Abstract
The scaling relations for solar-like oscillations provide a translation of the features of the stochastic low-degree modes of oscillation in the Sun to predict the features of solar-like oscillations in other stars with convective outer layers. This prediction is based on their stellar mass, radius and effective temperature. Over time, the original scaling relations have been reversed in their use from predicting features of solar-like oscillations to deriving stellar parameters. Updates to the scaling relations as well as their reference values have been proposed to accommodate for the different requirements set by the change in their use. In this review the suggestions for improving the accuracy of the estimates of stellar parameters through the scaling relations for solar-like oscillations are presented together with a discussion of pros and cons of different approaches.
Highlights
With the advent of high resolution spectrographs [e.g., UCLES (Diego et al, 1990), CORALIE (Queloz et al, 1999), HARPS (Pepe et al, 2000), UVES (Dekker et al, 2000), and SONG (Grundahl et al, 2007)] and dedicated space-based photometric missions [CoRoT (Michel et al, 1998), Kepler (Borucki et al, 2009), TESS (Ricker et al, 2014)] the number of stars for which solar-like oscillations have been observed has increased by several orders of magnitude from the single case of the Sun (Leighton et al, 1962) to several hundreds to thousands (e.g., Hekker et al, 2009; Chaplin et al, 2011; Yu et al, 2018) over the last few decades
Solar-like oscillations are stochastically excited by the turbulent convection in stars (e.g., Goldreich and Keeley, 1977; Goldreich and Kumar, 1988) with convective envelopes, i.e., in stars with effective temperatures below ∼ 6, 700 K
Some of the convective energy is transferred into energy of global oscillations, which reveal themselves as small amplitude oscillations at the stellar surface
Summary
With the advent of high resolution spectrographs [e.g., UCLES (Diego et al, 1990), CORALIE (Queloz et al, 1999), HARPS (Pepe et al, 2000), UVES (Dekker et al, 2000), and SONG (Grundahl et al, 2007)] and dedicated space-based photometric missions [CoRoT (Michel et al, 1998), Kepler (Borucki et al, 2009), TESS (Ricker et al, 2014)] the number of stars for which solar-like oscillations have been observed has increased by several orders of magnitude from the single case of the Sun (Leighton et al, 1962) to several hundreds to thousands (e.g., Hekker et al, 2009; Chaplin et al, 2011; Yu et al, 2018) over the last few decades. The main purpose of these relations was to predict the frequencies and amplitudes of the solar-like oscillations based on the known mass, radius, surface gravity, and effective temperature of the. Kjeldsen and Bedding (1995) presented a dedicated study in which they predicted the amplitude [both velocity amplitude vosc and luminosity amplitude (δL/L)λ at wavelength λ], frequency of maximum oscillation power (νmax) and large frequency separation ( ν) of other stars from scaling to the Sun, based on a linear adiabatic derivation. With the increase in the accuracy with which solar-like oscillations have been detected for a range of stars with different masses, metallicities, and effective temperatures, the inherent shortcomings of such relations, i.e., they rely on a homologous stellar structure between the target star and the reference, have been apparent. For this reason I focus here on the ν and νmax scaling relations
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