How the gradient of $M_{\rm d}$ versus UV field strength yields insights into the ages of protoplanetary disc populations

TL;DR

The paper tackles how external FUV photoevaporation shapes the median dust disc mass across protoplanetary disc populations and how this relation evolves with age and stellar mass. It uses 1D disc evolution models incorporating either viscosity or MHD winds, plus external and internal photoevaporation, to generate 1000-disc populations across a range of UV fields and turbulence strengths, then analyzes the resulting $M_{\rm dust,med}$ versus $F_{\rm FUV}$ gradients characterized by $\lambda_{\rm UV}$ and $C_{\rm UV}$. The authors find that both the gradient and intercept decline with age, with the rate of decline and the slope depending on $\alpha$, and that more massive stars exhibit steeper gradients; comparisons to the L1641 region constrain $\alpha$ to roughly $10^{-3.5}$–$10^{-2.5}$, while regional age differences may explain north-south variations. These results indicate that the observed gradient can serve as an age and mass diagnostic and provide a pathway to distinguishing viscous versus MHD-wind-dominated angular-momentum transport, given sufficiently precise stellar masses and ages.

Abstract

FUV radiation from massive stars launch photoevaporative winds from the outer regions of protoplanetary discs around other stars, removing gas and dust. Observations have identified a relation between the median dust disc mass and the external UV field strength. Here we use disc evolutionary models to explore how this relation evolves over time, and with respect to other stellar and disc properties. We find that the slope for the relationship $λ_{\rm UV}$ flattens over time as populations age, possibly explaining the differences seen between the L1641-N and L1641-S clusters in Orion A. We determine that $λ_{\rm UV}$ depends on the stellar mass where more massive stars exhibit steeper gradients than their lesser counterparts, in agreement with the differences seen between Herbig and T Tauri stars. Additionally, the strength of the mechanism for angular momentum transport, either viscosity or MHD disc winds, is found to significantly affect $λ_{\rm UV}$ with stronger $α$ values reducing $λ_{\rm UV}$ due to more material accreting on to the central stars in weaker UV environments. Estimates of $λ_{\rm UV}$ from observations of L1641 place preliminary constraints on $α$ to be between $10^{-3.5}$--$10^{-2.5}$, consistent with literature estimates. Further observations in different regions and better classifications of stellar masses will allow us to place stringent constraints on disc evolution properties, improving our understanding of how protoplanetary discs evolve.

Figures (4)

• Figure 1: Disc mass evolution tracks for a single population of viscously evolving ($\alpha=10^{-3}$) protoplanetary discs in a $10^{3} \rm G_0$ environment. The colour shows the frequency of discs with those masses as they temporally evolve. The black line shows the median disc mass.
• Figure 2: Median disc mass for a population of stars as a function of the UV field strength. Different colours represent different ages for the populations ranging between 0.5--3 Myr. The left-hand panel shows the relations for evolving viscous discs, whilst the right-hand panel represents MHD wind driven discs. The lines represent the fits to the data following equation \ref{['eq:fit']}.
• Figure 3: The gradient $\lambda_{\rm UV}$ (left-hand panel) and the intercept $C_{\rm UV}$ (right-hand panel) of the relation between the strength of the UV field and the median disc mass. Different colours denote different values of $\alpha$ for the simulated discs, with $\alpha=10^{-4}$ (blue), $\alpha=10^{-3.5}$ (red), $\alpha=10^{-3}$ yellow), $\alpha=10^{-2.5}$ (purple) and $\alpha=10^{-2}$ (green). Solid lines represent viscous discs, whilst dashed lines represent MHD wind driven discs. The grey patch represents the range in $\lambda_{\rm UV}$ and $C_{\rm UV}$ found by VanTerwisga23, with the black points showing the values found for specific regions.
• Figure 4: Same as Fig. \ref{['fig:gradients']} but showing the gradients for populations of different stellar masses ranging from 0.1--0.2 $\, {\rm M}_{\odot}$ to 0.9--1 $\, {\rm M}_{\odot}$. The value of $\alpha$ was set to $10^{-3}$.