Towards precise stellar ages: combining isochrone fitting with empirical gyrochronology
Ruth Angus, Timothy D. Morton, Daniel Foreman-Mackey, Jennifer van Saders, Jason Curtis, Stephen R. Kane, Megan Bedell, Rocio Kiman, David W. Hogg, John Brewer
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 stages than either method used in isolation. We demonstrate that the position of a star on the Hertzsprung- Russell or color-magnitude diagram can be combined with its rotation period to infer a precise age via both isochrone fitting and gyrochronology simultaneously. We show that incorporating rotation periods with 5% uncertainties into stellar evolution models improves age precision for FGK stars on the main sequence, and can, on average, provide age estimates up to three times more precise than isochrone fitting alone. In addition, we provide a new gyrochronology relation, calibrated to the Praesepe cluster and the Sun, that includes a variance model to capture the rotational behavior of stars whose rotation periods do not lengthen with the square-root of time, and parts of the Hertzsprung-Russell diagram where gyrochronology has not been calibrated. This publication is accompanied by an open source Python package, stardate, for inferring the ages of main-sequence and subgiant FGKM stars from rotation periods, spectroscopic parameters and/or apparent magnitudes and parallaxes.
Using a sample of 68 planet-hosting stars I carry out a comparison of isochrone fitting and gyrochronology to investigate whether tidal interactions between the stars and their planets are leading to underestimated ages using the latter method. I find a slight tendency for isochrones to produce older age estimates but find no correlation with tidal time-scale, although for some individual systems the effect of tides might be leading to more rapid rotation than expected from the stars' isochronal age, and therefore an underestimated gyrochronology age. By comparing to planetary systems in stell…
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 …
We present a program designed to obtain age-rotation measurements of solar-type dwarfs to be used in the calibration of gyrochronology relations at ages of several Gyr. This is a region of parameter space crucial for the large-scale study of the Milky Way, and where the only constraint available today is that provided by the Sun. Our program takes advantage of a set of wide binaries selected so that one component is an evolved star and the other is a main-sequence star of FGK type. In this way, we obtain the age of the system from the evolved star, while the rotational properties of the main s…
Among the available methods for dating stars, gyrochronology is a powerful one because it requires knowledge of only the star's mass and rotation period. Gyrochronology relations have previously been calibrated using young clusters, with the Sun providing the only age dependence, and are therefore poorly calibrated at late ages. We used rotation period measurements of 310 Kepler stars with asteroseismic ages, 50 stars from the Hyades and Coma Berenices clusters and 6 field stars (including the Sun) with precise age measurements to calibrate the gyrochronology relation, whilst fully accounting …
Age is a stellar parameter that is both fundamental and difficult to determine. Among middle-aged M dwarfs, the most prolific hosts of close-in and detectable exoplanets, gyrochronology is the most promising method to assign ages, but requires calibration by rotation-temperature sequences (gyrochrones) in clusters of known ages. We curated a catalog of 249 late K- and M-type (($T_{eff}$=3200-4200K) exoplanet host stars with established rotation periods, and applied empirical, temperature-dependent rotation-age relations based on relevant published gyrochrones, including one derived from observ…
The high-precision photometry from the CoRoT and Kepler satellites has led to measurements of surface rotation periods for tens of thousands of stars. Our main goal is to derive ages of thousands of field stars using consistent rotation period measurements in different gyrochronology relations. Multiple rotation periods are interpreted as surface differential rotation (DR). We re-analyze the sample of 24,124 Kepler stars from Reinhold et al. (2013) using different approaches based on the Lomb-Scargle periodogram. Each quarter (Q1-Q14) is treated individually using a prewhitening approach. Addi…
Accurate stellar ages are essential for our understanding of the star formation history of the Milky Way, Galactic chemical evolution, and to constrain exoplanet formation models. Gyrochronology, a relationship between stellar rotation and age, appears to offer a reliable age indicator for main sequence (MS) stars over the mass range of approximately 0.6 to 1.3 $M_\odot$. Those stars lose their angular momentum due to magnetic braking and as a result, their rotation speeds decrease with age. Although current gyrochronology relations are fairly well tested for young MS stars with masses greater…
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).
One of the most difficult properties to derive for stars is their age. For cool main-sequence stars, gyrochronology relations can be used to infer stellar ages from measured rotation pe- riods and HR Diagram positions. These relations have few calibrators with known ages for old, long rotation period stars. There is a significant sample of old Kepler objects of inter- est, or KOIs, which have both measurable surface rotation periods and precise asteroseismic measurements from which ages can be accurately derived. In this work we determine the age and the rotation period of solar-like pulsating…
The ages of the most common stars - low-mass (cool) stars like the Sun, and smaller - are difficult to derive because traditional dating methods use stellar properties that either change little as the stars age or are hard to measure. The rotation rates of all cool stars decrease substantially with time as the stars steadily lose their angular momenta. If properly calibrated, rotation therefore can act as a reliable determinant of their ages based on the method of gyrochronology. To calibrate gyrochronology, the relationship between rotation period and age must be determined for cool stars of …
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).
We report periods for 33 members of Blanco 1 as measured from KELT-South light curves, the first reported rotation periods for this benchmark zero-age-main-sequence open cluster. The distribution of these stars spans from late-A or early-F dwarfs to mid-K with periods ranging from less than a day to ~8 days. The rotation period distribution has a morphology similar to the coeval Pleiades cluster, suggesting the universal nature of stellar rotation distributions. Employing two different gyrochronology methods, we find an age of 146+13-14 Myr for the cluster. Using the same techniques, we infer …
Blue stragglers and other mass transfer/collision products are likely born with rapid rotation rates due to angular momentum transfer during mass-transfer, merger or collisional formation. However, less is known about the angular momentum evolution of these stars as they age. Here we compare rotation rates and post-formation ages of mass-transfer products to models of angular momentum evolution for normal main-sequence stars and collisionally formed blue stragglers. In our sample, we include both F- and G-type blue stragglers in the cluster NGC 188 and post-mass-transfer GK main-sequence stars…
Even with the diminished precision possible with only two reaction wheels, the Kepler spacecraft can obtain mmag level, time-resolved photometry of tens of thousands of sources. The presence of such a rich, large data set could be transformative for stellar astronomy. In this white paper, we discuss how rotation periods for a large ensemble of single and binary main- sequence dwarfs can yield a quantitative understanding of the evolution of stellar spin-down over time. This will allow us to calibrate rotation-based ages beyond ~1 Gyr, which is the oldest benchmark that exists today apart from …
This article aims to measure the age of planet-hosting stars (SWP) through stellar tracks and isochrones computed with the \textsl{PA}dova \& T\textsl{R}ieste \textsl{S}tellar \textsl{E}volutionary \textsl{C}ode (PARSEC). We developed algorithms based on two different techniques for determining the ages of field stars: \emph{isochrone placement} and \emph{Bayesian estimation}. Their application to a synthetic sample of coeval stars shows the intrinsic limits of each method. For instance, the Bayesian computation of the modal age tends to select the extreme age values in the isochrones grid. Th…
We present a catalog of ~100,000 periodic variable stars in TESS FFI data among members of widely distributed moving groups identified with Gaia in the previous papers in the series. By combining the periods from our catalog attributable to rotation with previously derived rotation periods for benchmark open clusters, we develop an empirical gyrochronology relation of angular momentum evolution that is valid for stars with ages 10-1000 Myr. Excluding stars rotating faster than 2 days, which we find are predominantly binaries, we achieve a typical age precision of ~0.2-0.3 dex and improving at …
Asteroseismological determinations of stellar ages have shown that old main-sequence dwarfs do not obey gyrochronology. Their rotation is slow compared to young stars but faster than gyrochronology predicts. This can be explained by the presence of a maximum rotation period beyond which the large-scale dynamo switches off and stops providing global magnetic fields necessary for stellar spindown. Assuming this explanation, the excess of stellar dynamo parameters over their marginal values can be estimated for given spectral type and rotation rate. The estimation gives the dynamo number for the …
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 present the results of photometric surveys for stellar rotation in the Hyades and in Praesepe, using data obtained as part of the SuperWASP exoplanetary transit-search programme.We determined accurate rotation periods for more than 120 sources whose cluster membership was confirmed by common proper motion and colour-magnitude fits to the clusters' isochrones. This allowed us to determine the effect of magnetic braking on a wide range of spectral types for expected ages of ~600Myr for the Hyades and Praesepe. Both clusters show a tight and nearly linear relation between J - Ks colour and rot…
ChronoFlow: A Data-Driven Model for Gyrochronology
David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto, Toronto, ON, Canada（多伦多大学天文学与天体物理学系）；Dunlap Institute of Astronomy & Astrophysics, University of Toronto, Toronto, ON, Canada（多伦多大学杜拉普天文与天体物理学研究所）；Department of Statistical Sciences, University of Toronto, Toronto, ON M5S 3G3, Canada（多伦多大学统计科学系）；Data Sciences Institute, University of Toronto, Toronto, ON, Canada（多伦多大学数据科学研究所）；Department of Physics, Lafayette College, Easton, PA, United States（拉法叶学院物理系）；Center for Astrophysics — Harvard & Smithsonian, Cambridge, MA 02138, USA（哈佛—史密松天体物理中心）；Department of Astronomy, The Ohio State University, Columbus, 140 W 18th Ave, OH 43210, USA（俄亥俄州立大学天文学系）；Center for Cosmology and Astroparticle Physics (CCAPP), The Ohio State University, 191 W. Woodruff Ave., Columbus, OH 43210, USA（俄亥俄州立大学宇宙学与天体粒子物理中心）；American Museum of Natural History, Central Park West, Manhattan, NY, USA（美国自然历史博物馆）；Center for Computational Astrophysics, Flatiron Institute, Manhattan, NY, USA（Flatiron研究所计算天体物理学中心）
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 …
We present a new, BVIc photometric survey of the young open cluster IC4665, which improves on previous studies of this young cluster by incorporating a rigorous standardization procedure, thus providing high-fidelity colors and magnitudes for cluster members. We use this new photometric dataset to reevaluate the properties (age and distance) of IC4665. Namely, using a statistical approach incorporating Tau^2 CMD modeling, we measure a pre-main-sequence isochrone age and distance of 36+-9 Myr and 360+-12 pc, as well as a upper-main-sequence turn-off age and distance of 42+-12 Myr and 357+-12 pc…
Employing photometric rotation periods for solar-type stars in NGC 1039 [M 34], a young, nearby open cluster, we use its mass-dependent rotation period distribution to derive the cluster's age in a distance independent way, i.e., the so-called gyrochronology method. We present an analysis of 55 new rotation periods,using light curves derived from differential photometry, for solar type stars in M 34. We also exploit the results of a recently-completed, standardized, homogeneous BVIc CCD survey of the cluster in order to establish photometric cluster membership and assign B-V colours to each ph…
We combine recently computed models of stellar evolution using a new treatment of rotation with a Bayesian statistical framework to constrain the ages and other properties of early-type stars. We find good agreement for early-type stars and clusters with known young ages, including beta Pictoris, the Pleiades, and the Ursa Majoris Moving Group. However, we derive a substantially older age for the Hyades open cluster (750+/-100 Myr compared to 625+/-50 Myr). This older age results from both the increase in main-sequence lifetime with stellar rotation and from the fact that rotating models near …
In this paper we apply a Bayesian technique to determine the best fit of stellar evolution models to find the main sequence turn off age and other cluster parameters of four intermediate-age open clusters: NGC 2360, NGC 2477, NGC 2660, and NGC 3960. Our algorithm utilizes a Markov chain Monte Carlo technique to fit these various parameters, objectively finding the best-fit isochrone for each cluster. The result is a high-precision isochrone fit. We compare these results with the those of traditional "by-eye" isochrone fitting methods. By applying this Bayesian technique to NGC 2360, NGC 2477, …
Gyrochronology allows the derivation of ages for cool main sequence stars based on their observed rotation periods and masses, or a suitable proxy thereof. It is increasingly well-explored for FGK stars, but requires further measurements for older ages and K-M-type stars. We study the nearby, 3 Gyr-old open cluster Ruprecht 147 to compare it with the previously-studied, but far more distant, NGC 6819 cluster, and especially to measure cooler stars than was previously possible there. We constructed an inclusive list of 102 cluster members from prior work, including Gaia DR2, and for which light…
We revisit the problem of low-mass pre-main-sequence (PMS) stellar evolution and its observational consequences for where stars fall on the Hertzsprung-Russell diagram (HRD). In contrast to most previous work, our models follow stars as they grow from small masses via accretion, and we perform a systematic study of how the stars' HRD evolution is influenced by their initial radius, by the radiative properties of the accretion flow, and by the accretion history, using both simple idealized accretion histories and histories taken from numerical simulations of star cluster formation. We compare o…
The knowledge of stellar ages directly impacts the characterization of a planetary system as it puts strong constraints on the moment when the system was born. Unfortunately, the determination of precise stellar ages is a very difficult task. Different methods can be used to do so (based on isochrones or chemical element abundances) but they usually provide large uncertainties. During its evolution a star goes through processes leading to loss of angular momentum but also changes in its magnetic activity. Building rotation, magnetic, age relations would be an asset to infer stellar ages model …
Age constraints are most often placed on globular clusters by comparing their CMDs with theoretical isochrones. The recent discoveries of detached, eclipsing binaries in such systems by the Cluster AgeS Experiment (CASE) provide new insights into their ages and, at the same time, much needed tests of stellar evolution models. We describe efforts to model the properties of the detached, eclipsing binary V69 in 47 Tuc and compare age constraints derived from stellar evolution models of V69A and B with ages obtained from fitting isochrones to the cluster CMD. We determine, under reasonable assump…
We have derived ages for 13 young (<30 Myr) star-forming regions and find they are up to a factor two older than the ages typically adopted in the literature. This result has wide-ranging implications, including that circumstellar discs survive longer (~10-12 Myr) and that the average Class I lifetime is greater (~1 Myr) than currently believed. For each star-forming region we derived two ages from colour-magnitude diagrams. First we fitted models of the evolution between the zero-age main-sequence and terminal-age main-sequence to derive a homogeneous set of main-sequence ages, distances and …
Although the means of the ages of stars in young groups determined from Li depletion often agree with mean ages determined from Hertzsprung - Russell diagram isochrones, there are often statistically significant differences in the ages of individual stars determined by the two methods. We find that inclusion of the effects of inhibition of convection due to the presence of magnetic fields leads to consistent ages for the individual stars. We illustrate how age consistency arises by applying our results to the βPictoris moving group. We find that, although magnetic inhibition of convection lead…
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 analo…
We report the discovery of two transiting brown dwarfs (BDs), TOI-811b and TOI-852b, from NASA's Transiting Exoplanet Survey Satellite mission. These two transiting BDs have similar masses, but very different radii and ages. Their host stars have similar masses, effective temperatures, and metallicities. The younger and larger transiting BD is TOI-811b at a mass of $M_b = 55.3 \pm 3.2{\rm M_J}$ and radius of $R_b = 1.35 \pm 0.09{\rm R_J}$ and it orbits its host star in a period of $P = 25.16551 \pm 0.00004$ days. Its age of $93^{+61}_{-29}$ Myr, which we derive from an application of gyrochron…
In this fourth paper of a series on the precision of ages of stellar populations obtained through the full-spectrum fitting technique, we present a first systematic analysis that compare the age, metallicity and reddening of star clusters obtained from resolved and unresolved data (namely colour-magnitude diagrams (CMDs) and integrated-light spectroscopy) using the same sets of isochrones. We investigate the results obtained with both Padova isochrones and MIST isochrones. We find that there generally is a good agreement between the ages derived from CMDs and integrated spectra. However, for m…
We report rotation periods for 20 cool (FGK) main sequence member stars of the 4 Gyr-old open cluster M 67 (= NGC 2682), obtained by analysing data from Campaign 5 of the K2 mission with the Kepler Space Telescope. The rotation periods delineate a sequence in the color-period diagram (CPD) of increasing period with redder color. This sequence represents a cross-section at the cluster age of the surface P = P (t, M), suggested in prior work to extend to at least solar age. The current Sun is located marginally (approx. one sigma) above M 67 in the CPD, as its relative age leads us to expect, an…
We present a catalogue of distances, masses and ages for $\sim3$ million stars in the second Gaia data release with spectroscopic parameters available from the large spectroscopic surveys: APOGEE, Gaia-ESO, GALAH, LAMOST, RAVE and SEGUE. We use a Bayesian framework to characterise the probability density functions of distance, mass and age using photometric, spectroscopic and astrometric information, supplemented with spectroscopic masses where available for giant stars. Furthermore, we provide posterior extinction estimates ($A_V$) to every star using published extinction maps as a prior inpu…
Absolute ages of young stars are important for many issues in pre-main sequence stellar and circumstellar evolution but are long recognized as difficult to derive and calibrate. In this paper, we use literature spectral types and photometry to construct empirical isochrones in HR diagrams for low-mass stars and brown dwarfs in the eta Cha, epsilon Cha, and TW Hya Associations and the beta Pic and Tuc-Hor Moving Groups. A successful theory of pre-main sequence evolution should match the shapes of the stellar loci for these groups of young stars. However, when comparing the combined empirical is…
By using the current photometric rotational data on eight galactic open clusters, we show that the evolutionary stellar model (isochrone) ages of these clusters are tightly correlated with the period shifts applied to the (B-V)_0 - P_rot ridges that optimally align these ridges to the one defined by Praesepe and the Hyades. On the other hand, when the traditional Skumanich-type multiplicative transformation is used, the ridges become far less aligned due to the age-dependent slope change introduced by the period multiplication. Therefore, we employ our simple additive gyro-age calibration on v…
Current spectroscopic surveys are producing large catalogs of chemical abundances for stars of all types. The yttrium to magnesium ratio, [Y/Mg], has emerged as a candidate age indicator for solar twins in the local stellar neighborhood. However, it is unclear whether it is a viable age diagnostic for more diverse stellar types, so we investigate [Y/Mg] as an age indicator for the FGK-type planet host stars observed by $Kepler$. We find that the [Y/Mg] "Clock" is most precise for solar twins, with a [Y/Mg]/Age slope of $m$ = $-$0.0370 $\pm$ 0.0071 dex/Gyr and $σ_{\mathrm{Age}}$ = 2.6 Gyr. We a…
The ages of the oldest and most metal-poor stars in the Milky Way bear important information on the age of the Universe and its standard model. We analyze a sample of 28 extremely metal-poor field stars in the solar vicinity culled from the literature and carefully determine their ages. To this aim, we critically make use of Gaia data to derive their distances and associated uncertainties. Particular attention has been paid to the estimate of the reddening and its effect on the derivation of stellar ages. We employed different reddenings and super-impose isochrones from different sources in th…
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…
A knowledge of stellar ages is crucial for our understanding of many astrophysical phenomena, and yet ages can be difficult to determine. As they become older, stars lose mass and angular momentum, resulting in an observed slowdown in surface rotation. The technique of 'gyrochronology' uses the rotation period of a star to calculate its age. However, stars of known age must be used for calibration, and, until recently, the approach was untested for old stars (older than 1 gigayear, Gyr). Rotation periods are now known for stars in an open cluster of intermediate age (NGC 6819; 2.5 Gyr old), an…
Isochrone-cloud fitting and asteroseismology of the Kepler open cluster NGC6866
Institute of Astronomy, KU Leuven（KU鲁汶大学天文学研究所）；Centre for Astrophysics, University of Southern Queensland（南昆士兰大学天体物理中心）；Department of Astrophysics, IMAPP, Radboud University Nijmegen（拉特罗布大学IMAPP天体物理学系）；Max Planck Institut für Astronomie（马克斯·普朗克天文学研究所）
Previous studies suggest that tidal interactions may be responsible for discrepancies between the ages of exoplanet host stars estimated using stellar models (isochronal ages) and age estimates based on the stars' rotation periods (gyrochronological ages). We have compiled a sample of 28 transiting exoplanet host stars with measured rotation periods. We use a Bayesian Markov chain Monte Carlo method to determine the joint posterior distribution for the mass and age of each star in the sample, and extend this method to include a calculation of the posterior distribution of the gyrochronological…
