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Circumbinary Planets Astronomy & Astrophysics manuscript no. cbp-orbit ©ESO 2020 December 8, 2020 Parking planets in circumbinary discs Anna B. T. Penzlin1, Wilhelm Kley1, Richard P. Nelson2 1 Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Germany 2 Astronomy Unit, School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK ABSTRACT The Kepler space mission discovered about a dozen planets orbiting around binary stars systems. Most of these cir- cumbinary planets lie near their instability boundaries at about 3 to 5 binary separations. Past attempts to match these final locations through an inward migration process were only successful for the Kepler-16 system. Here, we study 10 circumbinary systems and try to match the final parking locations and orbital parameters of the planets with a disc driven migration scenario. We performed 2D locally isothermal hydrodynamical simulations of circumbinary discs with embedded planets and followed their migration evolution using different values for the disc viscosity and aspect ratio. We found that for the six systems with intermediate binary eccentricities (0:1 ≤ ebin ≤ 0:21) the final planetary orbits matched the observations closely for a single set of disc parameters, specifically a disc viscosity of α = 10−4, and an aspect ratio of H=r ∼ 0:04. For these systems the planet masses were large enough to open at least a partial gap in their discs as they approach the binary, forcing the discs to become circularized and allowing for further migration towards the binary, leading to good agreement with the observed planetary orbital parameters. For systems with very small or large binary eccentricities the match was not as good because the very eccentric discs and large inner cavities in these cases prevented close-in planet migration. In test simulations with higher than observed planet masses better agreement could be found for those systems. The good agreement for 6 out of the 10 modelled systems, where the relative difference between observed and simulated final planet orbit is ≤ 10%, strongly supports the idea that planet migration in the disc brought the planets to their present locations. Key words. Hydrodynamics – Binaries: general – Accretion, accretion discs – Planets and satellites: formation – Protoplanetary discs 1. Introduction observed in perpendicular orbits yet, due to observational constraints. The first circumbinary planet (CBP) discovered by the Kepler space mission was Kepler-16b (Doyle et al. 2011). In-situ formation of planets at these close orbits around Since then about a dozen more circumbinary p-type plan- binaries are unlikely. Tidal forces close to the binary cause ets have been discovered (see overview in Martin(2019) perturbations in the inner disc that inhibit planetesimal and and Table1). In 2012, multiple CBPs around Kepler-47 dust accretion (Paardekooper et al. 2012; Silsbee & Rafikov were detected (Orosz et al. 2012b, 2019). Later, the Planet 2015; Meschiari 2012), and turbulence induced by hydro- Hunters project discovered a planet in a quadruple star sys- dynamical parametric instabilities can dramatically reduce tem PH1b, also named Kepler-64b (Schwamb et al. 2013). pebble accretion efficiencies (Pierens et al. 2020). A more The most recent discovery is TOI-1338b by the TESS mis- likely formation scenario is planet formation in the outer sion (Kostov et al. 2020). disc and subsequent disk-driven migration to the observed All of the above systems, and most of the discovered close orbits (Pierens & Nelson 2008; Bromley & Kenyon innermost CBPs, share a set of properties in their orbits. 2015). However, this does not in itself explain the particu- Firstly, they are in good alignment with the binary’s or- lar stopping positions of most CBPs. arXiv:2012.03651v1 [astro-ph.EP] 7 Dec 2020 bital plane, hinting at formation in a protoplanetary disc Several studies were already dedicated to investigate that was aligned with the binary. Secondly, the planetary planet migration in circumbinary discs (Pierens & Nelson orbits (the semi-major axes) are all near 3.5 binary separa- 2008, 2013; Kley & Haghighipour 2014, 2015; Kley et al. tions, which is close to the instability limit (Dvorak 1986). 2019). Due to gravitational torques the binary clears out Additionally, the eccentricities of the planetary orbits are an inner cavity and hence planet migration is stopped at small. All of this points to a common formation mechanism the inner edge of the disk at a location close to the bi- for most observed CBPs in aligned, coplanar discs. nary, but not yet matching the observations in most cases Concerning the general stability of circumbinary discs it studied. Numerical simulations showed that the inner disc’s has been suggested that, in addition to the coplanar situa- shape and hence the final planet orbital parameters depend tion, the perpendicular case is also a stable binary-disc con- on disc parameters such as viscosity and scale height, and figuration (Martin & Lubow 2017; Lubow & Martin 2018; the mass ratio and eccentricity of the binary (Mutter et al. Cuello & Giuppone 2019). However, no planets have been 2017; Thun & Kley 2018). Article number, page 1 of 9 A&A proofs: manuscript no. cbp-orbit Kepler 38 35 453 64 34 47 16 413 1661 TOI-1338 Mbin[Msun] 1.20 1.70 1.14 1.77 2.07 1.32 0.89 1.36 1.10 1.34 qbin 0.26 0.91 0.21 0.28 0.97 0.35 0.29 0.66 0.31 0.28 ebin 0.10 0.14 0.05 0.21 0.52 0.02 0.16 0.04 0.11 0.16 mp[mjup] 0.38 0.12 0.05 0.1 0.22 0.05 0.33 0.21 0.05 0.10 ap [abin] 3.16 3.43 4.26 3.64 4.76 3.53 3.14 3.55 3.39 3.49 ep 0.03 0.04 0.04 0.05 0.18 0.03 0.006 0.12 0.06 0.09 −5 mp=Mbin [×10 ] 30 7.1 4.3 5.4 10 3.7 35 15 4.6 6.8 Table 1: Table of observed circumbinary parameters. Mbin, qbin and ebin are the total mass, the mass ratio (M2=M1) and the eccentricity of the binary star, mp, ap, ep are the mass, semi-major axis and eccentricity of the planet on its orbit. (See reference Orosz et al.(2012a), Welsh et al.(2012), Welsh et al.(2015), Schwamb et al.(2013), Orosz et al.(2019), Doyle et al.(2011), Kostov et al.(2014), Kostov et al.(2020), Socia et al.(2020)) Two recent studies by Mutter et al.(2017) and Kley an inner cavity reaching to about 2:5 abin. Inside of this et al.(2019) were able to reproduce the observed CBP or- region the disc will be cleared due to the binary’s action. bits for Kepler-16b and Kepler-38b. In this work we plan to All discs are evolved initially for > 25 000 binary or- find a common formation scenario for most observed CBPs bits, Tbin, without a planet being present, depending on using a sample of 10 planets, as described in Table1. the specific system setup.A typical time scale for a locally To limit the parameter space, we will consider discs, in isothermal protoplanetary disc around a binary to reach agreement with the low α-viscosity that was observed in the a convergent quasi-equilibrium state is a few 10 000 Tbin. D-sharp survey (Dullemond et al. 2018) and scale heights Hence, we used in this work locally isothermal models as comparable to the results of Kley et al.(2019). There, we they converge faster than viscously heated radiative disc showed also that the geometry of the disc, specifically the which can need up to 200 000 Tbin, but eventually reach eccentricity of the inner cavity, can be influenced by an comparable final states with a pressure profil consistent embedded planet. Gap opening planets will circularize the with an unflared inner disc that has a constant aspect ra- disc while lighter planets or discs with higher viscosity will tio between 0.05 and 0.03 depending on the system, see have eccentric holes. We will explore the effect of a wider Kley et al.(2019) for details. During this initialization disc parameter range on the disc architecture in a future phase the binary is not influenced by the disc. As the fi- study. nal planetary orbits will depend on disc properties, we sim- To study the parking of planets we performed numeri- ulated discs for the observed systems in Table1 for dif- cal hydrodynamical simulations of circumbinary discs using ferent values of h and α. The viscously heated, radiative 3 different parameter sets for the disc physics in order to models in Kley et al.(2019) resulted in an unflared in- find a likely combination of viscosity and scale height that ner disc. Therefore we chose here a constant aspect ratio, results in disc shapes that allow for suitable stopping loca- h = H=R. Based on our previous experience (Thun & Kley tions of the planets. Hence, this study extends the work of 2018; Kley et al. 2019), we chose the following three com- Pierens & Nelson(2013) where they looked at a subset of 3 binations: h = 0:04; α = 10−3; h = 0:04; α = 10−4; and systems. The binary and planet parameters used in our sim- h = 0:03; α = 10−4, only for Kepler-38 we used addition- ulations are those given by the observations, as presented ally h = 0:05. in Table1. After the disc reached a convergent behaviour we added In Section2 the adopted model assumptions and ini- a planet with the observed mass (see Table1) in the outer tial conditions are defined.
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