Mapping the core mass function to the initial mass function

It has been shown that fragmentation within self-gravitating, turbulent molecular clouds (‘turbulent fragmentation’) can naturally explain the observed properties of protostellar cores, including the core mass function (CMF). Here, we extend recently developed analytic models for turbulent fragmentation to follow the time-dependent hierarchical fragmentation of self-gravitating cores, until they reach effectively infinite density (and form stars). We show that turbulent fragmentation robustly predicts two key features of the initial mass function (IMF). First, a high-mass power-law scaling very close to the Salpeter slope, which is a generic consequence of the scale-free nature of turbulence and self-gravity. We predict the IMF slope (−2.3) is slightly steeper than the CMF slope (−2.1), owing to the slower collapse and easier fragmentation of large cores. Secondly, a turnover mass, which is set by a combination of the CMF turnover mass (a couple solar masses, determined by the ‘sonic scale’ of galactic turbulence, and so weakly dependent on galaxy properties), and the equation of state (EOS). A ‘soft’ EOS with polytropic index γ < 1.0 predicts that the IMF slope becomes ‘shallow’ below the sonic scale, but fails to produce the full turnover observed. An EOS, which becomes ‘stiff’ at sufficiently low surface densities Σgas ∼ 5000 M_⊙ pc^(−2), and/or models, where each collapsing core is able to heat and effectively stiffen the EOS of a modest mass (∼0.02 M_⊙) of surrounding gas, are able to reproduce the observed turnover. Such features are likely a consequence of more detailed chemistry and radiative feedback

Comparing models for IMF variation across cosmological time in Milky Way-like galaxies

One of the key observations regarding the stellar initial mass function (IMF) is its near-universality in the Milky Way (MW), which provides a powerful way to constrain different star formation models that predict the IMF. However, those models are almost universally ‘cloud-scale’ or smaller – they take as input or simulate single molecular clouds (GMCs), clumps or cores, and predict the resulting IMF as a function of the cloud properties. Without a model for the progenitor properties of all clouds that formed the stars at different locations in the MW (including ancient stellar populations formed in high redshift, likely gas-rich dwarf progenitor galaxies that looked little like the Galaxy today), the predictions cannot be fully explored nor safely applied to ‘live’ cosmological calculations of the IMF in different galaxies at different cosmological times. We therefore combine a suite of high-resolution cosmological simulations (from the Feedback In Realistic Environments project), which form MW-like galaxies with reasonable star formation properties and explicitly resolve massive GMCs, with various proposed cloud-scale IMF models. We apply the models independently to every star particle formed in the simulations to synthesize the predicted IMF in the present-day galaxy. We explore models where the IMF depends on Jeans mass, sonic or ‘turbulent Bonnor–Ebert’ mass, fragmentation with a polytropic equation of state, or where it is self-regulated by protostellar feedback. We show that all of these models, except the feedback-regulated ones, predict far more variation (∼0.6–1 dex 1σ scatter in the IMF turnover mass) in the simulations than is observed in the MW

From the Top Down and Back Up Again: Star Cluster Structure from Hierarchical Star Formation

Young massive star clusters spanning $\sim 10^4 - 10^8 M_\odot$ in mass have been observed to have similar surface brightness profiles. 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 arbitrary initial profiles will tend to converge to a universal profile under hierarchical merging, owing to phase-space mixing obeying certain conservation constraints. 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 power-law spatial and kinematic scaling relations, these numerical experiments are able to reproduce the surface density profiles of observed young massive star clusters. Thus we provide physical motivation for the structure of young massive clusters within the paradigm of hierarchical star formation. This has important implications for the structure of nascent globular clusters.Comment: 16 pages, 10 figure

Can magnetized turbulence set the mass scale of stars?

Understanding the evolution of self-gravitating, isothermal, magnetized gas is crucial for star formation, as these physical processes have been postulated to set the initial mass function (IMF). We present a suite of isothermal magnetohydrodynamic (MHD) simulations using the GIZMO code that follow the formation of individual stars in giant molecular clouds (GMCs), spanning a range of Mach numbers found in observed GMCs (⁠M∼10−50⁠). As in past works, the mean and median stellar masses are sensitive to numerical resolution, because they are sensitive to low-mass stars that contribute a vanishing fraction of the overall stellar mass. The mass-weighted median stellar mass M₅₀ becomes insensitive to resolution once turbulent fragmentation is well resolved. Without imposing Larson-like scaling laws, our simulations find M₅₀∝∼M₀M⁻³α_(turb)SFE^(1/3) for GMC mass M₀, sonic Mach number M⁠, virial parameter α_(turb), and star formation efficiency SFE = M⋆/M₀. This fit agrees well with previous IMF results from the RAMSES, ORION2, and SPHNG codes. Although M₅₀ has no significant dependence on the magnetic field strength at the cloud scale, MHD is necessary to prevent a fragmentation cascade that results in non-convergent stellar masses. For initial conditions and SFE similar to star-forming GMCs in our Galaxy, we predict M₅₀ to be >20M⊙⁠, an order of magnitude larger than observed (⁠∼2M⊙⁠), together with an excess of brown dwarfs. Moreover, M₅₀ is sensitive to initial cloud properties and evolves strongly in time within a given cloud, predicting much larger IMF variations than are observationally allowed. We conclude that physics beyond MHD turbulence and gravity are necessary ingredients for the IMF

The Necessity of Feedback Physics in Setting the Peak of the Initial Mass Function

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 on to forming stars, arrests the fragmentation cascade and imposes a characteristic mass scale that is nearly independent of the time-evolution 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

Industry 4.0: Mining Physical Defects in Production of Surface-Mount Devices

With the advent of Industry 4.0, production processes have been endowed with intelligent cyber-physical systems generating massive amounts of streaming sensor data. Internet of Things technologies have enabled capturing, managing, and processing production data at a large scale in order to utilize this data as an asset for the optimization of production processes. In this work, we focus on the automatic detection of physical defects in the production of surfacemount devices. We show how to build a classification model based on random forests that efficiently detects defect products with a high degree of precision. In fact, the results of our preliminary experimental analysis indicate that our approach is able to correctly determine defects in a simulated production environment of surface-mount devices with a MCC score of 0.96. We investigate the feasibility of utilizing this approach in realistic settings. We believe that our approach will help to advance the production of surface-mount devices

Live Fast, Die Young: GMC lifetimes in the FIRE cosmological simulations of Milky Way-mass galaxies

We present the first measurement of the lifetimes of giant molecular clouds (GMCs) in cosmological simulations at z = 0, using the Latte suite of FIRE-2 simulations of Milky Way (MW) mass galaxies. We track GMCs with total gas mass ≳10⁵ M⊙ at high spatial (∼1 pc), mass (7100 M⊙), and temporal (1 Myr) resolution. Our simulated GMCs are consistent with the distribution of masses for massive GMCs in the MW and nearby galaxies. We find GMC lifetimes of 5–7 Myr, or 1–2 freefall times, on average, with less than 2 per cent of clouds living longer than 20 Myr. We find decreasing GMC lifetimes with increasing virial parameter, and weakly increasing GMC lifetimes with galactocentric radius, implying that environment affects the evolutionary cycle of GMCs. However, our GMC lifetimes show no systematic dependence on GMC mass or amount of star formation. These results are broadly consistent with inferences from the literature and provide an initial investigation into ultimately understanding the physical processes that govern GMC lifetimes in a cosmological setting