Accurate Stellar Ages Research Articles

A catalogue of asteroseismically calibrated ages for APOGEE DR17

Context. The formation history and evolution of the Milky Way through cosmological time is a complex field of research requiring the sampling of highly accurate stellar ages for all Galaxy components. Such highly reliable ages are starting to become available thanks to the synergy of asteroseismology, spectroscopy, stellar modelling, and machine learning analysis in the era of all-sky astronomical surveys. Aims. Our goal is to provide an accurate list of ages for the Main Red Star Sample of the APOGEE DR17 catalogue. In order to reach this goal, ages obtained under asteroseismic constraints are used to train a machine learning model. Methods. As our main objective is to obtain reliable age predictions without the need for asteroseismic parameters, the optimal choice of stellar non-asteroseismic parameters was investigated to obtain the best performances on the test set. The stellar parameters Teff and L, the abundances of [CI/N],[Mg/Ce], and [α/Fe], the U(LSR) velocity, and the vertical height from the Galactic plane ‘Z’ were used to predict ages with a categorical gradient boost decision trees model. The model was trained on two merged samples of the TESS Southern Continuous Viewing Zone and the Second APOKASC catalogue to avoid a data shift and to improve the reliability of the predictions. Finally, the model was tested on an independent data set of the K2 Galactic Archaeology Program. Results. A model with a median fractional age error of 20.8% is obtained. Its prediction variance between the validation and the training set is 4.77%. For stars older than 3 Gyr, the median fractional error in age ranges from 7% to 23%. For stars with ages ranging from 1 to 3 Gyr, the median fractional error in age ranges from 26% to 28%. For stars younger than 1 Gyr, the median fractional error is 43%. The optimised model applies to 125 445 stars from the Main Red Star Sample of the APOGEE DR17 catalogue. Our analysis of the ages confirms previous findings regarding the flaring of the young Galactic disc towards its outer regions. Additionally, we find an age gradient among the youngest stars within the Galactic plane. Finally, we identify two groups of a few metal-poor ([Fe/H] < −1 dex) young stars (Age < 2 Gyr) with similar peculiar chemical abundances and halo kinematics. These are likely the outcomes of the predicted third and latest episode of gas infall in the solar vicinity (~2.7 Gyr ago). Conclusions. We make a catalogue of asteroseismically calibrated ages for 125 445 red giants from the APOGEE DR17 catalogue available to the community. The analysis of the associated stellar parameters corroborates the predictions of different literature models.

The APO-K2 Catalog. II. Accurate Stellar Ages for Red Giant Branch Stars across the Milky Way

We present stellar age determinations for 4661 red giant branch stars in the APO-K2 catalog, derived using mass estimates from K2 asteroseismology from the K2 Galactic Archaeology Program and elemental abundances from the Apache Point Galactic Evolution Experiment survey. Our sample includes 17 of the 19 fields observed by K2, making it one of the most comprehensive catalogs of accurate stellar ages across the Galaxy in terms of the wide range of populations spanned by its stars, enabling rigorous tests of Galactic chemical evolution models. Taking into account the selection functions of the K2 sample, the data appear to support the age−chemistry morphology of stellar populations predicted by both inside-out and late-burst scenarios. We also investigate trends in age versus stellar chemistry and Galactic position, which are consistent with previous findings. Comparisons against APOKASC-3 asteroseismic ages show agreement to within ∼3%. We also discuss offsets between our ages and spectroscopic ages. Finally, we note that ignoring the effects of α-enhancement on stellar opacity (either directly or with the Salaris metallicity correction) results in an ∼10% offset in age estimates for the most α-enhanced stars, which is an important consideration for continued tests of Galactic models with this and other asteroseismic age samples.

Timing the formation of the galactic thin disc with asteroseismic stellar ages

ABSTRACT The formation of the extended thin disc is the most spectacular event of our Galaxy in the past ∼8 Gyr. To unveil this process, obtaining precise and accurate stellar ages for a large sample of stars is essential although challenging. In this work, we present the asteroseismic age determination of 5306 red giant branch stars using Kepler and LAMOST data, with a thorough examination of how the age determination is affected by the choice of different temperature scales and stellar models. Thanks to the high precision of the asteroseismic and spectroscopic parameters of our sample stars, we are able to achieve age determination with an average accuracy of 12 per cent. However, the age determination is sensitively dependent on the adopted temperature scale, as 50 K difference in effective temperature may cause larger than 10 per cent systematic uncertainty in the age estimates. Using the ages derived with the most plausible set of the temperature scale, we study the age distribution of the chemical thin disc stars, and present an estimate of the formation epoch of the first Galactic thin disc stars. We find that the first (oldest) thin disc stars have an age of $9.5^{+0.5(\rm rand.)+0.5(\rm sys.)}_{-0.4(\rm rand.)-0.3(\rm sys.)}$ Gyr, where the systematic uncertainties reflect ages estimated using different stellar evolutionary models. At this epoch, the Galactic thick disc was still forming stars, indicating there is a time window when both the thin and thick discs of our Galaxy were forming stars together. Moreover, we find that the first thin disc stars exhibit a broad distribution of Galactocentric radii, suggesting that the inner and outer thin discs began to form simultaneously.

A Monte Carlo Method for Evaluating Empirical Gyrochronology Models and Its Application to Wide Binary Benchmarks

Accurate stellar ages are essential for our understanding of the star formation history of the Milky Way and Galactic chemical evolution, as well as 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 0.6–1.3 M ⊙. Those stars lose their angular momentum due to magnetic braking and as a result their rotation speeds decrease with age. Although current gyrochronology relations have been fairly well tested for young MS stars with masses greater than 1 M ⊙, primarily in young open clusters, insufficient tests exist for older and lower mass MS stars. Binary stars offer the potential to expand and fill in the range of ages and metallicity over which gyrochronology can be empirically tested. In this paper, we demonstrate a Monte Carlo approach to evaluate gyrochronology models using binary stars. As examples, we used five previously published wide binary pairs. We also demonstrate a Monte Carlo approach to assess the precision and accuracy of ages derived from each gyrochronology model. For the traditional Skumanich models, the age uncertainties are σ age/age = 15%–20% for stars with B − V = 0.65 and σ age/age = 5%–10% for stars with B − V = 1.5 and rotation period P ≤ 20 days.

Deciphering the evolution of the Milky Way discs: Gaia APOGEE Kepler giant stars and the Besançon Galaxy Model

Context. Thanks to ongoing efforts to compute accurate stellar ages, we are able to characterise stars in different regions of the Milky Way. The Gaia and Kepler space-missions, along with ground-based spectroscopic surveys such as APOGEE, provide a unique way to study the chemo-kinematics relations as a function of age through the Galactic stellar populations and provide new constraints to Galactic evolution models. Aims. We investigate the properties of the double sequences of the Milky Way discs visible in the [α/Fe] versus [Fe/H] diagram, which are usually associated to the chemical thin and thick discs at the solar circle. In the framework of Galactic formation and evolution, we discuss the complex relationships between age, metallicity, [α/Fe], and the radial, azimuthal, and vertical components of the space velocities. Methods. We study stars with measured chemical and seismic properties from the APOGEE spectroscopic survey and the Kepler satellite, respectively. In addition, astrometry from the Gaia satellite is available for the majority of the sample. We separate the [α/Fe]−[Fe/H] diagram into three stellar populations: the thin disc, the high-α metal-poor thick disc, and the high-α metal-rich thick disc and characterise each of these in the age-chemo-kinematics parameter space. Because of the model-dependent nature of the ages inferred from asteroseismology, and because they depend on the quality of the input spectroscopic information, we compare results obtained from different APOGEE data releases (DR14 and DR16). We also use age determinations from two recent works in the literature. In addition, we use the Besançon stellar populations synthesis model to highlight selection biases and mechanisms (such as mergers and secular evolution) not included in the model. Results. The thin disc exhibits a flat age–metallicity relation while [α/Fe] increases with stellar age. We confirm no correlation between radial and vertical velocities with [Fe/H], [α/Fe], and age for each stellar population. Considering both samples, Vφ decreases with age for the thin disc, while Vφ increases with age for the high-α metal-poor thick disc. We show that this difference is not due to sample selection. Although the age distribution of the high-α metal-rich thick disc is very close to that of the high-α metal-poor thick disc between 7 and 14 Gyr, its kinematics seems to follow that of the thin disc. This feature, not predicted by the hypotheses included in the Besançon Galaxy Model, suggests a different origin and history for this population. Finally, we show that there is a maximum dispersion of the vertical velocity, σZ, with age for the high-α metal-poor thick disc around 8 Gyr. The comparisons with the Besançon Galaxy Model simulations suggest a more complex chemo-dynamical scheme to explain this feature, most likely including mergers and radial migration effects.

The AMBRE Project: Solar neighbourhood chemodynamical constraints on Galactic disc evolution

Context. The abundance of α-elements relative to iron ([α/Fe]) is an important fossil signature in Galactic archaeology for tracing the chemical evolution of disc stellar populations. High-precision chemical abundances, together with accurate stellar ages, distances, and dynamical data, are crucial to infer the Milky Way formation history. Aims. The aim of this paper is to analyse the chemodynamical properties of the Galactic disc using precise magnesium abundance estimates for solar neighbourhood stars with accurate Gaia astrometric measurements. Methods. We estimated ages and dynamical properties for 366 main sequence turn-off stars from the AMBRE Project using PARSEC isochrones together with astrometric and photometric values from Gaia DR2. We use precise global metallicities [M/H] and [Mg/Fe] abundances from a previous study in order to estimate gradients and temporal chemodynamic relations for these stars. Results. We find a radial gradient of −0.099 ± 0.031 dex kpc−1 for [M/H] and +0.023 ± 0.009 dex kpc−1 for the [Mg/Fe] abundance. The steeper [Mg/Fe] gradient than that found in the literature is a result of the improvement of the AMBRE [Mg/Fe] estimates in the metal-rich regime. In addition, we find a significant spread of stellar age at any given [Mg/Fe] value, and observe a clear correlated dispersion of the [Mg/Fe] abundance with metallicity at a given age. While for [M/H] ≤ − 0.2, a clear age–[Mg/Fe] trend is observed, more metal-rich stars display ages from 3 up to 12 Gyr, describing an almost flat trend in the [Mg/Fe]–age relation. Moreover, we report the presence of radially migrated and/or churned stars for a wide range of stellar ages, although we note the large uncertainties of the amplitude of the inferred change in orbital guiding radii. Finally, we observe the appearance of a second chemical sequence in the outer disc, 10–12 Gyr ago, populating the metal-poor, low-[Mg/Fe] tail. These stars are more metal-poor than the coexisting stellar population in the inner parts of the disc, and show lower [Mg/Fe] abundances than prior disc stars of the same metallicity, leading to a chemical discontinuity. Our data favour the rapid formation of an early disc that settled in the inner regions, followed by the accretion of external metal-poor gas –probably related to a major accretion event such as the Gaia-Enceladus/Sausage one– that may have triggered the formation of the thin disc population and steepened the abundance gradient in the early disc.

Uncertain times: the redshift–time relation from cosmology and stars

ABSTRACT Planck data provide precise constraints on cosmological parameters when assuming the base ΛCDM model, including a 0.17 per cent measurement of the age of the Universe, $t_0=13.797 \pm 0.023\, {\rm Gyr}$. However, the persistence of the ‘Hubble tension’ calls the base ΛCDM model’s completeness into question and has spurred interest in models such as early dark energy (EDE) that modify the assumed expansion history of the Universe. We investigate the effect of EDE on the redshift–time relation z↔t and find that it differs from the base ΛCDM model by at least ${\approx } 4{{\ \rm per\ cent}}$ at all t and z. As long as EDE remains observationally viable, any inferred t ← z or z ← t quoted to a higher level of precision do not reflect the current status of our understanding of cosmology. This uncertainty has important astrophysical implications: the reionization epoch – 10 > z > 6 – corresponds to disjoint lookback time periods in the base ΛCDM and EDE models, and the EDE value of t0 = 13.25 ± 0.17 Gyr is in tension with published ages of some stars, star clusters, and ultrafaint dwarf galaxies. However, most published stellar ages do not include an uncertainty in accuracy (due to, e.g. uncertain distances and stellar physics) that is estimated to be $\sim 7\!-\!10{{\ \rm per\ cent}}$, potentially reconciling stellar ages with $t_{0,\rm EDE}$. We discuss how the big data era for stars is providing extremely precise ages ($\lt 1{{\ \rm per\ cent}}$) and how improved distances and treatment of stellar physics such as convection could result in ages accurate to $4\!-\!5{{\ \rm per\ cent}}$, comparable to the current accuracy of t↔z. Such precise and accurate stellar ages can provide detailed insight into the high-redshift Universe independent of a cosmological model.

Uncovering the birth of the Milky Way through accurate stellar ages with Gaia

Knowledge of ages for stars formed over a galaxy's lifetime is fundamental to understand its formation and evolution. However, stellar ages are difficult to obtain since they cannot be measured from observations, being comparison with stellar models (Soderblom 2010) required. Alternatively, age distributions can be derived applying the robust technique of colour-magnitude diagram fitting (Gallart et al. 2005), till now mainly employed to study nearby galaxies. The new distances to individual Milky Way stars from the Gaia mission (Brown et al. 2018) have allowed us to use this technique to derive ages from a thick disk colour-magnitude diagram, and from the enigmatic, two-sequenced colour-magnitude diagram of the kinematically hot local halo (Babusiaux et al. 2018), which blue-sequence has been linked to a major accretion event (Haywood et al. 2018, Helmi et al. 2018). Because accurate ages were lacking, the time of the merger and its role on our Galaxy's early evolution remained unclear. We show that the stars in both halo sequences share identical age distributions, and are older than the bulk of thick disc stars. The sharp halo age cut 10 Gyr ago can be identified with the accretion of Gaia-Enceladus. Along with state-of-the-art cosmological simulations of galaxy formation (Brook et al. 2012), these robust ages allow us to order the early sequence of events that shaped our Galaxy, identifying the red-sequence as the first stars formed within the Milky Way progenitor which, because of their kinematics, can be described as its long sought in-situ halo.

The Gaia-ESO Survey: Age spread in the star forming region NGC 6530 from the HR diagram and gravity indicators

Context. In very young clusters, stellar age distribution is empirical proof of the duration of star cluster formation and thus it gives indications of the physical mechanisms involved in the star formation process. Determining the amount of interstellar extinction and the correct reddening law are crucial steps to derive fundamental stellar parameters and in particular accurate ages from the Hertzsprung-Russell diagram. Aims. In this context, we seek to derive accurate stellar ages for NGC 6530, the young cluster associated with the Lagoon Nebula to infer the star formation history of this region. Methods. We used the Gaia-ESO survey observations of the Lagoon Nebula, together with photometric literature data and Gaia DR2 kinematics, to derive cluster membership and fundamental stellar parameters. Using spectroscopic effective temperatures, we analysed the reddening properties of all objects and derived accurate stellar ages for cluster members. Results. We identified 652 confirmed and 9 probable members. The reddening inferred for members and non-members allows us to distinguish foreground objects, mainly main-sequence stars, and background objects, mainly giants, and to trace the three-dimensional structure of the nebula. This classification is in agreement with the distances inferred from Gaia DR2 parallaxes for these objects. Finally, we derive stellar ages for 382 confirmed cluster members for which we obtained the individual reddening values. In addition, we find that the gravity-sensitive γ index distribution for the M-type stars is correlated with stellar age. Conclusions. For all members with Teff < 5500 K, the mean logarithmic age is 5.84 (units of years) with a dispersion of 0.36 dex. The age distribution of stars with accretion or discs, i.e. classical T Tauri stars with excess (CTTSe), is similar to that of stars without accretion and without discs, i.e. weak T Tauri stars with photospheric emission (WTTSp). We interpret this dispersion as evidence of a real age spread since the total uncertainties on age determinations, derived from Monte Carlo simulations, are significantly smaller than the observed spread. This conclusion is supported by evidence of the decrease of the gravity-sensitive γ index as a function of stellar ages. The presence of a small age spread is also supported by the spatial distribution and kinematics of old and young members. In particular, members with accretion or discs, formed in the last 1 Myr, show evidence of subclustering around the cluster centre, in the Hourglass Nebula and in the M8-E region, suggesting a possible triggering of star formation events by the O-type star ionization fronts.

Asteroseismic modelling of the subgiant μ Herculis using SONG data: lifting the degeneracy between age and model input parameters

We model the oscillations of the SONG target |$\mu$| Herculis to estimate the parameters of the star. The ℓ = 1 mixed modes of |$\mu$| Her provide strong constraints on stellar properties. The mass and age given by our asteroseismic modelling are 1.10|$^{+0.11}_{-0.06}$| M⊙ and 7.55|$^{+0.96}_{-0.79}$| Gyr, respectively. The initial helium abundance is also constrained at around Yinit = 0.28, suggesting a ratio in the elements enrichment law (ΔY/ΔZ) around 1.3, which is closed to the solar value. The mixing-length parameter converges to about 1.7, which is ∼10 per cent lower than the solar value and consistent with the results from hydrodynamic simulations. Our estimates of stellar mass and age agree very well with the previous modelling results with different input physics. Adding asteroseismic information makes these determinations less model dependent than is typically the case when only surface information is available. Our studies of the model dependence (mass, initial helium and metallicity fractions, and the mixing-length parameter) of the age determination indicate that accurate stellar ages (≲10 per cent) can be expected from asteroseismic modelling for stars similar to |$\mu$| Her. The ℓ = 1 bumped modes, which are sensitive to the mean density of the helium core, provide a useful ‘clock’ that provides additional constraints on its age.

Closing remarks and Outlook

AbstractSome highlights are given of the IAU Symposium 334, Rediscovering our Galaxy, held in Potsdam, in July 2017: from the first stars fossil records found in the halo, the carbon-enhanced metal poor CEMP-no, to the cosmological simulations presenting possible scenarios for the Milky Way formation, passing through the chemo-dynamical models of the various components, thin and thick disks, box/peanut bulge, halo, etc. The domain is experiencing (or will be in the near future) huge improvements with precise and accurate stellar ages, provided by astero-seismology, precise stellar distances and kinematics (parallaxes and proper motions from GAIA), and the big data resulting from large surveys are treated with deep learning algorithms.

An improved age–activity relationship for cool stars older than a gigayear

Stars with convective envelopes display magnetic activity, which decreases over time due to the magnetic braking of the star. This age-dependence of magnetic activity is well-studied for younger stars, but the nature of this dependence for older stars is not well understood. This is mainly because absolute stellar ages for older stars are hard to measure. However, relatively accurate stellar ages have recently come into reach through asteroseismology. In this work we present X-ray luminosities, which are a measure for magnetic activity displayed by the stellar coronae, for 24 stars with well-determined ages older than a gigayear. We find 14 stars with detectable X-ray luminosities and use these to calibrate the age-activity relationship. We find a relationship between stellar X-ray luminosity, normalized by stellar surface area, and age that is steeper than the relationships found for younger stars, with an exponent of $-2.80 \pm 0.72$. Previous studies have found values for the exponent of the age-activity relationship ranging between -1.09 to -1.40, dependent on spectral type, for younger stars. Given that there are recent reports of a flattening relationship between age and rotational period for old cool stars, one possible explanation is that we witness a strong steepening of the relationship between activity and rotation.

Milky Way chemo‐dynamics in the era of Gaia

AbstractThe main goal of Galactic Archaeology is understanding the formation and evolution of the basic Galactic components. This requires sophisticated chemo‐dynamical modeling, where disc asymmetries (e.g., perturbations from the central bar, spirals arms, and infalling satellites) and non‐equilibrium processes are taken into account self‐consistently. Here we discuss the current status of Galactic chemo‐dynamical modeling and focus on a recent hybrid technique, which helps circumvent traditional problems with chemical enrichment and star formation encountered in fully self‐consistent cosmological simulations. We show that this model can account for a number of chemo‐kinematic relations in the Milky Way. In addition, we demonstrate that (1) our model matches well the observed age‐[α/Fe] and age‐[Fe/H] relations and (2) that the scatter in the age‐[Fe/H] relation cannot be simply explained by blurring (stars on apo‐ and pericenters visiting the solar vicinity) but significant radial migration (stars born elsewhere but ending up at the solar vicinity today because of a change in guiding radius) is needed. We emphasize the importance of accurate stellar ages, such as those obtained through asteroseismology by the CoRoT and Kepler missions, for breaking the degeneracy among different Galactic evolution scenarios.

The age–metallicity relation in the solar neighbourhood from a pilot sample of white dwarf–main sequence binaries

The age–metallicity relation (AMR) is a fundamental observational constraint for understanding how the Galactic disc formed and evolved chemically in time. However, there is not yet an agreement on the observational properties of the AMR for the solar neighbourhood, primarily due to the difficulty in obtaining accurate stellar ages for individual field stars. We have started an observational campaign for providing the much needed observational input by using wide white-dwarf–main-sequence (WDMS) binaries. White dwarfs are ‘natural’ clocks and can be used to derive accurate ages. Metallicities can be obtained from the main-sequence companions. Since the progenitors of white dwarfs and the main-sequence stars were born at the same time, WDMS binaries provide a unique opportunity to observationally constrain in a robust way the properties of the AMR. In this work we present the AMR derived from analysing a pilot sample of 23 WDMS binaries and provide clear observational evidence for the lack of correlation between age and metallicity at young and intermediate ages (0–7 Gyr).

Lithium Depletion Boundary Ages of Young Stars: Inconsistencies in Pre-Main Sequence Models

AbstractFor proper interpretations of various phenomena in young stars and planetary systems, knowledge of accurate stellar ages is very important. Among a handful of age dating methods commonly used for young (≲500 Myr) stars, lithium depletion boundary (LDB) ages have recently become the most cited and accepted age estimates. However, because of inconsistencies in theoretical evolutionary models, especially for lithium depletion calculations, one has to be cautious in using LDB ages. For a given luminosity, the lithium depletion process is too slow, causing LDB ages to appear older. Various stellar processes affect the surface lithium abundance, and these effects include star spots, accretion history, and magnetic fields. Until we have a self-consistent theoretical evolutionary model for young stars including all relevant stellar effects, caution should be taken when LDB ages are used.

Asteroseismology for “à la carte” stellar age-dating and weighing

In the context of CoRoT, Kepler, Gaia, TESS, and PLATO, precise and accurate stellar ages, masses and radii are of paramount importance. They are crucial to constrain scenarii of planetary formation and evolution.We aim at quantifying how detailed stellar modeling improves the accuracy and precision on age and mass of individual stars. We adopt a multifaceted approach where we examine how the number of observational constraints as well as the uncertainties on observations and on model input physics impact the age-dating and weighing. We modelled the exoplanet host-star HD52265, a MS, solar-like oscillator observed by CoRoT. We considered different sets of observational constraints (HR data, metallicity, seismic constraints). For each case, we determined the age, mass, and properties of HD52265 inferred from models, and quantified the impact of the models inputs. Our seismic analysis provides an age A=2.10-2.54 Gyr, a mass M=1.14-1.32 Msun, and a radius R=1.30-1.34 Rsun, which corresponds to uncertainties of 10, 7, and 1.5% respectively. Our seismic study provides constraints on surface convection, through the mixing-length found to be 12-15% smaller than the solar one. Because of helium-mass degeneracy, the initial He abundance is determined modulo the mass. The seismic mass of the exoplanet is found to be Mp sin i=1.17-1.26 MJup, much more precise than what can be derived by HR diagram inversion. We demonstrate that asteroseismology allows to improve the age accuracy compared to other methods. We emphasize that the knowledge of the mean properties of oscillations -as the large frequency separation- is not enough for deriving accurate ages. We need precise individual frequencies to narrow the age scatter due to model uncertainties. This strengthen the case for precise classical stellar parameters and frequencies as will be obtained by Gaia and PLATO.

THE DECAY OF DEBRIS DISKS AROUND SOLAR-TYPE STARS

We present a Spitzer MIPS study of the decay of debris disk excesses at 24 and 70 $\mu$m for 255 stars of types F4 - K2. We have used multiple tests, including consistency between chromospheric and X-ray activity and placement on the HR diagram, to assign accurate stellar ages. Within this spectral type range, at 24 $\mu$m, $13.6 \pm 2.8 \%$ of the stars younger than 5 Gyr have excesses at the 3$\sigma$ level or more, while none of the older stars do, confirming previous work. At 70 $\mu$m, $22.5 \pm 3.6\%$ of the younger stars have excesses at $ \ge$ 3 $\sigma$ significance, while only $4.7^{+3.7}_{-2.2}$% of the older stars do. To characterize the far infrared behavior of debris disks more robustly, we double the sample by including stars from the DEBRIS and DUNES surveys. For the F4 - K4 stars in this combined sample, there is only a weak (statistically not significant) trend in the incidence of far infrared excess with spectral type (detected fractions of 21.9$^{+4.8}_{-4.3}\%$, late F; 16.5$^{+3.9}_{-3.3}\%$, G; and 16.9$^{+6.3}_{-5.0}\%$, early K). Taking this spectral type range together, there is a significant decline between 3 and 4.5 Gyr in the incidence of excesses with fractional luminosities just under $10^{-5}$. There is an indication that the timescale for decay of infrared excesses varies roughly inversely with the fractional luminosity. This behavior is consistent with theoretical expectations for passive evolution. However, more excesses are detected around the oldest stars than is expected from passive evolution, suggesting that there is late-phase dynamical activity around these stars.