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--dispersion relation (AVR) to estimate average stellar ages for groupings of coeval stars. We calculate the vertical velocity dispersion of stars in bins of absolute magnitude, temperature, rotation period, and Rossby number and then convert velocity dispersion to kinematic age via an AVR. Using this method, we estimate gyro-kinematic ages for 29,949 Kepler stars with measured rotation periods. We are able to estimate ages for clusters and asteroseismic stars with an RMS of 1.22 Gyr and 0.26 Gyr respectively. With our Astraea machine learning algorithm, which predicts rotation periods, we suggest a new selection criterion (a weight of 0.15) to increase the size of the McQuillian et al. (2014) catalog of Kepler rotation periods by up to 25%. Using predicted rotation periods, we estimated gyro-kinematic ages for stars without measured rotation periods and found promising results by comparing 12 detailed age--element abundance trends with literature values.
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…
We revisit the photometric variability of stars in the M 67 field using Kepler/K2-Campaign-5 light curves. In our previous work, we limited the search area around M\,67 to that of a recent ground-based study. In the present work, we expand the search area and apply a more rigorous period-finding algorithm to determine the rotation periods of 98 main sequence cluster members from the same data. In addition, we derive periods of 40 stars from the K2SC detrended light curves. We determine the mean period of single sun-like main sequence cluster members to be $29.6 \pm 0.6$ d. Assuming the periods…
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)…
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…
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…
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…
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 …
The present work attempts to analytically explain the effects on the moment of inertia, $I$, caused by the evolution of stellar velocity in main-sequence stars. We have found that the effects linked to stellar oblateness can be estimated from the variation of the magnetic braking index denoted by $Δq$. We have also found that the effect of $\dot{I}$ is here a determining factor for understanding the delicate mechanisms that control the spin-down of stars in this evolutionary phase. We note that our models predict that the behaviour of the variations of the braking index is distinct when the st…
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…
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…
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 …
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…
We use asteroseismic data from the Kepler satellite to determine fundamental stellar properties of the 66 main-sequence targets observed for at least one full year by the mission. We distributed tens of individual oscillation frequencies extracted from the time series of each star among seven modelling teams who applied different methods to determine radii, masses, and ages for all stars in the sample. Comparisons among the different results reveal a good level of agreement in all stellar properties, which is remarkable considering the variety of codes, input physics and analysis methods emplo…
In this work we combine information from solar-like oscillations, high-resolution spectroscopy and Gaia astrometry to derive stellar ages, chemical abundances and kinematics for a group of seven metal-poor Red Giants and characterise them in a multidimensional chrono-chemo-dynamical space. Chemical abundance ratios were derived through classical spectroscopic analysis employing 1D LTE atmospheres on Keck/HIRES spectra. Stellar ages, masses and radii were calculated with grid-based modelling, taking advantage of availability of asteroseismic information from Kepler. The dynamical properties wer…
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 abundances of 21 elements in a sample of 13 bright FG dwarfs drawn from the Kepler LEGACY sample to examine the applicability of the abundance-age relations to stars with properties strongly departing from solar. These stars have precise asteroseismic ages that can be compared to the abundance-based estimates. We analyse the well-known binary 16 Cyg AB for validation purposes and confirm the existence of a slight metal enhancement (~0.02 dex) in the primary, which might arise from planetary formation/ingestion. We draw attention to systematic errors in some widely-used catalogues of…
The solar analogs 16 Cyg A and 16 Cyg B are excellent asteroseismic targets in the \Kepler field of view and together with a red dwarf and a Jovian planet form an interesting system. For these more evolved Sun-like stars we cannot detect surface rotation with the current \Kepler data but instead use the technique of asteroseimology to determine rotational properties of both 16 Cyg A and B. We find the rotation periods to be $23.8^{+1.5}_{-1.8} \rm \, days$ and $23.2^{+11.5}_{-3.2} \rm \, days$, and the angles of inclination to be $56^{+6}_{-5} \, ^{\circ}$ and $36^{+17}_{-7} \, ^{\circ}$, for …
In the past few years, the CoRoT and Kepler missions have carried out what is now called the space photometry revolution. This revolution is still ongoing thanks to K2 and will be continued by the Tess and Plato2.0 missions. However, the photometry revolution must also be followed by progress in stellar modelling, in order to lead to more precise and accurate determinations of fundamental stellar parameters such as masses, radii and ages. In this context, the long-lasting problems related to mixing processes in stellar interior is the main obstacle to further improvements of stellar modelling.…
We perform a search for wide binaries in the Kepler field with the prospect of providing new constraints for gyrochronology. First, we construct our base catalog by compiling astrometry for the stars observed by Kepler, and supplement it with parallaxes, radial velocities (RVs), and metallicities. We then mine our base catalog for wide binary candidates by matching the stars' proper motions, as well as parallaxes, RVs, and metallicities, if available. We mitigate the presence of chance alignments among our candidates by performing a comprehensive data-based contamination analysis in the proper…
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…
Obtaining accurate and precise masses and ages for large numbers of giant stars is of great importance for unraveling the assemblage history of the Galaxy. In this paper, we estimate masses and ages of 6940 red giant branch (RGB) stars with asteroseismic parameters deduced from \emph{Kepler} photometry and stellar atmospheric parameters derived from LAMOST spectra. The typical uncertainties of mass is a few per cent, and that of age is $\sim$\,20 per cent. The sample stars reveal two separate sequences in the age -- [$α$/Fe] relation -- a high--$α$ sequence with stars older than $\sim$\,8\,Gyr…
We examine the photometric variability of stars in the M 67 field using Kepler/K2-Campaign-5 light curves. Variabilities and periods were determined for 639 stars. The mean photometric period of 28 single Sun-like members stars in M 67 is 23.4 +/- 1.2 d. This corresponds to a gyro-age of 3.7 +/- 0.3 Gyr, assuming the periods can be associated with rotation. The intrinsic variabilities of the solar analogs are greater than the Sun's variability, as measure from VIRGO fluxes. We also find evidence that the single cluster members have a different distribution of variability than the binary member…
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…
We measure rotation periods for 12151 stars in the Kepler field, based on the photometric variability caused by stellar activity. Our analysis returns stable rotation periods over at least six out of eight quarters of Kepler data. This large sample of stars enables us to study the rotation periods as a function of spectral type. We find good agreement with previous studies and vsini measurements for F, G and K stars. Combining rotation periods, B-V color, and gyrochronology relations, we find that the cool stars in our sample are predominantly younger than ~1Gyr.
Continuous high-precision photometry of stars, provided by space missions such as CoRoT, Kepler, and K2, represents a unique way to study stellar rotation and magnetism. The coupling of these studies of the surface dynamics with asteroseismology is changing our view to surface and internal dynamics. In this proceedings I will provide the latest developments in the understanding of surface and internal rotation and magnetic fields. I will also discuss the possible discovery of strong internal magnetic fields of dynamo origin in the convective cores of stars above 1.2-1.4 solar masses. I will fi…
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 …
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 …
Asteroseismology has started to provide constraints on stellar properties that will be essential to accurately reconstruct the history of the Milky Way. Here we look at the information content in data sets representing current and future space missions (CoRoT, Kepler, K2, TESS, and PLATO) for red giant stars. We describe techniques for extracting the information in the frequency power spectrum and apply these techniques to {\it Kepler} data sets of different observing length to represent the different space missions. We demonstrate that for KIC 12008916, a low-luminosity red giant branch star,…
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 …
We embark on a detailed study of the lightcurves of Keplers most Earth-like exoplanet host stars using the full length of Kepler data. We derive rotation periods, photometric activity indices, flaring energies, mass loss rates, gyrochronological ages, X-ray luminosities and consider implications for the planetary magnetospheres and habitability. Furthermore, we present the detection of superflares in the lightcurve of Kepler-438, the exoplanet with the highest Earth Similarity Index to date. Kepler-438b orbits at a distance of 0.166AU to its host star, and hence may be susceptible to atmospher…
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）
We present a study of 33 {\it Kepler} planet-candidate host stars for which asteroseismic observations have sufficiently high signal-to-noise ratio to allow extraction of individual pulsation frequencies. We implement a new Bayesian scheme that is flexible in its input to process individual oscillation frequencies, combinations of them, and average asteroseismic parameters, and derive robust fundamental properties for these targets. Applying this scheme to grids of evolutionary models yields stellar properties with median statistical uncertainties of 1.2\% (radius), 1.7\% (density), 3.3\% (mas…
Red clump stars are fundamental distance indicators in astrophysics, although theoretical stellar models predict a dependence of absolute magnitudes with ages. This effect is particularly strong below 2 Gyr, but even above this limit a mild age dependence is still expected. We use seismically identified red clump stars in the Kepler field for which we have reliable distances, masses and ages from the SAGA survey to first explore this effect. By excluding red clump stars with masses larger than 1.6 Msun (corresponding to ages younger than 2 Gyr), we derive robust calibrations linking intrinsic …
We explore the relationships between the chemistry, ages, and locations of stars in the Galaxy using asteroseismic data from the K2 mission and spectroscopic data from the Apache Point Galactic Evolution Experiment survey. Previous studies have used giant stars in the Kepler field to map the relationship between the chemical composition and the ages of stars at the solar circle. Consistent with prior work, we find that stars with high [Alpha/Fe] have distinct, older ages in comparison to stars with low [Alpha/Fe]. We provide age estimates for red giant branch (RGB) stars in the Kepler field, w…
Binary star systems are important for understanding stellar structure and evolution, and are especially useful when oscillations can be detected and analysed with asteroseismology. However, only four systems are known in which solar-like oscillations are detected in both components. Here, we analyse the fifth such system, HD 176465, which was observed by Kepler. We carefully analysed the system's power spectrum to measure individual mode frequencies, adapting our methods where necessary to accommodate the fact that both stars oscillate in a similar frequency range. We also modelled the two sta…
