Asteroseismology of 16000 Kepler Red Giants: Global Oscillation Parameters, Masses, and Radii

The Kepler mission has provided exquisite data to perform an ensemble asteroseismic analysis on evolved stars. In this work we systematically characterize solar-like oscillations and granulation for 16,094 oscillating red giants, using end-of-mission long-cadence data. We produced a homogeneous catalog of the frequency of maximum power (typical uncertainty $\sigma_{\nu_{\rm max}}$=1.6\%), the mean large frequency separation ($\sigma_{\Delta\nu}$=0.6\%), oscillation amplitude ($\sigma_{\rm A}$=4.7\%), granulation power ($\sigma_{\rm gran}$=8.6\%), power excess width ($\sigma_{\rm width}$=8.8\%), seismically-derived stellar mass ($\sigma_{\rm M}$=7.8\%), radius ($\sigma_{\rm R}$=2.9\%), and thus surface gravity ($\sigma_{\log g}$=0.01 dex). Thanks to the large red giant sample, we confirm that red-giant-branch (RGB) and helium-core-burning (HeB) stars collectively differ in the distribution of oscillation amplitude, granulation power, and width of power excess, which is mainly due to the mass difference. The distribution of oscillation amplitudes shows an extremely sharp upper edge at fixed $\nu_{\rm max}$, which might hold clues to understand the excitation and damping mechanisms of the oscillation modes. We find both oscillation amplitude and granulation power depend on metallicity, causing a spread of 15\% in oscillation amplitudes and a spread of 25\% in granulation power from [Fe/H]=-0.7 to 0.5 dex. Our asteroseismic stellar properties can be used as reliable distance indicators and age proxies for mapping and dating galactic stellar populations observed by Kepler. They will also provide an excellent opportunity to test asteroseismology using Gaia parallaxes, and lift degeneracies in deriving atmospheric parameters in large spectroscopic surveys such as APOGEE and LAMOST.Comment: Accepted for publication in ApJS. Both table 1 and 2 are available for download as ancillary file

Mass and Age of Red Giant Branch Stars Observed with LAMOST and \emph{Kepler}

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 -- [$\alpha$/Fe] relation -- a high--$\alpha$ sequence with stars older than $\sim$\,8\,Gyr and a low--$\alpha$ sequence composed of stars with ages ranging from younger than 1\,Gyr to older than 11\,Gyr. We further investigate the feasibility of deducing ages and masses directly from LAMOST spectra with a machine learning method based on kernel based principal component analysis, taking a sub-sample of these RGB stars as a training data set. We demonstrate that ages thus derived achieve an accuracy of $\sim$\,24 per cent. We also explored the feasibility of estimating ages and masses based on the spectroscopically measured carbon and nitrogen abundances. The results are quite satisfactory and significantly improved compared to the previous studies.Comment: accepted by MNRA

Safe functional reactive programming through dependent types

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals. FRP is based on the synchronous dataflow paradigm and supports both continuous-time and discrete-time signals (hybrid systems).What sets FRP apart from most other languages for similar applications is its support for systems with dynamic structure and for higher-order reactive constructs. Statically guaranteeing correctness properties of programs is an attractive proposition. This is true in particular for typical application domains for reactive programming such as embedded systems. To that end, many existing reactive languages have type systems or other static checks that guarantee domain-specific properties, such as feedback loops always being well-formed. However, they are limited in their capabilities to support dynamism and higher-order data-flow compared with FRP. Thus, the onus of ensuring such properties of FRP programs has so far been on the programmer as established static techniques do not suffice. In this paper, we show how dependent types allow this concern to be addressed. We present an implementation of FRP embedded in the dependently-typed language Agda, leveraging the type system of the host language to craft a domain-specific (dependent) type system for FRP. The implementation constitutes a discrete, operational semantics of FRP, and as it passes the Agda type, coverage, and termination checks, we know the operational semantics is total, which means our type system is safe

Asteroseismology of the Hyades red giant and planet host epsilon Tauri

Asteroseismic analysis of solar-like stars allows us to determine physical parameters such as stellar mass, with a higher precision compared to most other methods. Even in a well-studied cluster such as the Hyades, the masses of the red giant stars are not well known, and previous mass estimates are based on model calculations (isochrones). The four known red giants in the Hyades are assumed to be clump (core-helium-burning) stars based on their positions in colour-magnitude diagrams, however asteroseismology offers an opportunity to test this assumption. Using asteroseismic techniques combined with other methods, we aim to derive physical parameters and the evolutionary stage for the planet hosting star epsilon Tau, which is one of the four red giants located in the Hyades. We analysed time-series data from both ground and space to perform the asteroseismic analysis. By combining high signal-to-noise (S/N) radial-velocity data from the ground-based SONG network with continuous space-based data from the revised Kepler mission K2, we derive and characterize 27 individual oscillation modes for epsilon Tau, along with global oscillation parameters such as the large frequency separation and the ratio between the amplitude of the oscillations measured in radial velocity and intensity as a function of frequency. The latter has been measured previously for only two stars, the Sun and Procyon. Combining the seismic analysis with interferometric and spectroscopic measurements, we derive physical parameters for epsilon Tau, and discuss its evolutionary status.Comment: 13 pages, 13 figures, 4 tables, accepted for publication in Astronomy & Astrophysic

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

International audienc

The K2-HERMES Survey: Age and Metallicity of the Thick Disc

Asteroseismology is a promising tool to study Galactic structure and evolution because it can probe the ages of stars. Earlier attempts comparing seismic data from the {\it Kepler} satellite with predictions from Galaxy models found that the models predicted more low-mass stars compared to the observed distribution of masses. It was unclear if the mismatch was due to inaccuracies in the Galactic models, or the unknown aspects of the selection function of the stars. Using new data from the K2 mission, which has a well-defined selection function, we find that an old metal-poor thick disc, as used in previous Galactic models, is incompatible with the asteroseismic information. We show that spectroscopic measurements of [Fe/H] and [$\alpha$/Fe] elemental abundances from the GALAH survey indicate a mean metallicity of $\log (Z/Z_{\odot})=-0.16$ for the thick disc. Here $Z$ is the effective solar-scaled metallicity, which is a function of [Fe/H] and [$\alpha$/Fe]. With the revised disc metallicities, for the first time, the theoretically predicted distribution of seismic masses show excellent agreement with the observed distribution of masses. This provides an indirect verification of the asteroseismic mass scaling relation is good to within five percent. Using an importance-sampling framework that takes the selection function into account, we fit a population synthesis model of the Galaxy to the observed seismic and spectroscopic data. Assuming the asteroseismic scaling relations are correct, we estimate the mean age of the thick disc to be about 10 Gyr, in agreement with the traditional idea of an old $\alpha$-enhanced thick disc.Comment: 21 pages, submitted to MNRA

Deep Learning Classification in Asteroseismology Using an Improved Neural Network: Results on 15000 Kepler Red Giants and Applications to K2 and TESS Data

Deep learning in the form of 1D convolutional neural networks have previously been shown to be capable of efficiently classifying the evolutionary state of oscillating red giants into red giant branch stars and helium-core burning stars by recognizing visual features in their asteroseismic frequency spectra. We elaborate further on the deep learning method by developing an improved convolutional neural network classifier. To make our method useful for current and future space missions such as K2, TESS and PLATO, we train classifiers that are able to classify the evolutionary states of lower frequency resolution spectra expected from these missions. Additionally, we provide new classifications for 8633 Kepler red giants, out of which 426 have previously not been classified using asteroseismology. This brings the total to 14983 Kepler red giants classified with our new neural network. We also verify that our classifiers are remarkably robust to suboptimal data, including low signal-to-noise and incorrect training truth labels.Comment: 12 pages, 14 figures, 4 tables. Accepted for publication in the Main Journal of MNRAS. The catalogue containing updated evolutionary state classifications of ~16000 Kepler red giants is available as an ancillary fil

Mixed-mode Ensemble Asteroseismology of Low-Luminosity Kepler Red Giants

We present measurements of the dipole mode asymptotic period spacing ($\Delta\Pi_1$), the coupling factor between p- and g- modes ($q$), the g-mode phase offset ($\epsilon_g$), and the mixed-mode frequency rotational splitting ($\delta\nu_{\mathrm{rot}}$) for 1,074 low-luminosity red giants from the Kepler mission. Using oscillation mode frequencies extracted from each star, we apply Bayesian optimization to estimate $\Delta\Pi_1$ from the power spectrum of the stretched period spectrum and to perform the subsequent forward modelling of the mixed-mode frequencies. With our measurements, we show that the mode coupling factor $q$ shows significant anti-correlation with both stellar mass and metallicity, and can reveal highly metal-poor stars. We present the evolution of $\epsilon_g$ up the lower giant branch up to before the luminosity bump, and find no significant trends in $\epsilon_g$ or $\delta\nu_{\mathrm{rot}}$ with stellar mass and metallicity in our sample. Additionally, we identify six new red giants showing anomalous distortions in their g-mode pattern. Our data products, code, and results are provided in a public repository.Comment: Accepted in the Astrophysical Journal. Code repository is at https://github.com/jsk389/BOChaMM and associated peakbagging data is publicly available at https://zenodo.org/record/788863