Nonlinear seismic scaling relations

Abstract

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 $\Delta \nu -$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 $\Delta {\nu }_{\mathrm{cor}}$ 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: $g/\sqrt{T_{\mathrm{eff}}}=({\nu }_{\max }/{\nu }_{\max ,\odot }{)}^{1.0075\pm 0.0021}$ and $\sqrt{\bar{\rho }}=(\Delta {\nu }_{\mathrm{cor}}/\Delta {\nu }_{\mathrm{cor},\odot })[\eta -(0.0085\pm 0.0025){\log }^2(\Delta {\nu }_{\mathrm{cor}}/\Delta {\nu }_{\mathrm{cor},\odot }){]}^{-1}$, where $g$, $T_{\mathrm{eff}}$, and $\bar{\rho }$ are in solar units, ${\nu }_{\max ,\odot }=3140\pm 5\mu$Hz and $\Delta {\nu }_{\mathrm{cor},\odot }=135.08\pm 0.02\mu$Hz , and $\eta$ is equal to one in case of RGB stars and $1.04\pm 0.01$ for RC stars.

arXiv comment19 pages, 13 figures, accepted for publication in A&A

References in corpus (85)

• MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics
• The K2 Mission: Characterization and Early results
• A large stellar evolution database for population synthesis studies. I. Scaled solar models and isochrones
• Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars
• Asteroseismology of Solar-Type and Red-Giant Stars
• Testing Scaling Relations for Solar-Like Oscillations from the Main Sequence to Red Giants using Kepler Data
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• Significantly improving stellar mass and radius estimates: A new reference function for the Δν scaling relation
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• On the surface physics affecting solar oscillation frequencies
• A New Method for the Asteroseismic Determination of the Evolutionary State of Red-Giant Stars
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• Oscillating red giants in eclipsing binary systems: empirical reference value for asteroseismic scaling relation
• Asteroseismic surface gravity for evolved stars
• Surface-effect corrections for oscillation frequencies of evolved stars
• vbyCaHbeta CCD Photometry of Clusters. VIII. The Super-Metal Rich, Old Open Cluster NGC 6791
• Bayesian Asteroseismology of 23 Solar-Like Kepler Targets
• Testing Asteroseismic Scaling Relations using Eclipsing Binaries in Star Clusters and the Field
• KIC 9246715: The Double Red Giant Eclipsing Binary With Odd Oscillations
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• The Physical Parameters of the Retired A Star HD185351
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• Determining the Age of the Kepler Open Cluster NGC 6819 With a New Triple System and Other Eclipsing Binary Stars
• Confronting uncertainties in stellar physics II. exploring differences in main-sequence stellar evolution tracks
• On the asymptotic acoustic-mode phase in red-giant stars and its dependence on evolutionary state
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