The Kepler space mission discovered about a dozen planets orbiting around binary stars systems. Most of these circumbinary 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 ($0.1 \le e_{bin}\le 0.21$) 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 $H/r \sim 0.04$. 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 $\leq 10\%$, strongly supports the idea that planet migration in the disc brought the planets to their present locations.
We present the results of two-fluid hydrodynamical simulations of circumbinary discs consisting of gas and dust, with and without embedded planets, to examine the influence of the dust on the structure of the tidally truncated inner cavity and on the parking locations of migrating planets. In this proof-of-concept study, we consider Kepler-16 and -34 analogues, and examine dust fluids with Stokes numbers in the range $10^{-4} \le St \le 10^{-1}$ and dust-to-gas ratios of 0.01 and 1. For the canonical dust-to-gas ratio of 0.01, we find the inclusion of the dust has only a minor effect on the ca…
The recent detection of the third planet in Kepler-47 has shown that binary stars can host several planets in circumbinary orbits. To understand the evolution of such systems we have performed two-dimensional hydrodynamic simulations of the circumbinary disc with two embedded planets for several Kepler systems. In two cases, Kepler-47 and -413, the planets are captured in a 1:1 mean-motion resonance at the planet parking position near the inner edge of the disc. The orbits are fully aligned, have mean eccentricities of about 0.25 to 0.30, and the planets are entangled in a horseshoe type of mo…
Resonant locking of two planets is an expected outcome of convergent disc migration. The planets subsequently migrate together as a resonant pair. In the context of circumbinary planets, the disc is truncated internally by the binary. If there were only a single planet, then this inner disc edge would provide a natural parking location. However, for two planets migrating together in resonance there will be a tension between the inner planet stopping at the disc edge, and the outer planet continuing to be torqued inwards. In this paper we study this effect, showing that the outcome is a functio…
As of today ten circumbinary planets orbiting solar type main sequence stars have been discovered. Nearly all of them orbit around the central binary very closely to the region of instability where it is difficult to form them in situ. It is assumed that they formed further out and migrated to their observed position. We extend previous studies to a more realistic thermal disc structure and determine what parameter influence the final parking location of a planet around a binary star. We perform two-dimensional numerical simulations of viscous accretion discs around a central binary that inclu…
Martin & Lubow (2017) showed through simulations that an initially tilted disc around an eccentric binary can evolve to polar alignment in which the disc lies perpendicular to the binary orbital plane. We apply linear theory to show both analytically and numerically that a nearly polar aligned low mass circumbinary disc evolves to polar alignment and determine the alignment timescale. Significant disc evolution towards the polar state around moderately eccentric binaries can occur for typical protostellar disc parameters in less than a typical disc lifetime for binaries with orbital periods of…
Most stars form in binaries and the evolution of their discs remains poorly understood. To shed light on this subject, we carry out 3D ideal MHD simulations with the AMR code FLASH of binary star formation for separations of $10-20\,\mathrm{AU}$. We run a simulation with no initial turbulence (NT), and two with turbulent Mach numbers of $\mathcal{M} = σ_v/c_s = 0.1$ and $0.2$ (T1 and T2) for $5000\,\mathrm{yr}$ after protostar formation. By the end of the simulations the circumbinary discs in NT and T1, if any, have radii of $\lesssim20\,\mathrm{AU}$ with masses $\lesssim0.02\,\mathrm{M}_\odot…
We use three dimensional simulations with coupled hydrodynamics and Monte Carlo radiative transfer to show that shadows cast by the inner disc in broken circumbinary discs move within a confined range of position angles on the outer disc. Over time, shadows appear to rock back and forth in azimuth as the inner disc precesses. The effect occurs because the inner disc precesses around a vector that is not the angular momentum vector of the outer disc. We relate our findings to recent observations of shadows in discs.
Nearly all young stars are initially surrounded by `protoplanetary' discs of gas and dust, and in the case of single stars at least 30\% of these discs go on to form planets. The process of protoplanetary disc formation can result in initial misalignments, where the disc orbital plane is different to the stellar equator in single star systems, or to the binary orbital plane in systems with two stars. A quirk of the dynamics means that initially misaligned `circumbinary' discs -- those that surround two stars -- are predicted to evolve to one of two possible stable configurations, one where the…
We present hydrodynamical simulations to model the accretion flow from a polar circumbinary disc onto a high eccentricity ($e=0.78$) binary star system with near unity mass ratio ($q=0.83$), as a model for binary HD 98800 BaBb. We compare the polar circumbinary disc accretion flow with the previously studied coplanar case. In the coplanar case, the circumbinary disc becomes eccentric and the accretion alternates from being dominant onto one binary member to the other. For the polar disc case involving a highly eccentric binary, we find that the circumbinary disc retains its initially low eccen…
Recent observations have shown that circumstellar and circumbinary discs in young stellar binaries are often misaligned with respect to the binary orbital plane. We analyze the tidal truncation of such misaligned discs due to torques applied to the disc at the Lindblad resonances from the tidal forcings of the binary. We consider eccentric binaries with arbitrary binary-disc inclination angles. We determine the dependence of the tidal forcing strengths on the binary parameters and show that they are complicated non-monotonic functions of eccentricity and inclination. We adopt a truncation crit…
Eccentric gaseous discs are unstable to a parametric instability involving the resonant interaction between inertial-gravity waves and the eccentric mode in the disc. We present 3D global hydrodynamical simulations of inviscid circumbinary discs that form an inner cavity and become eccentric through interaction with the central binary. The parametric instability grows and generates turbulence that transports angular momentum with stress parameter $α\sim 5 \times 10^{-3}$ at distances $\lesssim 7 \;a_{bin} $, where $a_{bin}$ is the binary semi-major axis. Vertical turbulent diffusion occurs at …
Up to present date, no circumbinary planet around contact binaries were discovered neither by transit method nor by the minima times variation, although they are known having third component stars around. We thus ask: where are the circumbinary planets of contact binaries? By considering the physical and geometrical parameters we simulated the light curves of contact binaries with possible transiting circumbinary jovian planets. It seems either the circumbinary jovian planets are not formed around contact binaries, probably due to dynamical effects of the binary and third component stars, or t…
A test particle orbit around an eccentric binary has two stationary states in which there is no nodal precession: coplanar and polar. Nodal precession of a misaligned test particle orbit centres on one of these stationary states. A low mass circumbinary disc undergoes the same precession and moves towards one of these states through dissipation within the disc. For a massive particle orbit, the stationary polar alignment occurs at an inclination less than $90^{\circ}$, this is the prograde-polar stationary inclination. A sufficiently high angular momentum particle has an additional higher incl…
No circumbinary planets have been discovered smaller than 3 Earth radii, yet planets of this small size comprise over 75% of the discoveries around single stars. The observations do not prove the non-existence of small circumbinary planets, but rather they are much harder to find than around single stars, because their transit timing variations are much larger than the transit durations. We present STANLEY: an automated algorithm to find small circumbinary planets. It employs custom methods to detrend eclipsing binary light curves and stack shallow transits of variable duration and interval us…
The abundance and properties of planets orbiting binary stars - circumbinary planets - are largely unknown because they are difficult to detect with currently available techniques. Results from the Kepler satellite and other studies indicate a minimum occurrence rate of circumbinary giant planets of ~10 %, yet only a handful are presently known. Here, we study the potential of ESA's Gaia mission to discover and characterise extrasolar planets orbiting nearby binary stars by detecting the binary's periodic astrometric motion caused by the orbiting planet. We expect that Gaia will discover hundr…
We analyze the eccentric response of a low mass coplanar circumbinary disc to secular tidal forcing by a Keplerian eccentric orbit central binary. The disc acquires a forced eccentricity whose magnitude depends on the properties of the binary and disc. The largest eccentricities occur when there is a global apsidal resonance in the disc. The driving frequency by the binary is its apsidal frequency that is equal to zero. A global resonance occurs when the disc properties permit the existence of a zero apsidal frequency free eccentric mode. Resonances occur for different free eccentric modes tha…
Gas and dust in inclined orbits around binaries experience precession induced by the binary gravitational torque. The difference in precession between gas and dust alters the radial drift of weakly coupled dust and leads to density enhancements where the radial drift is minimised. We explore this phenomenon using 3D hydrodynamical simulations to investigate the prominence of these `dust traffic jams' and the evolution of the resulting dust sub-structures at different disc inclinations and binary eccentricities. We then derive evolution equations for the angular momentum of warped dust discs an…
We present a 3D hydrodynamics study of gravitational instabilities (GIs) in a 0.14 M$_{\odot}$ circumbinary protoplanetary disc orbiting a 1 M$_{\odot}$ star and a 0.02 M$_{\odot}$ brown dwarf companion. We examine the thermodynamical state of the disc and determine the strengths of GI-induced density waves, nonaxisymmetric density structures, mass inflow and outflow, and gravitational torques. Results are compared with a parallel simulation of a protoplanetary disc without the brown dwarf binary companion. Simulations are performed using CHYMERA, a radiative 3D hydrodynamics code. The onset o…
How does the cavity size in circumbinary discs depend on disc and binary properties? We investigate by simulating disc cavities carved by binary companions using smoothed particle hydrodynamics (SPH). We find that a cavity is quickly opened on the dynamical time, while the cavity size is set on the viscous time. In agreement with previous findings, we find long term cavity sizes of 2-5 times the binary semi-major axis, increasing with eccentricity and decreasing with disc aspect ratio. When considering binaries inclined with respect to the disc we find three regimes: i) discs that evolve towar…
Stellar binaries represent a substantial fraction of stellar systems, especially among young stellar objects. Accordingly, binaries play an important role in setting the architecture of a large number of protoplanetary discs. Binaries in coplanar and polar orientations with respect to the circumbinary disc are stable configurations and could induce non-axisymmetric structures in the dust and gas distributions. In this work, we suggest that the structures shown in the central region of the protoplanetary disc HD 169142 are produced by the presence of an inner stellar binary and a circumbinary (…
Although most of the circumbinary planets detected by the Kepler spacecraft are on orbits that are closely aligned with the binary orbital plane, the systems Kepler-413 and Kepler-453 exhibit small misalignments of $\sim 2.5^\circ$. One possibility is that these planets formed in a circumbinary disc whose midplane was inclined relative to the binary orbital plane. Such a configuration is expected to lead to a warped and twisted disc, and our aim is to examine the inclination evolution of planets embedded in these discs. We employed 3D hydrodynamical simulations that examine the disc response t…
In recent years an increasing number of observational studies have hinted at the presence of warps in protoplanetary discs, however a general comprehensive description of observational diagnostics of warped discs was missing. We performed a series of 3D SPH hydrodynamic simulations and combined them with 3D radiative transfer calculations to study the observability of warps in circumbinary discs, whose plane is misaligned with respect to the orbital plane of the central binary. Our numerical hydrodynamic simulations confirm previous analytical results on the dependence of the warp structure on…
Planets and satellites orbiting a binary system exist in the solar system and extrasolar planetary systems. Their orbits can be significantly different from Keplerian orbits, if they are close to the binary and the secondary-to-primary mass ratio is high. A proper description of a circumbinary orbit is in terms of the free eccentricity $e_{\rm free}$ at the epicyclic frequency $κ_0$, forced eccentricity $e_{\rm forced}$ at the mean motion $n_0$, and oscillations at higher frequencies forced by the non-axisymmetric components of the binary's potential. We show that accurate numerical values for…
The recent discovery of planets orbiting main sequence binaries will provide crucial constraints for theories of binary and planet formation. The formation pathway for these planets is complicated by uncertainties in the formation mechanism of the host stars. In this paper, we compare the dynamical states of single and binary star planetary systems. Specifically, we pose two questions: (1) What does it mean for a circumbinary system to be dynamically packed? (2) How many systems are required to differentiate between a population of packed or sparse planets? We determine when circumbinary syste…
Almost a dozen circumbinary planets have been found transiting eclipsing binaries. For the first time the observational bias of this sample is calculated with respect to the mass ratio of the host binaries. It is shown that the mass ratio affects transit detection in multiple, sometimes subtle ways, through stability and dynamics of orbits, dilution of transit depths and the geometric transit and eclipse probabilities. Surprisingly though, it is found that these effects largely cancel out. Consequently, the transit detections in the Kepler mission are essentially unbiased with respect to mass …
The Search for Planets Orbiting Two Stars (SPOTS) survey aims to study the formation and distribution of planets in binary systems by detecting and characterizing circumbinary planets and their formation environments through direct imaging. With the SPHERE Extreme Adaptive Optics instrument, a good contrast can be achieved even at small (<300 mas) separations from bright stars, which enables studies of planets and disks in a separation range that was previously inaccessible. Here, we report the discovery of resolved scattered light emission from the circumbinary disk around the well-studied yo…
Dust Growth in Binary Systems: Inhibition of dust settling and growth in circumbinary discs
Univ. Grenoble Alpes, CNRS, IPAG（格勒诺布尔阿尔卑斯大学）；Université Lyon 1, ENS de Lyon, CNRS, CRAL（里昂第一大学）；School of Physics and Astronomy, Monash University（蒙纳士大学）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学）；Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma（俄克拉荷马大学）；LIRA, Observatoire de Paris, Universite PSL（巴黎天文台）
We carry out numerical simulations of circumbinary discs, solving the viscous hydrodynamics equations on a polar grid covering an extended disc outside the binary co-orbital region. We use carefully controlled outer boundary conditions and long-term integrations to ensure that the disc reaches a quasi-steady state, in which the time-averaged mass accretion rate onto the binary, $\langle\dot{M}\rangle$, matches the mass supply rate at the outer disc. We focus on binaries with comparable masses and a wide range of eccentricities ($e_\mathrm{B}$). For $e_\mathrm{B} \lesssim 0.05$, the mass accret…
The evolution of circumbinary discs and planets is often studied using two-dimensional (2D) numerical simulations, although recent work suggests that 3D effects may significantly alter the structure of the inner cavity created by the binary. In this study, we present the results of 3D hydrodynamical simulations of circumbinary discs that orbit around analogues of the Kepler-16 and Kepler-34 systems, including the effect of stellar heating and radiative cooling on the thermal disc structure. We find that compared to their 2D counterparts, the structures of the cavities in 3D circumbinary disc m…
The inner-most regions of circumbinary discs are unstable to a parametric instability whose non-linear evolution is hydrodynamical turbulence. This results in significant particle stirring, impacting on planetary growth processes such as the streaming instability or pebble accretion. In this paper, we present the results of three-dimensional, inviscid global hydrodynamical simulations of circumbinary discs with embedded particles of 1 cm size. Hydrodynamical turbulence develops in the disc, and we examine the effect of the particle back-reaction on vertical dust. We find that higher solid-to-g…
We present the results of 2-dimensional hydrodynamic simulations of self-gravitating circumbinary discs around binaries whose parameters match those of the circumbinary planet-hosting systems Kepler-16, -34 and -35. Previous work has shown that non-self-gravitating discs in these systems form an eccentric precessing inner cavity due to tidal truncation by the binary, and planets which form at large radii migrate until stalling at this cavity. While this scenario appears to provide a natural explanation for the observed orbital locations of the circumbinary planets, previous simulations have fa…
IRAS~04158+2805 has long been thought to be a very low mass T-Tauri star (VLMS) surrounded by a nearly edge-on, extremely large disc. Recent observations revealed that this source hosts a binary surrounded by an extended circumbinary disc with a central dust cavity. In this paper, we combine ALMA multi-wavelength observations of continuum and $^{12}$CO line emission, with H$α$ imaging and Keck astrometric measures of the binary to develop a coherent dynamical model of this system. The system features an azimuthal asymmetry detected at the western edge of the cavity in Band~7 observations and a…
The nearby V4046 Sgr spectroscopic binary hosts a gas-rich disc known for its wide cavity and dusty ring. We present high resolution ($\sim$20 mas or 1.4 au) ALMA observations of the 1.3mm continuum of V4046 Sgr which, combined with SPHERE--IRDIS polarised images and a well-sampled spectral energy distribution (SED), allow us to propose a physical model using radiative transfer (RT) predictions. The ALMA data reveal a thin ring at a radius of 13.15$\pm$0.42 au (Ring13), with a radial width of 2.46$\pm$0.56 au. Ring13 is surrounded by a $\sim$10 au-wide gap, and it is flanked by a mm-bright out…
Context. Dynamical studies suggest that most circumbinary discs (CBDs) should be coplanar. However, some theoretical works show that under certain conditions a CBD can become polar, which means that its rotation vector is orthogonal with respect to the binary orbital plane. Interestingly, very recent observations show that polar CBDs exist in nature (e.g. HD 98800). Aims. We test the predictions of CBD alignment around eccentric binaries based on linear theory. In particular, we compare prograde and retrograde CBD configurations. Then, assuming planets form in these systems, we thoroughly char…
The presence of planets in binary systems poses interesting problems for planet formation theories, both in cases where planets must have formed in very compact discs around the individual stars and where they are located near the edge of the stable circumbinary region, where in situ formation is challenging. Dust dynamics is expected to play an important role in such systems, since dust trapping at the inner edge of circumbinary discs could aid in situ formation, but would simultaneously starve the circumstellar discs of the solid material needed to form planets. Here we investigate the dynam…
The structure and evolution of gas flows within the cavity of a circumbinary disk (CBD) surrounding the stellar components in eccentric binaries are examined via two-dimensional hydrodynamical simulations. The degree to which gas fills the cavity between the circumstellar disks (CSDs) and the CBD is found to be greater for highly eccentric systems, in comparison to low-eccentricity systems, reflecting the spatial extent over which mass enters into the cavity throughout the orbit. The pattern of the gas flow in the cavity differs for eccentric binaries from that of binaries in a circular orbit.…
A key discovery of the Kepler mission is of the circumbinary planets known as "Tatooines", which appear to be well aligned with their host stars' orbits. Whether this alignment is due to initially coplanar circumbinary planet-forming discs (i.e. nature), or subsequent alignment of initially misaligned discs by warping the inner disc or torquing the binary (i.e. nurture), is not known. Tests of which scenario dominates may be possible by observing circumbinary Kuiper belt analogues ("debris discs"), which trace the plane of the primordial disc. Here, the 140 au diameter circumbinary debris disc…
We study, by means of numerical simulations and analysis, the details of the accretion process from a disc onto a binary system. We show that energy is dissipated at the edge of a circumbinary disc and this is associated with the tidal torque that maintains the cavity: angular momentum is transferred from the binary to the disc through the action of compressional shocks and viscous friction. These shocks can be viewed as being produced by fluid elements which drift into the cavity and, before being accreted, are accelerated onto trajectories that send them back to impact the disc. The rate of …
We analyse the evolution of a mildly inclined circumbinary disc that orbits an eccentric orbit binary by means of smoother particle hydrodynamic (SPH) simulations and linear theory. We show that the alignment process of an initially misaligned circumbinary disc around an eccentric orbit binary is significantly different than around a circular orbit binary and involves tilt oscillations. The more eccentric the binary, the larger the tilt oscillations and the longer it takes to damp these oscillations. A circumbinary disc that is only mildly inclined may increase its inclination by a factor of a…
Numerous circumbinary planets have been discovered in surveys of transiting planets. Often, these planets are found to orbit near to the zone of dynamical instability, close to the central binary. The existence of these planets has been explained by hydrodynamical simulations that show that migrating circumbinary planets, embedded in circumbinary discs, halt at the central cavity that is formed by the central binary. Transit surveys are naturally most sensitive to finding circumbinary planets with the shortest orbital periods. The future promise of detecting longer period systems using radial-…
Recent discoveries of circumbinary planets in Kepler data show that there is a viable channel of planet formation around binary main sequence stars. Motivated by these discoveries, we have investigated the caustic structures and detectability of circumbinary planets in microlensing events. We have produced a suite of animations of caustics as a function of the projected separation and angle of the binary host to efficiently explore caustic structures over the entire circumbinary parameter space. Aided by these animations, we have derived a semi-empirical analytic expression for the location of…
Misaligned circumbinary discs around unequal-mass eccentric binaries: alignment, morphology, and binary accretion variability
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma（俄克拉荷马大学霍默·L·多格物理与天文学系）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Dipartimento di Fisica, Università degli Studi di Milano（米兰大学物理系）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Department of Physics and Astronomy, University of Victoria（维多利亚大学物理与天文学系）；CSST Science Center for the Guangdong-Hong Kong-Macau Greater Bay Area, Sun Yat-sen University（中山大学粤港澳大湾区空间科学中心）
Circumbinary disc observations and simulations show large, eccentric inner cavities. Recent work has shown that the shape and size of these cavities depend on the aspect ratio and viscosity of the disc, as well as the binary eccentricity and mass ratio. It has been further shown that, for gaps created by planets, the cooling timescale significantly affects the shape and size of the gap. In this study, we consider the effect of different cooling models on the cavity shape in a circumbinary disc. We compare locally isothermal and radiatively cooled disc models to ones with a parametrised cooling…
