The survivorship bias of protoplanetary disc populations

Internal photoevaporation causes an apparent increase in the median total disc mass with time

¹ Dipartimento di Fisica ‘Aldo Pontremoli’, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
² European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching bei München, Germany
³ Max-Planck Institute for Astronomy (MPIA), Königstuhl 17, 69117 Heidelberg, Germany
⁴ Fakultat für Physik, Ludwig-Maximilians-Universität München, Scheinersts. 1, 81679 München, Germany
⁵ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40122 Bologna, Italy
⁶ INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy

^★ Corresponding author: lorenzo.malanga@unimi.it

Received: 26 March 2025
Accepted: 6 May 2025

Abstract

The evolution of protoplanetary discs has a substantial impact on theories of planet formation. To date, neither of the two main competing evolutionary models – namely, the viscous-photoevaporative paradigm nor the MHD winds model – has been ruled out by observations. Due to the high number of sources observed by large surveys, population synthesis is a powerful tool to distinguish the evolution mechanism in observations. We explored the evolution of the mass distribution of synthetic populations under the assumption of turbulence-driven accretion and dispersal caused by internal photoevaporation. We find that the rapid removal of light discs often results in an apparent increase in the median mass of the surviving disc population. This occurs both when disc properties are independent of each other, and when typical correlations between these quantities and stellar mass are assumed. Furthermore, as MHD wind-driven accretion rarely manifests the same features, this serves as a signature of the viscous-photoevaporative evolution when dispersal proceeds from the inside out. Therefore, we propose the evolution of median mass as a new method to distinguish this model in observed populations. The median accretion rate, which decreases with time, does not show this survivorship bias. Moreover, we introduce a new criterion that estimates disc lifetime as a function of initial conditions and an analytical relation to predict whether internal photoevaporation triggers an inside-out or an outside-in dispersal. We verify both analytical relations with numerical simulations.