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Marc H. Pinsonneault

Publications and source records attributed to Marc H. Pinsonneault.

At least 73 records · Page 4Linked to original sources

Core-Envelope Coupling in Intermediate-Mass Core-Helium Burning Stars

Stars between two and three solar masses rotate rapidly on the main sequence, and the detection of slow core and surface rotation in the core-helium burning phase for these stars places strong constraints on their angular momentum transport and loss. From a detailed asteroseismic study of the mixed-dipole mode pattern in a carefully selected, representative sample of stars, we find that slow core rotation rates in the range reported by prior studies are a general phenomenon and not a selection effect. We show that the core rotation rates of these stars decline strongly with decreasing surface gravity during the core He-burning phase. We argue that this is a model-independent indication of significant rapid angular momentum transport between the cores and envelopes of these stars. We see a significant range in core rotation rates at all surface gravities, with little evidence for a convergence towards a uniform value. We demonstrate using evolutionary models that measured surface rotation periods are a biased tracer of the true surface rotation distribution, and argue for using stellar models for interpreting the contrast between core and surface rotation rates. The core rotation rates we measure do not have a strong mass or metallicity dependence. We argue that the emerging data strongly favors a model where angular momentum transport is much more efficient during the core He burning phase than in the shell burning phases which precede and follow it.

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TESS Asteroseismology of the known red-giant host stars HD 212771 and HD 203949

The Transiting Exoplanet Survey Satellite (TESS) is performing a near all-sky survey for planets that transit bright stars. In addition, its excellent photometric precision enables asteroseismology of solar-type and red-giant stars, which exhibit convection-driven, solar-like oscillations. Simulations predict that TESS will detect solar-like oscillations in nearly 100 stars already known to host planets. In this paper, we present an asteroseismic analysis of the known red-giant host stars HD 212771 and HD 203949, both systems having a long-period planet detected through radial velocities. These are the first detections of oscillations in previously known exoplanet-host stars by TESS, further showcasing the mission's potential to conduct asteroseismology of red-giant stars. We estimate the fundamental properties of both stars through a grid-based modeling approach that uses global asteroseismic parameters as input. We discuss the evolutionary state of HD 203949 in depth and note the large discrepancy between its asteroseismic mass ($M_\ast = 1.23 \pm 0.15\,{\rm M}_\odot$ if on the red-giant branch or $M_\ast = 1.00 \pm 0.16\,{\rm M}_\odot$ if in the clump) and the mass quoted in the discovery paper ($M_\ast = 2.1 \pm 0.1\,{\rm M}_\odot$), implying a change $>30\,\%$ in the planet's mass. Assuming HD 203949 to be in the clump, we investigate the planet's past orbital evolution and discuss how it could have avoided engulfment at the tip of the red-giant branch. Finally, HD 212771 was observed by K2 during its Campaign 3, thus allowing for a preliminary comparison of the asteroseismic performances of TESS and K2. We estimate the ratio of the observed oscillation amplitudes for this star to be $A_{\rm max}^{\rm TESS}/A_{\rm max}^{\rm K2} = 0.75 \pm 0.14$, consistent with the expected ratio of $\sim0.85$ due to the redder bandpass of TESS.

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Comparison of the Asteroseismic Mass Scale of Red Clump Giants with Photometric Mass Estimates

Asteroseismology can provide joint constraints on masses and radii of individual stars. While this approach has been extensively tested for red giant branch (RGB) stars, it has been more difficult to test for helium core-burning red-clump (RC) giants because of the lack of fundamental calibrators. To provide independent mass estimates, we utilize a number of widely used horizontal-branch (HB) models in the literature, and derive photometric masses from a comparison with $griBVI_CJHK_s$ photometry. Our selected models disagree with each other on the predicted mass-luminosity-temperature relation. We adopt first-order corrections on colors and magnitudes to minimize the dispersion between different models by forcing models to match the observed location in the solar-metallicity cluster M67. Even for these calibrated models, however, the internal consistency between models deteriorates at higher metallicities, and photometric masses become smaller than asteroseismic masses, as seen from metal-rich field RC stars with Gaia parallaxes. Similarly, the average photometric mass for metal-rich NGC 6791 stars ranges from $0.7\ M_\odot$ to $1.1\ M_\odot$, depending on the specific set of models employed. An ensemble average of the photometric masses ($0.88\pm0.16\ M_\odot$) in NGC 6791 is marginally consistent with the asteroseismic mass ($1.16\pm0.04\ M_\odot$). There is a clear tension between the masses that one would predict from photometry for metal-rich field RC stars, asteroseismic masses, and those that would be expected from the ages of stars in the Galactic disk populations and canonical RGB mass loss. We conclude that standard RC models need to be re-examined in light of these powerful new data sets.

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Dynamical heating across the Milky Way disc using APOGEE and $\it{Gaia}$

The kinematics of the Milky Way disc as a function of age are well measured at the solar radius, but have not been studied over a wider range of Galactocentric radii. Here, we measure the kinematics of mono-age, mono-$\mathrm{[Fe/H]}$ populations in the low and high $\mathrm{[α/Fe]}$ discs between $4 \lesssim R \lesssim 13$ kpc and $|z| \lesssim 2$ kpc using 65,719 stars in common between APOGEE DR14 and $\it{Gaia}$ DR2 for which we estimate ages using a Bayesian neural network model trained on asteroseismic ages. We determine the vertical and radial velocity dispersions, finding that the low and high $\mathrm{[α/Fe]}$ discs display markedly different age--velocity-dispersion relations (AVRs) and shapes $σ_z/σ_R$. The high $\mathrm{[α/Fe]}$ disc has roughly flat AVRs and constant $σ_z/σ_R = 0.64\pm 0.04$, whereas the low $\mathrm{[α/Fe]}$ disc has large variations in this ratio which positively correlate with the mean orbital radius of the population at fixed age. The high $\mathrm{[α/Fe]}$ disc component's flat AVRs and constant $σ_z/σ_R$ clearly indicates an entirely different heating history. Outer disc populations also have flatter radial AVRs than those in the inner disc, likely due to the waning effect of spiral arms. Our detailed measurements of AVRs and $σ_z/σ_R$ across the disc indicate that low $\mathrm{[α/Fe]}$, inner disc ($R \lesssim 10\,\mathrm{kpc}$) stellar populations are likely dynamically heated by both giant molecular clouds and spiral arms, while the observed trends for outer disc populations require a significant contribution from another heating mechanism such as satellite perturbations. We also find that outer disc populations have slightly positive mean vertical and radial velocities, likely because they are part of the warped disc.

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Confirmation of the ${\rm \it Gaia}$ DR2 parallax zero-point offset using asteroseismology and spectroscopy in the ${\rm \it Kepler}$ field

We present an independent confirmation of the zero-point offset of ${\rm \it Gaia}$ Data Release 2 (DR2) parallaxes using asteroseismic data of evolved stars in the ${\rm \it Kepler}$ field. Using well-characterized red giant branch (RGB) stars from the APOKASC-2 catalogue we identify a ${\rm \it Gaia}$ astrometric pseudo-color ($ν_{\rm eff}$)- and ${\rm \it Gaia}$ $G$-band magnitude-dependent zero-point offset of $\varpi_{\rm seis} - \varpi_{Gaia} = 52.8 \pm 2.4 {\rm\ (rand.)} \pm 8.6 {\rm\ (syst.)} - (150.7 \pm 22.7)(ν_{\rm eff} - 1.5) - (4.21 \pm 0.77)(G - 12.2) μ{\rm as}$, in the sense that ${\rm \it Gaia}$ parallaxes are too small. The offset is found in high and low-extinction samples, as well as among both shell H-burning red giant stars and core He-burning red clump stars. We show that errors in the asteroseismic radius and temperature scales may be distinguished from errors in the ${\rm \it Gaia}$ parallax scale. We estimate systematic effects on the inferred global ${\rm \it Gaia}$ parallax offset, $c$, due to radius and temperature systematics, as well as choices in bolometric correction and the adopted form for ${\rm \it Gaia}$ parallax spatial correlations. Because of possible spatially-correlated parallax errors, as discussed by the ${\rm \it Gaia}$ team, our ${\rm \it Gaia}$ parallax offset model is specific to the ${\rm \it Kepler}$ field, but broadly compatible with the magnitude- and color-dependent offset inferred by the ${\rm \it Gaia}$ team and several subsequent investigations using independent methods.

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Constraining Metallicity-dependent Mixing and Extra Mixing using [C/N] in Alpha-Rich Field Giants

Internal mixing on the giant branch is an important process which affects the evolution of stars and the chemical evolution of the galaxy. While several mechanisms have been proposed to explain this mixing, better empirical constraints are necessary. Here, we use [C/N] abundances in 26097 evolved stars from the SDSS-IV/APOGEE-2 Data Release 14 to trace mixing and extra mixing in old field giants with -1.7< [Fe/H] < 0.1. We show that the APOGEE [C/N] ratios before any dredge-up occurs are metallicity dependent, but that the change in [C/N] at the first dredge-up is metallicity independent for stars above [Fe/H] ~ -1. We identify the position of the red giant branch (RGB) bump as a function of metallicity, note that a metallicity-dependent extra mixing episode takes place for low-metallicity stars ([Fe/H] <-0.4) 0.14 dex in log g above the bump, and confirm that this extra mixing is stronger at low metallicity, reaching $Δ$ [C/N] = 0.58 dex at [Fe/H] = -1.4. We show evidence for further extra mixing on the upper giant branch, well above the bump, among the stars with [Fe/H] < -1.0. This upper giant branch mixing is stronger in the more metal-poor stars, reaching 0.38 dex in [C/N] for each 1.0 dex in log g. The APOGEE [C/N] ratios for red clump (RC) stars are significantly higher than for stars at the tip of the RGB, suggesting additional mixing processes occur during the helium flash or that unknown abundance zero points for C and N may exist among the red clump RC sample. Finally, because of extra mixing, we note that current empirical calibrations between [C/N] ratios and ages cannot be naively extrapolated for use in low-metallicity stars specifically for those above the bump in the luminosity function.

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Rapid Rotation in the Kepler Field: Not a Single Star Phenomenon

Tens of thousands of rotation periods have been measured in the Kepler fields, including a substantial fraction of rapid rotators. We use Gaia parallaxes to distinguish photometric binaries (PBs) from single stars on the unevolved lower main sequence, and compare their distribution of rotation properties to those of single stars both with and without APOGEE spectroscopic characterization. We find that 59% of stars with 1.5 day < P < 7 day lie 0.3 mag above the main sequence, compared with 28% of the full rotation sample. The fraction of stars in the same period range is 1.7 $\pm$ 0.1% of the total sample analyzed for rotation periods. Both the photometric binary fraction and the fraction of rapid rotators are consistent with a population of non-eclipsing short period binaries inferred from Kepler eclipsing binary data after correcting for inclination. This suggests that the rapid rotators are dominated by tidally-synchronized binaries rather than single-stars obeying traditional angular momentum evolution. We caution against interpreting rapid rotation in the Kepler field as a signature of youth. Following up this new sample of 217 candidate tidally-synchronized binaries will help further understand tidal processes in stars.

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APOGEE [C/N] Abundances Across the Galaxy: Migration and Infall from Red Giant Ages

We present [C/N]-[Fe/H] abundance trends from the SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey, Data Release 14 (DR14), for red giant branch stars across the Milky Way Galaxy (MW, 3 kpc $<$ R $<$ 15 kpc). The carbon-to-nitrogen ratio (often expressed as [C/N]) can indicate the mass of a red giant star, from which an age can be inferred. Using masses and ages derived by Martig et al., we demonstrate that we are able to interpret the DR14 [C/N]-[Fe/H] abundance distributions as trends in age-[Fe/H] space. Our results show that an anti-correlation between age and metallicity, which is predicted by simple chemical evolution models, is not present at any Galactic zone. Stars far from the plane ($|$Z$|$ $>$ 1 kpc) exhibit a radial gradient in [C/N] ($\sim$ $-$0.04 dex/kpc). The [C/N] dispersion increases toward the plane ($σ_{[C/N]}$ = 0.13 at $|$Z$|$ $>$ 1 kpc to $σ_{[C/N]}$ = 0.18 dex at $|$Z$|$ $<$ 0.5 kpc). We measure a disk metallicity gradient for the youngest stars (age $<$ 2.5 Gyr) of $-$0.060 dex/kpc from 6 kpc to 12 kpc, which is in agreement with the gradient found using young CoRoGEE stars by Anders et al. Older stars exhibit a flatter gradient ($-$0.016 dex/kpc), which is predicted by simulations in which stars migrate from their birth radii. We also find that radial migration is a plausible explanation for the observed upturn of the [C/N]-[Fe/H] abundance trends in the outer Galaxy, where the metal-rich stars are relatively enhanced in [C/N].

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APOGEE Data Releases 13 and 14: Stellar Parameter and Abundance Comparisons With Independent Analyses

Data from the SDSS-IV / Apache Point Observatory Galactic Evolution Experiment (APOGEE-2) have been released as part of SDSS Data Releases 13 (DR13) and 14 (DR14). These include high resolution H-band spectra, radial velocities, and derived stellar parameters and abundances. DR13, released in August 2016, contained APOGEE data for roughly 150,000 stars, and DR14, released in August 2017, added about 110,000 more. Stellar parameters and abundances have been derived with an automated pipeline, the APOGEE Stellar Parameter and Chemical Abundance Pipeline (ASPCAP). We evaluate the performance of this pipeline by comparing the derived stellar parameters and abundances to those inferred from optical spectra and analysis for several hundred stars. For most elements -- C, Na, Mg, Al, Si, S, Ca, Cr, Mn, Ni -- the DR14 ASPCAP analysis have systematic differences with the comparisons samples of less than 0.05 dex (median), and random differences of less than 0.15 dex (standard deviation). These differences are a combination of the uncertainties in both the comparison samples as well as the ASPCAP-analysis. Compared to the references, magnesium is the most accurate alpha-element derived by ASPCAP, and shows a very clear thin/thick disk separation, while nickel is the most accurate iron-peak element (besides iron).

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Testing Angular Momentum Transport and Wind Loss in Intermediate Mass Core Helium Burning Stars

Stars between two and three solar masses rotate rapidly on the main sequence, and their rotation rates in the core helium burning (secondary clump) phase can therefore be used to test models of angular momentum loss used for gyrochronology in a new regime. Because both their core and surface rotation rates can be measured, these stars can also be used to set strong constraints on angular momentum transport inside stars. We find that they are rotating slower than angular momentum conservation and rigid rotation would predict. Our results are insensitive to the degree of core-envelope coupling because of the small moment of inertia of the radiative core. We discuss two possible mechanisms for slowing down the surfaces of these stars: (1) substantial angular momentum loss, and (2) radial differential rotation in the surface convection zone. Modern angular momentum loss prescriptions used for solar-type stars predict secondary clump surface rotation rates in much better agreement with the data than prior variants used in the literature, and we argue that such enhanced loss is required to understand the combination of core and surface rotation rates. However, we find that the assumed radial differential rotation profile in convective regions has a strong impact on the predicted surface rotation rates, and that a combination of enhanced loss and radial differential rotation in the surface convection zone is also consistent with the data. We discuss future tests that can quantify the impact of both phenomena. Current data tentatively suggests that some combination of the two processes fits the data better than either one alone.

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The Second APOKASC Catalog: The Empirical Approach

We present a catalog of stellar properties for a large sample of 6676 evolved stars with APOGEE spectroscopic parameters and \textit{Kepler} asteroseismic data analyzed using five independent techniques. Our data includes evolutionary state, surface gravity, mean density, mass, radius, age, and the spectroscopic and asteroseismic measurements used to derive them. We employ a new empirical approach for combining asteroseismic measurements from different methods, calibrating the inferred stellar parameters, and estimating uncertainties. With high statistical significance, we find that asteroseismic parameters inferred from the different pipelines have systematic offsets that are not removed by accounting for differences in their solar reference values. We include theoretically motivated corrections to the large frequency spacing ($Δν$) scaling relation, and we calibrate the zero point of the frequency of maximum power ($ν_{\rm max}$) relation to be consistent with masses and radii for members of star clusters. For most targets, the parameters returned by different pipelines are in much better agreement than would be expected from the pipeline-predicted random errors, but 22\% of them had at least one method not return a result and a much larger measurement dispersion. This supports the usage of multiple analysis techniques for asteroseismic stellar population studies. The measured dispersion in mass estimates for fundamental calibrators is consistent with our error model, which yields median random and systematic mass uncertainties for RGB stars of order 4\%. Median random and systematic mass uncertainties are at the 9\% and 8\% level respectively for RC stars.

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Forward Modeling of the Kepler Stellar Rotation Period Distribution: Interpreting Periods from Mixed and Biased Stellar Populations

Stellar surface rotation carries information about stellar parameters---particularly ages---and thus the large rotational datasets extracted from Kepler timeseries represent powerful probes of stellar populations. In this article, we address the challenge of interpreting such datasets with a forward-modeling exercise. We combine theoretical models of stellar rotation, a stellar population model for the galaxy, and prescriptions for observational bias and confusion to predict the rotation distribution in the Kepler field under standard "vanilla" assumptions. We arrive at two central conclusions: first, that standard braking models fail to reproduce the observed distribution at long periods, and second, that the interpretation of the period distribution is complicated by mixtures of unevolved and evolved stars and observational uncertainties. By assuming that the amplitude and thus detectability of rotational signatures is tied to the Rossby number, we show that the observed period distribution contains an apparent "Rossby edge" at $\textrm{Ro}_{thresh} = 2.08$, above which long-period, high-Rossby number stars are either absent or undetected. This $\textrm{Ro}_{thresh}$ is comparable to the Rossby number at which van Saders et al. (2016) observed the onset of weakened magnetic braking, and suggests either that this modified braking is in operation in the full Kepler population, or that stars undergo a transition in spottedness and activity at a very similar Rossby number. We discuss the observations necessary to disentangle these competing scenarios. (abridged)

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The K2 M67 Study: A Curiously Young Star in an Eclipsing Binary in an Old Open Cluster

We present an analysis of a slightly eccentric ($e=0.05$), partially eclipsing long-period ($P = 69.73$ d) main sequence binary system (WOCS 12009, Sanders 1247) in the benchmark old open cluster M67. Using Kepler K2 and ground-based photometry along with a large set of new and reanalyzed spectra, we derived highly precise masses ($1.111\pm0.015$ and $0.748\pm0.005 M_\odot$) and radii ($1.071\pm0.008\pm0.003$ and $0.713\pm0.019\pm0.026 R_\odot$, with statistical and systematic error estimates) for the stars. The radius of the secondary star is in agreement with theory. The primary, however, is approximately $15\%$ smaller than reasonable isochrones for the cluster predict. Our best explanation is that the primary star was produced from the merger of two stars, as this can also account for the non-detection of photospheric lithium and its higher temperature relative to other cluster main sequence stars at the same $V$ magnitude. To understand the dynamical characteristics (low measured rotational line broadening of the primary star and the low eccentricity of the current binary orbit), we believe that the most probable (but not the only) explanation is the tidal evolution of a close binary within a primordial triple system (possibly after a period of Kozai-Lidov oscillations), leading to merger approximately 1Gyr ago. This star appears to be a future blue straggler that is being revealed as the cluster ages and the most massive main sequence stars die out.

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M Dwarf rotation from the ${\it K2}$ young clusters to the field. I. A Mass-Rotation Correlation at 10 Myr

Recent observations of the low-mass rotation distributions of the Pleiades and Praesepe clusters have revealed a ubiquitous correlation between mass and rotation, such that late M dwarfs rotate an order-of-magnitude faster than early M dwarfs. In this paper, we demonstrate that this mass-rotation correlation is present in the 10 Myr Upper Scorpius association, as revealed by new ${\it K2}$ rotation measurements. Using rotational evolution models we show that the low-mass ($0.1-0.6 M_{\odot}$) rotation distribution of the 125 Myr Pleiades cluster can only be produced if it hosted an equally strong mass-rotation correlation at 10 Myr. This suggests that physical processes important in the early pre-main sequence (star formation, accretion, disk-locking) are primarily responsible for the M dwarf rotation morphology, and not quirks of later angular momentum evolution. Such early mass trends must be taken into account when constructing initial conditions for future studies of stellar rotation. Finally, we show that the average M star loses $\sim 25-40$% of its angular momentum between 10 and 125 Myr, a figure accurately and generically predicted by modern solar-calibrated wind models. Their success rules out a lossless pre-main sequence, and validates the extrapolation of magnetic wind laws designed for solar-type stars to the low-mass regime at early times.

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Evidence for spatially-correlated ${\it Gaia}$ parallax errors in the ${\it Kepler}$ field

We present evidence for a spatially-dependent systematic error in the first data release of ${\it Gaia}$ parallaxes based on comparisons to asteroseismic parallaxes in the ${\it Kepler}$ field, and present a parametrized model of the angular dependence of these systematics. We report an error of $0.059^{+0.004}_{-0.004}$mas on scales of 0.3deg, which decreases for larger scales to become $0.011^{+0.006}_{-0.004}$mas at 8deg. This is consistent with the $\sim2\%$ zeropoint offset for the whole sample discussed by Huber et al., and is compatible with the effect predicted by the ${\it Gaia}$ team. Our results are robust to dust prescriptions and choices in temperature scales used to calculate asteroseismic parallaxes. We also do not find evidence for significant differences in the signal when using red clump versus red giant stars. Our approach allows us to quantify and map the correlations in an astrophysically interesting field, resulting in a parametrized model of the spatial systematics that can be used to construct a covariance matrix for any work that relies upon TGAS parallaxes.

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The Correlation Between Mixing Length and Metallicity on the Giant Branch: Implications for Ages in the Gaia Era

In the updated APOGEE-Kepler catalog, we have asteroseismic and spectroscopic data for over 3000 first ascent red giants. Given the size and accuracy of this sample, these data offer an unprecedented test of the accuracy of stellar models on the post-main-sequence. When we compare these data to theoretical predictions, we find a metallicity dependent temperature offset with a slope of around 100 K per dex in metallicity. We find that this effect is present in all model grids tested and that theoretical uncertainties in the models, correlated spectroscopic errors, and shifts in the asteroseismic mass scale are insufficient to explain this effect. Stellar models can be brought into agreement with the data if a metallicity dependent convective mixing length is used, with $ Δα_{\rm ML, YREC} \sim 0.2$ per dex in metallicity, a trend inconsistent with the predictions of three dimensional stellar convection simulations. If this effect is not taken into account, isochrone ages for red giants from the Gaia data will be off by as much as a factor of 2 even at modest deviations from solar metallicity ([Fe/H]=$-$0.5).

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On Lithium-Rich Red Giants. II. Engulfment on the Giant Branch of Trumpler 20

The Gaia-ESO survey recently reported on a large sample of lithium (Li) abundance determinations for evolved stars in the rich open cluster Trumpler 20. They argue for a scenario where virtually all stars experience post main sequence mixing and Li is preserved in only two objects. We present an alternate explanation, where Li is normal in the vast majority of cluster stars and anomalously high in these two cases. We demonstrate that the Li upper limits in the red giants can be explained with a combination of main sequence depletion and standard dredge-up, and that they are close to the detected levels in other systems of similar age. In our framework, the two detected giants are anomalously Li-rich, and we propose that both could have been produced by the engulfment of a substellar mass companion of 16(+6-10) M_J. This would imply that ~5% of 1.8 solar mass stars in this system, and by extension elsewhere, should have substellar mass companions of high mass that could be engulfed at some point in their lifetimes. We discuss future tests that could confirm or refute this scenario.

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Boron Abundances Across the "Li-Be Dip" in the Hyades

Dramatic deficiencies of Li in the mid-F dwarf stars of the Hyades cluster were discovered by Boesgaard & Tripicco. Boesgaard & King discovered corresponding, but smaller, deficiencies in Be in the same narrow temperature region in the Hyades. With the Space Telescope Imaging Spectrograph on the Hubble Space Telescope we investigate B abundances in the Hyades F stars to look for a potential B dip using the B I resonance line at 2496.8 A. The light elements, Li, Be, and B, are destroyed inside stars at increasingly hotter temperatures: 2.5, 3.5, and 5x10^6 K respectively. Consequently, these elements survive to increasingly greater depths in a star and their surface abundances indicate the depth and thoroughness of mixing in the star. We have (re)determined Li abundances/upper limits for 79 Hyades dwarfs, Be for 43 stars, and B in five stars. We find evidence for a small drop in the B abundance across the Li-Be dip. The B abundances for the four stars in the temperature range 6100-6730 K fit the B-Be correlation found previously by Boesgaard et al. Models of rotational mixing produce good agreement with the relative depletions of Be and B in the dip region. We have compared our nLTE B abundances for the three high B stars on either side of the Li-Be dip with those found by Duncan et al. for the two Hyades giants. This confirms the factor of ~10 decline in the B abundance in the Hyades giants as predicted by dilution due to the deepening of the surface convection zone.

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