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# The Effects of Magnetic Activity and Tidal Forces on Solar-like Oscillations in Red Giant Binaries

Abstract

Of the 18 known red giants in eclipsing binaries (RG/EBs), four do not show solar-like oscillations. These four also have the most signs of magnetic activity and tidal forces. A handful of the rest show suppressed oscillation modes with moderate levels of magnetism and tides. This paper uses Kepler light curves, high-resolution spectra, and stellar evolution modeling to demonstrate this trend and discuss the physical mechanisms responsible. Comments welcome. [Abstract placeholder]

## Introduction

\label{intro}
• Why red giants in eclipsing binaries are useful

• Why we care about understanding when solar-like oscillations can happen

• Why we think tides and stellar activity affect solar-like oscillations and how we can use models constrained by observations to investigate

In the absence of external influences, all evolved giant stars with a convective outer layer should theoretically exhibit solar-like oscillations. However, that is clearly not the case. Approximately one fifth of the known RG/EBs do not show any solar-like oscillation activity at all (Gaulme et al., 2014). The fraction of single evolved stars without confirmed binary companions that lack oscillations is unknown. Gaulme et al. (2014) proposed that stronger tidal interactions from short-period binaries and increased magnetic activity on spotty giants are linked to absent or damped solar-like oscillations. Now that the oscillating and non-oscillating binaries alike have been well-characterized globally (Frandsen et al., 2013; Rawls et al., 2016; Gaulme et al., 2016), we can use the available observations to explore how magnetically active each system is, how stellar evolution likely proceeded, and what role tidal forces have played over time.

In this paper, we perform an in-depth study of 18 red giants in eclipsing binaries (hereafter RG/EBs) which exhibit a range of orbital periods and solar-like oscillation behavior. Section \ref{review} revisits the dynamic eclipsing binary models based on Kepler light curves and radial velocity curves as well as the stellar atmosphere models from high-resolution spectra used to derive physical parameters for these RG/EBs. In Section \ref{magnetic}, we quantify each system’s magnetic activity photometrically and spectroscopically. Section \ref{tides} presents 1D stellar evolution models for each system, which are subsequently used to quantify each system’s level of tidal forces acting over time. We discuss how magnetic activity, tides, and solar-like oscillations are linked in Section \ref{discuss}, and Section \ref{conclusion} summarizes our results.

## Physical parameters of the RG/EBs

\label{review}

### Binary modeling

Gaulme et al. (2016) and Rawls et al. (2016) used JKTEBOP (Southworth et al., 2009) and the Eclipsing Light Curve (ELC) program (Orosz et al., 2000) to simultaneously fit a combination of light curves and radial velocity observations for a total of 17 RG/EBs observed by Kepler. Frandsen et al. (2013) did the same for KIC 8410637, which brings the total to 18. For the 14 systems with radial velocity curves for both stars, this gives a full dynamic solution: orbital period $$P_{\textrm{orb}}$$, zeropoint $$T_{0}$$, orbital inclination $$i$$, eccentricity and argument of periastron (parameterized as $$e\sin\omega$$ and $$e\cos\omega$$), component masses, component radii, and the effective temperature ratio. Of the 18 total systems, 14 have red giants that exhibit solar-like oscillations, which were analyzed in Gaulme et al. (2014); Gaulme et al. (2016) to derive global asteroseismic parameters.

In this work, we adopt the masses and radii reported in Frandsen et al. (2013); Gaulme et al. (2016); Rawls et al. (2016) from dynamic eclipsing binary models for the 14 double-lined systems. We further adopt the masses and radii from Gaulme et al. (2016) for the four single-lined systems which were derived by combining the asteroseismic scaling relations with the mass function and inclination from eclipse modeling. We note that the single-lined binaries’ masses and radii have larger systematic uncertainties than their double-lined counterparts because the asteroseismic scaling relations are known to overestimate mass by about 15% and radius by about 5%, on average, for evolved stars (Gaulme et al., 2016).

To ensure consistent results between the binary modeling programs JKTEBOP (Southworth, 2013) used in Gaulme et al. (2016) and ELC (Orosz et al., 2000) used in Rawls et al. (2016), we model a representative subset of seven RG/EBs using ELC with differential evolution Monte Carlo Markov Chain optimizers (DE-MCMC, Ter Braak, 2006). The input datasets are identical to those described in Gaulme et al. (2016): detrended Kepler light curves and radial velocity curves from the ARCES spectrograph and APOGEE. For KICs 9291629 and 9970396, we include eight and 12 binned $$BVRI$$ photometry points, respectively, from the 1 m robotic telescope at APO. These observations were taken in and out of eclipse to better constrain the stellar flux ratios. Detailed descriptions of these new observations and the ELC modeling technique are available in Rawls (2016), Chapter 3.

Using ELC, we find a full dynamic solution for seven systems with 16 free parameters: $$P_{\textrm{orb}}$$, $$T_{\textrm{conj}}$$, $$i$$, $$e\cos\omega$$, $$e\sin\omega$$, the temperature of one star ($$T_{\textrm{eff},1}$$ or $$T_{\textrm{eff},2}$$), the mass of one star $$M_{1}$$, the amplitude of one star’s radial velocity curve $$K_{1}$$, the fractional radii of each star, $$R_{1}/a$$ and $$R_{2}/a$$, the temperature ratio $$T_{2}/T_{1}$$, the Kepler contamination factor, and stellar limb darkening parameters for the triangularly parameterized quadratic law (Kipping, 2013). One of the seven RG/EBs modeled with ELC, KIC 8702921, is a single-lined binary, and we fit the same 16 free parameters but note that the mass ratio, component masses, scale of the system, and component radii are unconstrained. For each system, the ELC optimization run is continued long enough to compute more than 400,000 models and arrive at a robust global solution.

The stellar masses all agree within one sigma with those from Gaulme et al. (2016) and the stellar radii generally agree within two sigma. We present all the masses and radii in Table \ref{tab:mrcompare} and show the consistency of the two binary modeling techniques in Figure \ref{fig:mrcompare}. There are four stars which do not have radii that agree within two sigma: both stars in KIC 3955867 and the main sequence companion stars in KICs 7037405 and 9291629. They are shown as open circles in the right portion of Figure \ref{fig:mrcompare}, where it can be seen that two are slightly larger in ELC than JKTEBOP and two are slightly smaller. The offset is not systematic, and can be attributed to a difference in how stellar atmospheric parameters are modeled in the two techniques over the broad Kepler bandpass. The JKTEBOP models in Gaulme et al. (2016) assume a fixed quadratic limb darkening law for the main sequence star and fit only the first order term for the quadratic law of the red giant. On the other hand, ELC fits the reparameterized quadratic limb darkening law (Kipping, 2013) for both stars together with a model stellar atmosphere integrated over the Kepler bandpass to set the intensity at the stellar surface normals. The error bars for stellar radii from both methods are likely underestimated because neither limb darkening parameterization is an accurate representation of reality.