On the Structure and Mass Delivery Towards Circumplanetary Discs Matthäus Schulik,1 Anders Johansen,1 Bertram Bitsch,2 Elena Lega3 Michiel Lambrechts1
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Astronomy & Astrophysics manuscript no. cpds c ESO 2020 March 31, 2020 On the structure and mass delivery towards circumplanetary discs Matthäus Schulik,1 Anders Johansen,1 Bertram Bitsch,2 Elena Lega3 Michiel Lambrechts1 1 Lund Observatory, Box 43, Sölvegatan 27, SE-22100 Lund, Sweden e-mail: [email protected] 2 Max-Planck Institut für Astronomie, Königsstuhl 17, 69117 Heidelberg, Germany 3 Laboratoire Lagrange, UMR7293, Université de la Côte d’Azur, Boulevard de la Observatoire, 06304 Nice Cedex 4, France Received ... ABSTRACT Circumplanetary discs (CPDs) form around young gas giants and are thought to be the sites of moon formation as well as an interme- diate reservoir of gas that feeds the growth of the gas giant. How the physical properties of such CPDs are affected by the planetary mass and the overall opacity is relatively poorly understood. In order to clarify this, we use the global radiation hydrodynamics code FARGOCA, with a grid structure that allows resolving the planetary gravitational potential sufficiently well for a CPD to form. We then study the gas flows and density/temperature structures that emerge as a function of planet mass, opacity and potential depth. Our results indicate interesting structure formation for Jupiter-mass planets at low opacities, which we subsequently analyse in de- tail. Using an opacity level that is 100 times lower than that of ISM dust, our Jupiter-mass protoplanet features an envelope that is sufficiently cold for a CPD to form, and a free-fall region separating the CPD and the circumstellar disc emerges. Interestingly, this free-fall region appears to be a result of supersonic erosion of outer envelope material, as opposed to the static structure formation that one would expect at low opacities. Our analysis reveals that the planetary spiral arms seem to pose a significant pressure barrier that needs to be overcome through radiative cooling in order for gas to free-fall onto the CPD. The circulation inside the CPD is near-keplerian and modified by the presence of CPD spiral arms. The same is true when we deepen the planetary potential depth, which in turn increases the planetary luminosity, quenches the formation of a free-fall region and decreases the rotation speed of the envelope by 10%. For high opacities we recover results from the literature, finding an essentially featureless hot envelope. With this work, we demonstrate the first simulation and analysis of a complete detachment process of a protoplanet from its parent disc in a 3D radiation hydrodynamics setting. Key words. giant planet formation – simulations – radiation hydrodynamics 1. Introduction cretion rates into the planetary Hill spheres and in turn also to regulate CPD and planet growth (D’Angelo & Lubow 2008). Circumplanetary discs (CPDs) are rotationally supported discs, On the other hand, radiative feedback from the growing consisting of gas and dust, that are thought to form around planet and CPD into the CSD is inevitable, with potentially ob- massive host protoplanets. This formation process involves gas servable consequences for the CSD chemistry (Cleeves et al. from the parent circumstellar disc (CSD), in which the planet 2015). is formed, being accreted into the Hill sphere of the planet. In- The study of such a triplet system of planet – CPD – CSD side the Hill sphere, the gas is unable to finalize its fall onto the must therefore be performed numerically, in order to access all planet as the gas cannot easily get rid of its angular momentum available physical information. with respect to the planet, thus forming a disc (Tanigawa et al. Because of the inherent complexity of simulating this prob- 2012). The recent discovery of a massive protoplanet with an lem, hydrodynamical simulations are usually either limited in the associated mass of possibly circumplanetary material in PDS70 number of CSD orbits they can compute, or in the physics that (Keppler et al. 2018; Haffert et al. 2019; Isella et al. 2019) has is being computed. In this endeavour, a number of interesting stirred renewed interest into the properties of this class of ob- milestones exist: jects. D’Angelo et al.(2003) used the system of 2D Euler equa- tions with a cooling prescription and found various CPD struc- CPDs have been long recognized as potential sites for the tures with spirals in them. Contrary to this work, Ayliffe & Bate formation of regular moon populations around giant planets (2009a) found no CPD spiral arms in a global, 3D radiation (Canup & Ward 2006; Shibaike et al. 2019; Ronnet & Johansen hydrodynamics setting, arguing that they disappear due to the 2020). Because they are directly coupled to the global CSD increase in degrees of freedom for the flow in 3D. Tanigawa gas flows, CPDs are thought to be possible bottlenecks for fur- et al.(2012) found a disk at keplerian rotation in their isother- ther growth of giant planets. Those global flows can exhibit su- mal 3D simulation. Gressel et al.(2013) showed in a comparison personic spiral arm shocks as the planet orbits relative to the of global isothermal, adiabatic-hydrodynamic and MHD simula- CPD medium (Goldreich & Tremaine 1978), and once the planet tions that isothermal simulations favour highly-keplerian disc ro- grows massive enough those shocks perturb the global flows tation and strong flattening of the CPDs. Zhu et al.(2016) found sufficiently to open gaps in the gas distribution (Goldreich & again spiral arms in highly resolved radial-azimuthal 2D runs Tremaine 1980). Those gaps are thought to further limit the ac- with a cooling prescription as function of optical depth, identi- Article number, page 1 of 18 A&A proofs: manuscript no. cpds Table 1: Simulation runs used in this paper. The relation of the particularly important if the CPD is accreting onto the planet runs with the science questions posed in this work are explained and at the same time is replenished from the CSD. Earlier au- in Sec.1 and parameters are explained in Sec.2. thors have often assumed that the mass accreted by the planet is a fraction of the mass entering either the Bondi or the Hill Label mP=mJup mP=m⊕ r˜s Opacities* radius (D’Angelo & Lubow 2008; Owen & Menou 2016), CPD occurrence but a more recent study (Lambrechts et al. 2019) shows that m1 0.06 20 0.1 1.0/0.01 the mass flux through the Hill sphere and the actual accretion m2 0.2 60 0.1 0.01 rate can differ by a factor of up to 100, with this number ap- m3 0.3 90 0.1 1.0/0.01 proaching ∼0.1 when the planetary mass reaches ∼1MJ. We m4 0.4 120 0.1 1.0/0.01 use runs C1/C2 and H1/H2 to extend this idea and measure m5 0.75 240 0.1 1.0/0.01 the mass and accretion rates of the CPDs and compare them Main simulations to those of the planets. C1 ("nominal") 1 360 0.1 0.01 – What is the influence of the variation of dust opacity on prop- H1 ("high opacity") 1 360 0.1 1.0 erties of the CPD? Is there an influence from the CSD on the H2 ("deep") 1 360 0.025 0.01 accretion process? Discs at different ages are able to provide C2 ("Bell & Lin") 1 360 0.1 0.01 differing amounts of dust to already formed protoplanetary envelopes (Brauer et al. 2008; Birnstiel et al. 2012). How- ever, the full time evolution of CPDs in 3D radiative hydro- (*) Opacities used: numbers denote constant opacities κ for all 2 −1 dynamics simulations is currently not accessible on modern simulations in cm g , except for simulation C2, which uses hardware. This problem is even more severe if one would Bell & Lin opacities reduced by the factor in the table. All sim- consider the evolution of the full disc, including stellar irra- ulation runs have an unperturbed CSD surface density Σ0 = −2 diation and the evolution of the size distribution of the dust. 100 g cm at the planets position. Simulation letters refer to Thus we take a simplified approach and compare a dust-rich the purpose or expected simulation outcome: m="mass survey", (run H1) and dust-poor (run C1) scenario. We also perform C="cold", H="hot" two support parameter simulations, investigating deep plan- etary potentials (run H2) and more realistic, non-constant opacities, given by Bell & Lin(1994) (run C2). fied them to be triggered by the tidal action from the host star We structure this paper as follows in order to address those ques- and measured accretion rates onto the planet through the CPD. tions. In Section2 we describe our methods, the used set of sim- The same study also investigated the effects of the optical depth ulations and justify parameter choices. Section3 describes how on the CPD properties in detail by changing the CPD mass. An the envelopes of protoplanets of varying masses and envelope interesting result from their approach of varying the CPD mass opacities flatten and rotate. Section4 describes and analyses our is that the temperature changes with the optical depth. The tem- nominal simulation run, which presents most of the novel and perature in turn controls the spiral arms attack angle, which is interesting physics features. Subsequently, Section5 discusses in their study responsible for the ongoing accretion of the CPD how those features change when using different simulation pa- into the planet. Subsequently, Szulágyi et al.(2016) clarified in rameters and establishes the robustness of our nominal results. 3D radiation hydrodynamics runs that the occurrence of CPDs, That section also presents results for CPD masses, mass profiles as opposed to spherical envelopes around giant planets, is linked and accretion rates, together with reflections upon those.