Using EUV driven external photoevaporation to test viscous evolution of protoplanetary discs

TL;DR

This work seeks to distinguish viscous disc evolution from MHD-wind–driven evolution by exploiting EUV external photoevaporation as a diagnostic. Using analytical diffusion-based theory and 1D numerical simulations, the authors show that viscous discs naturally evolve toward a tight correlation where the accretion rate onto the star matches the external photoevaporative mass-loss rate, $\dot{M}_{acc}\approx\dot{M}_{pe}$, while MHD-wind discs do not exhibit this one-to-one link. The study provides a practical observational test requiring joint measurements of $\dot{M}_{acc}$ and $\dot{M}_{pe}$ for the same discs, with clear predictions for ONC-like environments and for discs at varying distances from ionizing sources. By applying this diagnostic, researchers can robustly constrain the dominant angular momentum transport mechanism in protoplanetary discs and advance our understanding of disc evolution and planet formation.

Abstract

Protoplanetary discs are thought to evolve either through angular momentum transport driven by viscous processes or through angular momentum removal induced by magnetohydrodynamic (MHD) winds. One proposed method to distinguish between these two evolutionary pathways is by comparing mass accretion rates and disc sizes, but observational constraints complicate this distinction. In this study, we investigate how extreme ultraviolet (EUV) external photoevaporation affects the evolution of protoplanetary discs, particularly in environments such as the Orion Nebula Cluster. Using a combination of analytical derivations and 1D numerical simulations, we explore the impact of externally induced mass-loss on disc structure and accretion dynamics. We demonstrate that, in the viscous scenario, there exists a clear, near one-to-one correlation between the mass-loss rate due to external photoevaporative outflows and the mass accretion rate onto the central star. In contrast, MHD wind-driven discs do not exhibit such trend, leading to a distinct evolutionary path. External photoevaporative mass-loss rates and mass accretion rates can both be accurately measured for a population of discs, without a strong model dependence. Thus, our findings provide a robust observational test to distinguish between viscous and MHD wind-driven disc evolution, offering a new approach to constraining angular momentum transport mechanisms in protoplanetary discs. Applying this diagnostic observationally requires joint measurements of $\dot{M}_{\rm acc}$ and $\dot{M}_{\rm pe}$ for the same objects, which are currently scarce in bright HII regions due to contamination and sensitivity limitations.

Figures (10)

• Figure 1: Relevant timescales as a function of disc size for a viscously evolving disc. The viscous timescale (dark navy line) scales as $t_{\nu} \propto R_{\rm d}$, while the timescale for the evolution of the disc's outer radius due to EUV-driven external photoevaporation (yellow solid line) scales as $t_{\rm edge, EUV} \propto R_{\rm d}^{-1/2}$. For an FUV-dominated photoevaporative outflow (orange dashed line), instead, $t_{\rm edge, FUV}$ is independent of $R_{\rm d}$.
• Figure 2: Disc surface density as a function of $x$, at different time steps. It comes from the analytic solution to Eq. \ref{['eq:dimentionless_evolution']}, illustrating the effect of an external photoevaporative outflow at the outer boundary.
• Figure 3: Evolution of the disc surface density profiles for the viscous ($\alpha_{\rm SS}=10^{-3}$) and wind-driven scenarios (top and middle panels, respectively) for an initial disc mass of 0.2 M$_{\odot}$ and scaling radius of 20 au. The disc is located at 0.3 pc from the irradiating source. The dashed black lines in the top and middle panels indicate the evolution of the disc in the absence of external photoevaporation, for each corresponding scenario. The bottom panel shows the evolution of the disc radius and disc mass: squares are used for the viscously evolving discs and circles for the wind-driven discs. Coloured lines and points correspond to $t=0, 0.1, 0.5, 1.0, 2.0, 2.5, 3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2, 4.4$ Myr.
• Figure 4: Evolution of the disc outer radius for the viscous and MHD wind-driven discs presented in Figure \ref{['fig:disc_evolution_0.3pc_alpha1e-3']}. The red dash-dotted line marks the location at which the viscous disc transitions from a photoevaporation-dominated regime to viscous-dominated evolution (see Figure \ref{['fig:timescales']} and Section \ref{['sec:timescales']}).
• Figure 5: Evolution of the mass accretion (blue) and photoevaporative mass-loss (red) rates with respect to the disc size, for the disc presented in Figure \ref{['fig:disc_evolution_0.3pc_alpha1e-3']}. Solid and dashed lines represent the results for the viscous and MHD wind-driven disc, respectively. The blue solid line with lower opacity indicates the values of mass accretion rates for a disc that is not undergoing external photoevaporation. The grey dotted line shows the scaling $\dot{M} \propto R_{\rm d}^{3/2}$. The black arrow indicates time evolution, with the coloured dots highlighting the $t=0$ point.