Stellar feedback in the star formation–gas density relation: Comparison between simulations and observations

Abstract

The impact of stellar feedback on the Kennicutt-Schmidt (KS) law, which relates the star formation rate (SFR) to the surface gas density, is a topic of ongoing debate. The interpretation of high-resolution observations of individual clouds is challenging due to the various processes at play simultaneously and inherent biases. Therefore, a numerical investigation is necessary to understand the role of stellar feedback and identify observable signatures. In this study we investigate the impact of stellar feedback on the KS law, aiming to identify distinct signatures that can be observed and analysed. By employing magnetohydrodynamic simulations of an isolated cloud, we specifically isolate the effects of high-mass star radiation feedback and protostellar jets. High-resolution numerical simulations are a valuable tool for isolating the impact of stellar feedback on the star formation process, while also allowing us to assess how observational biases may affect the derived relation. We used high-resolution (<0.01 pc) magnetohydrodynamic numerical simulations of a 10$^4\ cloud and followed its evolution under different feedback prescriptions. The set of simulations contained four types of feedback: one with only protostellar jets, one with ionising radiation from massive stars (>8 odot $), one with the combination of the two, and one without any stellar feedback. In order to compare these simulations with the existing observational results, we analysed their evolution by adopting the same techniques applied in the observational studies. Then, we simulated how the same analyses would change if the data were affected by typical observational biases: counting young stellar objects (YSO) to estimate the SFR, the limited resolution for the column density maps, and a sensitivity threshold for detecting faint embedded YSOs. Our analysis reveals that the presence of stellar feedback strongly influences the shape of the KS relation and the star formation efficiency per free-fall time (eff ). The impact of feedback on the relation is primarily governed by its influence on the cloud's structure. Additionally, the evolution of eff throughout the star formation event suggests that variations in this quantity can mask the impact of feedback in observational studies that do not account for the evolutionary stage of the clouds. Although the eff measured in our clouds is higher than what is usually observed in real clouds, upon applying prescriptions to mimic observational biases we recover a good agreement with the expected values. From that, we can infer that observations tend to underestimate the total SFR. Moreover, this likely indicates that the physics included in our simulations is sufficient to reproduce the basic mechanisms that contribute to setting eff . We demonstrate the interest of employing numerical simulations to address the impact of early feedback on star formation laws and to correctly interpret observational data. This study will be extended to other types of molecular clouds and ionising stars, sampling different feedback strengths, to fully characterise the impact of regions on star formation.