Initial Mass Function Variations Research Articles

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.

The effect of the environment-dependent IMF on the formation and metallicities of stars over the cosmic history

Recent observational and theoretical studies indicate that the stellar initial mass function (IMF) varies systematically with the environment (star formation rate – SFR, metallicity). Although the exact dependence of the IMF on those properties is likely to change with improving observational constraints, the reported trend in the shape of the IMF appears robust. We present the first study aiming to evaluate the effect of the IMF variations on the measured cosmic SFR density (SFRD) as a function of metallicity and redshift,fSFR(Z,z). We also study the expected number and metallicity of white dwarf, neutron star, and black hole progenitors under different IMF assumptions. Applying the empirically driven IMF variations described by the integrated galactic IMF (IGIMF) theory, we revisefSFR(Z,z) obtained in our previous study that assumed a universal IMF. We find a lower SFRD at high redshifts and a higher fraction of metal-poor stars being formed than previously determined. In the local Universe, our calculation applying the IGIMF theory suggests more white dwarf and neutron star progenitors in comparison with the universal IMF scenario, while the number of black hole progenitors remains unaffected.

Variations of the stellar Initial Mass Function in semi-analytic models: Implications for the mass assembly of galaxies in the GAEA model

AbstractA 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 synthetic photometry assuming a universal IMF. This provides a self-consistent interpretation for the observed mismatch between photometrically inferred stellar masses of local early-type galaxies and those derived by dynamical and spectroscopic studies. At higher redshifts, the assumption of a variable IMF has a deep impact on our ability to reconstruct the evolution of the galaxy stellar mass function and the star formation history of galaxies.

Chemical evolution of elliptical galaxies with a variable IMF

Growing evidence in recent years suggests a systematic variation of the stellar initial mass function (IMF), being top-heavy for starburst galaxies and possibly bottom-heavy for massive ellipticals. Galaxy chemical evolution simulations adopting an invariant canonical IMF face difficulty in simultaneously reproducing the metallicity and α-enhancement of the massive elliptical galaxies. Applying a variable IMF that changes with time is a promising solution, however, it is non-trivial to couple a variable IMF theory with the existing galaxy evolution codes. Here we present the first open source simulation code which recalculates the galaxy-wide IMF at each time step according to the integrated galactic IMF (IGIMF) theory where the galaxy-wide IMF depends on the galactic star formation rate and metallicity. The resulting galaxy-wide IMF and metal abundance evolve with time. With this pilot work, we explore the effect of the IGIMF theory on galaxy chemical evolution in comparison with an invariant IMF.

IMF radial gradients in most massive early-type galaxies

ABSTRACT 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 initial mass function (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 ∼ 0.05, with central velocity dispersion in the range 300 ≲ σ ≲ 350 km s−1. Using state-of-the-art stellar population synthesis models, we fit a number of spectral indices, from different chemical species (including TiO and Na indices), to constrain the IMF slope (i.e. the fraction of low-mass stars), as a function of galactocentric distance, over a radial range out to ∼4 kpc. ETGs in our sample show a significant correlation of IMF slope and surface mass density. The bottom-heavy population (i.e. an excess of low-mass stars in the IMF) is confined to central galaxy regions with surface mass density above $\rm \sim 10^{10}\, M_\odot \, kpc^{-2}$, or, alternatively, within a characteristic radius of ∼2 kpc. Radial distance, in physical units, and surface mass density are the best correlators to IMF variations, with respect to other dynamical (e.g. velocity dispersion) and stellar population (e.g. metallicity) properties. Our results for the most massive galaxies suggest that there is no single parameter that fully explains variations in the stellar IMF, but IMF radial profiles at z ∼ 0 rather result from the complex formation and mass accretion history of galaxy inner and outer regions.

13C/18O ratio as a litmus test of stellar IMF variations in high-redshift starbursts

AbstractDetermining the shape of the stellar initial mass function (IMF) and whether it is constant or varies in space and time is the Holy Grail of modern astrophysics, with profound implications for all theories of star and galaxy formation. On a theoretical ground, the extreme conditions for star formation (SF) encountered in the most powerful starbursts in the Universe are expected to favour the formation of massive stars. Direct methods of IMF determination, however, cannot probe such systems, because of the severe dust obscuration affecting their starlight. The next best option is to observe CNO bearing molecules in the interstellar medium at millimetre/ submillimetre wavelengths, which, in principle, provides the best indirect evidence for IMF variations. In this contribution, we present our recent findings on this issue. First, we reassess the roles of different types of stars in the production of CNO isotopes. Then, we calibrate a proprietary chemical evolution code using Milky Way data from the literature, and extend it to discuss extragalactic data. We show that, though significant uncertainties still hamper our knowledge of the evolution of CNO isotopes in galaxies, compelling evidence for an IMF skewed towards high-mass stars can be found for galaxy-wide starbursts. In particular, we analyse a sample of submillimetre galaxies observed by us with the Atacama Large Millimetre Array at the peak of the SF activity of the Universe, for which we measure 13C/18O⋍1. This isotope ratio is especially sensitive to IMF variations, and is little affected by observational uncertainties. At the end, ongoing developments of our work are briefly outlined.

Measuring the stellar initial mass function

AbstractThe birth of stars and the formation of galaxies are cornerstones of modern astrophysics. While much is known about how galaxies globally and their stars individually form and evolve, one fundamental property that affects both remains elusive. This is problematic because this key property, the stellar initial mass function (IMF), is a key tracer of the physics of star formation that underpins almost all of the unknowns in galaxy and stellar evolution. It is perhaps the greatest source of systematic uncertainty in star and galaxy evolution. The past decade has seen a growing number and variety of methods for measuring or inferring the shape of the IMF, along with progressively more detailed simulations, paralleled by refinements in the way the concept of the IMF is applied or conceptualised on different physical scales. This range of approaches and evolving definitions of the quantity being measured has in turn led to conflicting conclusions regarding whether or not the IMF is universal. Here I summarise the growing wealth of approaches to our understanding of this fundamental property that defines so much of astrophysics, and highlight the importance of considering potential IMF variations, reinforcing the need for measurements to quantify their scope and uncertainties carefully. I present a new framework to aid the discussion of the IMF and promote clarity in the further development of this fundamental field.

Fornax 3D project: a two-dimensional view of the stellar initial mass function in the massive lenticular galaxy FCC 167

The stellar initial mass function (IMF) regulates the baryonic cycle within galaxies, and is a key ingredient for translating observations into physical quantities. Although it was assumed to be universal for decades, there is now growing observational evidence showing that the center of massive early-type galaxies hosts a larger population of low-mass stars than is expected based on observations from the Milky Way. Moreover, these variations in the IMF have been found to be related to radial metallicity variations in massive galaxies. We present here a two-dimensional stellar population analysis of the massive lenticular galaxy FCC 167 (NGC 1380) as part of the Fornax3D project. Using a newly developed stellar population fitting scheme, we derive a full two-dimensional IMF map of an early-type galaxy. This two-dimensional analysis allows us go further than a radial analysis, showing how the metallicity changes along a disk-like structure while the IMF follows a distinct, less disky distribution. Thus, our findings indicate that metallicity cannot be the sole driver of the observed radial IMF variations. In addition, a comparison with the orbital decomposition shows suggestive evidence of a coupling between stellar population properties and the internal dynamical structure of FCC 167, where metallicity and IMF maps seem to track the distribution of cold and warm orbits, respectively.

Initial Mass Function Variation in Two Elliptical Galaxies Using Near-infrared Tracers

Abstract Using integral field spectroscopy, we demonstrate that gravity-sensitive absorption features in the zJ band (0.9–1.35 μm) can constrain the low-mass stellar initial mass function (IMF) in the cores of two elliptical galaxies, M85 and M87. Compared to the visible bands, the near-infrared (NIR) is more sensitive to light from low-mass dwarf stars, whose relative importance is the primary subject of the debate over IMF variations in nearby galaxies. Our analysis compares the observed spectra to the latest stellar population synthesis models by employing two different methods: equivalent widths and spectral fitting. We find that the IMF slopes in M85 are similar to the canonical Milky Way IMF with a median IMF-mismatch parameter α K = 1.26. In contrast, we find that the IMF in M87 is steeper than a Salpeter IMF with α K = 2.77. The derived stellar population parameters, including the IMF slopes, are consistent with those from recent results in the visible bands based on spectroscopic and kinematic techniques. Certain elemental abundances, e.g., Na and Fe, have dramatic effects on the IMF-sensitive features and therefore the derived IMF slopes. We show evidence for a high [Na/H] ∼ 0.65 dex in the core of M85 from two independent Na i absorption features. The high Na abundance may be the result of a recent galactic merger involving M85. This suggests that including [Na/H] in the stellar population model parameters is critical for constraining the IMF slopes in M85. These results confirm the viability of using NIR absorption features to investigate IMF variation in nearby galaxies.

Comparing IMF-sensitive indices of intermediate-mass quiescent galaxies in various environments

ABSTRACT Using samples drawn from the Sloan Digital Sky Survey, we study for the first time the relation between large-scale environments (clusters, groups, and voids) and the stellar initial mass function (IMF). We perform an observational approach based on the comparison of IMF-sensitive indices of quiescent galaxies with similar mass in varying environments. These galaxies are selected within a narrow redshift interval (0.020 < z < 0.055) and spanning a range in velocity dispersion from 100 to 200 km s−1. The results of this paper are based upon analysis of composite spectra created by stacking the spectra of galaxies, binned by their velocity dispersion and redshift. The trends of spectral indices as measured from the stacked spectra, with respect to velocity dispersion, are compared in different environments. We find a lack of dependence of the IMF on the environment for intermediate-mass galaxy regime. We verify this finding by providing a more quantitative measurement of the IMF variations among galactic environments using MILES stellar population models with a precision of ΔΓb ∼ 0.2.

SDSS-IV MaNGA: stellar initial mass function variation inferred from Bayesian analysis of the integral field spectroscopy of early-type galaxies

We analyze the stellar initial mass functions (IMF) of a large sample of early type galaxies (ETGs) provided by MaNGA. The large number of IFU spectra of individual galaxies provide high signal-to-noise composite spectra that are essential for constraining IMF and to investigate possible radial gradients of the IMF within individual galaxies. The large sample of ETGs also make it possible to study how the IMF shape depends on various properties of galaxies. We adopt a novel approach to study IMF variations in ETGs, use Bayesian inferences based on full spectrum fitting. The Bayesian method provides a statistically rigorous way to explore potential degeneracy in spectrum fitting, and to distinguish different IMF models with Bayesian evidence. We find that the IMF slope depends systematically on galaxy velocity dispersion, in that galaxies of higher velocity dispersion prefer a more bottom-heavy IMF, but the dependence is almost entirely due to the change of metallicity, $Z$, with velocity dispersion. The IMF shape also depends on stellar age, $A$, but the dependence is completely degenerate with that on metallicity through a combination $AZ^{-1.42}$. Using independent age and metallicity estimates we find that the IMF variation is produced by metallicity instead of age. The IMF near the centers of massive ETGs appears more bottom-heavy than that in the outer parts, while a weak opposite trend is seen for low-mass ETGs. Uncertainties produced by star formation history, dust extinction, $\alpha$-element abundance enhancement and noise in the spectra are tested.

Is it possible to reconcile extragalactic IMF variations with a universal Milky Way IMF?

Abstract One of the most robust observations of the stellar initial mass function (IMF) is its near-universality in the Milky Way and neighbouring galaxies. But recent observations of early-type galaxies can be interpreted to imply a ‘bottom-heavy’ IMF, while others of ultrafaint dwarfs could imply a ‘top-heavy’ IMF. This would impose powerful constraints on star formation models. We explore what sort of ‘cloud-scale’ IMF models could possibly satisfy these constraints. We utilize simulated galaxies that reproduce (broadly) the observed galaxy properties, while they also provide the detailed star formation history and properties of each progenitor star-forming cloud. We then consider generic models where the characteristic mass of the IMF is some arbitrary power-law function of progenitor cloud properties, along with well-known literature IMF models which scale with Jeans mass, ‘turbulent Bonnor–Ebert mass’, temperature, the opacity limit, metallicity, or the ‘protostellar heating mass’. We show that no IMF models currently in the literature – nor any model where the turnover mass is an arbitrary power-law function of a combination of cloud temperature/density/size/metallicity/velocity dispersion/magnetic field – can reproduce the claimed IMF variation in ellipticals or dwarfs without severely violating observational constraints in the Milky Way. Specifically, they predict too much variation in the ‘extreme’ environments of the Galaxy compared to that observed. Either the IMF varies in a more complicated manner, or alternative interpretations of the extragalactic observations must be explored.

Recovering stellar population parameters via different population models and stellar libraries

Three basic ingredients are required to generate a simple stellar population (SSP) library, i.e., an initial mass function (IMF), a stellar evolution model/isochrones, and an empirical/theoretical stellar spectral library. However, there are still some uncertainties to the determination and understanding of these ingredients. We perform the spectral fitting to test the relative parameter offsets between these uncertainties using two different stellar population models, two different empirical stellar libraries, two different isochrones, and the Salpeter and Chabrier IMFs. Based on these setups, we select five SSP libraries generated with the Galaxev/STELIB and Vazdekis/MILES models, and apply them to the pPXF full-spectrum fitting of both MaNGA and mock spectra. We find that: 1) Compared to the Galaxev/STELIB model, spectral fitting qualities with the Vazdekis/MILES model have significant improvements for those metal-rich (especially over-solar) spectra, which cause better reduced $\chi^2$ distributions and more precisely fitted absorption lines. This might due to the lack of metal rich stars in the empirical STELIB library, or code improvement of the Vazdekis model. 2) When applying the Vazdekis/MILES model for spectral fitting, the IMF variation will lead to not only a systematic offset in $M_*/L_r$, but also offsets in age and metallicity, and these offsets increase with increasing stellar population ages. However, the IMF-variation caused metallicity offsets disappear in the case of Galaxev/STELIB based libraries. 3) The Padova2000 model provides a better match to the MaNGA galaxy spectra at [M/H]$_L<-1.0$, while the BaSTI model match the local galaxy spectra better at [M/H]$_L>-1.0$. Current tests suggest that spectral fitting with the Vazdekis/MILES+BaSTI combination would be a better choice for local galaxies.

Initial mass function variations cannot explain the ionizing spectrum of low metallicity starbursts

Aims. Observations of both galaxies in the distant Universe and local starbursts are showing increasing evidence for very hard ionizing spectra that stellar population synthesis models struggle to reproduce. Here we explore the effects of the assumed stellar initial mass function (IMF) on the ionizing photon output of young populations at wavelengths below key ionization energy thresholds. Methods. We use a custom set of binary population and spectral synthesis (BPASS) models to explore the effects of IMF assumptions as a function of metallicity, IMF slope, upper mass limit, IMF power law break mass and sampling. Results. We find that while the flux capable of ionizing hydrogen is only weakly dependent on IMF parameters, the photon flux responsible for the He II and O VI lines is far more sensitive to assumptions. In our current models this flux arises primarily from helium and Wolf-Rayet stars which have partially or fully lost their hydrogen envelopes. The timescales for formation and evolution of both Wolf Rayet stars and helium dwarfs, and hence inferred population age, are affected by choice of model IMF. Even the most extreme IMFs cannot reproduce the He II ionizing flux observed in some high redshift galaxies, suggesting a source other than stellar photospheres. Conclusions. We caution that detailed interpretation of features in an individual galaxy spectrum is inevitably going to be subject to uncertainties in the IMF of its contributing starbursts. We remind the community that the IMF is fundamentally a statistical construct, and that stellar population synthesis models are most effective when considering entire galaxy populations rather than individual objects.

The Stellar Membership of the Taurus Star-forming Region*

Abstract The high-precision astrometry from the second data release of the Gaia mission has made it possible to greatly improve the census of members of nearby clusters and associations. I have applied the Gaia data to the Taurus star-forming region, refining the sample of known members and identifying candidates for undiscovered members. The resulting samples of members and candidates provide the best constraints to date on the distribution of ages and the initial mass function (IMF) in Taurus. Several studies over the last 30 years have proposed the existence of a population of older stars (≳10 Myr) that is associated with the Taurus clouds. The data from Gaia demonstrate that such a population does not exist. Meanwhile, previous IMF estimates for small fields surrounding the Taurus aggregates have exhibited a surplus of K7–M0 stars (0.7–0.8 M ⊙) relative to star-forming clusters such as IC 348 and the Orion Nebula Cluster. However, that difference disappears when the new census of the entire region is considered, which should be complete for spectral types earlier than M6–M7 at A J &lt; 1. Thus, there is little variation in the stellar IMF across the 3–4 orders of magnitude in stellar density that are present in nearby star-forming regions. Finally, I note that the proper motions of two previously known members, KPNO 15 and 2MASS J04355209 + 2255039, indicate that they may have been ejected from the same location within the L1536 cloud ∼7200 years ago.

Calibrated, cosmological hydrodynamical simulations with variable IMFs III: spatially resolved properties and evolution

Recent spatially-resolved observations of massive early-type galaxies (ETGs) have uncovered evidence for radial gradients of the stellar initial mass function (IMF), ranging from super-Salpeter IMFs in the centre to Milky Way-like beyond the half-light radius, $r_e$. We compare these findings with our new cosmological, hydrodynamical simulations based on the EAGLE model that self-consistently vary the IMF on a per-particle basis such that it becomes either bottom-heavy (LoM-50) or top-heavy (HiM-50) in high-pressure environments. These simulations were calibrated to reproduce inferred IMF variations such that the IMF becomes "heavier" due to either excess dwarf stars or stellar remnants, respectively, in galaxies with increasing stellar velocity dispersion. In agreement with observations, both simulations produce negative radial IMF gradients, transitioning from high to low excess mass-to-light ratio (MLE) at around $r_e$. We find negative metallicity radial gradients for both simulations, but positive and flat [Mg/Fe] gradients in LoM-50 and HiM-50, respectively. Measured in radial bins, the MLE increases strongly with local metallicity for both simulations, in agreement with observations. However, the local MLE increases and decreases with local [Mg/Fe] in LoM-50 and HiM-50, respectively. These qualitative differences can be used to break degeneracies in the manner with which the IMF varies in these high-mass ETGs. At $z=2$, we find that the MLE has a higher and lower normalization for bottom- and top-heavy IMF variations, respectively. We speculate that a hybrid of our LoM and HiM models may be able to reconcile observed IMF diagnostics in star-forming galaxies and ETGs.

Impact of inter-correlated initial binary parameters on double black hole and neutron star mergers

The distributions of the initial main-sequence binary parameters are one of the key ingredients in obtaining evolutionary predictions for compact binary (BH–BH/BH–NS/NS–NS) merger rates. Until now, such calculations were done under the assumption that initial binary parameter distributions were independent. For the first time, we implement empirically derived inter-correlated distributions of initial binary parameters primary mass (M1), mass ratio (q), orbital period (P), and eccentricity (e). Unexpectedly, the introduction of inter-correlated initial binary parameters leads to only a small decrease in the predicted merger rates by a factor of ≲2–3 relative to the previously used non-correlated initial distributions. The formation of compact object mergers in the isolated classical binary evolution favours initial binaries with stars of comparable masses (q ≈ 0.5–1) at intermediate orbital periods (log P (days) = 2–4). New distributions slightly shift the mass ratios towards lower values with respect to the previously used flat q distribution, which is the dominant effect decreasing the rates. New orbital periods (∼1.3 more initial systems within log P (days) = 2–4), together with new eccentricities (higher), only negligibly increase the number of progenitors of compact binary mergers. Additionally, we discuss the uncertainty of merger rate predictions associated with possible variations of the massive-star initial mass function (IMF). We argue that evolutionary calculations should be normalized to a star formation rate (SFR) that is obtained from the observed amount of UV light at wavelength 1500 Å (an SFR indicator). In this case, contrary to recent reports, the uncertainty of the IMF does not affect the rates by more than a factor of ∼2. Any change to the IMF slope for massive stars requires a change of SFR in a way that counteracts the impact of IMF variations on compact object merger rates. In contrast, we suggest that the uncertainty in cosmic SFR at low metallicity can be a significant factor at play.

Calibrated, cosmological hydrodynamical simulations with variable IMFs – II. Correlations between the IMF and global galaxy properties

The manner in which the stellar initial mass function (IMF) scales with global galaxy properties is under debate. We use two hydrodynamical, cosmological simulations to predict possible trends for two self-consistent variable IMF prescriptions that respectively become locally bottom-heavy or top-heavy in high-pressure environments. Both simulations have been calibrated to reproduce the observed correlation between central stellar velocity dispersion and the excess mass-to-light ratio (MLE) relative to a Salpeter IMF by increasing the mass fraction of, respectively, dwarf stars or stellar remnants. We find trends of MLE with galaxy age, metallicity and [Mg/Fe] that agree qualitatively with observations. Predictions for correlations with luminosity, half-light radius, and black hole mass are presented. The significance of many of these correlations depends sensitively on galaxy selection criteria such as age, luminosity, and morphology. For an IMF with a varying high-mass end, some of these correlations are stronger than the correlation with the birth ISM pressure (the property that governs the form of the IMF), because in this case the MLE has a strong age dependence. Galaxies with large MLE tend to have overmassive central black holes. This indicates that the abnormally high MLE observed in the centres of some high-mass galaxies does not imply that overmassive BHs are merely the result of incorrect IMF assumptions, nor that excess M/L ratios are solely the result of overmassive BHs. Satellite galaxies tend to scatter toward high MLE due to tidal stripping, which may have significant implications for the inferred stellar masses of ultracompact dwarf galaxies.