Protoplanetary disc population synthesis I. Constraining disc parameters to reproduce disc observations

TL;DR

This study addresses how to reproduce observed protoplanetary disc fractions and accretion rates by tuning disc evolution parameters in a population synthesis framework. It demonstrates that a stellar-mass–dependent viscosity, modeled as α = α_0 M_*^a with a ≈ 1.8 and a biased distribution of α_0, is necessary to recover the observed Ṁ*–M_* relation; including external photoevaporation and a time-varying star formation rate further shapes the distribution of accretion rates and allows low-mass discs to maintain high accretion. A stellar-mass cut-off is used to mimic distance-related observational biases in disc fractions. The results imply that both stellar mass and environment regulate disc evolution and have downstream consequences for planet formation, with extended star formation explaining high accretion in older regions like Upper Scorpius.

Abstract

Context. Protoplanetary discs are the birthplaces of planets. Recent studies highlight the role of stellar mass sampling in determining disc lifetimes from the observed fraction of stars with discs. Low-mass stars tend to host longer-lived discs, allowing planet formation via solid accretion. Observations also reveal a strong correlation between stellar (and substellar) mass and accretion rate, typically following $\dot{M}\propto M_\star^2$. Aims. We aim to identify the optimal parameters of a disc evolution model that reproduces both the observed disc fractions and accretion rates in young stellar populations. Methods. We performed a population synthesis study exploring different dependencies of the viscosity parameter $α$ on stellar mass. Disc evolution includes viscous accretion and photoevaporation (internal and external). Initial disc masses and radii were drawn from observationally motivated distributions, while stellar masses followed a given distribution and a time-dependent star formation rate (SFR) was introduced. Results. Matching observed disc fractions and accretion trends requires $α$ to increase with stellar mass. External photoevaporation is necessary to produce low-mass discs with high accretion rates, and a time-dependent SFR enhances accretion in young clusters while extending disc lifetimes in older ones. A stellar mass cut-off reproduces the distance-dependent biases in observed disc fractions. Conclusions. Both stellar and environmental effects are essential to explain the observed properties of protoplanetary discs. A stellar-mass-dependent viscosity reproduces the $\dot{M}$-$M_\star$ relation, while external photoevaporation and extended star formation histories shape the accretion rate distribution across environments.

Figures (14)

• Figure 1: The orange line represents the probability density of the star formation rate from coleman2022dispersal. The blue histograms show the discrete probability apply for our population synthesis.
• Figure 2: The blue line represents the probability density of the disc masses (in term of the the mass of the host star) obtained by tychoniec2018vla. The dark blue histograms correspond to the disc mass sample for our population synthesis.
• Figure 3: Linear probability distribution for the $\log \alpha_{0}$ between -4 and -2. This distribution favors the presence of high viscosity discs in our population synthesis.
• Figure 4: Top panels. Disc population synthesis results without considering a prolonged SFR. Bottom panels. Results adopting a SFR with a characteristic timescale $t_{\rm d}= 1$ Myr. Left column. Fraction of stars with discs as a function of the age of the cluster. Blue, green and orange points correspond to observations of young stellar clusters within 200 pc, between 200--500 pc and between 500-1000 pc, respectively. The red line represents the fit to cluster within 200 pc Pfalzner_2022. The black line corresponds to the results obtained by MamajekE. The dashed lines represent the results of our population synthesis for different values of the minimum stellar mass considered. The orange, green and blue dashed lines correspond to the minimum stellar masses of $M_{*,m}=1,\,0.1$ and 0.004$M_{\odot}$, respectively. Center column. Histogram (or color density map) for the stellar mass accretion rate as a function of the disc mass at 1.5 Myr from the population synthesis. Orange, magenta, pink, and red points represents the observations compiled in manara2023ASPC. Right column. Stellar mass accretion rate against stellar mass, also at 1.5 Myr of the synthesis evolution. The orange line represents the fit to the observations manara2023ASPC, while the gray line is the fit to our results.
• Figure 5: Similar to Fig.\ref{['Fig:reference']}, but considering the $\alpha$-viscosity parameter as a function of the stellar mass ($\alpha = \alpha_{0} \times M_{*}^{1.8}$) and considering a SFR with $t_{\rm d}= 1$ Myr. The top row corresponds to the results for the population synthesis adopting a uniform distribution for $\alpha_0$, while the bottom row corresponds to consider a linear distribution for $\alpha_0$. In both cases the range of the $\log \alpha_0$ is between -4 and -2.