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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.
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Seismology of stars that exhibit solar-like oscillations develops a growing interest with the wealth of observational results obtained with the CoRoT and Kepler space-borne missions. In this framework, relations between asteroseismic quantities and stellar parameters provide a unique opportunity to derive model-independent determinations of stellar parameters (e.g., masses and radii) for a large sample of stars. I review those scaling relations with particular emphasis on the underlying physical processes governing those relations, as well as their uncertainties.
Scaling relations between asteroseismic quantities and stellar parameters are essential tools for studying stellar structure and evolution. We will address two of them, namely, the relation between the large frequency separation ($Delta u$) and the mean density ($bar{rho}$) as well as the relation between the frequency of the maximum in the power spectrum of solar-like oscillations ($ u_{rm max}$) and the cut-off frequency ($ u_{rm c}$). For the first relation, we will consider the possible sources of uncertainties and explore them with the help of a grid of stellar models. For the second one, we will show that the basic physical picture is understood and that departure from the observed relation arises from the complexity of non-adiabatic processes involving time-dependent treatment of convection. This will be further discussed on the basis of a set of 3D hydrodynamical simulation of surface convection.
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.
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.
Faber-Jackson and Tully-Fisher scaling relations for elliptical and spiral galaxy samples up to z=1 provide evidence for a differential behaviour of galaxy evolution with mass. In compliance with the downsizing scenario, the stellar populations of less massive galaxies display a stronger evolution than the more massive ones. For spirals, this may be attributed to a suppressed star formation efficiency in small dark matter halos. For ellipticals, star formation must have been negligible at least during the past ~4Gyr in all environments.
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