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Register a new userA seismic scaling relation for stellar age
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Earl Patrick Bellinger
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A simple solar scaling relation for estimating the ages of main-sequence stars from asteroseismic and spectroscopic data is developed. New seismic scaling relations for estimating mass and radius are presented as well, including a purely seismic radius scaling relation (i.e., no dependence on temperature). The relations show substantial improvement over the classical scaling relations and perform similarly well to grid-based modeling.
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Owing to their simplicity and ease of application, seismic scaling relations are widely used to determine the properties of stars exhibiting solar-like oscillations, such as solar twins and red giants. So far, no seismic scaling relations for determining the ages of red giant stars have been developed. Such relations would be desirable for galactic archaeology, which uses stellar ages to map the history of the Milky Way. The ages of red giants must instead be estimated with reference to grids of theoretical stellar models, which can be computationally intensive. Here I present an exhaustive search for scaling age relations involving different combinations of observable quantities. The candidate scaling relations are calibrated and tested using more than 1,000 red giant stars whose ages were obtained via grid-based modeling. I report multiple high-quality scaling relations for red giant branch stars, the best of which are shown to be approximately as accurate as grid-based modeling with typical uncertainties of 15%. Additionally, I present new scaling mass and radius relations for red giants as well.
In recent years the global seismic scaling relations for the frequency of maximum power and for the large frequency separation have caught the attention of various fields of astrophysics. With the exquisite photometry of textit{Kepler}, the uncertainties in the seismic observables are small enough to estimate masses and radii with a precision of only a few per cent. Even though this seems to work quite well for main-sequence stars, there is empirical evidence, mainly from studies of eclipsing binary systems, that the seismic scaling relations overestimate the mass and radius of red giants by about 15 and 5%, respectively. Model-based corrections of the $Delta u -$scaling reduce the problem but do not solve it. We re-examine the global oscillation parameters of the giants in the binary systems in order to determine their seismic fundamental parameters and find them to agree with the dynamic parameters from the literature if we adopt nonlinear scalings. We note that a curvature and glitch corrected $Delta u_mathrm{cor}$ should be preferred over a local or average values. We then compare the observed seismic parameters of the cluster giants to those scaled from independent measurements and find the same nonlinear behaviour as for the eclipsing binaries. Our final proposed scaling relations are based on both samples and cover a broad range of evolutionary stages from RGB to RC stars: $g/sqrt{T_mathrm{eff}} = ( u_mathrm{max}/ u_mathrm{max,odot})^{1.0075pm0.0021}$ and $sqrt{barrho} = (Delta u_mathrm{cor}/Delta u_mathrm{cor,odot})[eta - (0.0085pm0.0025) log^2 (Delta u_mathrm{cor}/Delta u_mathrm{cor,odot})]^{-1}$, where $g$, $T_mathrm{eff}$, and $barrho$ are in solar units, $ u_mathrm{max,odot}=3140pm5mu$Hz and $Delta u_mathrm{cor,odot}=135.08pm0.02mu$Hz , and $eta$ is equal to one in case of RGB stars and $1.04pm0.01$ for RC stars.
The scaling relations between global asteroseismic observables and stellar properties are widely used to estimate masses and radii of stars exhibiting solar-like oscillations. Since the mass and radius of the Sun are known independently, the Sun is commonly used as a reference to scale to. However, the validity of the scaling relations depends on the homology between the star under study and the reference star. Solar-like oscillators span a wide range of masses and metallicities, as well as evolutionary phases. Most of these stars are therefore not homologous to the Sun. This leads to errors of up to 10% (5%) in mass (radius) when using the asteroseismic scaling relations with the Sun as the reference. In this paper we derive a reference function to replace the solar-reference value used in the large-frequency-separation scaling relation. Our function is the first that depends on both effective temperature and metallicity, and is applicable from the end of the main sequence to just above the bump on the red giant branch. This reference function improves the estimates of masses and radii determined through scaling relations by a factor of 2, i.e. allows masses and radii to be recovered with an accuracy of 5% and 2%, respectively.
We identify member stars of more than 90 open clusters in the LAMOST survey. With the method of Fang et al.(2018), the chromospheric activity (CA) indices logRCaK for 1091 member stars in 82 open clusters and logRH{alpha} for 1118 member stars in 83 open clusters are calculated. The relations between the average logRCaK, logRH{alpha} in each open cluster and its age are investigated in different Teff and [Fe/H] ranges. We find that CA starts to decrease slowly from logt = 6.70 to logt = 8.50, and then decreases rapidly until logt = 9.53. The trend becomes clearer for cooler stars. The quadratic functions between logR and logt with 4000K < Teff < 5500K are constructed, which can be used to roughly estimate ages of field stars with accuracy about 40% for logRCaK and 60% for logRH{alpha}.
The disk mass is among the most important input parameter for every planet formation model to determine the number and masses of the planets that can form. We present an ALMA 887micron survey of the disk population around objects from 2 to 0.03Msun in the nearby 2Myr-old Chamaeleon I star-forming region. We detect thermal dust emission from 66 out of 93 disks, spatially resolve 34 of them, and identify two disks with large dust cavities of about 45AU in radius. Assuming isothermal and optically thin emission, we convert the 887micron flux densities into dust disk masses, hereafter Mdust. We find that the Mdust-Mstar relation is steeper than linear with power law indices 1.3-1.9, where the range reflects two extremes of the possible relation between the average dust temperature and stellar luminosity. By re-analyzing all millimeter data available for nearby regions in a self-consistent way, we show that the 1-3 Myr-old regions of Taurus, Lupus, and Chamaeleon I share the same Mdust-Mstar relation, while the 10Myr-old Upper Sco association has a steeper relation. Theoretical models of grain growth, drift, and fragmentation reproduce this trend and suggest that disks are in the fragmentation-limited regime. In this regime millimeter grains will be located closer in around lower-mass stars, a prediction that can be tested with deeper and higher spatial resolution ALMA observations.
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