The impact of disc photoevaporation on the long-term evolution of giant planets in mean motion resonances

TL;DR

This work investigates how disc photoevaporation shapes the long-term evolution and stability of giant planets in mean motion resonances using 2D hydrodynamic simulations with a photoevaporation sink. By varying disc mass, viscosity, planet mass, and resonance type, it identifies a threshold photoevaporation strength above which gas depletion in the common gap weakens planet–disc torques and slows migration, stabilizing otherwise fragile resonances (notably the $3:2$ case) while often raising planetary eccentricities. The results show a complex, system-dependent landscape: in massive discs, resonances can be quickly disrupted absent strong PE, whereas in lighter discs PE-induced gap depletion can preserve resonance and alter eccentricity growth; the $2:1$ resonance is generally robust but can destabilize under high disc mass with strong PE due to torque imbalances. These findings have implications for the final orbital architectures of wide-separation giant planet systems and for Gaia’s ability to detect resonant configurations, offering testable predictions on libration amplitudes and eccentricities.

Abstract

We investigate the long-term impact of disc photoevaporation on the dynamical stability and evolution of giant planet pairs in mean motion resonances. Using two-dimensional hydrodynamical simulations with FARGO3D, in which we have included mass-loss due to photoevaporation, we explore a parameter space covering disc mass, viscosity, planet mass, and resonance type. We find that strong photoevaporation depletes gas in the common gap between the planets, slowing migration and suppressing planet-disc interactions that typically lead to resonance breaking and eccentricity damping. This stabilising effect is most significant for 3:2 resonances, which are more prone to disruption due to the reduced planet spacing. In contrast, 2:1 resonances are generally more robust but can still be destabilised at high disc mass and moderate-to-strong photoevaporation due to asymmetric torques. Photoevaporation can therefore stabilise resonances that would otherwise break, or conversely disrupt resonances that are natively more stable. Even in cases where photoevaporation does not directly affect resonance stability, it typically results in increased planetary eccentricities. These results highlight the complex, system-dependent nature of resonance evolution, with implications for the final orbital architectures of giant planet systems and their detectability via astrometry from missions such as Gaia.

Figures (15)

• Figure 1: The photoevaporation mass loss profile used in our simulations for each photoevaporation strength, from alexander_dust_2007. The initial planet profiles are indicated for the fiducial setup (see section \ref{['results']}). These profiles are only valid in the diffuse radiation field regime, where photoevaporation only happens from the upper layers of the disc. This model prescribes mass loss at radii $\gtrsim$ 0.1 $R_\text{g}$. Given the disc inner boundary is at 1 AU, this means that the entirety of the simulated disc experiences mass loss. The planets are at about 10 AU, where this surface mass loss rate is roughly an order of magnitude weaker than at its peak in the inner disc, although the typical local mass-loss rate $\sim R^2\dot{\Sigma}_{\text{PE}}$ is larger.
• Figure 2: Surface density profiles of the disc at different snapshots, with time shown indicating the time after photoevaporation was activated. The top row shows a disc without photoevaporation and the bottom row shows the results of a disc with $\dot{M}_{\text{PE}} = 10^{-8} \mathrm{M_{\odot}.yr^{-1}}$. The impact of photoevaporation is clear in the common gap at 0.036 Myr, making it deeper. Once the gap is depleted (0.099 Myr onwards), the inner disc is very quickly dispersed since the flow of mass from the outer disc is insufficient to replenish it.
• Figure 3: The azimuthally averaged disc surface density profiles at 0.15 Myr after photoevaporation is activated for each photoevaporation strength. The inner disc boundary surface density drops in all cases due to the boundary conditions, but is more strongly depleted (by a factor of about 10) in the strong photoevaporation case. We notice a two order of magnitude drop of the surface density in the common gap only in the case of strong photoevaporation.
• Figure 4: Comparing the local photoevaporative depletion timescales ($\Sigma/\dot{\Sigma}_{\text{PE}}$) for medium and strong photoevaporation. Outside the gap, only the strong photoevaporation timescale is below the viscous time, explaining the features in Fig. \ref{['fig:1Dsurfdens']}. In the gap region, both strong and medium photoevaporation timescales are below the viscous timescale. Planetary torques contribute to accretion and are not taken into account, explaining why we do not observe any gap deepening in Fig. \ref{['fig:1Dsurfdens']} for medium photoevaporation. The photoevaporation timescale is an order of magnitude lower for strong photoevaporation, explaining why this is the only setup with a deeper gap in the presence of photoevaporation.
• Figure 5: Evolution of the resonant angle (top), planet period ratio (middle) and inner planet eccentricity in the nominal case (bottom). The first phase of the simulation has the planets clear out a gap without any other interactions. During this phase, the pattern in the resonant angle plot is due to the output sampling frequency and has no physical significance. The second phase starts when the planets migrate until they reach resonance (0.1 Myr). At this point, photoevaporation is activated and the simulation enters phase 3. With weak or no photoevaporation, the resonant angle oscillations become larger and larger: a sign of resonance breaking. The period ratio also takes values further and further away from exact commensurability and the eccentricity slowly drops. Strong photoevaporation limits all of these effects, with the eccentricity climbing and the resonance remaining stable until the inner disc dissipates.