The time evolution of $M_{\mathrm{d}}/\dot M$ in protoplanetary discs as a way to disentangle between viscosity and MHD winds

TL;DR

This study proposes a method to distinguish between viscous and MHD wind models in protoplanetary disks by analyzing the evolution of the $M_{d}/\dot M$ ratio, using analytical and numerical simulations to identify observable differences.

Contribution

The paper introduces a novel approach combining analytical and 1D simulations to differentiate between viscous and MHD wind-driven disk evolution based on $M_{d}/\dot M$ spread over time.

Findings

The $M_{d}/\dot M$ spread decreases over time in both models.

The decrease is less pronounced in MHD-dominated populations.

Current observations favor the wind model, but future measurements may change this conclusion.

Abstract

As the classic viscous paradigm for protoplanetary disk accretion is challenged by the observational evidence of low turbulence, the alternative scenario of MHD disk winds is being explored as potentially able to reproduce the same observed features traditionally explained with viscosity. Although the two models lead to different disk properties, none of them has been ruled out by observations - mainly due to instrumental limitations. In this work, we present a viable method to distinguish between the viscous and MHD framework based on the different evolution of the distribution in the disk mass ($M_{\mathrm{d}}$) - accretion rate ($\dot M$) plane of a disk population. With a synergy of analytical calculations and 1D numerical simulations, performed with the population synthesis code \texttt{Diskpop}, we find that both mechanisms predict the spread of the observed ratio $M_{\mathrm{d}}/\dot M$ in a disk population to decrease over time; however, this effect is much less pronounced in MHD-dominated populations as compared to purely viscous populations. Furthermore, we demonstrate that this difference is detectable with the current observational facilities: we show that convolving the intrinsic spread with the observational uncertainties does not affect our result, as the observed spread in the MHD case remains significantly larger than in the viscous scenario. While the most recent data available show a better agreement with the wind model, ongoing and future efforts to obtain direct gas mass measurements with ALMA and ngVLA will cause a reassessment of this comparison in the near future.