Initial Mass Function Variations Research Articles

MaNGA DynPop – V. The dark-matter fraction versus stellar velocity dispersion relation and stellar initial mass function variations in galaxies: dynamical models and full spectrum fitting of integral-field spectroscopy

ABSTRACT Using the final Mapping Nearby Galaxies at Apache Point Observatory sample of 10K galaxies, we investigate the dark matter (DM) fraction fDM within one half-light radius Re for about 6K galaxies with good kinematics spanning a wide range of morphologies and stellar velocity dispersion. We employ two techniques to estimate fDM: (i) Jeans anisotropic modelling (JAM), which performs DM decomposition based on stellar kinematics and (ii) comparing the total dynamical mass-to-light ratios (M/L)JAM and (M*/L)SPS from stellar population synthesis (SPS). We find that both methods consistently show a significant trend of increasing fDM with decreasing σe and low fDM at larger σe. For 235 early-type galaxies with the best models, we explore the variation of stellar initial mass function (IMF) by comparing the stellar mass-to-light ratios from JAM and SPS. We confirm that the stellar mass excess factor αIMF increases with σe, consistent with previous studies that reported a transition from Chabrier-like to Salpeter IMF among galaxies. We show that the αIMF trend cannot be driven by M*/L or IMF gradients as it persists when allowing for radial gradients in our model. We find no evidence for the total M/L increasing toward the centre. We detect weak positive correlations between αIMF and age, but no correlations with metallicity. We stack galaxy spectra according to their αIMF to search for differences in IMF-sensitive spectral features (e.g. the $\rm Na_{\rm I}$ doublet). We only find marginal evidence for such differences, which casts doubt on the validity of one or both methods to measure the IMF.

The universal variability of the stellar initial mass function probed by the TIMER survey

The debate about the universality of the stellar initial mass function (IMF) revolves around two competing lines of evidence. While measurements in the Milky Way, an archetypal spiral galaxy, seem to support an invariant IMF, the observed properties of massive early-type galaxies (ETGs) favor an IMF somehow sensitive to the local star-formation conditions. However, the fundamental methodological and physical differences between the two approaches have hampered a comprehensive understanding of IMF variations. Here, we describe an improved modeling scheme that, for the first time, allows consistent IMF measurements across stellar populations with different ages and complex star-formation histories (SFHs). Making use of the exquisite MUSE optical data from the TIMER survey and powered by the MILES stellar population models, we show the age, metallicity Mg/Fe and IMF slope maps of the inner regions of NGC\,3351, a spiral galaxy with a mass similar to that of the Milky Way. The measured IMF values in NGC\,3351 follow the expectations from a Milky Way-like IMF, although they simultaneously show systematic and spatially coherent variations, particularly for low-mass stars. In addition, our stellar population analysis reveals the presence of metal-poor and Mg-enhanced star-forming regions that appear to be predominantly enriched by the stellar ejecta of core-collapse supernovae. Our findings therefore showcase the potential of detailed studies of young stellar populations to provide the means to better understand the early stages of galaxy evolution and, in particular, the origin of the observed IMF variations beyond and within the Milky Way.

Dynamical Stellar Mass-to-light Ratio Gradients: Evidence for Very Centrally Concentrated IMF Variations in ETGs?

Evidence from different probes of the stellar initial mass function (IMF) of massive early-type galaxies (ETGs) has repeatedly converged on IMFs more bottom heavy than in the Milky Way (MW). This consensus has come under scrutiny due to often contradictory results from different methods on the level of individual galaxies. In particular, a number of strong lensing probes are ostensibly incompatible with a non-MW IMF. Radial gradients of the IMF—related to gradients of the stellar mass-to-light ratio ϒ—can potentially resolve this issue. We construct Schwarzschild models allowing for ϒ-gradients in seven massive ETGs with MUSE and SINFONI observations. We find dynamical evidence that ϒ increases toward the center for all ETGs. The gradients are confined to subkiloparsec scales. Our results suggest that constant-ϒ models may overestimate the stellar mass of galaxies by up to a factor of 1.5. For all except one galaxy, we find a radius where the total dynamical mass has a minimum. This minimum places the strongest constraints on the IMF outside the center and appears at roughly 1 kpc. We consider the IMF at this radius characteristic for the main body of each ETG. In terms of the IMF mass-normalization α relative to a Kroupa IMF, we find on average an MW-like IMF 〈α main〉 = 1.03 ± 0.19. In the centers, we find concentrated regions with increased mass normalizations that are less extreme than previous studies suggested, but still point to a Salpeter-like IMF, 〈α cen〉 = 1.54 ± 0.15.

The metallicity dependence of the stellar initial mass function

ABSTRACT During star formation, dust plays the crucial role of coupling gas to stellar radiation fields, allowing radiation feedback to influence gas fragmentation and thus the stellar initial mass function (IMF). Variations in dust abundance therefore provide a potential avenue by which variation in galaxy metallicity might affect the IMF. In this paper, we present a series of radiation-magnetohydrodynamic simulations in which we vary the metallicity and thus the dust abundance from 1 per cent of solar to 3× solar, spanning the range from the lowest metallicity dwarfs to the most metal-rich early-type galaxies (ETGs) found in the local Universe. We design the simulations to keep all dimensionless parameters constant so that the interaction between feedback and star-forming environments of varying surface density and metallicity is the only factor capable of breaking the symmetry between the simulations and modifying the IMF, allowing us to isolate and understand the effects of each environmental parameter cleanly. We find that shifts in the IMF with varying metallicity at a fixed surface density are smaller than the shifts in varying surface density at a fixed surface metallicity. We also find that metallicity-induced IMF variations are too small to explain the mass-to-light ratio shifts seen in the ETGs. We therefore conclude that metallicity variations are much less important than variations in surface density in driving changes in the IMF and that the latter rather than the former are most likely responsible for the IMF variations found in ETGs.

Effect of the initial mass function on the dynamical SMBH mass estimate in the nucleated early-type galaxy FCC 47

Supermassive black holes (SMBHs) and nuclear star clusters (NSCs) co-exist in many galaxies. While the formation history of the black hole is essentially lost, NSCs preserve their evolutionary history imprinted onto their stellar populations and kinematics. Studying SMBHs and NSCs in tandem might help us to ultimately reveal the build-up of galaxy centres. In this study, we combine large-scale VLT/MUSE and high-resolution adaptive-optics-assisted VLT/SINFONI observations of the early-type galaxy FCC 47 with the goal being to assess the effect of a spatially (non-)variable initial mass function (IMF) on the determination of the mass of the putative SMBH in this galaxy. We achieve this by performing DYNAMITE Schwarzschild orbit-superposition modelling of the galaxy and its NSC. In order to properly take account of the stellar mass contribution to the galaxy potential, we create mass maps using a varying stellar mass-to-light ratio derived from single stellar population models with fixed and with spatially varying IMFs. Using the two mass maps, we estimate black hole masses of (7.1−1.1+0.8) × 107 M⊙ and (4.4−2.1+1.2) × 107 M⊙ at 3σ signifance, respectively. Compared to models with constant stellar-mass-to-light ratio, the black hole masses decrease by 15% and 48%, respectively. Therefore, a varying IMF, both in its functional form and spatially across the galaxy, has a non-negligible effect on the SMBH mass estimate. Furthermore, we find that the SMBH in FCC 47 has probably not grown over-massive compared to its very over-massive NSC.

INSPIRE: INvestigating Stellar Population In RElics – IV. The initial mass function slope in relics

ABSTRACTIn the last decade, growing evidence has emerged supporting a non-universal stellar initial mass function (IMF) in massive galaxies, with a larger number of dwarf stars with respect to the Milky Way (bottom-heavy IMF). However, a consensus about the mechanisms that cause IMF variations is yet to be reached. Recently, it has been suggested that stars formed early-on in cosmic time, via a star formation burst, could be characterized by a bottom-heavy IMF. A promising way to confirm this is to use relics, ultra-compact massive galaxies, almost entirely composed by these ‘pristine’ stars. The INvestigating Stellar Population In RElics (INSPIRE) Project aims at assembling a large sample of confirmed relics, that can serve as laboratory to investigate on the conditions of star formation in the first 1–3 Gyr of the Universe. In this third INSPIRE paper, we build a high signal-to-noise spectrum from five relics, and one from five galaxies with similar sizes, masses, and kinematical properties, but characterized by a more extended star formation history (non-relics). Our detailed stellar population analysis suggests a systematically bottom-heavier IMF slope for relics than for non-relics, adding new observational evidence for the non-universality of the IMF at various redshifts and further supporting the above proposed physical scenario.

Stellar initial mass function varies with metallicity and time.

Most structural and evolutionary properties of galaxies strongly rely on the stellar initial mass function (IMF), namely the distribution of the stellar mass formed in each episode of star formation1-4. The IMF shapes the stellar population in all stellar systems, and so has become one of the most fundamental concepts of modern astronomy. Both constant and variable IMFs across different environments have been claimed despite a large number of theoretical5-7 and observational efforts8-15. However, the measurement of the IMF in Galactic stellar populations has been limited by the relatively small number of photometrically observed stars, leading to high uncertainties12-16. Here we report a star-counting result based on approximately 93,000 spectroscopically observed M-dwarf stars, an order of magnitude more than previous studies, in the 100-300 parsec solar neighbourhood. We find unambiguous evidence of a variable IMF that depends on both metallicity and stellar age. Specifically, the stellar population formed at early times contains fewer low-mass stars compared with the canonical IMF, independent of stellar metallicities. In more recent times, however, the proportion of low-mass stars increases with stellar metallicity. The variable abundance of low-mass stars in our Milky Way establishes a powerful benchmark for models of star formation and can heavily affect results in Galactic chemical-enrichment modelling, mass estimation of galaxies and planet-formation efficiency.

A common origin for the fundamental plane of quiescent and star-forming galaxies in the EAGLE simulations

ABSTRACT We use the EAGLE cosmological simulations to perform a comprehensive and systematic analysis of the z = 0.1 fundamental plane (FP), the tight relation between galaxy size, mass, and velocity dispersion. We first measure the total mass and velocity dispersion (including both random and rotational motions) within the effective radius to show that simulated galaxies obey a total mass FP that is very close to the virial relation ($\lt 10{{\ \rm per\ cent}}$ deviation), indicating that the effects of non-homology are weak. When we instead use the stellar mass, we find a strong deviation from the virial plane, which is driven by variations in the dark matter content. The dark matter fraction is a smooth function of the size and stellar mass, and thereby sets the coefficients of the stellar mass FP without substantially increasing the scatter. Hence, both star-forming and quiescent galaxies obey the same FP, with equally low scatter ($0.02\,$dex). We employ simulations with a variable stellar initial mass function (IMF) to show that IMF variations have a modest additional effect on this FP. Moreover, when we use luminosity-weighted mock observations of the size and spatially integrated velocity dispersion, the inferred FP changes only slightly. However, the scatter increases significantly, due to the luminosity-weighting and line-of-sight projection of the velocity dispersions, and measurement uncertainties on the half-light radii. Importantly, we find significant differences between the simulated FP and observations, which likely reflects a systematic difference in the stellar mass distributions. Therefore, we suggest the stellar mass FP offers a simple test for cosmological simulations, requiring minimal post-processing of simulation data.

Environmental variation of the low-mass IMF.

We use a series of magnetohydrodynamic simulations including both radiative and protostellar outflow feedback to study environmental variation of the initial mass function (IMF). 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 outflows are more effective at suppressing the formation of massive stars in higher surface density environments. The combined effect of these two trends is towards an IMF with a lower characteristic mass and a narrower overall mass range in high surface density environments. We discuss the implications for these findings for the interpretation of observational evidence of IMF variation in early type galaxies.

The Fornax3D project: intrinsic correlations between orbital properties and the stellar initial mass function

ABSTRACT Variations of the stellar initial mass function (IMF) in external galaxies have been inferred from a variety of independent probes. Yet the physical conditions causing these variations remain largely unknown. In this work, we explore new spatially resolved measurements of the IMF for three edge-on lenticular galaxies in the Fornax cluster. We utilize existing orbit-based dynamical models in order to fit the new IMF maps within an orbital framework. We find that, within each galaxy, the high-angular momentum disc-like stars exhibit an IMF which is rich in dwarf stars. The centrally concentrated pressure-supported orbits exhibit similarly dwarf-rich IMF. Conversely, orbits at large radius which have intermediate angular momentum exhibit IMF which are markedly less dwarf-rich relative to the other regions of the same galaxy. Assuming that the stars which reside, in the present-day, on dynamically hot orbits at large radii are dominated by accreted populations, we interpret these findings as a correlation between the dwarf-richness of a population of stars, and the mass of the host in which it formed. Specifically, deeper gravitational potentials would produce more dwarf-rich populations, resulting in the relative deficiency of dwarf stars which originated in the lower mass accreted satellites. The central and high-angular momentum populations are likely dominated by in situ stars, which were formed in the more massive host itself. There are also global differences between the three galaxies studied here, of up to ∼0.3 dex in the IMF parameter ξ. We find no local dynamical or chemical property which alone can fully account for the IMF variations.

The MASSIVE Survey. XVI. The Stellar Initial Mass Function in the Center of MASSIVE Early-type Galaxies

The stellar initial mass function (IMF) is a fundamental property in the measurement of stellar masses and galaxy star formation histories. In this work, we focus on the most massive galaxies in the nearby universe . We obtain high-quality Magellan/LDSS-3 long-slit spectroscopy with a wide wavelength coverage of 0.4–1.01 μm for 41 early-type galaxies (ETGs) in the MASSIVE survey and derive high signal-to-noise spectra within an aperture of R e/8. Using detailed stellar synthesis models, we constrain the elemental abundances and stellar IMF of each galaxy through full spectral modeling. All the ETGs in our sample have an IMF that is steeper than a Milky Way (Kroupa) IMF. The best-fit IMF mismatch parameter, α IMF = (M/L)/(M/L)MW, ranges from 1.1 to 3.1, with an average of 〈α IMF〉 = 1.84, suggesting that on average, the IMF is more bottom heavy than Salpeter. Comparing the estimated stellar masses with the dynamical masses, we find that most galaxies have stellar masses that are smaller than their dynamical masses within the 1σ uncertainty. We complement our sample with lower-mass galaxies from the literature and confirm that is positively correlated with , , and . From the combined sample, we show that the IMF in the centers of more massive ETGs is more bottom heavy. In addition, we find that is positively correlated with both [Mg/Fe] and the estimated total metallicity [Z/H]. We find suggestive evidence that the effective stellar surface density ΣKroupa might be responsible for the variation of α IMF. We conclude that σ, [Mg/Fe], and [Z/H] are the primary drivers of the global stellar IMF variation.

Implications of a Temperature-dependent Initial Mass Function. I. Photometric Template Fitting

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 increasing redshift. Additionally, subpopulations of ULIRGs, quiescent and star-forming galaxies are compared with predictions of stellar population feedback and show clear qualitative similarities to the evolution of dust temperatures.

EDGE: The sensitivity of ultra-faint dwarfs to a metallicity-dependent initial mass function

ABSTRACT 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 newborn stellar populations becomes top-heavy, increasing the efficiency of supernova and photoionization feedback in regulating star formation. This results in a 100-fold reduction of the final stellar mass of the dwarf compared to a canonical IMF, at fixed dynamical mass. The increase in the feedback budget is none the less met by increased metal production from more numerous massive stars, leading to nearly constant iron content at z = 0. A metallicity-dependent IMF therefore provides a mechanism to produce low-mass ($\rm M_{\star }\sim 10^3 \rm M_{\odot }$), yet enriched ($\rm [Fe/H]\approx -2$) field dwarf galaxies, thus opening a self-consistent avenue to populate the plateau in $\rm [Fe/H]$ at the faintest end of the mass–metallicity relation.

Fornax 3D project: Assessing the diversity of IMF and stellar population maps within the Fornax Cluster

The stellar initial mass function (IMF) is central to our interpretation of astronomical observables and to our understanding of most baryonic processes within galaxies. The universality of the IMF, suggested by observations in our own Milky Way, has been thoroughly revisited due to the apparent excess of low-mass stars in the central regions of massive quiescent galaxies. As part of the efforts within the Fornax 3D project, we aim to characterize the two-dimensional IMF variations in a sample of 23 quiescent galaxies within the Fornax cluster. For each galaxy in the sample, we measured the mean age, metallicity, [Mg/Fe], and IMF slope maps from spatially resolved integrated spectra. The IMF maps show a variety of behaviors and internal substructures, roughly following metallicity variations. However, metallicity alone is not able to fully explain the complexity exhibited by the IMF maps. In particular, for relatively metal-poor stellar populations ([M/H] ≲ −0.1), the slope of the IMF seems to depend on the (specific) star formation rate at which stars were formed. Moreover, metallicity maps have systematically higher ellipticities than IMF slope ones. At the same time, both metallicity and IMF slope maps have at the same time higher ellipticities than the stellar light distribution in our sample of galaxies. In addition we find that, regardless of the stellar mass, every galaxy in our sample shows a positive radial [Mg/Fe] gradient. This results in a strong [Fe/H]–[Mg/Fe] relation, similar to what is observed in nearby, resolved galaxies. Since the formation history and chemical enrichment of galaxies are causally driven by changes in the IMF, our findings call for a physically motivated interpretation of stellar population measurements based on integrated spectra that take into account any possible time evolution of the stellar populations.

Mild radial variations of the stellar IMF in the bulge of M31

ABSTRACT Using new, homogeneous, long-slit spectroscopy in the wavelength range from ∼0.35 to $\sim 1 \, \mu$m, we study radial gradients of optical and near-infrared (NIR) initial mass function (IMF)-sensitive features along the major axis of the bulge of M31, out to a galactocentric distance of ∼200 arcsec (∼800 pc). Based on state-of-the-art stellar population synthesis models with varying Na abundance ratio, we fit a number of spectral indices, from different chemical species (including TiO’s, Ca, and Na indices), to constrain the low-mass (≲0.5 M⊙) end slope (i.e. the fraction of low-mass stars) of the stellar IMF, as a function of galactocentric distance. Outside a radial distance of ∼10 arcsec, we infer an IMF similar to a Milky Way-like distribution, while at small galactocentric distances, an IMF radial gradient is detected, with a mildly bottom-heavy IMF in the few inner arcsec. We are able to fit Na features (both NaD and $\rm Na\,{\small I}8190$), without requiring extremely high Na abundance ratios. $\rm [Na/Fe]$ is ∼0.4 dex for most of the bulge, rising up to ∼0.6 dex in the innermost radial bins. Our results imply an overall, luminosity-weighted, IMF and mass-to-light ratio for the M31 bulge, consistent with those for a Milky Way-like distribution, in contrast to results obtained, in general, for most massive early-type galaxies.

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 STAR FORmation in Gaseous Environments 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 ${\gt}500\, \mathrm{M}_{\rm \odot }$. 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 as 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.

Stellar initial mass function variation in massive early-type galaxies: the potential role of the deuterium abundance

ABSTRACT The observed stellar initial mass function (IMF) appears to vary, becoming bottom-heavy in the centres of the most massive, metal-rich early-type galaxies. It is still unclear what physical processes might cause this IMF variation. In this paper, we demonstrate that the abundance of deuterium in the birth clouds of forming stars may be important in setting the IMF. We use models of disc accretion on to low-mass protostars to show that those forming from deuterium-poor gas are expected to have zero-age main-sequence masses significantly lower than those forming from primordial (high deuterium fraction) material. This deuterium abundance effect depends on stellar mass in our simple models, such that the resulting IMF would become bottom-heavy – as seen in observations. Stellar mass loss is entirely deuterium free and is important in fuelling star formation across cosmic time. Using the Evolution and Assembly of GaLaxies and their Environments (EAGLE) simulation we show that stellar mass-loss-induced deuterium variations are strongest in the same regions where IMF variations are observed: at the centres of the most massive, metal-rich, passive galaxies. While our analysis cannot prove that the deuterium abundance is the root cause of the observed IMF variation, it sets the stage for future theoretical and observational attempts to study this possibility.

Evidence for Initial Mass Function Variation in Massive Early-Type Galaxies

The initial mass function (IMF), describing the distribution of birth masses of stars, plays a pivotal role in establishing the observable properties of galaxies. This article reviews the evidence for variation in the IMF of massive early-type galaxies (ETGs), especially from spectroscopic studies and from dynamical and gravitational lensing measurements over the past decade. The principal conclusions are as follows: ▪ The spectra of massive ETGs depart from the predictions of models with Milky Way–like IMFs in a way that is best reproduced by assuming a steeper (bottom-heavy) IMF below ∼1 M⊙. ▪ Lensing and dynamical models, assuming a constant mass-to-light ratio for the stellar component, infer heavy IMFs, superficially supporting the result from spectra. ▪ The spectroscopic signal exhibits a steep gradient, however, and may be confined to the innermost region with scales ≲2 kpc; such internal variation in the stellar mass-to-light ratio would invalidate a key assumption of most dynamics and lensing studies. ▪ For masses above the main sequence turnoff in ancient populations (≳1 M⊙), there is little evidence for a steeper IMF in massive ETGs or their high-redshift progenitors; rather, a slightly shallower slope is preferred in this regime from several different arguments. ▪ Steep internal gradients may be responsible for some of the apparent discrepancies between different methods and also point to the cause of the IMF variation being restricted to conditions specific to the in situ formation phase of ETG cores.

The Kinematics of Massive Quiescent Galaxies at 1.4 < z < 2.1: Dark Matter Fractions, IMF Variation, and the Relation to Local Early-type Galaxies*

Abstract We study the dynamical properties of massive quiescent galaxies at 1.4 < z < 2.1 using deep Hubble Space Telescope WFC3/F160W imaging and a combination of literature stellar velocity dispersion measurements and new near-infrared spectra obtained using the K-band Multi Object Spectrograph (KMOS) on the ESO Very Large Telescope. We use these data to show that the typical dynamical-to-stellar mass ratio has increased by ∼0.2 dex from z = 2 to the present day, and we investigate this evolution in the context of possible changes in the stellar initial mass function (IMF) and/or fraction of dark matter contained within the galaxy effective radius, f DM[<r e]. Comparing our high-redshift sample to their likely descendants at low redshift, we find that f DM[<r e] has increased by a factor of more than 4 since z ≈ 1.8, from f DM[<r e] = 6.6% ± 1.0% to ∼24%. The observed increase appears robust to changes in the methods used to estimate dynamical masses or match progenitors and descendants. We quantify possible variation of the stellar IMF through the offset parameter α, defined as the ratio of dynamical mass in stars to the stellar mass estimated using a Chabrier IMF. We demonstrate that the correlation between stellar velocity dispersion and α reported among quiescent galaxies at low redshift is already in place at z = 2, and we argue that subsequent evolution through (mostly minor) merging should act to preserve this relation while contributing significantly to galaxies’ overall growth in size and stellar mass.

Can magnetized turbulence set the mass scale of stars?

ABSTRACT 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 ($\mathcal {M} \sim 10\!-\!50$). 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 $M_\mathrm{50} \,\, \buildrel\propto \over \sim \,\,M_\mathrm{0} \mathcal {M}^{-3} \alpha _\mathrm{turb}\, \mathrm{SFE}^{1/3}$ for GMC mass M0, sonic Mach number $\mathcal {M}$, virial parameter αturb, 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 $\gt 20 \, \mathrm{M}_{\odot }$, an order of magnitude larger than observed ($\sim 2 \, \mathrm{M}_\odot$), 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.