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

The onset of planet formation is actively under debate. Recent mass measurements of disks around protostars suggest an early start of planet formation in the 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 the Class 0/I disks indicates 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 prescribe the evolution of the disk and the protostar from Class 0 to Class II phase and calculate the disk temperature using radiative transfer models at various stages of the evolution. We use 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. Particularly, we find that if a planet up to ${\sim}5$ M$_{\oplus}$ in the inner ${\sim}5$ au or up to ${\sim}10-50$ M$_{\oplus}$ at radii ${\gtrsim}5$ au was already formed in the early protostellar phase ($t< 2\times 10^5$ 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 ${\sim}50\%$ - could be elevated temperatures rather than the absence of planets.