Heavy Initial Mass Function Research Articles

Recovery of the low- and high-mass end slopes of the IMF in massive early-type galaxies using detailed elemental abundances

ABSTRACT Star formation in the early Universe has left its imprint on the chemistry of observable stars in galaxies. We derive elemental abundances and the slope of the low-mass end of the initial mass function (IMF) for a sample of 25 very massive galaxies, separated into brightest cluster galaxies (BCGs) and their massive satellites. The elemental abundances of BGCs and their satellites are similar, but for some elements, satellite galaxies show a correlation with the global velocity dispersion. Using a subset of derived elemental abundances, we model the star formation histories of these galaxies with chemical evolution models, and predict the high-mass end slope of the IMF and star formation time-scales. The high-mass end IMF slope of the satellite galaxies correlates with the global velocity dispersion. The low- and the high-mass end IMF slopes are weakly correlated in a general sense that top heavy IMFs are paired with bottom heavy IMFs. Our results do not necessarily imply that the IMF was simultaneously bottom and top heavy. Instead, our findings can be considered consistent with a temporal variation in the IMF, where, for massive galaxies, the high-mass end IMF slope is representative of the very early age and the low-mass end slope of the later star formation. The small but noticeable differences between the BCGs and the satellites in terms of their elemental abundances and IMF slopes, together with their stellar kinematical properties, suggest somewhat different formation pathways, where BCGs experience more major, gas-free mergers.

Dark matter haloes of massive elliptical galaxies at z ∼ 0.2 are well described by the Navarro–Frenk–White profile

ABSTRACT We investigate the internal structure of elliptical galaxies at z ∼ 0.2 from a joint lensing–dynamics analysis. We model Hubble Space Telescope images of a sample of 23 galaxy–galaxy lenses selected from the Sloan Lens ACS (SLACS) survey. Whereas the original SLACS analysis estimated the logarithmic slopes by combining the kinematics with the imaging data, we estimate the logarithmic slopes only from the imaging data. We find that the distribution of the lensing-only logarithmic slopes has a median 2.08c ± 0.03 and intrinsic scatter 0.13 ± 0.02, consistent with the original SLACS analysis. We combine the lensing constraints with the stellar kinematics and weak lensing measurements, and constrain the amount of adiabatic contraction in the dark matter (DM) haloes. We find that the DM haloes are well described by a standard Navarro–Frenk–White halo with no contraction on average for both of a constant stellar mass-to-light ratio (M/L) model and a stellar M/L gradient model. For the M/L gradient model, we find that most galaxies are consistent with no M/L gradient. Comparison of our inferred stellar masses with those obtained from the stellar population synthesis method supports a heavy initial mass function (IMF) such as the Salpeter IMF. We discuss our results in the context of previous observations and simulations, and argue that our result is consistent with a scenario in which active galactic nucleus feedback counteracts the baryonic-cooling-driven contraction in the DM haloes.

Predicting the observability of population III stars with ELT-HARMONI via the helium 1640 Å emission line

ABSTRACT Population III (Pop. III) stars, as of yet, have not been detected, however as we move into the era of extremely large telescopes this is likely to change. One likely tracer for Pop. III stars is the He iiλ1640 emission line, which will be detectable by the HARMONI spectrograph on the European Extremely Large Telescope (ELT) over a broad range of redshifts (2 ≤ z ≤ 14). By post-processing galaxies from the cosmological, AMR-hydrodynamical simulation newhorizon with theoretical spectral energy distributions (SED) for Pop. III stars and radiative transfer (i.e. the Yggdrasil Models and cloudy look-up tables, respectively) we are able to compute the flux of He iiλ1640 for individual galaxies. From mock 10 h observations of these galaxies we show that HARMONI will be able to detect Pop. III stars in galaxies up to z ∼ 10 provided Pop. III stars have a top heavy initial mass function (IMF). Furthermore, we find that should Pop. III stars instead have an IMF similar to those of the Pop. I stars, the He iiλ1640 line would only be observable for galaxies with Pop. III stellar masses in excess of $10^{7}\, {\rm M}_\odot$, average stellar age $\lt 1\, {\rm Myr}$ at z = 4. Finally, we are able to determine the minimal intrinsic flux required for HARMONI to detect Pop. III stars in a galaxy up to z = 10.

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.

Calibrated, cosmological hydrodynamical simulations with variable IMFs I: Method and effect on global galaxy scaling relations

The recently inferred variations in the stellar initial mass function (IMF) among local high-mass early-type galaxies may require a reinterpretation of observations of galaxy populations and may have important consequences for the predictions of models of galaxy formation and evolution. We present a new pair of cosmological, hydrodynamical simulations based on the EAGLE model that self-consistently adopt an IMF that respectively becomes bottom- or top-heavy in high-pressure environments for individual star-forming gas particles. In such models, the excess stellar mass-to-light ($M/L$) ratio with respect to a reference IMF is increased due to an overabundance of low-mass dwarf stars or stellar remnants, respectively. Crucially, both pressure-dependent IMFs have been calibrated to reproduce the observed trends of increasing excess $M/L$ with central stellar velocity dispersion ($\sigma_e$) in early-type galaxies, while maintaining agreement with the observables used to calibrate the EAGLE model, namely the galaxy luminosity function, half-light radii of late-type galaxies, and black hole masses. We find that while the $M/L$ excess is a good measure of the IMF for low-mass slope variations, it depends strongly on the age of the stellar population for high-mass slope variations. The normalization of the [Mg/Fe]$-\sigma_e$ relation is decreased (increased) for bottom- (top-)heavy IMF variations, while the slope is not strongly affected. Bottom-heavy variations have little impact on galaxy metallicities, half-light radii of early-type galaxies, or star formation rates, while top-heavy variations significantly increase these quantities for high-mass galaxies, leading to tension with observations.

KINETyS II: Constraints on spatial variations of the stellar initial mass function from K-band spectroscopy

We investigate the spatially resolved stellar populations of a sample of seven nearby massive Early-type galaxies (ETGs), using optical and near infrared data, including K-band spectroscopy. This data offers good prospects for mitigating the uncertainties inherent in stellar population modelling by making a wide variety of strong spectroscopic features available. We report new VLT-KMOS measurements of the average empirical radial gradients out to the effective radius in the strengths of the Ca I 1.98$\mu$m and 2.26$\mu$m features, the Na I 2.21$\mu$m line, and the CO 2.30$\mu$m bandhead. Following previous work, which has indicated an excess of dwarf stars in the cores of massive ETGs, we pay specific attention to radial variations in the stellar initial mass function (IMF) as well as modelling the chemical abundance patterns and stellar population ages in our sample. Using state-of-the-art stellar population models we infer an [Fe/H] gradient of -0.16$\pm$0.05 per dex in fractional radius and an average [Na/Fe] gradient of -0.35$\pm$0.09. We find a large but radially-constant enhancement to [Mg/Fe] of $\sim$ 0.4 and a much lower [Ca/Fe] enhancement of $\sim$ 0.1. Finally, we find no significant IMF radial gradient in our sample on average and find that most galaxies in our sample are consistent with having a Milky Way-like IMF, or at most a modestly bottom heavy IMF (e.g. less dwarf enriched than a single power law IMF with the Salpeter slope).

KINETyS: Constraining spatial variations of the stellar initial mass function in early-type galaxies ★

The heavyweight stellar initial mass function (IMF) observed in the cores of massive early-type galaxies (ETGs) has been linked to formation of their cores in an initial swiftly-quenched rapid starburst. However, the outskirts of ETGs are thought to be assembled via the slow accumulation of smaller systems in which the star formation is less extreme; this suggests the form of the IMF should exhibit a radial trend in ETGs. Here we report radial stellar population gradients out to the half-light radii of a sample of eight nearby ETGs. Spatially resolved spectroscopy at 0.8-1.35{\mu}m from the VLT's KMOS instrument was used to measure radial trends in the strengths of a variety of IMF-sensitive absorption features (including some which are previously unexplored). We find weak or no radial variation in some of these which, given a radial IMF trend, ought to vary measurably, e.g. for the Wing-Ford band we measure a gradient of +0.06$\pm$0.04 per decade in radius. Using stellar population models to fit stacked and individual spectra, we infer that the measured radial changes in absorption feature strengths are primarily accounted for by abundance gradients which are fairly consistent across our sample (e.g. we derive an average [Na/H] gradient of -0.53$\pm$0.07). The inferred contribution of dwarf stars to the total light typically corresponds to a bottom heavy IMF, but we find no evidence for radial IMF variations in the majority of our sample galaxies.

Optical spectroscopy and initial mass function of z = 0.4 red galaxies

Spectral absorption features can be used to constrain the stellar initial mass function (IMF) in the integrated light of galaxies. Spectral indices used at low redshift are in the far red, and therefore increasingly hard to detect at higher and higher redshifts as they pass out of atmospheric transmission and CCD detector wavelength windows. We employ IMF-sensitive indices at bluer wavelengths. We stack spectra of red, quiescent galaxies around $z=0.4$, from the DEEP2 Galaxy Redshift Survey. The $z=0.4$ red galaxies have 2 Gyr average ages so that they cannot be passively evolving precursors of nearby galaxies. They are slightly enhanced in C and Na, and slightly depressed in Ti. Split by luminosity, the fainter half appears to be older, a result that should be checked with larger samples in the future. We uncover no evidence for IMF evolution between $z=0.4$ and now, but we highlight the importance of sample selection, finding that an SDSS sample culled to select archetypal elliptical galaxies at z$\sim$0 is offset toward a more bottom heavy IMF. Other samples, including our DEEP2 sample, show an offset toward a more spiral galaxy-like IMF. All samples confirm that the reddest galaxies look bottom heavy compared with bluer ones. Sample selection also influences age-color trends: red, luminous galaxies always look old and metal-rich, but the bluer ones can be more metal-poor, the same abundance, or more metal-rich, depending on how they are selected.

Dominant dark matter and a counter-rotating disc: MUSE view of the low-luminosity S0 galaxy NGC 5102

The kinematics and stellar populations of the low-mass nearby S0 galaxy NGC 5102 are studied from integral field spectra taken with the Multi-Unit Spectroscopic Explorer (MUSE). The kinematic maps reveal for the first time that NGC 5102 has the characteristic 2 sigma peaks indicative of galaxies with counter-rotating discs. This interpretation is quantitatively confirmed by fitting two kinematic components to the observed spectra. Through stellar population analysis we confirm the known young stellar population in the centre and find steep age and metallicity gradients. We construct axisymmetric Jeans anisotropic models of the stellar dynamics to investigate the initial mass function (IMF) and the dark matter halo of the galaxy. The models show that this galaxy is quite different from all galaxies previously studied with a similar approach: even within the half-light radius, it cannot be approximated with the self-consistent mass-follows-light assumption. Including an NFW dark matter halo, we need a heavy IMF and a dark matter fraction of 0.37+-0.04 within a sphere of one effective radius to describe the stellar kinematics. The more general model with a free slope of the dark matter halo shows that slope and IMF are degenerate, but indicates that a light weight IMF (Chabrier-like) and a higher dark matter fraction, with a steeper (contracted) halo, fit the data better. Regardless of the assumptions about the halo profile, we measure the slope of the total mass density to be -1.75+-0.04. This is shallower than the slope of -2 of an isothermal halo and shallower than published slopes for more massive early type galaxies.

The SINFONI Nearby Elliptical Lens Locator Survey: discovery of two new low-redshift strong lenses and implications for the initial mass function in giant early-type galaxies★

We present results from a blind survey to identify strong gravitational lenses among the population of low-redshift early-type galaxies. The SINFONI Nearby Elliptical Lens Locator Survey (SNELLS) uses integral-field infrared spectroscopy to search for lensed emission line sources behind massive lens candidates at $z$<0.055. From 27 galaxies observed, we have recovered one previously-known lens (ESO325-G004) at $z$=0.034, and discovered two new systems, at $z$=0.031 and $z$=0.052. All three lens galaxies have high velocity dispersions (\sigma>300 km/s) and \alpha-element abundances ([Mg/Fe]>0.3). From the lensing configurations we derive total J-band mass-to-light ratios of 1.8$\pm$0.1, 2.1$\pm$0.1 and 1.9$\pm$0.2 within the $\sim$2 kpc Einstein radius. Correcting for estimated dark-matter contributions, and comparing to stellar population models with a Milky Way (Kroupa) initial mass function (IMF), we determine the "mass excess factor", \alpha. Assuming the lens galaxies have "old" stellar populations (10$\pm$1 Gyr), the average IMF mass factor is $\langle\alpha\rangle$=1.10$\pm$0.08$\pm$0.10, where the first error is random and the second is systematic. If we instead fit the stellar populations from 6dF optical survey spectra, all three galaxies are consistent with being old, but the age errors are 3-4 Gyr, due to limited signal-to-noise. The IMF constraints are therefore looser in this case, with $\langle\alpha\rangle$ = $1.23^{+0.16}_{-0.13}\pm{0.10}$. Our results are thus consistent with a Kroupa IMF (\alpha=1.00) on average, and strongly reject very heavy IMFs with \alpha>2. A Salpeter IMF (\alpha=1.55) is inconsistent at the 3.5$\sigma$ level if the galaxies are old, but cannot be excluded using age constraints derived from the currently-available optical spectra.

Variations in the initial mass function in early-type galaxies: a critical comparison between dynamical and spectroscopic results

Abstract I present a comparison between published dynamical (ATLAS3D) and spectroscopic (Conroy &amp; van Dokkum) constraints on the stellar initial mass function (IMF) in early-type galaxies, using the 34 galaxies in common between the two works. Both studies infer an average IMF mass factor α (the stellar mass relative to a Kroupa-IMF population of similar age and metallicity) greater than unity, i.e. both methods favour an IMF which is heavier than that of the Milky Way, on average over the sample. However, on a galaxy-by-galaxy basis, there is no correlation between α inferred from the two approaches. I investigate how the two estimates of α are correlated systematically with the galaxy velocity dispersion, σ, and with the Mg/Fe abundance ratio. The spectroscopic method, based on the strengths of metal absorption lines, yields a correlation only with metal abundance ratios: at fixed Mg/Fe, there is no residual correlation with σ. The dynamical method, applied to exactly the same galaxy sample, yields the opposite result: the IMF variation correlates only with dynamics, with no residual correlation with Mg/Fe after controlling for σ. Hence, although both methods indicate a heavy IMF on average in ellipticals, they lead to incompatible results for the systematic trends, when applied to the same set of galaxies. The sense of the disagreement could suggest that one (or both) of the methods has not accounted fully for the main confounding factors, i.e. element abundance ratios or dark matter contributions. Alternatively, the poor agreement might indicate additional variation in the detailed shape of the IMF, beyond what can currently be inferred from the spectroscopic features.

EVIDENCE FOR A CONSTANT INITIAL MASS FUNCTION IN EARLY-TYPE GALAXIES BASED ON THEIR X-RAY BINARY POPULATIONS,

A number of recent studies have proposed that the stellar initial mass function (IMF) of early type galaxies varies systematically as a function of galaxy mass, with higher mass galaxies having bottom heavy IMFs. These bottom heavy IMFs have more low-mass stars relative to the number of high mass stars, and therefore naturally result in proportionally fewer neutron stars and black holes. In this paper, we specifically predict the variation in the number of black holes and neutron stars based on the power-law IMF variation required to reproduce the observed mass-to-light ratio trends with galaxy mass. We then test whether such variations are observed by studying the field low-mass X-ray binary populations (LMXBs) of nearby early-type galaxies. In these binaries, a neutron star or black hole accretes matter from a low-mass donor star. Their number is therefore expected to scale with the number of black holes and neutron stars present in a galaxy. We find that the number of LMXBs per K-band light is similar among the galaxies in our sample. These data therefore demonstrate the uniformity of the slope of the IMF from massive stars down to those now dominating the K-band light, and are consistent with an invariant IMF. Our results are inconsistent with an IMF which varies from a Kroupa/Chabrier like IMF for low mass galaxies to a steep power-law IMF (with slope $x$=2.8) for high mass galaxies. We discuss how these observations constrain the possible forms of the IMF variations and how future Chandra observations can enable sharper tests of the IMF.

The cosmic evolution of the IMF under the Jeans conjecture with implications for massive galaxies

We examine the cosmic evolution of a stellar initial mass function (IMF) in galaxies that varies with the Jeans mass in the interstellar medium, paying particular attention to the K-band stellar mass to light ratio (M/L_K) of present-epoch massive galaxies. We calculate the typical Jeans mass using high-resolution hydrodynamic simulations coupled with a fully radiative model for the ISM, which yields a parameterisation of the IMF characteristic mass as a function of galaxy star formation rate (SFR). We then calculate the star formation histories of galaxies utilising an equilibrium galaxy growth model coupled with constraints on the star formation histories set by abundance matching models. We find that at early times, energetic coupling between dust and gas drive warm conditions in the ISM, yielding bottom-light/top- heavy IMFs associated with large ISM Jeans masses for massive star-forming galaxies. Owing to the remnants of massive stars that formed during the top-heavy phases at early times, the resultant M/L_K(sigma) in massive galaxies at the present epoch is increased relative to the non- varying IMF case. At late times, lower cosmic ray fluxes allow for cooler ISM temperatures in massive galaxies, and hence newly formed clusters will exhibit bottom-heavy IMFs, further increasing M/L_K(sigma). Our central result is hence that a given massive galaxy may go through both top-heavy and bottom-heavy IMF phases during its lifetime, though the bulk of the stars form during a top-heavy phase. Qualitatively, the variations in M/L_K(sigma) with galaxy mass are in agreement with observations, however, our model may not be able to account for bottom-heavy mass functions as indicated by stellar absorption features.

Dynamics of the disks of nearby galaxies

AbstractI describe how the dynamics of galactic disks can be inferred by imaging and spectroscopy. Next I demonstrate that the decomposition of the rotation curves of spiral galaxies into the contributions by the various components of the galaxies is highly degenerate. Constraints on the decomposition can be found by considering implications for the dynamics of the galactic disks. An important diagnostic is the Toomre Q stability parameter which controls the stability of a galactic disk against local Jeans collapse. I also show how the density wave theory of galactic spiral arms can be employed to constrain the mass of a galactic disk. Applying both diagnostics to the example of NGC2985 and discussing also the implied massto‐light ratio I demonstrate that the inner parts of the galaxy, where the optical disk resides, are dominated by baryons. When I apply this method to the disks of low surface brightness galaxies, I find unexpectedly high mass‐to light ratios. These could be explained by population synthesis models which assume a bottom heavy initial mass function similar to the recently proposed ‘integrated galactic initial mass function’. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The dependence of the IMF on the density- temperature relation of pre-stellar gas

AbstractIt has been recently shown by several authors that fragmentation of pre-stellar gas (i.e. at densities from 104 to 1010 particles cm−3 and temperatures of order 10-30 K) depends on the gas thermodynamics much more than it was anticipated in earlier studies, in which only an isothermal behaviour has been assumed for the gas. Here we review the results of a number of numerical hydrodynamic simulations (e.g. Li et al. 2003, Jappsen et al. 2005, Bonnell et al. 2006) in which departure from isothermality has been attempted by employing a polytropic equation of state (eos) with exponent different from unity. In particular, in these studies it has been shown that the dominant fragmentation scale of pre-stellar gas, and hence the peak of the initial mass function (IMF), depends on a polytropic exponent that changes value, from below to above unity, at a critical density (Larson 2005). Furthermore, this piecewise polytropic eos depends on the gas metallicity and fundamental constants. Therefore, the peak of the IMF depends, in turn, also on the gas metallicity and fundamental constants rather than on initial conditions, as it has been previously suggested (e.g. Larson 1995). Hence, we are for the first time in a position to infer theoretically the notion of a universal IMF (at least for its low-mass end).We also present two test cases in which a non-isothermal eos has been used in the context of smoothed particle hydrodynamic (SPH) numerical simulations. In the first case star formation is triggered by means of low-mass clump collisions. These calculations have shown that clump collisions can be a relatively efficient mechanism for the formation of solar-mass protostars and their lower-mass companions (efficiency greater or of order 20-25%; Kitsionas &amp; Whitworth 2006). We have also found that in such collisions protostars form mainly by fragmentation of dense filaments along which it is likely that pairs of protostars capture each other in close binaries surrounded by circumbinary discs. In the second case, the use of a polytropic eos with a varying exponent appropriate for the metallicity of starburst regions (Spaans &amp; Silk 2000, 2005) is shown to be sufficient to obtain a top heavy IMF similar to that observed e.g. in the Galactic centre (Klessen, Spaans &amp; Jappsen 2006). These are preliminary results in the direction of revisiting earlier isothermal calculations that were resolving all densities up to the opacity limit for fragmentation (e.g. Bate et al. 2002ab, 2003), this time also taking into account the thermal properties of the gas in the density range between 104 and 1010 particles cm−3. The next step would be to include self-consistent radiation transport in the calculations, the first attempts for which are already in the making (e.g. Whitehouse &amp; Bate 2004).

Near-infrared properties ofi-drop galaxies in theHubble Ultra Deep Field

We analyse near-infrared Hubble Space Telescope (HST)/Near-Infrared Camera and Multi-Object Spectrometer F110W (J) and F160W (H) band photometry of a sample of 27 i′-drop candidate z≃ 6 galaxies in the central region of the HST/Advanced Camera for Surveys Ultra Deep Field. The infrared colours of the 20 objects not affected by near neighbours are consistent with a high-redshift interpretation. This suggests that the low-redshift contamination of this i′-drop sample is smaller than that observed at brighter magnitudes, where values of 10–40 per cent have been reported. The J–H colours are consistent with a slope flat in fν(fλ∝λ−2), as would be expected for an unreddened starburst. However, there is evidence for a marginally bluer spectral slope (fλ∝λ−2.2), which is perhaps indicative of an extremely young starburst (∼10 Myr old) or a top heavy initial mass function and little dust. The low levels of contamination, median photometric redshift of z∼ 6.0 and blue spectral slope, inferred using the near-infrared data, support the validity of the assumptions in our earlier work in estimating the star formation rates, and that the majority of the i-drop candidates galaxies lie at z∼ 6.

Generic Spectrum and Ionization Efficiency of a Heavy Initial Mass Function for the First Stars

We calculate the generic spectral signature of an early population of massive stars at high redshifts. For metal-free stars with mass above 300 M☉, we find that the combined spectral luminosity per unit stellar mass is almost independent of the mass distribution of these stars. To zeroth order, the generic spectrum resembles a blackbody with an effective temperature of ~105 K, making these stars highly efficient at ionizing hydrogen and helium. The production rate of ionizing radiation per stellar mass by stars more massive than ~300 M☉ is larger by ~1 order of magnitude for hydrogen and He I and by ~2 orders of magnitude for He II than the emission from a standard initial mass function. This would result in unusually strong hydrogen and helium recombination lines from the surrounding interstellar medium. It could also alleviate the current difficulty of ionizing the intergalactic medium at z 6 with the cosmic star formation rate inferred at somewhat lower redshifts.