Hidden under a warm blanket: If planets existed in protostellar disks, they would hardly produce observable substructures

¹ European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching, Germany
² Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
³ Dipartimento di Fisica ‘Aldo Pontremoli’, Università degli Studi di Milano, via G. Celoria 16, 20133 Milano, Italy

^★ Corresponding author: pooneh.nazari@eso.org

Received: 14 June 2024
Accepted: 31 January 2025

Abstract

The onset of planet formation is actively under debate. Recent mass measurements of disks around protostars suggest an early start for planet formation in class 0/I disks. However, dust substructures, one possible signature of forming planets, are rarely observed in the young class 0/I disks, while they are ubiquitous in the mature class II disks. It is not clear whether the lack of dust substructures in class 0/I disks indicates an absence of planets or whether it is due to other physical effects such as temperature and dust opacity. Here, we consider the effect of temperature on the ability of planets to produce dust substructures. We prescribed the evolution of the disk and the protostar from class 0 to the class II phase and calculated the disk temperature using radiative transfer models at various stages of the evolution. We used the mid-plane temperature to calculate the disk scale height and the minimum planet mass needed to open observable dust gaps using the thermal criterion. We find that this minimum planet mass decreases as a function of time. In particular, we find that if a planet up to ∼5 M_⊕ in the inner ∼5 au or up to ∼10−50 M_⊕ at radii ≳5 au were already formed in the early protostellar phase (t < 2 × 10⁵ yr), it would barely produce any dust substructures. We conclude that a major contribution to the observed lack of substructures (if produced by planets) in the early protostellar phase – lowering their frequency by ∼50% – could be elevated temperatures rather than the absence of planets.