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Register a new userThe sensitivity of stellar feedback to IMF averaging versus IMF sampling in galaxy formation simulations
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Matthew C. Smith
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Galaxy formation simulations frequently use Initial Mass Function (IMF) averaged feedback prescriptions, where star particles are assumed to represent single stellar populations that fully sample the IMF. This approximation breaks down at high mass resolution, where stochastic variations in stellar populations become important. We discuss various schemes to populate star particles with stellar masses explicitly sampled from the IMF. We use Monte Carlo numerical experiments to examine the ability of the schemes to reproduce an input IMF in an unbiased manner while conserving mass. We present our preferred scheme which can easily be added to pre-existing star formation prescriptions. We then carry out a series of high resolution isolated simulations of dwarf galaxies with supernovae, photoionization and photoelectric heating to compare the differences between using IMF averaged feedback and explicitly sampling the IMF. We find that if supernovae are the only form of feedback, triggering individual supernovae from IMF averaged rates gives identical results to IMF sampling. However, we find that photoionization is more effective at regulating star formation when IMF averaged rates are used, creating more, smaller H II regions than the rare, bright sources produced by IMF sampling. We note that the increased efficiency of the IMF averaged feedback versus IMF sampling is not necessarily a general trend and may be reversed depending on feedback channel, resolution and other details. However, IMF sampling is always the more physically motivated approach. We conservatively suggest that it should be used for star particles less massive than $sim500,mathrm{M_odot}$.
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(abridged) We develop a model which describes the coevolution of the mass function of dense cores and of the IMF in a protocluster clump. In the model, cores injected in the clump evolve under the effect of gas accretion. Accretion onto the cores follows a time-dependent accretion rate that describes accretion in a turbulent medium. Once the accretion timescales of cores exceed their contraction timescales, they are turned into stars. We include the effect of feedback by the newly formed massive stars through their stellar winds. A fraction of the winds energy is assumed to counter gravity and disperse the gas from the protocluster and as a consequence, quench further star formation. The latter effect sets the final IMF of the cluster. We apply our model to a clump that is expected to resemble the progenitor clump of the Orion Nebula Cluster (ONC). Our model is able to reproduce both the shape and normalization of the ONCs IMF and the mass function of dense cores in Orion. The complex features of the ONCs IMF,i.e., a shallow slope in the mass range ~0.3-2.5 Msol,a steeper slope in the mass range ~2.5-12 Msol, and a nearly flat tail at the high mass end are reproduced. The model predicts a rapid star formation process with an age spread for the stars of 2.3 10^5 yr which is consistent with the fact that 80% of the ONCs stars have ages of <=0.3 Myr. The model predicts a primordial mass segregation with the most massive stars being born in the region between 2-4 times the core radius of the cluster. In parallel, the model also reproduces, simultaneously, the mass function of dense cores in Orion. We study the effects of varying the model parameters on the resulting IMF and show that the IMF of stellar clusters is expected to show significant variations, provided variations in the clumps and cores properties exist.
Some ultra-compact dwarf galaxies have large dynamical mass to light (M/L) ratios and also appear to contain an overabundance of LMXB sources, and some Milky Way globular clusters have a low concentration and appear to have a deficit of low-mass stars. These observations can be explained if the stellar IMF becomes increasingly top-heavy with decreasing metallicity and increasing gas density of the forming object. The thus constrained stellar IMF then accounts for the observed trend of metallicity and M/L ratio found amongst M31 globular star clusters. It also accounts for the overall shift of the observationally deduced galaxy-wide IMF from top-light to top-heavy with increasing star formation rate amongst galaxies. If the IMF varies similarly to deduced here, then extremely young very massive star-burst clusters observed at a high redshift would appear quasar-like (Jerabkova et al. 2017) .
Various heuristic approaches to model unresolved supernova (SN) feedback in galaxy formation simulations exist to reproduce the formation of spiral galaxies and the overall inefficient conversion of gas into stars. Some models, however, require resolution dependent scalings. We present a sub-resolution model representing the three major phases of supernova blast wave evolution $-$free expansion, energy conserving Sedov-Taylor, and momentum conserving snowplow$-$ with energy scalings adopted from high-resolution interstellar-medium simulations in both uniform and multiphase media. We allow for the effects of significantly enhanced SN remnant propagation in a multiphase medium with the cooling radius scaling with the hot volume fraction, $f_{mathrm{hot}}$, as $(1 - f_{mathrm{hot}})^{-4/5}$. We also include winds from young massive stars and AGB stars, Stromgren sphere gas heating by massive stars, and a gas cooling limiting mechanism driven by radiative recombination of dense HII regions. We present initial tests for isolated Milky-Way like systems simulated with the GADGET based code SPHgal with improved SPH prescription. Compared to pure thermal SN input, the model significantly suppresses star formation at early epochs, with star formation extended both in time and space in better accord with observations. Compared to models with pure thermal SN feedback, the age at which half the stellar mass is assembled increases by a factor of 2.4, and the mass loading parameter and gas outflow rate from the galactic disk increase by a factor of 2. Simulation results are converged for a two order of magnitude variation in particle mass in the range (1.3$-$130)$times 10^4$ solar masses.
Over the past years observations of young and populous star clusters have shown that the stellar initial mass function (IMF) can be conveniently described by a two-part power-law with an exponent alpha_2 = 2.3 for stars more massive than about 0.5 Msol and an exponent of alpha_1 = 1.3 for less massive stars. A consensus has also emerged that most, if not all, stars form in stellar groups and star clusters, and that the mass function of these can be described as a power-law (the embedded cluster mass function, ECMF) with an exponent beta ~2. These two results imply that the integrated galactic IMF (IGIMF) for early-type stars cannot be a Salpeter power-law, but that they must have a steeper exponent. An application to star-burst galaxies shows that the IGIMF can become top-heavy. This has important consequences for the distribution of stellar remnants and for the chemo-dynamical and photometric evolution of galaxies. In this contribution the IGIMF theory is described, and the accompanying contribution by Pflamm-Altenburg, Weidner & Kroupa (this volume) documents the applications of the IGIMF theory to galactic astrophysics.
We address the turbulent fragmentation scenario for the origin of the stellar initial mass function (IMF), using a large set of numerical simulations of randomly driven supersonic MHD turbulence. The turbulent fragmentation model successfully predicts the main features of the observed stellar IMF assuming an isothermal equation of state without any stellar feedback. As a test of the model, we focus on the case of a magnetized isothermal gas, neglecting stellar feedback, while pursuing a large dynamic range in both space and timescales covering the full spectrum of stellar masses from brown dwarfs to massive stars. Our simulations represent a generic 4 pc region within a typical Galactic molecular cloud, with a mass of 3000 Msun and an rms velocity 10 times the isothermal sound speed and 5 times the average Alfven velocity, in agreement with observations. We achieve a maximum resolution of 50 au and a maximum duration of star formation of 4.0 Myr, forming up to a thousand sink particles whose mass distribution closely matches the observed stellar IMF. A large set of medium-size simulations is used to test the sink particle algorithm, while larger simulations are used to test the numerical convergence of the IMF and the dependence of the IMF turnover on physical parameters predicted by the turbulent fragmentation model. We find a clear trend toward numerical convergence and strong support for the model predictions, including the initial time evolution of the IMF. We conclude that the physics of isothermal MHD turbulence is sufficient to explain the origin of the IMF.
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