In the pedestal of a tokamak, the sharp radial gradients of density and temperature can give rise to poloidal variation in the density of impurities. At the same time, the flow of the impurity species is modified relative to the conventional neoclassical result. In this paper, these changes to the density and flow of a collisional impurity species are calculated for the case when the main ions are in the plateau regime. In this regime it is found that the impurity density can be higher at either the inboard or outboard side. This finding differs from earlier results for banana-or PfirschSchlüter-regime main ions, in which case the impurity density is always higher at the inboard side in the absence of rotation. Finally, the modifications to the impurity flow are also given for the other regimes of main-ion collisionality.
A popular theory of star formation is gravito-turbulent fragmentation, in which self-gravitating structures are created by turbulence-driven density fluctuations. Simple theories of isothermal fragmentation successfully reproduce the core mass function (CMF) which has a very similar shape to the initial mass function (IMF) of stars. However, numerical simulations of isothermal turbulent fragmentation thus far have not succeeded in identifying a fragment mass scale that is independent of the simulation resolution. Moreover, the fluid equations for magnetized, self-gravitating, isothermal turbulence are scale-free, and do not predict any characteristic mass. In this paper we show that, although an isothermal self-gravitating flow does produce a CMF with a mass scale imposed by the initial conditions, this scale changes as the parent cloud evolves. In addition, the cores that form undergo further fragmentation and after sufficient time forget about their initial conditions, yielding a scale-free pure power-law distribution dN/dM ∝ M −2 for the stellar IMF. We show that this problem can be alleviated by introducing additional physics that provides a termination scale for the cascade. Our candidate for such physics is a simple model for stellar radiation feedback. Radiative heating, powered by accretion onto forming stars, arrests the fragmentation cascade and imposes a characteristic mass scale that is nearly independent of the timeevolution or initial conditions in the star-forming cloud, and that agrees well with the peak of the observed IMF. In contrast, models that introduce a stiff equation of state for denser clouds but that do not explicitly include the effects of feedback do not yield an invariant IMF.
We analyse the first giant molecular cloud (GMC) simulation to follow the formation of individual stars and their feedback from jets, radiation, winds, and supernovae, using the STARFORGE framework in the GIZMO code. We evolve the GMC for $\sim 9 \rm Myr$, from initial turbulent collapse to dispersal by feedback. Protostellar jets dominate feedback momentum initially, but radiation and winds cause cloud disruption at $\sim 8{{\ \rm per\ cent}}$ star formation efficiency (SFE), and the first supernova at $8.3 \rm Myr$ comes too late to influence star formation significantly. The per-freefall SFE is dynamic, accelerating from 0 to $\sim 18{{\ \rm per\ cent}}$ before dropping quickly to <1 per cent, but the estimate from YSO counts compresses it to a narrower range. The primary cluster forms hierarchically and condenses to a brief (∼1 Myr) compact ($\sim 1 \rm pc$) phase, but does not virialize before the cloud disperses, and the stars end as an unbound expanding association. The initial mass function resembles the Chabrier (2005) form with a high-mass slope α = −2 and a maximum mass of 55M⊙. Stellar accretion takes $\sim 400 \rm kyr$ on average, but $\gtrsim 1\rm Myr$ for >10M⊙ stars, so massive stars finish growing latest. The fraction of stars in multiples increases as a function of primary mass, as observed. Overall, the simulation much more closely resembles reality, compared to previous versions that neglected different feedback physics entirely. But more detailed comparison with synthetic observations will be needed to constrain the theoretical uncertainties.
We present STARFORGE (STAR FORmation in Gaseous Environments): a new numerical framework for 3D radiation MHD simulations of star formation that simultaneously follow the formation, accretion, evolution, and dynamics of individual stars in massive giant molecular clouds (GMCs) while accounting for stellar feedback, including jets, radiative heating and momentum, stellar winds, and supernovae. We use the GIZMO code with the MFM mesh-free Lagrangian MHD method, augmented with new algorithms for gravity, timestepping, sink particle formation and accretion, stellar dynamics, and feedback coupling. We survey a wide range of numerical parameters/prescriptions for sink formation and accretion and find very small variations in star formation history and the IMF (except for intentionally-unphysical variations). Modules for mass-injecting feedback (winds, SNe, and jets) inject new gas elements on-the-fly, eliminating the lack of resolution in diffuse feedback cavities otherwise inherent in Lagrangian methods. The treatment of radiation uses GIZMO’s radiative transfer solver to track 5 frequency bands (IR, optical, NUV, FUV, ionizing), coupling direct stellar emission and dust emission with gas heating and radiation pressure terms. We demonstrate accurate solutions for SNe, winds, and radiation in problems with known similarity solutions, and show that our jet module is robust to resolution and numerical details, and agrees well with previous AMR simulations. STARFORGE can scale up to massive (>105M⊙) GMCs on current supercomputers while predicting the stellar (≳ 0.1M⊙) range of the IMF, permitting simulations of both high- and low-mass cluster formation in a wide range of conditions.
Young massive star clusters spanning ∼ 10 4 − 10 8 M in mass have been observed to have similar surface brightness profiles. We show that recent hydrodynamical simulations of star cluster formation have also produced star clusters with this structure. We argue analytically that this type of mass distribution arises naturally in the relaxation from a hierarchically-clustered distribution of stars into a monolithic star cluster through hierarchical merging. We show that initial profiles of finite maximum density will tend to produce successively shallower power-law profiles under hierarchical merging, owing to certain conservation constraints on the phase-space distribution. We perform N-body simulations of a pairwise merger of model star clusters and find that mergers readily produce the shallow surface brightness profiles observed in young massive clusters. Finally, we simulate the relaxation of a hierarchically-clustered mass distribution constructed from an idealized fragmentation model. Assuming only powerlaw spatial and kinematic scaling relations, these numerical experiments are able to reproduce the surface density profiles of observed young massive star clusters. Thus we bolster the physical motivation for the structure of young massive clusters within the paradigm of hierarchical star formation. This could have important implications for the structure and dynamics of nascent globular clusters.
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