The 3D time evolution of the dust size distribution in protostellar envelopes

¹ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
² Institute of Space Sciences (ICE), CSIC, Campus UAB, Carrer de Can Magrans s/n, 08193 Barcelona, Spain
³ ICREA, Pg. Lluís Companys 23, Barcelona, Spain

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 16 September 2025
Accepted: 11 January 2026

Abstract

Context. Dust plays a fundamental role during protostellar collapse and disk and planet formation. Recent observations suggest that efficient dust growth can begin early in the protostellar envelopes, potentially even before the formation of the disk. Three-dimensional models of protostellar evolution that address multi-size dust growth, gas and dust dynamics, and magnetohydrodynamics (MHD) are required to characterize the dust evolution in the embedded stages of star formation.

Aims. We aim to establish a new framework for dust evolution models that follow in 3D the dust size distribution in both time and space, i.e., MHD models that describe the formation and evolution of star–disk systems at low numerical cost.

Methods. We coupled the COALA dust evolution module that uses the Smoluchowski equations to RAMSES numerical computations, performing the first 3D MHD simulation of protostellar collapse that simultaneously includes polydisperse dust growth modeled by the Smoluchowski equation and dust dynamics in the terminal velocity approximation.

Results. We note that, locally in the protostellar collapse, the dust size distribution deviates significantly from the Mathis–Rumpl–Nordsieck (MRN) distribution due to dust growth. Ice-coated micron-sized grains can rapidly grow in the envelope and survive by not entering the fragmentation regime. The evolution of the dust size distribution is highly inhomogeneous due to the turbulent nature of the collapse and the development of favorable locations, such as outflow cavity walls, which locally enhance the dust-to-gas ratio.

Conclusions. We analyzed the first 3D non-ideal MHD simulations that self-consistently account for dust dynamics and growth during the protostellar stage. Very early in the lifetime of a young embedded protostar, micron-sized grains can grow, and locally the dust size distribution deviates from the initial MRN shape. This new numerical method opens the possibility of treating gas and dust dynamics with dust growth simultaneously in 3D simulations at a low numerical cost for several astrophysical environments.