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A Triple Origin for the Lack of Tight Coplanar Circumbinary Planets Around Short-Period Binaries

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A Triple Origin for the Lack of Tight Coplanar Circumbinary Planets Around Short-Period Binaries Mon. Not. R. Astron. Soc. 000, 1–24 (2015) Printed July 15, 2021 (MN LATEX style file v2.2) A triple origin for the lack of tight coplanar circumbinary planets around short-period binaries Adrian S. Hamers1⋆, Hagai B. Perets2 and Simon F. Portegies Zwart1 1Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, The Netherlands 2Technion - Israel Institute of Technology, Haifa 32000, Israel MNRAS 455, 3, 3180-3200 (2016) Accepted 2015 October 20. Received 2015 October 20; in original form 2015 June 5 ABSTRACT Transiting circumbinary planets are more easily detected around short-period than long-period binaries, but none have yet been observed by Kepler orbiting binaries with periods shorter than seven days. In triple systems, secular Kozai-Lidov cycles and tidal friction (KLCTF) have been shown to reduce the inner orbital period from ∼ 104 to a few days. Indeed, the majority of short-period binaries are observed to possess a third stellar companion. Using secular evolution analysis and population synthesis, we show that KLCTF makes it unlikely for circumbinary transiting planets to exist around short-period binaries. We find the following outcomes. (1) Sufficiently massive planets in tight and/or coplanar orbits around the inner binary can quench the KL evolution because they induce precession in the inner binary. The KLCTF process does not take place, preventing the formation of a short-period binary. (2) Secular evolution is not quenched and it drives the planetary orbit into a high eccentricity, giving rise to an unstable configuration, in which the planet is most likely ejected from the system. (3) Secular evolution is not quenched but the planet survives the KLCTF evolution. Its orbit is likely to be much wider than the currently observed inner binary orbit, and is likely to be eccentric and inclined with respect to the inner binary. These outcomes lead to two main conclusions: (1) it is unlikely to find a massive planet on a tight and coplanar orbit around a short-period binary, and (2) the properties of circumbinary planets in short-period binaries are constrained by secular evolution. Key words: gravitation – celestial mechanics – planet-star interactions – stars: kinematics and dynamics. 1 INTRODUCTION sion (Martin & Triaud 2015). Because of this bias, many circumbinary planets are expected to have been observed arXiv:1506.02039v2 [astro-ph.EP] 9 Jun 2016 An increasing number of transiting circumbinary planets around short-period Kepler eclipsing binaries. However, so around solar-type main-sequence (MS) binary stars are be- far, none have been found. ing discovered by the Kepler mission. Currently, 10 such If the apparent lack of (nearly) coplanar circumbinary planets are known (see Table A1; top rows). The orbital planets around close binaries is intrinsic and not related to periods of the stellar binaries in the systems discovered (yet unknown) observational bias(es), then this raises the so far have a mean value of 20.4 d; the shortest period is question of its origin. The following two observations suggest 7.45 d (Kepler 47; Orosz et al. 2012a). In contrast, the Ke- that this origin is related to the (MS) evolution of solar-type pler eclipsing binaries without circumbinary planets typically triple star systems. have shorter orbital periods, with a mean period of 2.8 d. There exists a bias for detecting more transiting circumbi- nary planets around shorter-period binaries because (1) the The fraction of tertiary companions to spectroscopic • shorter period results in more transits in a given amount binaries is a strong function of the inner period, increasing of time, and (2) the binary precession period is only a few from 0.34 for inner periods PA > 12 d to 0.96 for PA < 3d years long, resulting in intersecting binary and planet orbits (Tokovinin et al. 2006). For the Kepler eclipsing binaries in (as seen in the plane of the sky) during the Kepler mis- particular, the tertiary fraction for inner binaries with pe- riods . 3 d is 20% (Rappaport et al. 2013; Conroy et al. ∼ 2014). The latter studies are limited (by observing time) ⋆ E-mail: [email protected] to triples with outer periods . 3 yr. The complete tertiary c 2015 RAS 2 Adrian S. Hamers, Hagai B. Perets and Simon F. Portegies Zwart fraction for these Kepler binaries, i.e. including any outer period, is likely much larger. In the survey of Tokovinin (2014), a peak is found in • the (inner) period distribution around 3 d. As shown by Fabrycky & Tremaine (2007); Naoz & Fabrycky (2014), this peak in the period distribution can be explained by the com- bination of the secular gravitational torque of the tertiary companion and tidal friction in the inner binary. The former, through Kozai-Lidov (KL) oscillations (Lidov 1962; Kozai 1962), can excite the inner binary orbit to high eccentric- ity. Consequently, tides are much more effective, leading to tidal dissipation and shrinkage of the orbit, and, eventually, to a tight and (nearly) circular orbit. In this scenario, the precursors of the binaries affected by KL cycles with tides have orbital periods ranging roughly between 10 and 104 d. The lower limit of 10 d of precursor binaries is right in the ballpark of the orbital periods of the currently observed Kepler systems with transiting circumbinary planets. Also, there are a number of observed wider systems orbited by at least one circumbinary planet; some of them are listed in Figure 1. A schematic depiction (not to scale) of the hierarchi- Table A1 (bottom rows). Therefore, a large fraction of these cal configuration of the systems considered in this paper. The precursor binaries might have a circumbinary planet in a circumbinary planet (m3) orbits the inner binary (m1 and m2); stable orbit in-between the ‘inner’ and ‘outer’ stellar orbits the outermost star (m3), in the outer binary, orbits the centre of (henceforth, we refer to the inner and outer stellar binaries mass of the inner binary+planet system. simply as the ‘inner’ and ‘outer’ binaries; see also Fig. 1). Here, we show that in these stellar triples with a cir- detections of transiting Kepler circumbinary planets around cumbinary planet around the inner binary, the planet can short-period binaries. strongly affect the secular orbital evolution of the inner bi- The goal of this paper is to quantify the above argu- nary compared to the situation without a planet, provided ment. The organization is as follows. In Section 2, we briefly that certain conditions are met (see below). This ‘shielding’ describe our methods and assumptions. In Section 3, we effect arises from a quenching of the eccentricity oscillations study the secular gravitational dynamics of stellar triples in the inner binary induced by the torque of the outer bi- with a circumbinary planet, and we quantify the conditions nary, because of precession induced from the circumbinary when the planet can affect the inner binary. In order to planet. The shielding effect is similar to the quenching of KL evaluate the effect of circumbinary planets in a population oscillations in stellar triples because of additional sources of of triples in the field, we carry out a population synthesis orbital precession (notably, precession associated with gen- study in Section 4. We discuss our results in Section 5, where eral relativity, tidal bulges and/or stellar rotation). In some we also describe, using direct N-body integrations, the fate cases, however, resonances can occur that enhance the ec- of circumbinary planets that become unstable because of centricity oscillations in the inner binary (such resonances secular evolution. We conclude in Section 6. can also occur in isolated triples in conjunction with general We remark that nearing the completion of this pa- relativity; Naoz et al. 2013b). per, we became aware of two similar and independent Typically, shielding of KL oscillations by the presence studies on the lack of circumbinary planets around short- of the planet is only effective for massive planets that are period binaries in stellar triples by Martin et al. (2015) and in a (nearly) coplanar and tight orbit with respect to the Mu˜noz & Lai (2015). inner binary. This implies the following two scenarios for the secular evolution of the system. If the precursor binary is orbited by a massive planet in 2 METHODS AND ASSUMPTIONS • a tight and coplanar orbit, then planet shielding can prevent the binary from shrinking through the combined effects of We model the system of a circumbinary planet orbiting KL cycles and tidal friction (KLCTF). the inner binary in a stellar triple system as a hierarchi- On the other hand, if the planet is of low mass and in cal quadruple system in the ‘triple-single’ configuration, • an inclined and wide orbit with respect to the inner binary, which we studied previously in Hamers et al. (2015) (here- then shielding is typically ineffective, and the binary can after HPAPZ15). In the latter work, the Hamiltonian of the shrink through KLCTF to become a short-period binary. system was derived and expanded in terms of the ratios of the three binary separations rA, rB and rC, where, by as- Assuming that short-period binaries are produced through sumption, rC rB rA. In the current context, binary A ≫ ≫ KLCTF, then this implies an intrinsic lack of massive plan- corresponds to the inner binary, binary B to the orbit of the ets in tight and coplanar circumbinary orbits (i.e. strongly planet around the inner binary, and binary C to the orbit shielding planets), whereas far-away and inclined low-mass of the tertiary star around the centre of mass of the inner circumbinary planets (i.e. weakly shielding planets) could binary+planet system (evidently, the latter nearly coincides still be abundant.
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