Probing tiny convective cores with the acoustic modes of lowest degree

Abstract

Solar-like oscillations are expected to be excited in stars of up to about 1.6 solar masses. Most of these stars will have convective cores during their main-sequence evolution. At the edges of these convective cores, there is a rapid variation in the sound speed, which influences the frequencies of acoustic oscillations. In this paper we build on earlier work to investigate the impact that these rapid structural variations have on different p-mode frequency combinations, involving modes of low degree. In particular, we adopt a different expression to describe the sound speed variation at the edge of the core, which we show more closely reproduces the profiles derived from the equilibrium models. We analyse the impact of this change on the frequency perturbation derived for radial modes. Moreover, we consider three different small frequency separations involving modes of degree l = 0, 1, 2, 3, l = 0, 1, and l = 0, 2, and show that they are all significantly affected by the sharp sound speed variation at the edge of the core. In particular, we confirm that the frequency derivative of the diagnostic tool that combines modes of degree up to 3 can potentially be used to infer the amplitude of the relative sound speed variation directly at the edge of the core. We show that at high frequencies the other two diagnostic tools can be up to a few μHz smaller than what would be expected in the absence of the rapid structural variation at the edge of the core. Also, we show that the absolute values of their frequency derivatives are significantly increased, in a manner that strongly depends on stellar age.

Stellar model fits and inversions

“…Cunha & Metcalfe (2007) derived a diagnostic applicable to this case and showed that it provided a measure of stellar age. This and similar diagnostic quantities were further analysed by Cunha & Brandão (2011). A similar analysis was carried out by Silva Aguirre et al (2011), demonstrating the potential of such diagnostics to constrain the size of the convective core, including the effects of semiconvection which remain a serious uncertainty in the modelling of stellar evolution.…”

Constraining mixing processes in stellar cores using asteroseismology

“…In their work, Cunha & Metcalfe (2007) find that the sharp discontinuity formed at the edge of the convective core has a direct impact on the slope of their proposed quantity when plotted against frequency, showing that the absolute value of the slope increases as a function of the size of the chemical discontinuity (and therefore with decreasing amount of central hydrogen content). Since observing l = 3 modes is very challenging owing to severe amplitude reduction, Cunha & Brandão (2011) extended this study by using the small frequency separations defined in Eqs. (12) and (13) and analyzing the changes in the slope, reaching the same conclusions as Cunha & Metcalfe (2007).…”

Inferring properties of small convective cores in main-sequence solar-like pulsators

“…As anticipated from the work of Cunha & Brandão (2011), there is a strong dependence of |S {∆ν dr 0213 }| on A δ . Nevertheless, that relation deviates from linear and shows significant dispersion, particularly for larger values of A δ .…”

“…In the case of stars with a convective core we expect that the frequency derivatives of the diagnostic tools taken at their maximum absolute value are a measure of A δ (Cunha & Brandão, 2011). We introduce here a new quantity S {i}, which we shall name 'slope', which is a measure of the frequency derivative of a diagnostic tool 'i', at its maximum absolute value.…”