# Meredith L. Rawls,11Department of Astronomy, New Mexico State University, P.O. Box 30001, MSC 4500, Las Cruces, NM 88003, USA; mrawls@nmsu.edu Patrick Gaulme,22Apache Point Observatory, 2001 Apache Point Road, P.O. Box 59, Sunspot, NM 88349, USA$${}^{,}$$11Department of Astronomy, New Mexico State University, P.O. Box 30001, MSC 4500, Las Cruces, NM 88003, USA Jean McKeever,11Department of Astronomy, New Mexico State University, P.O. Box 30001, MSC 4500, Las Cruces, NM 88003, USA Jason Jackiewicz,11Department of Astronomy, New Mexico State University, P.O. Box 30001, MSC 4500, Las Cruces, NM 88003, USA Jerome A. Orosz,33Department of Astronomy, San Diego State University, 5500 Campanile Drive, San Diego, CA 91945, USA Enrico Corsaro,44Laboratoire AIM, CEA/DSM – CNRS – Univ. Paris Diderot – IRFU/SAp, Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France$${}^{,}$$55Instituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife, Spain$${}^{,}$$66Universidad de La Laguna, Departamento de Astrofísica, 38206 La Laguna, Tenerife, Spain Paul G. Beck,44Laboratoire AIM, CEA/DSM – CNRS – Univ. Paris Diderot – IRFU/SAp, Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France Benoît Mosser,77LESIA, Observatoire de Paris, PSL Research University, CNRS, Université Pierre et Marie Curie, Université Paris Diderot, 92195 Meudon, France David W. Latham,88Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA and Christian A. Latham88Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA

Abstract

We combine Kepler photometry with ground-based spectra to present a comprehensive dynamical model of the double red giant eclipsing binary KIC 9246715. While the two stars are very similar in mass ($$M_{1}=2.171\begin{subarray}{c}+0.006\\ -0.008\end{subarray}\ M_{\odot}$$, $$M_{2}=2.149\begin{subarray}{c}+0.006\\ -0.008\end{subarray}\ M_{\odot}$$) and radius ($$R_{1}=8.37\begin{subarray}{c}+0.03\\ -0.07\end{subarray}\ R_{\odot}$$, $$R_{2}=8.30\begin{subarray}{c}+0.04\\ -0.03\end{subarray}\ R_{\odot}$$), an asteroseismic analysis finds one main set of solar-like oscillations with unusually low-amplitude, wide modes. A second set of oscillations from the other star may exist, but this marginal detection is extremely faint. Because the two stars are nearly twins, KIC 9246715 is a difficult target for a precise test of the asteroseismic scaling relations, which yield $$M=2.17\pm 0.14\ M_{\odot}$$ and $$R=8.26\pm 0.18\ R_{\odot}$$. Both stars are consistent with the inferred asteroseismic properties, but we suspect the main oscillator is Star 2 because it is less active than Star 1. We find evidence for stellar activity and modest tidal forces acting over the 171-day eccentric orbit, which are likely responsible for the essential lack of solar-like oscillations in one star and weak oscillations in the other. Mixed modes indicate the main oscillating star is on the secondary red clump (a core-He-burning star), and stellar evolution modeling supports this with a coeval history for a pair of red clump stars. This system is a useful case study and paves the way for a detailed analysis of more red giants in eclipsing binaries, an important benchmark for asteroseismology.

stars: activity — binaries: eclipsing — stars: evolution — stars: fundamental parameters — stars: individual (KIC 9246715) — stars: oscillations

Accepted for publication in The Astrophysical Journal, December 2015
Published February 2016, Rawls et al. 2016, ApJ, 818, 108
Blog post summary for the public: http://wp.me/p3H1S0-6X
AAS Nova Highlight: http://aasnova.org/2016/02/17/sizing-up-red-giant-twins

## Introduction

\label{intro}

Mass and radius are often-elusive stellar properties that are critical to understanding a star’s past, present, and future. Eclipsing binaries are the only astrophysical laboratories that allow for a direct measurement of these and other fundamental physical parameters. Recently, however, observing solar-like oscillations in stars with convective envelopes has opened a window to stellar interiors and provided a new way to measure global stellar properties. A pair of asteroseismic scaling relations use the Sun as a benchmark between these oscillations and a star’s effective temperature to yield mass and radius (Kjeldsen et al., 1995; Huber et al., 2010; Mosser et al., 2013).

While both the mass and radius scaling relations are useful, it is important to test their validity. Recent work has investigated the radius relation by comparing the asteroseismic large-frequency separation $$\Delta\nu$$ and stellar radius between models and simulated data (e.g. Stello et al., 2009; White et al., 2011; Miglio et al., 2013), and by comparing asteroseismic radii with independent radius measurements such as interferometry or binary star modeling (e.g. Huber et al., 2011; Huber et al., 2012; Silva Aguirre et al., 2012). All of these find that radius estimates from asteroseismology are precise within a few percent, with greater scatter for red giants than main sequence stars. The mass scaling relation remains relatively untested. Most studies test the $$\Delta\nu$$ scaling with average stellar density and not the scaling of $$\nu_{\rm{max}}$$ (the asteroseismic frequency of maximum oscillation power) with stellar surface gravity, because the latter has a less-secure theoretical basis It(Belkacem et al., 2011)—.is not yet possible to reliably predict oscillation mode amplitudes as a function of frequency (Christensen-Dalsgaard, 2012). One study by Frandsen et al. (2013) did test both scaling laws with the red giant eclipsing binary KIC 8410637. They found good agreement between Keplerian and asteroseismic mass and radius, but a more recent analysis from Huber (2014) indicates that the asteroseismic density of KIC 8410637 is underestimated by $$\sim$$7 % (1.8 $$\sigma$$, accounting for the density uncertainties), which results in an overestimate of the radius by $$\sim$$9 % (2.7 $$\sigma$$) and mass by $$\sim$$17 % (1.9 $$\sigma$$). Additional benchmarks for the asteroseismic scaling relations are clearly needed.

Evolved red giants are straightforward to characterize through pressure-mode solar-like oscillations in their convective zones, and red giant asteroseismology is quickly becoming an important tool to study stellar populations throughout the Milky Way (for a review of this topic, see Chaplin et al., 2013). Compared to main-sequence stars, red giants oscillate with larger amplitudes and longer periods—several hours to days instead of minutes. Oscillations appear as spikes in the amplitude spectrum of a light curve that is sampled both frequently enough and for a sufficiently long duration. Therefore, observations from the Kepler space telescope taken every 29.4 minutes (long-cadence) over many 90-day quarters are ideal for asteroseismic studies of red giant stars.

Kepler’s primary science goal is to find Earth-like exoplanets orbiting sun-like stars (Borucki et al., 2010). However, in addition to successes in planet-hunting and suitability for red giant asteroseismology, Kepler is also incredibly useful for studies of eclipsing binary stars. Kepler has discovered numerous long-period eclipsing systems from consistent target monitoring over several years (Prša et al., 2011; Slawson et al., 2011). Eclipsing binaries are important tools for understanding fundamental stellar properties, testing stellar evolutionary models, and determining distances. When radial velocity curves exist for both stars in an eclipsing binary, along with a well-sampled light curve, the inclination is precisely constrained and a full orbital solution with masses and radii can be found. Kepler’s third law applied in this way is the only direct method for measuring stellar masses.

Taken together, red giants in eclipsing binaries (hereafter RG/EBs) that exhibit solar-like oscillations are ideal testbeds for asteroseismology. There are presently 18 known RG/EBs that show solar-like oscillations (Hekker et al., 2010; Gaulme et al., 2013; Gaulme et al., 2014; Beck et al., 2014;