Nonlinear seismic scaling relations.

摘要: In recent years the global seismic scaling relations for frequency of maximum power and large separation have caught attention various fields astrophysics. With exquisite photometry \textit{Kepler}, uncertainties in observables are small enough to estimate masses radii with a precision only few per cent. Even though this seems work quite well main-sequence stars, there is empirical evidence, mainly from studies eclipsing binary systems, that overestimate mass radius red giants by about 15 5\%, respectively. Model-based corrections $\Delta\nu -$scaling reduce problem but do not solve it. We re-examine oscillation parameters systems order determine their fundamental find them agree dynamic literature if we adopt nonlinear scalings. note curvature glitch corrected $\Delta\nu_\mathrm{cor}$ should be preferred over local or average values. then compare observed cluster those scaled independent measurements same behaviour as binaries. Our final proposed based on both samples cover broad range evolutionary stages RGB RC stars: $g/\sqrt{T_\mathrm{eff}} = (\nu_\mathrm{max}/\nu_\mathrm{max,\odot})^{1.0075\pm0.0021}$ $\sqrt{\bar\rho} (\Delta\nu_\mathrm{cor}/\Delta\nu_\mathrm{cor,\odot})[\eta - (0.0085\pm0.0025) \log^2 (\Delta\nu_\mathrm{cor}/\Delta\nu_\mathrm{cor,\odot})]^{-1}$, where $g$, $T_\mathrm{eff}$, $\bar\rho$ solar units, $\nu_\mathrm{max,\odot}=3140\pm5\mu$Hz $\Delta\nu_\mathrm{cor,\odot}=135.08\pm0.02\mu$Hz , $\eta$ equal one case stars $1.04\pm0.01$ stars.