Environmental interactions in Class II systems and their impact on the disk-planet architecture

Technical Summary: Environmental Interactions in Class II Systems and Their Impact on the Disk-Planet Architecture

Problem Statement
Protoplanetary disks (PPDs) are often modeled as isolated systems, yet observational evidence suggests that approximately 55% of disks in regions like Taurus interact with nearby stars or infalling interstellar gas. While the effects of stellar flybys and gas infall have been studied in the context of early planet formation (Class 0/I) or late-stage debris disks, the intermediate Class II phase—where a substantial gaseous disk coexists with already-formed planets—remains largely unexplored. This paper investigates how these environmental perturbations alter the architecture of Class II systems, specifically focusing on the dynamical evolution of the gas and dust components and their subsequent impact on embedded planets. The study aims to determine if such interactions leave persistent dynamical signatures that could explain the formation of narrow, eccentric debris disks observed in later evolutionary stages.

Methodology
The authors performed three-dimensional hydrodynamical simulations using the Phantom smoothed particle hydrodynamics (SPH) code. The simulation setup modeled a representative Class II system inspired by the general structural characteristics of PDS 70, consisting of:

• A central star ($2 M_\odot$).
• A gas and dust disk extending from 120 to 220 au, initialized with a surface density profile $\Sigma \propto r^{-1}$ and a total gas mass of $10^{-3} M_\odot$.
• Two planets in a 2:1 mean-motion resonance (MMR), with masses of $1 M_{Jup}$ each.
• Five dust species with grain sizes ranging from 9.48 to 1580 $\mu$m, treated using a "dust-as-particles" approach to self-consistently account for dust back-reaction on the gas.

The simulations evolved for 100 outer-planet orbital periods ($T_{out}$) to establish a stable disk-planet configuration. Subsequently, two distinct environmental perturbation scenarios were introduced and evolved for an additional 200 $T_{out}$ (total 300 $T_{out}$):

1. Infall: A gaseous cloudlet (mass $10^{-3} M_\odot$) on a parabolic, prograde, coplanar trajectory with a pericenter of 440 au.
2. Flyby: A passing star ($1 M_\odot$) on a parabolic, prograde, coplanar trajectory with a pericenter of 440 au.
   A control simulation ("Isolated") without external perturbations was also conducted for comparison.

Key Results

• Gas Disk Dynamics:

  • Infall: The infalling cloudlet replenished the disk, increasing its total mass, angular momentum, and energy by approximately 10% and 20%, respectively. This led to a pronounced azimuthal gas overdensity and a significant increase in the Angular Momentum Deficit (AMD), indicating strong dynamical excitation. The excitation persisted for $\sim70 T_{out}$ due to continuous accretion.
  • Flyby: The stellar encounter tidally truncated the disk, removing angular momentum (a $\sim30\%$ drop) and energy. The perturbation was short-lived, with the system relaxing to a steady state in fewer than 5 $T_{out}$.

• Dust Morphology and Dynamics:

  • Infall: The additional gas supply and impact overcame the planetary barrier, allowing the smallest dust grains to migrate inward and form a secondary ring interior to the inner planet. The dust disk developed a coherent, eccentric structure where coupled grains ($St \ll 1$) and decoupled grains ($St \gg 1$) exhibited distinct eccentricity evolutions. The largest grains retained high eccentricities even as the gas circularized.
  • Flyby: The encounter drove gas and dust inward, compressing the dust distribution radially. Unlike the infall case, this scenario produced an inner ring for intermediate-sized grains ($34.1$ and $122 \mu$m) but not the smallest. The flyby induced a broader outer ring and a double-ringed structure for specific grain sizes, driven by radial dynamical excitation.

• Planetary Accretion:

  • Infall: The accretion rate of the inner planet increased significantly (nearly doubling), while the outer planet's accretion was suppressed relative to the isolated case. This is attributed to the injection of angular momentum by the infalling material, which increased gas velocities and hindered efficient accretion by the outer planet.
  • Flyby: Both planets experienced a substantial increase in accretion rates (outer planet $\sim2.5\times$, inner planet $\sim2\times$). The flyby facilitated the inward transport of solid material across planetary orbits, suggesting enhanced solid enrichment and potential changes in planetary metallicity.

Significance and Claims
The paper claims that environmental interactions during the Class II phase can fundamentally reshape disk-planet systems, imprinting dynamical signatures that may persist into the debris disk phase. Specifically:

1. Origin of Eccentric Debris Disks: The study suggests that narrow, eccentric debris disks (such as those around Fomalhaut) may originate from environmental perturbations (infall or flybys) during the PPD phase, rather than solely from secular evolution driven by eccentric planets. The simulations show that both mechanisms can produce coherent, eccentric dust distributions that align with the forced eccentricity of the outer planet.
2. Dust as a Tracer: The results highlight that dust grains with high Stokes numbers (large grains) retain dynamical imprints (eccentricity and pericenter alignment) longer than the gas, potentially tracing the location of planetesimal formation and the history of environmental interactions.
3. Planetary Evolution: The paper posits that flybys may enhance the solid accretion and metallicity of forming planets, while infall events preferentially alter the growth of inner planets.

The authors conclude that while their study utilized a specific set of parameters (coplanar, prograde interactions), the identified structural and dynamical signatures provide a plausible mechanism for the formation of eccentric debris disks and offer a framework for interpreting multi-wavelength observations of systems like HL Tau, ISO-Oph 2, and AS 205.