Testing the Breakdown of the Asteroseismic Scaling Relations in Luminous Red Giants

Nearly all cool, evolved stars are solar-like oscillators, and fundamental stellar properties can be inferred from these oscillations with asteroseismology. Scaling relations are commonly used to relate global asteroseismic properties, the frequency of maximum power $ν_{max}$ and the large frequency separation $Δν$, to stellar properties. Mass, radius, and age can then be inferred with the addition of stellar spectroscopy. There is excellent agreement between seismic radii and fundamental data on the lower red giant branch and red clump. However, the scaling relations appear to breakdown in luminous red giant stars. We attempt to constrain the contributions of the asteroseismic parameters to the observed breakdown. We test the $ν_{max}$ and $Δν$ scaling relations separately, by using stars of known mass and radius in star clusters and the Milky Way's high-$α$ sequence. We find evidence that the $Δν$-scaling relation contributes to the observed breakdown in luminous giants more than the $ν_{max}$ relation. We test different methods of mapping the observed $Δν$ to the mean density via a correction factor, $F_{Δν}$ and find a $\approx 1 - 3\%$ difference in the radii in the luminous giant regime depending on the technique used to measure $F_{Δν}$. The differences between the radii inferred by these two techniques are too small on the luminous giant branch to account for the inflated seismic radii observed in evolved giant stars. Finally, we find that the $F_{Δν}$ correction is insensitive to the adopted mixing length, chosen by calibrating the models to observations of $T_{eff}$.