Disc Fragmentation. III. The need for a new paradigm for formation of planets within close binary systems

Abstract

Dozens of planets and brown dwarfs are known to orbit one component of tight stellar binaries ($a_{\rm bin} \lesssim 20$ au), despite circumstellar discs in such systems being truncated to radii of only $\sim (0.2-5)$ au. This presents a challenge to classical planet formation models, which assume planets form after their host stars within stable discs. We propose instead that planet formation and binary formation are concurrent outcomes of gravitational fragmentation in massive circumstellar discs. In this scenario, rapid disc growth driven by infall from the parent molecular cloud leads to fragmentation at radii of tens of au, producing planetary-mass objects that migrate inward. Continued disc growth produces a dominant "oligarch" fragment that undergoes accretion runaway to become the secondary star. During this process, dynamical interactions eject many lower-mass planets, producing free-floating planets (FFPs), while others survive if they migrate sufficiently close to the primary star before destabilisation. Using numerical simulations, we show that survival depends strongly on formation time and mass. Planets formed early and those with masses $> 1-3M_j$ are preferentially retained, whereas lower-mass planets ($<0.1M_j$) are typically ejected. This mechanism naturally explains why low-mass planets are more deficient in tight binaries than gas giants, and predicts that FFPs have a steeper mass function than bound planets within binaries.

Figures (12)

• Figure 1: Schematic illustration of the model. (a) Several planets (the smaller blue circles) and the secondary seed ("oligarch", the larger brown circle) are born at $\sim 50-100$ au disc of the circum-primary disc. The innermost planet has migrated the deepest because it had been born first and/or it is more massive than the other planets. (b) The oligarch begins its rapid inward migration, while also gaining mass rapidly by gas accretion. It ejects one FFP and (may) have captured one of the planets on a bound orbit; (c) The final configuration of the system. The oligarch opens a deep gap/hole in the disc, and stops its rapid inward migration. The innermost planet survives as an S-type circumprimary planet. The outermost planet remains stranded at large radii as a wide orbit P-type planet.
• Figure 2: The density for the disc at different times. White dots with black edges indicate the inserted objects. Panels: $t=2.1$ kyr, the insertion of planet P1 in the clump; $t=3.2$ kyr, P1 decouples from the disrupted clump and migrates inward; $t=3.9$ kyr, the secondary S1 is inserted into a massive and dense clump that migrated to $R\approx 16$ au, whereas low mass planet P2 is inserted in a dense filament.
• Figure 3: Left: Time evolution of the secondary’s orbital radius and mass. The left y-axis shows the orbital radius (blue curve), while the right y-axis shows the secondary mass (red curve). Right: Orbital radii of the secondary and planets in the simulation. The grey shaded region indicates the radially unstable range according to the criterion of Holman_Wiegert_99. The grey dotted line marks $t=3.9\,\mathrm{kyr}$, when the secondary and the other planet was injected.
• Figure 4: Surface density field of the disc at $t = 5.2\,\mathrm{kyr}$. Note that the figure is centred on the secondary. The primary star is towards the top left corner of the figure, inside the (white) inner boundary region. The white dashed lines trace the trajectories of S1 and P2 in the frame fixed on the primary, while arrows indicate their velocities. The separation of P2 and S1 at the closest approach is $0.6\,\mathrm{au}$.
• Figure 5: The Toomre $Q$-parameter field for the relaxed disc at $t = 14\,\mathrm{kyr}$.