STARFORGE: the effects of protostellar outflows on the IMF

Abstract

The initial mass function (IMF) of stars is a key quantity affecting almost every field of astrophysics, yet it remains unclear what physical mechanisms determine it. We present the first runs of the STARFORGE project, using a new numerical framework to follow the formation of individual stars in giant molecular clouds (GMCs) using the GIZMO code. Our suite includes runs with increasingly complex physics, starting with isothermal ideal magnetohydrodynamics (MHD) and then adding non-isothermal thermodynamics and protostellar outflows. We show that without protostellar outflows the resulting stellar masses are an order of magnitude too high, similar to the result in the base isothermal MHD run. Outflows disrupt the accretion flow around the protostar, allowing gas to fragment and additional stars to form, thereby lowering the mean stellar mass to a value similar to that observed. The effect of jets upon global cloud evolution is most pronounced for lower-mass GMCs and dense clumps, so while jets can disrupt low-mass clouds, they are unable to regulate star formation in massive GMCs, as they would turn an order unity fraction of the mass into stars before unbinding the cloud. Jets are also unable to stop the runaway accretion of massive stars, which could ultimately lead to the formation of stars with masses >500 M⊙. Although we find that the mass scale set by jets is insensitive to most cloud parameters (i.e., surface density, virial parameter), it is strongly dependent on the momentum loading of the jets (which is poorly constrained by observations) as well the the temperature of the parent cloud, which predicts slightly larger IMF variations than observed. We conclude that protostellar jets play a vital role in setting the mass scale of stars, but additional physics are necessary to reproduce the observed IMF.

The dynamics and outcome of star formation with jets, radiation, winds, and supernovae in concert

“…In Grudić et al (2021a) (hereafter Paper I) we introduced the more-advanced STARFORGE 1 framework for the GIZMO code, combining modules for gravity, N-body dynamics, MHD, radiative transfer, cooling and chemical physics, (proto-)stellar evolution, and feedback in the form of accretion-and fusion-powered radiation from stars and protostars, stellar winds, protostellar jets, and core-collapse supernovae. And in Guszejnov et al (2021) (hereafter Paper II) we used STAR-FORGE to re-run our GMC models with the addition of realistic ISM cooling/heating physics and protostellar jet feedback, finding that jet feedback in particular is crucial for moderating the growth of individual stars and recovering a realistic IMF, in agreement with other IMF studies with jet feedback (Hansen et al 2012;Krumholz et al 2012;Myers et al 2013;Federrath et al 2014;Mathew & Federrath 2021).…”

“…Overall, where key hallmarks of star formation are concerned, such as the IMF, star formation efficiency, stellar accretion, star cluster kinematics, and stellar multiplicity, we have reached the point where there is no longer any blatantly unphysical prediction from the model that must be fixed with additional physics, as was the case before various important mechanisms like magnetic fields and feedback were accounted for (Guszejnov et al 2018(Guszejnov et al , 2020(Guszejnov et al , 2021. On some level, the simulation successfully reproduces these key phenomenaif and only if such physics is included.…”

“…The first massive stars have finished accreting by 4Myr, clearing out their environment via feedback and ionizing their immediate surroundings, but the influence of feedback on the morphology, kinematics, and thermal state of the cloud is still limited. The velocity map shows that the cloud is permeated by high-velocity outflows, but this difficult to see in the gas or dust mass-weighted morphology (Krumholz et al 2012;Guszejnov et al 2021).…”

Seeds don’t sink: even massive black hole ‘seeds’ cannot migrate to galaxy centres efficiently

“…To do so, we re-calculate the trajectories of a huge number of BH "test particles," taking background potentials from the simulations and adding an analytic DF force explicitly in post-processing, during which we apply a newly developed DF estimator that is discussed in a companion paper (Ma et al in prep.). We approximate the N-body dynamics of a seed of mass M with an acceleration aM = aext + adf, where aext is the "normal" external gravitational acceleration on a test particle (computed identically to how the forces 3 We enable the additional improvements to the gravitational timestep criteria, tidal force treatment, tree-opening, and integration accuracy detailed in Guszejnov et al (2020); where they were developed for simulations of star formation which require accurate evolution of stellar binaries and multiples, and set the force softening of the BH seeds to a very small value (10 −3 pc) to represent real sink particles while using adaptive force softening for all other types to represent a smooth background. Detailed studies have shown that using adaptive softening as we do to ensure a smooth background force and with the more strict timestep and integration accuracy criteria used here, DF-like forces can be accurately captured for BHs with masses 10 times the background particle mass, while with less accurate integration often used in cosmological simulations which do not intend to resolve few-body effects, the pre-factor is more like ∼ 100 (van den Bosch et al 1999;Colpi et al 2007;Boylan-Kolchin et al 2008;Hopkins et al 2018;Pfister et al 2019;Barausse et al 2020;Boldrini et al 2020).…”

The Single-Cloud Star Formation Relation

“…On the other hand, if a KS relation does hold within single clouds, particularly those containing no stars massive enough to produce supernovae, this implies that some smaller-scale or more universal mechanism inhibits star formation within individual molecular clouds. These mechanisms include turbulence, magnetic fields (Krumholz & McKee 2005;Federrath & Klessen 2012) or stellar feedback in the form of protostellar outflows, stellar winds and ionizing radiation (Krumholz et al 2012b;Federrath 2015;Xu et al 2020;Guszejnov et al 2021).…”