A&A 647, A187 (2021) Astronomy https://doi.org/10.1051/0004-6361/202040055 & c A. Noll et al. 2021 Astrophysics Probing core overshooting using subgiant asteroseismology: The case of KIC10273246 A. Noll, S. Deheuvels, and J. Ballot IRAP, Université de Toulouse, CNRS, CNES, UPS, Toulouse, France e-mail: [email protected] Received 3 December 2020 / Accepted 26 January 2021 ABSTRACT Context. The size of convective cores remains uncertain, despite their substantial influence on stellar evolution, and thus on stellar ages. The seismic modeling of young subgiants can be used to obtain indirect constraints on the core structure during main sequence, thanks to the high probing potential of mixed modes. Aims. We selected the young subgiant KIC10273246, observed by Kepler, based on its mixed-mode properties. We thoroughly modeled this star, with the aim of placing constraints on the size of its main-sequence convective core. A corollary goal of this study is to elaborate a modeling technique that is suitable for subgiants and can later be applied to a larger number of targets. Methods. We first extracted the parameters of the oscillation modes of the star using the full Kepler data set. To overcome the challenges posed by the seismic modeling of subgiants, we propose a method that is specifically tailored to subgiants with mixed modes and uses nested optimization. We then applied this method to perform a detailed seismic modeling of KIC10273246. Results. We obtain models that show good statistical agreements with the observations, both seismic and non-seismic. We show that including core overshooting in the models significantly improves the quality of the seismic fit, optimal models being found for αov = 0:15. Higher amounts of core overshooting strongly worsen the agreement with the observations and are thus firmly ruled out. We also find that having access to two g-dominated mixed modes in young subgiants allows us to place stronger constraints on the gradient of molecular weight in the core and on the central density. Conclusions. This study confirms the high potential of young subgiants with mixed modes to investigate the size of main-sequence convective cores. It paves the way for a more general study including the subgiants observed with Kepler, TESS, and eventually PLATO. Key words. asteroseismology – convection – stars: evolution – stars: interiors – stars: individual: KIC10273246 1. Introduction (2016) found that αov, the ratio between dov and Hp, increases with mass for stars under 2 M before reaching a plateau. How- One of the most important current open questions in stellar ever, this result is still debated (Constantino & Baraffe 2018, physics is the extent of convective cores. Several physical pro- Claret & Torres 2019). cesses are known to extend the convective core boundaries Over the last decade, asteroseismology allowed us to beyond the standard Schwarzschild limit. The most frequently probe the structure of stellar cores. Thanks to the data of quoted are overshooting of ascending blobs of fluids due to their CoRoT (Baglin et al. 2006), Kepler (Borucki et al. 2010) and inertia, rotational mixing or semi-convection. All these processes now TESS (Ricker et al. 2014) missions, we have been able remain poorly described by theory, and the way they interact is to precisely measure the oscillation frequencies of numer- understood even less. They are therefore generally modeled, in ous pulsators. The study of pressure (p) modes in low- stellar evolution codes, as an extension of the mixed core over a mass main sequence (MS) stars, showed the need for core distance dov, which is often referred to as the distance of over- overshooting to correctly reproduce the observed frequencies shoot, even though other processes can contribute as well. In (Goupil et al. 2011, Deheuvels et al. 2010, Silva Aguirre et al. practice, this can either be achieved by simply extending the 2013). Deheuvels et al.(2016), modeling several MS stars, fully mixed central region, or by treating overshooting as a dif- found that αov increases with the mass. Moreover, gravity (g) fusive process, following a behavior found in numerical sim- mode pulsators, like slowly-pulsating B (SPB) stars, are interest- ulations (Freytag et al. 1996). In both cases, a free parameter ing targets to constrain the additional mixing around convective controlling the extent of the additional mixing is required. cores. Indeed, gravity modes probe the inner chemical structure Observations are therefore necessary to better constrain those of the star and allow detailed investigation of the convective core processes. extensions. Moravveji et al.(2015, 2016), when modeling SPB Initial constraints have been obtained thanks to the study stars, found that overshoot was necessary, and they favored dif- of the HR diagram of clusters (see e.g., Maeder & Mermilliod fusive overshooting over a simple extension of the central mixed 1981, VandenBerg et al. 2006), and the modeling of eclipsing region. binaries (Claret & Torres 2016). Most of those studies favor Post-main-sequence stars are another way to put constraints adding overshooting, to various extents. Typically, dov is around on the amount of overshooting. Once the central hydrogen is 0:2 Hp, where Hp is the pressure scale height. Claret & Torres exhausted, nuclear energy production stops, leaving an inert A187, page 1 of 14 Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A&A 647, A187 (2021) radiative helium core. This core then contracts, heating the modes than p-dominated modes, and for which ng is of the order surrounding hydrogen layers of the star until shell burning starts. of several tens (e.g., Mosser et al. 2012). At that moment, the star begins its subgiant phase, and evolves The frequencies of mixed modes are mostly determined by on a nuclear timescale for masses below about 1:5 solar masses two structural features of the star. The first is the g-mode (G) (M ). For stars that are close to the terminal-age main sequence cavity, which is delimited by the Brunt-Väisälä frequency N. The (TAMS), the structure and the evolution remain highly influ- second is the evanescent zone between the g-mode and p-mode enced by the properties of the MS convective core. Interestingly, (P) cavities, the latter being delimited by the Lamb frequency S l. the star begins to exhibit mixed modes at that moment. These The G cavity affects the frequency of the g-mode that is modes behave like gravity modes in the internal propagation involved in the mixed mode frequency. G-mode frequencies, in cavity and pressure modes in the outer one. Thus, they allow the asymptotic theory, can be approximated by us to finely probe the deepest layers of the star, all the while p Z r being observable. This and the proximity of the subgiant to the l(l + 1) 2 N ν ≈ dr; (1) TAMS make the mixed modes of young subgiants valuable data n;l 2 2π (n − 1=2) r r in studying the extension of convective cores. 1 Another particularity of mixed modes is their very fast evolu- l being the degree of the mode, r1 and r2 the turning points in tion, compared to the nuclear evolution timescale of the subgiant the G cavity, and r the local radius of the star. In our case, ng is phase. Indeed, mixed mode frequencies change dramatically low for the observed modes, so the asymptotic expression given over the course of a few million years. This makes their seismic in Eq. (1) should not apply. However, it has been shown that modeling challenging. Recently, increasing efforts have been it can provide qualitative information about the behavior of the made to model subgiants (Huber et al. 2019; Stokholm et al. mixed mode frequencies (Deheuvels et al. 2010). It tells us that 2019; Metcalfe et al. 2020; Deheuvels et al. 2020; Li et al. 2019, g-dominated modes should give strong constraints on the Brunt- 2020), driven by both their great physical interest and the sud- Väisälä frequency in the G cavity. One can write it in the follow- den increase of seismic data for these stars. Most of those works ing form (e.g., Kippenhahn et al. 2012): focused on finding the optimal stellar parameters for one or sev- eral subgiants. So far, few studies have used subgiants as tools to 2 gδ φ test stellar physics, mainly due to the challenges of their model- N = rad − r + rµ ; (2) Hp δ ing, as mentioned above. Deheuvels & Michel(2011) successfully constrained αov where g is the local gravity, δ = −(@ ln ρ/∂ ln T)P,µ, φ = from a subgiant observed by CoRoT, HD 49385, which exhibits (@ ln ρ/∂ ln µ)P;T , rad = (@ ln T=@ ln P)ad, r = @ ln T=@ ln P; and only one g-dominated mode and is therefore very close to the rµ = @ ln µ/∂ ln P. The Brunt-Väisälä frequency consequently TAMS. They found that either no overshooting, or a model with carries information about both the thermal (two first terms in αov = 0:19 were giving equally good results. In this work, we parentheses) and compositional structure (last term) of the star. modeled a young subgiant, KIC10273246, which was observed The evanescent zone affects the coupling between the two by Kepler over almost 1000 days. That star exhibits two g- cavities, whose strength is linked to the size of this region and dominated modes, which allows us to better constrain its inner the value of N inside it (e.g., Unno et al. 1989). Using a toy structure.