The IMF of stellar clusters: effects of accretion and feedback
Sami Dib, Mohsen Shadmehri, Paolo Padoan, G. Maheswar, D. K. Ojha, Fazeleh Khajenabi
备注：
accepted to MNRAS. 22 pages, 17 figures. 2 new sections added to better present the model parameters and compare to previous work. Some figures are now better presented. Main conclusions unchanged
(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 wind's 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 ONC's IMF and the mass function of dense cores in Orion. The complex features of the ONC's 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 ONC's 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.
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 ou…
We perform a series of three-dimensional, magnetohydrodynamical (MHD) simulations of star cluster formation including gravity, turbulence, magnetic fields, stellar radiative heating and outflow feedback. We observe that the inclusion of protostellar outflows (1) reduces the star formation rate by a factor of $\sim2$, (2) increases fragmentation, and (3) shifts the initial mass function (IMF) to lower masses by a factor of $2.0\pm0.2$, without significantly affecting the overall shape of the IMF. The form of the sink particle (protostellar objects) mass distribution obtained from our simulation…
Explaining the initial mass function (IMF) of stars is a long-standing problem in astrophysics. The number of complex mechanisms involved in the process of star cluster formation, such as turbulence, magnetic fields and stellar feedback, make understanding and modeling the IMF a challenging task. In this paper, we aim to assert the importance of stellar heating feedback in the star cluster formation process and its effect on the shape of the IMF. We use an analytical sub-grid model to implement the radiative feedback in fully three-dimensional magnetohydrodynamical (MHD) simulations of star cl…
TODDLERS 2.0: Stellar feedback and observables across diverse IMFs, binary populations, and cloud environments
Département de Physique, de Génie Physique et d’Optique, Université Laval（拉瓦尔大学物理、物理工程与光学系）；Centre de Recherche en Astrophysique du Québec (CRAQ)（魁北克天体物理学研究中心）
Observational and theoretical arguments increasingly suggest that the initial mass function (IMF) of stars may depend systematically on environment, yet most galaxy formation models to date assume a universal IMF. Here we investigate simulations of the formation of Milky Way analogues run with an empirically derived metallicity-dependent IMF and the moving-mesh code AREPO in order to characterize the associated uncertainties. In particular, we compare a constant Chabrier and a varying metallicity-dependent IMF in cosmological, magneto-hydrodynamical zoom-in simulations of Milky Way-sized halos…
Using high-resolution simulations from the FIRE-2 (Feedback In Realistic Environments) project, we study the effects of discreteness in stellar feedback processes on the evolution of galaxies and the properties of the interstellar medium (ISM). We specifically consider the discretization of supernovae (SNe), including hypernovae (HNe), and sampling the initial mass function (IMF). We study these processes in cosmological simulations of dwarf galaxies with $z=0$ stellar masses $M_{\ast}\sim 10^{4}-3\times10^{6}\,M_\odot$ (halo masses $\sim 10^{9}-10^{10}\,M_\odot$). We show that the discrete na…
Star formation is regulated through a variety of feedback processes. In this study, we treat feedback by X-rays and discuss its implications. Our aim is to investigate whether star formation is significantly affected when a star forming cloud resides in the vicinity of a strong X-ray source. We perform an Eulerian grid simulation with embedded Lagrangian sink particles of a collapsing molecular cloud near a massive, 10^7 M_o black hole. The chemical and thermal changes caused by radiation are incorporated into the FLASH code. When there is strong X-ray feedback the star forming cloud fragments…
We report on a series of numerical simulations of gas clouds with self-gravity forming sink particles, adopting an isothermal equation of state to isolate the effects of gravity from thermal physics on the resulting sink mass distributions. Simulations starting with supersonic velocity fluctuations develop sink mass functions with a high-mass power-law tail $dN/d\log M \propto M^Γ$, $Γ= -1 \pm 0.1$, independent of the initial Mach number of the velocity field. Similar results but with weaker statistical significance hold for a simulation starting with initial density fluctuations. This mass fu…
Cosmological simulations are reaching the resolution necessary to study ultra-faint dwarf galaxies. Observations indicate that in small populations, the stellar initial mass function (IMF) is not fully populated; rather, stars are sampled in a way that can be approximated as coming from an underlying probability density function. To ensure the accuracy of cosmological simulations in the ultra-faint regime, we present an improved treatment of the IMF. We implement a self-consistent, stochastically populated IMF in cosmological hydrodynamic simulations. We test our method using high-resolution s…
We review star formation in molecular clouds and describe why magnetic fields may be important and how they can influence filamentary structure and the column density probability distribution function (PDF). We also comment on the origin of the stellar and substellar initial mass function (IMF), which may require explanations beyond a simple Jeans length argument in turbulent molecular clouds. A mathematical model of the modified lognormal power-law (MLP) distribution function provides a framework within which to connect accretion processes with the IMF.
In the present work we examined the hypothesis that, a core mass function (CMF), such as the one deduced for cores in the Orion molecular cloud (OMC), could possibly be the primogenitor of the stellar initial mass function (IMF). Using the rate of accretion of a protostar from its natal core as a free parameter, we demonstrate its quintessential role in determining the shape of the IMF. By varying the rate of accretion, we show that a stellar mass distribution similar to the universal IMF could possibly be generated starting from either a typical CMF such as the one for the OMC, or a uniform d…
A universal stellar initial mass function (IMF) should not be expected from theoretical models of star formation, but little conclusive observational evidence for a variable IMF has been uncovered. In this paper, a parameterization of the IMF is introduced into photometric template fitting of the COSMOS2015 catalog. The resulting best-fit templates suggest systematic variations in the IMF, with most galaxies exhibiting top-heavier stellar populations than in the Milky Way. At fixed redshift, only a small range of IMFs are found, with the typical IMF becoming progressively top-heavier with incr…
Bright Galaxies at Cosmic Dawn: A Cloud-Scale Star Formation Model Unifying Variable SFE, IMFs, and Stochasticity
Max Planck Institut für Astrophysik（马克斯·普朗克天体物理学研究所）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Cosmic Dawn Center (DAWN)（宇宙黎明中心）；Department of Astrophysics, University of Vienna（维也纳大学天体物理系）
FORGE'd in FIRE III: The IMF in Quasar Accretion Disks from STARFORGE
California Institute of Technology（加州理工学院）；Carnegie Observatories（卡内基观测站）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of California, San Diego（加利福尼亚大学圣迭戈分校）
We use a series of magnetohydrodynamic simulations including both radiative and protostellar outflow feedback to study the environmental variation of the initial mass function. The simulations represent a carefully-controlled experiment whereby we keep all dimensionless parameters of the flow constant except for those related to feedback. We show that radiation feedback suppresses the formation of lower mass objects more effectively as the surface density increases, but this only partially compensates for the decreasing Jeans mass in denser environments. Similarly, we find that protostellar ou…
We present an analysis of star-forming gas cores in an SPH simulation of a Giant Molecular Cloud. We identify cores using their deep potential wells. This yields a smoother distribution with clearer boundaries than density. Additionally, this gives an indication of future collapse, as bound potential cores (p-cores) represent the earliest stages of fragmentation in molecular clouds. We find that the mass function of the p-cores resembles the stellar IMF and the observed clump mass function, although p-core masses (~0.7 Msol) are smaller than typical density clumps. The bound p-cores are genera…
One of the key mysteries of star formation is the origin of the stellar initial mass function (IMF). The IMF is observed to be nearly universal in the Milky Way and its satellites, and significant variations are only inferred in extreme environments, such as the cores of massive elliptical galaxies. In this work we present simulations from the STARFORGE project that are the first cloud-scale RMHD simulations that follow individual stars and include all relevant physical processes. The simulations include detailed gas thermodynamics, as well as stellar feedback in the form of protostellar jets,…
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 which formed the stars at different locations in the MW (including ancient stellar populations…
We describe the use of our chemical evolution model to reproduce the abundance patterns observed in a catalog of elliptical galaxies from the SDSS DR4. The model assumes ellipticals form by fast gas accretion, and suffer a strong burst of star formation followed by a galactic wind which quenches star formation. Models with fixed IMF failed in simultaneously reproducing the observed trends with the galactic mass. So, we tested a varying IMF; contrary to the diffused claim that the IMF should become bottom heavier in more massive galaxies, we find a better agreement with data by assuming an inve…
Magnetic fields play an important role in the dynamics of present-day molecular clouds. Recent work has shown that magnetic fields are equally important for primordial clouds, which form the first stars in the Universe. While the primordial magnetic field strength on cosmic scales is largely unconstrained, theoretical models strongly suggest that a weak seed field existed in the early Universe. We study how the amplification of such a weak field can influence the evolution of accretion discs around first stars, and thus affect the primordial initial mass function (IMF). We perform a suite of 3…
Low-mass population III (PopIII) stars of $\lesssim 0.8 M_{\odot}$ could survive up until the present. Non-detection of low-mass PopIII stars in our Galaxy has already put a stringent constraint on the initial mass function (IMF) of PopIII stars, suggesting that PopIII stars have a top-heavy IMF. On the other hand, some claims that the lack of such stars stems from metal enrichment of their surface by accretion of heavy elements from interstellar medium (ISM). We investigate effects of the stellar wind on the metal accretion onto low-mass PopIII stars because accretion of the local ISM onto th…
Using new long-slit spectroscopy obtained with X-Shooter at ESO-VLT, we study, for the first time, radial gradients of optical and Near-Infrared IMF-sensitive features in a representative sample of galaxies at the very high-mass end of the galaxy population. The sample consists of seven early-type galaxies (ETGs) at $z\sim0.05$, with central velocity dispersion in the range $300<σ<350$km/s. Using state-of-art stellar population synthesis models, we fit a number of spectral indices, from different chemical species (including TiO's and Na indices), to constrain the IMF slope (i.e. the fraction o…
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 dwa…
The possibility that the stellar initial mass function (IMF) arises mostly from cloud structure is investigated with fractal Brownian motion (fBm) clouds that have power-law power spectra. An fBm cloud with a realistic projected power spectrum slope of $β=2.8$ is found to have a mass function for clumps exceeding a threshold density that is a power-law with a slope of $α=2.35$, the same as in the Salpeter IMF. Any hierarchically structured cloud has a clump mass function with about the same slope. This result implies that turbulent interstellar clouds produce dense substructure with the observ…
We investigate the star formation and chemical evolution in the early universe by considering the merging history of the Galaxy in the ΛCDM scenario according to the extended Press-Schechter theory. We give some possible constraints from comparisons with observation of extremely metal-poor (EMP) stars. We demonstrate that (1) The hierarchical structure formation can explain the characteristics of the observed metallicity distribution function (MDF) including a break around [Fe/H]~-4. (2) A high mass IMF of peak mass ~10Msun with the contribution of binaries, derived from the statistics of carb…
Self-regulated galaxy evolution within a self-consistently varying galaxy-wide IMF
Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn（波恩大学赫尔姆霍兹射线与核物理研究所）；Argelander-Institut für Astronomie, Universität Bonn（波恩大学阿尔格兰德天文学研究所）；Astronomical Institute, Faculty of Mathematics and Physics, Charles University（查理大学数学与物理学院天文研究所）；Department of Astrophysics, University of Vienna（维也纳大学天体物理学系）
We introduce a new multi-power-law distribution for the Initial Mass Function (IMF) to explore its potential properties. It follows on prior work that introduced mechanisms accounting for mass accretion in star formation, developed within the framework of general evolution equations for the mass distribution of accreting and non-accreting (proto)stars. This paper uses the same fundamental framework to demonstrate that the interplay between a mass-dependent and a time-dependent step-like dropout rate from accretion leads to IMFs that exhibit multiple power laws for an exponential mass growth. W…
Using self-consistent chemodynamical simulations including star formation, supernova feedback, and chemical enrichment, I show the dependence of cosmic star formation and chemical enrichment histories on the initial mass function (IMF). The effects of Pop-III IMF can be only seen in the elemental abundance ratios at z>4 or [Fe/H]<-2. The preferable IMF has a flatter slope in the case of high star formation rate (SFR) and smaller upper-mass (~20Msun) in the case of low SFR, which is consistent with the observed elemental abundances of dwarf spheroidal galaxies. However, the [alpha/Fe] problem o…
We introduce a new dual power law (DPL) probability distribution function for the mass distribution of stellar and substellar objects at birth, otherwise known as the initial mass function (IMF). The model contains both deterministic and stochastic elements, and provides a unified framework within which to view the formation of brown dwarfs and stars resulting from an accretion process that starts from extremely low mass seeds. It does not depend upon a top down scenario of collapsing (Jeans) masses or an initial lognormal or otherwise IMF-like distribution of seed masses. Like the modified lo…
A wealth of observations recently challenged the notion of a universal stellar initial mass function (IMF) by showing evidences in favour of a variability of this statistical indicator as a function of galaxy properties. I present predictions from the semi-analytic model GAEA (GAlaxy Evolution and Assembly), which features (a) a detailed treatment of chemical enrichment, (b) an improved stellar feedback scheme, and (c) implements theoretical prescriptions for IMF variations. Our variable IMF realizations predict intrinsic stellar masses and mass-to-light ratios larger than those estimated from…
Motivated by the observed bottom-light initial mass function (IMF) in faint dwarfs, we study how a metallicity-dependent IMF affects the feedback budget and observables of an ultra-faint dwarf galaxy. We model the evolution of a low-mass ($\approx 8 \, \times \, 10^{8} \, \rm M_{\odot}$) dark matter halo with cosmological, zoomed hydrodynamical simulations capable of resolving individual supernovae explosions, which we complement with an empirically motivated subgrid prescription for systematic IMF variations. In this framework, at the low gas metallicities typical of faint dwarfs, the IMF of …
Star cluster formation is unlikely to be a sudden event: instead, matter will flow to a cluster's formation site over an extended period, even as stars form and inject energy to the region. A cluster's gaseous precursor must persist under the competing influences of accretion and feedback for several crossing times, insofar as star formation is a slow process. The new-born stellar cluster should therefore preserve a memory of this competition. Using analytical approximations we assess the dynamical state of the gas, mapping regimes in which various types of feedback are weak or strong. Protost…
A model of core-clump accretion with equally likely stopping describes star formation in the dense parts of clusters, where models of isolated collapsing cores may not apply. Each core accretes at a constant rate onto its protostar, while the surrounding clump gas accretes as a power of protostar mass. Short accretion flows resemble Shu accretion, and make low-mass stars. Long flows resemble reduced Bondi accretion and make massive stars. Accretion stops due to environmental processes of dynamical ejection, gravitational competition, and gas dispersal by stellar feedback, independent of initia…
We investigate the physics that drives the gas accretion rates onto galaxies at the centers of dark matter haloes using the EAGLE suite of hydrodynamical cosmological simulations. We find that at redshifts $z{\le}2$ the accretion rate onto the galaxy increases with halo mass in the halo mass range $10^{10}-10^{11.7}M_{\odot}$, flattens between the halo masses $10^{11.7}-10^{12.7}M_{\odot}$, and increases again for higher-mass haloes. However, the galaxy gas accretion does not flatten at intermediate halo masses when AGN feedback is switched off. To better understand these trends, we develop a …
One model for the origin of typical galactic star clusters such as the Orion Nebula Cluster (ONC) is that they form via the rapid, efficient collapse of a bound gas clump within a larger, gravitationally-unbound giant molecular cloud. However, simulations in support of this scenario have thus far have not included the radiation feedback produced by the stars; radiative simulations have been limited to significantly smaller or lower density regions. Here we use the ORION adaptive mesh refinement code to conduct the first ever radiation-hydrodynamic simulations of the global collapse scenario fo…
It is speculated that the accretion of material onto young protostars is episodic. We present a computational method to include the effects of episodic accretion in radiation hydrodynamic simulations of star formation. We find that during accretion events protostars are "switched on", heating and stabilising the discs around them. However, these events typically last only a few hundred years, whereas the intervals in between them may last for a few thousand years. During these intervals the protostars are effectively "switched off", allowing gravitational instabilities to develop in their disc…
In this work, we derive the stellar initial mass function (IMF) from the superposition of mass distributions of dense cores, generated through gravoturbulent fragmentation of unstable clumps in molecular clouds (MCs) and growing through competitive accretion. MCs are formed by the turbulent cascade in the interstellar medium at scales L from 100 down to ~0.1 pc. Their internal turbulence is essentially supersonic and creates clumps with a lognormal distribution of densities n. Our model is based on the assumption of a power-law relationship between clump mass and clump density: n~m^x, where x …
Star formation in the centers of galaxies is thought to yield massive stars with a possibly top-heavy stellar mass distribution. It is likely that magnetic fields play a crucial role in the distribution of stellar masses inside star-forming molecular clouds. In this context, we explore the effects of magnetic fields, with a typical field strength of 38 microG, such as in RCW 38, and a field strength of 135 microG, similar to NGC 2024 and the infrared dark cloud G28.34+0.06, on the initial mass function (IMF) near (< 10 pc) a 10^7 solar mass black hole. Using these conditions, we perform a seri…
While the stellar Initial Mass Function (IMF) appears to be close to universal within the Milky Way galaxy, it is strongly suspected to be different in the primordial Universe, where molecular hydrogen cooling is less efficient and the gas temperature can be higher by a factor of 30. In between these extreme cases, the gas temperature varies depending on the environment, metallicity and radiation background. In this paper we explore if changes of the gas temperature affect the IMF of the stars considering fragmentation and accretion. The fragmentation behavior depends mostly on the Jeans mass …
We review current theories for the origin of the Stellar Initial Mass Function (IMF) with particular focus on the extent to which the IMF can be considered universal across various environments. To place the issue in an observational context, we summarize the techniques used to determine the IMF for different stellar populations, the uncertainties affecting the results, and the evidence for systematic departures from universality under extreme circumstances. We next consider theories for the formation of prestellar cores by turbulent fragmentation and the possible impact of various thermal, hy…
It is usually assumed that the stellar initial mass function (IMF) takes a universal form and that there exists a direct mapping between this and the distribution of natal core masses (the core mass function, CMF). The IMF and CMF have been best characterized in the Solar neighborhood. Beyond 500~pc from the Sun, in diverse environments where metallicity varies and massive star feedback may dominate, the IMF has been measured only incompletely and imprecisely, while the CMF has hardly been measured at all. In order to establish if the IMF and CMF are indeed universal and related to each other,…
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 include runs with increasingly complex physics, starting with isothermal ideal magnetohydrodynamic (MHD) and then adding non-isothermal thermodynamics and protostellar outflows. We show that without protostellar outflows the resulting stell…
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 turbul…
We introduce a new model for the accretion and feedback of supermassive black hole (SMBH) binaries to the KETJU code, which enables us to resolve the evolution of SMBH binaries down to separations of tens of Schwarzschild radii in gas-rich galaxy mergers. Our subgrid binary accretion model extends the widely used Bondi--Hoyle--Lyttleton accretion into the binary phase and incorporates preferential mass accretion onto the secondary SMBH, which is motivated by results from small-scale hydrodynamical circumbinary disc simulations. We perform idealised gas-rich disc galaxy merger simulations using…
We numerically investigate the effect of feedback from the ionizing radiation heating from massive stars on the evolution of giant molecular clouds (GMCs) and their star formation efficiency (SFE). We find that the star-forming regions within the GMCs are invariably formed by gravitational contraction. After an initial period of contraction, the collapsing clouds begin forming stars, whose feedback evaporates part of the clouds' mass, opposing the continuing accretion from the infalling gas. The competition of accretion against dense gas consumption by star formation (SF) and evaporation by th…
We examine gas accretion and subsequent star formation in representative galaxies from the McMaster Unbiased Galaxy Simulations (Stinson et al. 2010). Accreted gas is bimodal with a natural temperature division at $10^5$ K, near the peak of the cooling curve. Cold-mode accretion dominates inflows at early times, creating a peak in total accretion at redshift z=2-4 and declining exponentially below z$\sim$2. Hot-mode accretion peaks near z=1-2 and declines gradually. Hot-mode exceeds cold-mode accretion at z$\sim$1.8 for all four galaxies rather than when the galaxy reaches a characteristic mas…
Protostars grow in mass by accreting material through their discs, and this accretion is initially their main source of luminosity. The resulting radiative feedback heats the environments of young protostars, and may thereby suppress further fragmentation and star formation. There is growing evidence that the accretion of material onto protostars is episodic rather than continuous; most of it happens in short bursts that last up to a few hundred years, whereas the intervals between these outbursts of accretion could be thousands of years. We have developed a model to include the effects of epi…
Turbulence is a critical ingredient for star formation, yet its role for the initial mass function (IMF) is not fully understood. Here we perform magnetohydrodynamical (MHD) simulations of star cluster formation including gravity, turbulence, magnetic fields, stellar heating and outflow feedback to study the influence of the mode of turbulence driving on IMF. We find that simulations that employ purely compressive turbulence driving (COMP) produce a higher fraction of low-mass stars as compared to simulations that use purely solenoidal driving (SOL). The characteristic (median) mass of the sin…
Stars do not generally form in isolation. Instead, they form in clusters, and in these clustered environments newborn stars can have profound effects on one another and on their parent gas clouds. Feedback from clustered stars is almost certainly responsible for a number of otherwise puzzling facts about star formation: that it is an inefficient process that proceeds slowly when averaged over galactic scales; that most stars disperse from their birth sites and dissolve into the galactic field over timescales $\ll 1$ Gyr; and that newborn stars follow an initial mass function (IMF) with a disti…
