Dust Growth in Binary Systems: Inhibition of dust settling and growth in circumbinary discs

Technical Summary: Density-driven Dust Growth in Binary Systems

Problem Statement
While sub-structures in protoplanetary discs are routinely observed, the specific impact of stellar multiplicity on dust evolution remains poorly quantified. In binary systems, tidal interactions alter the density structure of discs, creating a distinct dynamical environment compared to single-star systems. Although binary-disc interactions can create pressure bumps that trap dust, they also induce perturbations that may increase collisional velocities, potentially leading to fragmentation rather than growth. Previous studies have largely focused on gas dynamics or utilized simplified dust prescriptions that neglect the feedback between particle growth, disc structure, and dynamics. This work addresses the gap in understanding how the density structures induced by companions promote or inhibit dust coagulation and the subsequent conditions for planetesimal formation via the streaming instability.

Methodology
The authors performed 3D hydrodynamical simulations using the Smoothed Particle Hydrodynamics (SPH) code PHANTOM. The simulations employed a "dust-as-a-mixture" scheme to model a population of 1.5 million gas and dust particles.

• Dust Physics: The model utilized a monodisperse implementation where grains evolve in size based on collisions driven by gas turbulence. The relative collision velocity ($V_{rel}$) was calculated analytically based on turbulent velocity and Stokes number, compared against a fragmentation velocity threshold ($V_{frag} = 15$ m s$^{-1}$, consistent with icy grains). Growth was treated as perfect coagulation, while fragmentation was smoothed to allow progressive mass loss.
• Simulation Setups: Five configurations were simulated:
  1. IB0 & IB5: Circumbinary discs (orbiting both stars) with binary eccentricities ($e_{bin}$) of 0 and 0.5, respectively. The binary had a mass ratio $q=0.75$ and semi-major axis $a_{bin}=5$ au.
  2. OB0 & OB5: Circumstellar discs (orbiting one star) perturbed by an external companion ($0.1 M_{\odot}$) at $a_{bin}=100$ au, with $e_{bin}=0$ and 0.5.
  3. ref: A control case of a disc orbiting a single star ($1 M_{\odot}$).
• Initial Conditions: Discs were initialized with a surface density profile, a gas mass of $0.05 M_{\odot}$, and an initial dust grain size of $60 \mu$m. Simulations evolved for 29 kyr (approx. 2635 binary periods for circumbinary cases) after an initial relaxation phase.

Key Results

1. Density Structure and Mixing:

   • Circumbinary Discs (IB): The inner binary creates an eccentric cavity and induces significant radial and vertical mixing. Dust is depleted in the inner regions ($\lesssim 10-15$ au) and forms a plateau between 10 and 40 au. The binary excites eccentricity in the inner disc, driving turbulent motions that hinder efficient vertical settling and radial drift.
   • Circumstellar Discs (OB): Dust rapidly drifts inward and settles toward the midplane, accumulating at the inner disc edge. In eccentric binaries (OB5), radial drift is enhanced, leading to sharper truncation and higher dust density peaks compared to circular binaries.

2. Grain Growth:

   • Circumbinary Discs: Dust growth is significantly inhibited. The maximum grain size reached is up to five times smaller than in isolated discs. This limitation arises because the binary-induced mixing prevents grains from settling and drifting effectively, keeping them in a regime where they are constantly stirred and unable to reach the high densities required for sustained growth.
   • Circumstellar Discs: Grain growth is comparable to, or slightly enhanced by, the isolated case. In OB5, the maximum grain size is approximately 1.7 times larger than in the reference case, correlating with the higher dust density achieved due to enhanced drift and accumulation.

3. Streaming Instability (SI) and Clumping:

   • Circumbinary Discs: The conditions required to trigger the non-resonant streaming instability (dust-to-gas ratio $\delta_{dg} \gtrsim 1$) are not met anywhere in the disc. The vertical mixing and lower dust densities prevent the onset of strong clumping.
   • Circumstellar Discs: Regions close to the midplane ($z < 1$ au) and extending to $\sim 15$ au satisfy the criteria for the streaming instability. The mass of dust convertible into planetesimals in these regions is comparable between isolated discs and those in binary systems (OB0 and OB5), suggesting that external companions do not significantly alter the potential for planetesimal formation via SI in circumstellar discs.

Significance and Conclusions
The paper concludes that the density structure of a disc is the primary driver of dust growth in these systems.

• Circumbinary Planets: The inhibition of dust growth and the failure to meet streaming instability conditions in the inner regions of circumbinary discs suggest that core accretion is unlikely to occur in situ near the dynamical stability limit. This supports the hypothesis that observed P-type planets near the stability limit formed at larger separations and migrated inward, or formed via gravitational instability.
• Circumstellar Planets: Perturbations from external companions only marginally affect density-driven dust growth compared to isolated systems. Consequently, the formation of S-type planets via core accretion remains viable in the inner regions of circumstellar discs, provided the companion does not truncate the disc so severely that it removes the reservoir of material.

The authors note that these results represent upper limits on grain size, as the current formalism neglects the contribution of non-Keplerian disc kinematics (e.g., differential drift and vertical motions induced by the binary) to the relative collision velocities, which would likely further suppress growth in circumbinary discs. Future work will address these kinematic contributions to provide quantitative predictions.