decays over the main-sequence life of cool stars due to the stellar spin-down driven by magnetic braking. The evolution of chromospheric emission is well-studied for younger stars, but difficulties in determining the ages of older cool stars on the main sequence have complicated such studies for older stars in the past. Here we report on chromospheric Ca II H and K line measurements for 26 main-sequence cool stars with asteroseismic ages older than a gigayear and spectral types F and G. We find that for the G stars and the cooler F-type stars which still have convecti…
Calibration of the [C/N] and [Y/Mg] chemical clocks with asteroseismic ages from the TESS space mission
Institute of Theoretical Physics and Astronomy, Vilnius University（维尔纽斯大学理论与天体物理研究所）；Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University（奥胡斯大学物理学与天文学系恒星天体物理学中心）
We present estimates of distances, ages and masses for over 6 million stars. These estimates are derived from the combination of spectrophotometric data and Gaia eDR3 parallaxes. For that, we used the previously published Unified tool to estimate Distances, Ages, and Masses (UniDAM).
In this first work attempts to analytically explain the effects on the magnetic braking index, $q$, caused by the evolution of stellar velocity in main-sequence stars, and estimated by de Freitas \& De Medeiros (2013). We have found that the effect of $q$ is here a determining factor for understanding the delicate mechanisms that control the spin-down of stars as a function of the mass of stars. We note that our models predict that the calculated ages are distinct from gyrochronology ages. Indeed, the gyro-ages are measured considering only the canonical value of the Skumanich relation ($q$=3)…
We propose a new model to determine the ages and masses of red giant branch (RGB) stars from the low-resolution large sky area multi-object fiber spectroscopic telescope (LAMOST) spectra. The ages of RGB stars are difficult to determine using classical isochrone fitting techniques in the Hertzsprung-Russell diagram, because isochrones of RGB stars are tightly crowned. With the help of the asteroseismic method, we can determine the masses and ages of RGB stars accurately. Using the ages derived from the asteroseismic method, we train a deep learning model based on DenseNet to calculate the ages…
Older Ages for 23 Pre-Main Sequence Stars in Upper Scorpius Using Dynamical Mass-Constrained Stellar Evolutionary Models
University of Arizona（亚利桑那大学）；National Radio Astronomy Observatory（国家射电天文台）；California Institute of Technology（加州理工学院）；National Taiwan Normal University（台湾师范大学）
We present a method to build a probability density function (pdf) for the age of a star based on its peculiar velocities $U$, $V$ and $W$ and its orbital eccentricity. The sample used in this work comes from the Geneva-Copenhagen Survey (GCS) which contains both the spatial velocities, orbital eccentricities and isochronal ages for about $14\,000$ stars. Using the GCS stars, we fitted the parameters that describe the relations between the distributions of kinematical properties and age. This parametrization allows us to obtain an age probability from the kinematical data. From this age pdf, we…
We present a Bayesian implementation of isochrone fitting in deriving stellar ages and masses, incorporating absolute K magnitude ($\rm M_K$) derived from 2MASS photometry and Gaia DR1 parallax and differentiation between initial bulk metallicity and present day surface metallicity, with allowance for incorporating further constraints (e.g., asteroseismology) when available. As a test, we re-computed stellar ages and masses of $\sim 4000$ stars in the solar neighbourhood from six well-studied literature samples using both Hipparcos and TGAS parallaxes. Our ages are found to be compatible with …
We select from Paper I a sample of 306 massive star clusters observed with the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) in the vicinity fields of M31 and M33 and determine their metallicities, ages and masses. Metallicities and ages are estimated by fitting the observed integrated spectra with stellar synthesis population (SSP) models with a pixel-to-pixel spectral fitting technique. Ages for most young clusters are also derived by fitting the multi-band photometric measurements with model spectral energy distributions (SEDs). The estimated cluster ages span a wide ra…
It is well-known that fitting the Color Magnitude Diagrams (CMDs) to the theoretical isochrones is the main method to determine star cluster ages. However, when the CMDs are not available, the Spectral Energy Distribution (SED)-fitting technique is the only other approach, although it suffers the age-metallicity-reddening degeneracy. In this work, we gather the ages, metallicities and masses of dozens of M31 star clusters from the CMD-fitting with HST images from the literatures for comparison. We check the reliability of the SED-fitting results with different models, i.e., Bruzual \& Charlot …
The Serpens Molecular Cloud is one of the most active star-forming regions within 500 pc, with over one thousand of YSOs at different evolutionary stages. The ages of the member stars inform us about the star formation history of the cloud. In this paper, we develop a spectral energy distribution (SED) fitting method for nearby evolved (diskless) young stars from members of the Pleiades to estimate their ages, with a temperature scale adopted from APOGEE spectra. When compared with literature temperatures of selected YSOs in Orion, the SED fits to cool (<5000 K) stars have temperatures that di…
Oxygen and carbon are important elements in stellar populations. Their behavior refers to the formation history of the stellar populations. C and O abundances would also obviously influence stellar opacities and the overall metal abundance $Z$. With observed high-quality spectroscopic properties, we construct stellar models with C and O elements, to give more accurate ages for 70 metal-poor dwarfs, which have been determined to be high-$α$ halo, low-$α$ halo and thick-disk stars. Our results show that high-$α$ halo stars are relatively older than low-$α$ halo stars by around 2.0 Gyr. The thick…
We present a new age-dating technique that combines gyrochronology with isochrone fitting to infer ages for FGKM main-sequence and subgiant field stars. Gyrochronology and isochrone fitting are each capable of providing relatively precise ages for field stars in certain areas of the Hertzsprung-Russell diagram: gyrochronology works optimally for cool main-sequence stars, and isochrone fitting can provide precise ages for stars near the main-sequence turnoff. Combined, these two age-dating techniques can provide precise and accurate ages for a broader range of stellar masses and evolutionary st…
Apache Point Observatory follow-up of ACcelerating Candidate ExopLanet host Stars (APO ACCELS): Ages for 166 Accelerating Stars in the Northern Hemisphere
In the era of large stellar spectroscopic surveys, there is emphasis on deriving not only stellar abundances but also ages for millions of stars. In the context of Galactic archeology, stellar ages provide a direct probe of the formation history of the Galaxy. We use the stellar evolution code MESA to compute models with atomic diffusion--with and without radiative acceleration--and extra mixing in the surface layers. The extra mixing consists of both density-dependent turbulent mixing and envelope overshoot mixing. Based on these models we argue that it is important to distinguish between ini…
Main sequence turn-off (MSTO) stars are good tracers of Galactic populations since their ages can be reliably estimated from atmospheric parameters. Based on the GALAH survey, we use the Yale Rotation Evolution Code to determine ages of 2926 MSTO stars with mean age uncertainty $\sim$10\% considering the variation of C and O abundances. Ages of CO-poor stars are systematically affected by $\sim$10\% due to the C and O abundances, globally shifting to $\sim$0.5 Gyr older compared to the results using solar metal-mixture. Of the stars with \mbox{[Fe/H] $\sim$0.3-0.5} or \mbox{[O/Fe]~$\leq$~-0.25…
There is growing evidence that star clusters can no longer be considered simple stellar populations (SSPs). Intermediate and old age clusters are often found to have extended main sequence turn-offs (eMSTOs) which are difficult to explain with single age isochrones, an effect attributed to rotation. In this paper, we provide the first characterisation of this effect in young (<20Myr) clusters. We determine ages for 4 young massive clusters (2 LMC, 2 Galactic) by three different methods: using the brightest single turn-off (TO) star; using the luminosity function (LF) of the TO; and by using th…
We use models of stellar angular momentum evolution to determine ages for $\sim500$ stars in the APOGEE-\textit{Kepler} Cool Dwarfs sample. We focus on lower main-sequence stars, where other age-dating tools become ineffective. Our age distributions are compared to those derived from asteroseismic and giant samples and solar analogs. We are able to recover gyrochronological ages for old, lower-main-sequence stars, a remarkable improvement over prior work in hotter stars. Under our model assumptions, our ages have a median relative uncertainty of $14\%$, comparable to the age precision inferred…
Age is a fundamental parameter of stars, yet in many cases ages of individual stars are presented without robust estimates of the uncertainty. We have developed a Bayesian framework, BAFFLES, to produce the age posterior for a star from its calcium emission strength (log($R'_{HK}$)) or lithium abundance (Li EW) and $B-V$ color. We empirically determine the likelihood functions for calcium and lithium as functions of age from literature measurements of stars in benchmark clusters with well-determined ages. We use a uniform prior on age which reflects a uniform star formation rate. The age poste…
