Physical Properties of the Eclipsing Binary KIC 9851944: Abstract and Intro

25 May 2024

This paper is available on arxiv under CC 4.0 license.


(1) Z. Jennings, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK (E-mail:;

(2) J. Southworth, Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK;

(3) K. Pavlovski, Department of Physics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia;

(4) T. Van Reeth, Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.


Stars that are both pulsating and eclipsing offer an important opportunity to better understand many of the physical phenomena that occur in stars, because it is possible to measure the pulsation frequencies of stars for which the masses and radii are known precisely and accurately. KIC 9851944 is a double-lined detached eclipsing binary containing two F-stars which show both pressure and gravity mode pulsations. We present an analysis of new high-resolution spectroscopy of the system and high-quality light curves from the Kepler and TESS space missions. We determine the masses and effective temperatures of the stars to 0.6% precision, and their radii to 1.0% and 1.5% precision. The secondary component is cooler, but larger and more massive than the primary so is more evolved; both lie inside the δ Scuti and γ Doradus instability strips. We measure a total of 133 significant pulsation frequencies in the light curve, including 14 multiplets that each contain between 3 and 19 frequencies. We find evidence for tidal perturbations to some of the p- and g-modes, attribute a subset of the frequencies to either the primary or secondary star, and measure a buoyancy radius and near-core rotational frequency for the primary component. KIC 9851944 is mildly metal-rich and MIST isochrones from the MESA evolutionary code agree well with the observed properties of the system for an age of 1.25 Gyr.

Key words: stars: oscillations — stars: variables: Scuti — binaries: eclipsing — binaries: spectroscopic — stars: fundamental parameters


Binary and multiple systems make up the vast majority of all observed medium- and high-mass (M > 1.15M⊙) stellar objects in the galaxy (Duchêne & Kraus 2013). For double-lined spectroscopic binary systems (SB2s), where light emitted from both components is visible in the stellar spectrum, the radial velocity (RV) variations of each component throughout the orbit can be measured. Combining this with the analysis of the light variability due to geometrical effects when the components also eclipse one another, i.e., eclipsing binaries (EBs), can lead to estimations of the mass and radius to within 1% (Torres et al. 2010), making these objects our best source of precise fundamental stellar parameters. Since the methods used to derive the properties of the components in double-lined eclipsing binaries (DLEBs) do not rely on theoretical stellar models, these objects are critical for testing and verifying stellar evolution theory (Pols et al. 1997; Pourbaix 2000; Lastennet & Valls-Gabaud 2002; de Mink et al. 2007).

Such measurements for the masses and radii of stars allow for a precise determination of evolutionary status and age (e.g., Higl & Weiss 2017) and the calibration of interior physics. As examples, the mass dependence of convective core overshoot- ⋆ E-mail: ing (Claret & Torres 2016, 2017, 2018, 2019), and the amount of core mixing in massive stars has been probed using DLEBs (Pavlovski et al. 2018; Tkachenko et al. 2020).

It has been known since the 1970s that stellar pulsations occur in the components of EBs (e.g., Tempesti 1971, for the system AB Cassiopeiae). Oscillation signals measured in the light curves of pulsating stars can be studied using asteroseismology. This is an alternative way by which accurate stellar parameters can be derived (Aerts et al. 2010) and is a powerful tool for probing the internal structures of stars (Aerts et al. 2017; Chaplin & Miglio 2013). The analysis of space-based photometry of pulsating stars has revealed information about important phenomena such as internal rotation, core overshooting and angular momentum transport (e.g., Saio et al. 2015; Lovekin & Guzik 2017).

It is advantageous to study pulsating stars in EBs because analysing the intrinsic variability due to oscillations of the stellar interior and atmosphere as well as the light variability during eclipses leads to independent constraints on theoretical models (Guo et al. 2019; Liakos 2021; Miszuda et al. 2022). The parameters derived from EBs can also be used to constrain the seismic models (e.g., Sekaran et al. 2020), and this can be useful, for example, in mode identification for δ Scuti stars which is difficult (Streamer et al. 2018; Murphy et al. 2021). The complimentary nature of these two methods of analysis makes pulsating stars in EBs (particularly DLEBs) the best objects to use to refine our knowledge of stellar structure and evolution (Guo et al. 2016). Lampens (2021) and Southworth (2021) have reviewed the impact of space missions on the study of EBs with pulsating components, and on binary stars in general, respectively.

δ Scuti stars are a class of short-period (15 min to 8 h; Uytterhoeven et al. 2011; Aerts et al. 2010), multiperiodic pressure mode (p-mode) pulsators. They are dwarfs or subgiants located at the lower end of the classical instability strip in the Hertzsprung-Russell (HR) diagram (Breger 2000; Dupret et al. 2005; Murphy et al. 2019). Their spectral types are A2 to F5, corresponding to typical effective temperatures (Teffs) of 6500 – 9500 K (Liakos 2021). Their masses range from 1.5 to 2.5M⊙ (Aerts et al. 2010; Yang et al. 2021), which places them in the transition region between lower-mass stars with radiative cores and thick outer convection zones, and massive stars with convective cores and thin outer convective zones (Yang et al. 2021). They thus provide an opportunity to study the structure and evolution of stars in this transition region (Bowman & Kurtz 2018). Low-order, non-radial modes are generally observed for these stars and these modes are driven by the κ mechanism acting in the partial ionization zone of He II (Pamyatnykh 1999; Breger 2000; Antoci et al. 2014; Murphy et al. 2020). Higher-order non-radial pulsations have been observed in some δ Scuti stars such as τ Peg (Kennelly et al. 1998), where the κ mechanism may not be sufficient to explain the modes, and may instead be attributed to the turbulent pressure in the hydrogen convective zone (Antoci et al. 2014; Grassitelli et al. 2015).

The γ Doradus class of pulsators are also located at the lower end of the classical instability strip in the HR diagram; they exist near the red edge of the δ Scuti instability strip (Yang et al. 2021). Such stars pulsate with typical periods between 8 and 80 h (Handler 1999) in high order gravity modes (g-modes) (Kaye et al. 1999), believed to be excited by the interaction of convection and pulsations (e.g. Guzik et al. 2000; Grigahcène et al. 2005; Dupret et al. 2005). Typical masses are between 1.3 and 1.8 M⊙ (Hong et al. 2022; Aerts et al. 2023) with spectral types of F5 to A7. The high radial order of their pulsations puts them in the asymptotic regime, meaning their oscillations are equally spaced in period for non-rotating, non-magnetic, chemically homogeneous stars (Tassoul 1980). Deviations from a homogeneous spacing emerge due to chemical gradients and rotation (Sekaran et al. 2020), where the former are influenced by the effects of diffusive mixing; mixing reduces the steepness of chemical gradients. Period spacing diagrams can therefore be used to derive information on chemical composition gradients, internal rotation rates and diffusive mixing processes (e.g. Bouabid et al. 2013; Bedding et al. 2015; Saio et al. 2015; Van Reeth et al. 2016; Ouazzani et al. 2017; Li et al. 2019; Miglio et al. 2008; Moravveji et al. 2015; Sekaran et al. 2021).

Space missions such as Kepler (Koch et al. 2010; Borucki et al. 2010), CoRoT (Baglin et al. 2006) and TESS (Ricker et al. 2015), have delivered a large amount of photometric data with precisions unachievable from the ground. The unprecedented precision has allowed for the detection of extremely low-amplitude frequencies (Murphy et al. 2013; Bowman & Kurtz 2018) while long sequences of continuous observations (Lehmann et al. 2013) means that longer-period pulsations, such as those typical of γ Doradus stars, can be studied. The overlap of the δ Scuti and γ Doradus instability strips supports the existence of δ Scuti/γ Doradus hybrids (Breger & Beichbuchner 1996; Handler & Shobbrook 2002; Yang et al. 2021). These were expected to be rare, based on early calculations by Dupret et al. (2005), but the lower detection thresholds provided by space missions has led to the discovery that such behaviour is indeed common (Uytterhoeven et al. 2011; Grigahcène et al. 2010; Bradley et al. 2015; Balona et al. 2015; Guo et al. 2019). Later calculations by Xiong et al. (2016) conform better with these findings.

Hybrids have great potential for asteroseismology (Schmid & Aerts 2016). The p-modes probe the stellar envelope while the g-modes carry information about the near-core regions (Yang et al. 2021; Grigahcène et al. 2010; Saio et al. 2015; Kurtz et al. 2014). The behaviour also means that information about two different driving mechanisms can be obtained (Hong et al. 2022).

KIC 9851944 is an EB showing δ Scuti/γ Doradus hybrid pulsation signatures. Therefore, the object is an ideal candidate for testing our understanding of stellar structure and evolution given the large amount of constraints that can be obtained due to the advantages associated with hybrid behaviour as well as binarity. KIC 9851944 is included in the Kepler Eclipsing Binary Catalogue (KEBC; Prša et al. 2011; Kirk et al. 2016), as well as a study by Matson et al. (2017) who presented RVs for 41 Kepler EBs. Gies et al. (2012, 2015) studied the eclipse times for KIC 9851944 and found no evidence of apsidal motion or a third body; the object was also included in a catalogue of precise eclipse times of 1279 Kepler EBs by Conroy et al. (2014)

This work aims to be complementary to the work by Guo et al. (2016) on KIC 9851944; we additionally include observations by TESS in our photometric analysis and combine this with the analysis of high-resolution (R = 60000) spectroscopic observations. Section 2 outlines the photometric and spectroscopic observations. We determine the orbital ephemeris based on the photometric observations in Section 3. In Section 4 we analyse RVs derived from the spectroscopic observations and in Section 5 we present the spectroscopic analysis. The analysis of the photometric light curves is given in section 6 and in Section 7 we present the physical properties of the system. An investigation of the pulsations is given in Section 8. The discussion and conclusion are given in Sections 9 and 10, respectively.