Initial Mass Function Variations Research Articles

AGN feedback and the origin of the α enhancement in early-type galaxies – insights from the GAEA model

Abstract We take advantage of our recently published model for GAlaxy Evolution and Assembly (GAEA) to study the origin of the observed correlation between [α/Fe] and galaxy stellar mass. In particular, we analyse the role of radio-mode active galactic nuclei (AGN) feedback, which recent work has identified as a crucial ingredient to reproduce observations. In GAEA, this process introduces the observed trend of star formation histories extending over shorter time-scales for more massive galaxies, but does not provide a sufficient condition to reproduce the observed α enhancements of massive galaxies. In the framework of our model, this is possible only by assuming that any residual star formation is truncated for galaxies more massive than 1010.5 M⊙. This results, however, in even shorter star formation time-scales for the most massive galaxies, which translate in total stellar metallicities significantly lower than observed. Our results demonstrate that (i) trends of [α/Fe] ratios cannot be simply converted into relative time-scale indicators; and (ii) AGN feedback cannot explain alone the positive correlation between [α/Fe] and galaxy mass/velocity dispersion. Reproducing simultaneously the mass–metallicity relation and the α enhancements observed pose a challenge for hierarchical models, unless more exotic solutions are adopted such as metal-rich winds or a variable initial mass function.

Radial gradients in initial mass function sensitive absorption features in the Coma brightest cluster galaxies

Using the Oxford Short Wavelength Integral Field specTrograph (SWIFT), we trace radial variations of initial mass function (IMF) sensitive absorption features of three galaxies in the Coma cluster. We obtain resolved spectroscopy of the central 5kpc for the two central brightest-cluster galaxies (BCGs) NGC4889, NGC4874, and the BCG in the south-west group NGC4839, as well as unresolved data for NGC4873 as a low-$\sigma_*$ control. We present radial measurements of the IMF-sensitive features sodium NaI$_{\rm{SDSS}}$, calcium triplet CaT and iron-hydride FeH0.99, along with the magnesium MgI0.88 and titanium oxide TiO0.89 features. We employ two separate methods for both telluric correction and sky-subtraction around the faint FeH feature to verify our analysis. Within NGC4889 we find strong gradients of NaI$_{\rm{SDSS}}$ and CaT but a flat FeH profile, which from comparing to stellar population synthesis models, suggests an old, $\alpha$-enhanced population with a Chabrier, or even bottom-light IMF. The age and abundance is in line with previous studies but the normal IMF is in contrast to recent results suggesting an increased IMF slope with increased velocity dispersion. We measure flat NaI$_{\rm{SDSS}}$ and FeH profiles within NGC4874 and determine an old, possibly slightly $\alpha$-enhanced and Chabrier IMF population. We find an $\alpha$-enhanced, Chabrier IMF population in NGC4873. Within NGC4839 we measure both strong NaI$_{\rm{SDSS}}$ and strong FeH, although with a large systematic uncertainty, suggesting a possible heavier IMF. The IMFs we infer for these galaxies are supported by published dynamical modelling. We stress that IMF constraints should be corroborated by further spectral coverage and independent methods on a galaxy-by-galaxy basis.

Circumstellar dust, PAHs and stellar populations in early-type galaxies: insights fromGALEXandWISE

A majority of early-type galaxies contain interstellar dust, yet the origin of this dust, and why the dust sometimes exhibits unusual polycyclic aromatic hydrocarbon (PAH) ratios, remains a mystery. If the dust is internally produced, it likely originates from the large number of AGB stars associated with the old stellar population. We present GALEX and WISE elliptical aperture photometry of $\sim310$ early-type galaxies with Spitzer mid-infrared spectroscopy and/or ancillary data from ATLAS3D, to characterize their circumstellar dust and the shape of the radiation field that illuminates the interstellar PAHs. We find that circumstellar dust is ubiquitous in early-type galaxies, which indicates some tension between stellar population age estimates and models for circumstellar dust production in very old stellar populations. We also use dynamical masses from ATLAS3D to show that WISE W1 (3.4 $\mu$m) mass-to-light ratios are consistent with the initial mass function variation found by previous work. While the stellar population differences in early-type galaxies correspond to a range of radiation field shapes incident upon the diffuse dust, the ratio of the ionization-sensitive $7.7\mu$m to $11.3\mu$m PAH feature does not correlate with the shape of the radiation field, nor to variations with the size-sensitive $11.3\mu$m to $17\mu$m ratio. The $7.7\mu$m to $11.3\mu$m PAH ratio does tend to be smaller in galaxies with proportionally greater $H_2$ emission, which is evidence that processing of primarily smaller grains by shocks is responsible for the unusual ratios, rather than substantial differences in the overall PAH size or ionization distribution.

NEW CONSTRAINTS ON A COMPLEX RELATION BETWEEN GLOBULAR CLUSTER COLORS AND ENVIRONMENT

ABSTRACT We present an analysis of high-quality photometry for globular clusters (GCs) in the Virgo cluster core region, based on data from the Next Generation Virgo Cluster Survey (NGVS) pilot field, and in the Milky Way (MW), based on Very Large Telescope/X-Shooter spectrophotometry. We find significant discrepancies in color–color diagrams between sub-samples from different environments, confirming that the environment has a strong influence on the integrated colors of GCs. GC color distributions along a single color are not sufficient to capture the differences we observe in color–color space. While the average photometric colors become bluer with increasing radial distance to the cD galaxy M87, we also find a relation between the environment and the slope and intercept of the color–color relations. A denser environment seems to produce a larger dynamic range in certain color indices. We argue that these results are not due solely to differential extinction, Initial Mass Function variations, calibration uncertainties, or overall age/metallicity variations. We therefore suggest that the relation between the environment and GC colors is, at least in part, due to chemical abundance variations, which affect stellar spectra and stellar evolution tracks. Our results demonstrate that stellar population diagnostics derived from model predictions which are calibrated on one particular sample of GCs may not be appropriate for all extragalactic GCs. These results advocate a more complex model of the assembly history of GC systems in massive galaxies that goes beyond the simple bimodality found in previous decades.

Implications of a variable IMF for the interpretation of observations of galaxy populations

We investigate the effect of a metallicity-dependent stellar initial mass function (IMF), as deduced observationally by Martin-Navarro et al. (2015c), on the inferred stellar masses and star formation rates (SFRs) of a representative sample of 186,886 SDSS galaxies. Relative to a Chabrier IMF, for which we show the implied masses to be close to minimal, the inferred masses increase in both the low- and high-metallicity regimes due to the addition of stellar remnants and dwarf stars, respectively. The resulting galaxy stellar mass function (GSMF) shifts toward higher masses by 0.5 dex, without affecting the high-mass slope (and thus the need for effective quenching). The implied low-redshift SFR density increases by an order of magnitude. However, these results depend strongly on the assumed IMF parametrisation, which is not directly constrained by the observations. Varying the low-end IMF slope instead of the high-end IMF slope, while maintaining the same dwarf-to-giant ratio, results in a much more modest GSMF shift of 0.2 dex and a 10 per cent increase in the SFR density relative to the Chabrier IMF. A bottom-heavy IMF during the late, metal-rich evolutionary stage of a galaxy would help explain the rapid quenching and the bimodality in the galaxy population by on the one hand making galaxies less quenched (due to the continued formation of dwarf stars) and on the other hand reducing the gas consumption timescale. We conclude that the implications of the observational evidence for a variable IMF could vary from absolutely dramatic to mild but significant.

RADIAL TRENDS IN IMF-SENSITIVE ABSORPTION FEATURES IN TWO EARLY-TYPE GALAXIES: EVIDENCE FOR ABUNDANCE-DRIVEN GRADIENTS

ABSTRACT Samples of early-type galaxies show a correlation between stellar velocity dispersion and the stellar initial mass function (IMF) as inferred from gravity-sensitive absorption lines in the galaxies’ central regions. To search for spatial variations in the IMF, we have observed two early-type galaxies with Keck/LRIS and measured radial gradients in the strengths of absorption features from 4000–5500 Å and 8000–10000 Å. We present spatially resolved measurements of the dwarf-sensitive spectral indices Na I (8190 Å) and Wing-Ford FeH (9915 Å), as well as indices for species of H, C2, CN, Mg, Ca, TiO , and Fe. Our measurements show a metallicity gradient in both objects, and Mg/Fe consistent with a shallow gradient in α-enhancement, matching widely observed trends for massive early-type galaxies. The Na I index and the CN1 index at 4160 Å exhibit significantly steeper gradients, with a break at r ∼ 0.1 r eff ( r ∼ 300 pc). Inside this radius, Na I strength increases sharply toward the galaxy center, consistent with a rapid central rise in [Na/Fe]. In contrast, the ratio of the FeH to Fe index strength decreases toward the galaxy center. This behavior cannot be reproduced by a steepening IMF inside of 0.1 r eff if the IMF is a single power law. While gradients in the mass function above ∼ 0.4 M ⊙ may occur, exceptional care is required to disentangle these IMF variations from the extreme variations in individual element abundances near the galaxies’ centers.

Radial constraints on the initial mass function from TiO features and Wing–Ford band in early-type galaxies

At present, the main challenge to the interpretation of variations in gravity-sensitive line strengths as driven by a non-universal initial mass function (IMF), lies in understanding the effect of other parameters describing unresolved stellar populations, such as elemental abundance ratios. We combine various TiO-based, IMF-sensitive indicators in the optical and NIR spectral windows, along with the FeH-based Wing-Ford band to break this degeneracy. We obtain a significant radial trend of the IMF slope in XSG1, a massive early-type galaxy (ETG), with velocity dispersion sigma~300km/s, observed with the VLT/X-SHOOTER instrument. In addition, we constrain both the shape and normalization of the IMF based only on a stellar population analysis. We robustly rule out a single power-law to describe the IMF, whereas a power law tapered off to a constant value at low masses (defined as a bimodal IMF) is consistent with all the observational spectroscopic data and with the stellar M/L constraints based on the Jeans Anisotropic Modelling method. The IMF in XSG1 is bottom-heavy in the central regions (corresponding to a bimodal IMF slope Gb~3, or a mass normalization mismatch parameter alpha~2), changing towards a standard Milky-Way like IMF (Gb~1.3; alpha~1) around half of the effective radius. This result, combined with previous observations of local IMF variations in massive ETGs, reflects the varying processes underlying the formation of this type of galaxies, between the central core and the outer regions.

MERGER RATES OF DOUBLE NEUTRON STARS AND STELLAR ORIGIN BLACK HOLES: THE IMPACT OF INITIAL CONDITIONS ON BINARY EVOLUTION PREDICTIONS

The initial mass function (IMF), binary fraction, and distributions of binary parameters (mass ratios, separations, and eccentricities) are indispensable inputs for simulations of stellar populations. It is often claimed that these are poorly constrained, significantly affecting evolutionary predictions. Recently, dedicated observing campaigns have provided new constraints on the initial conditions for massive stars. Findings include a larger close binary fraction and a stronger preference for very tight systems. We investigate the impact on the predicted merger rates of neutron stars and black holes. Despite the changes with previous assumptions, we only find an increase of less than a factor of 2 (insignificant compared with evolutionary uncertainties of typically a factor of 10-100). We further show that the uncertainties in the new initial binary properties do not significantly affect (within a factor of 2) our predictions of double compact object merger rates. An exception is the uncertainty in IMF (variations by a factor of 6 up and down). No significant changes in the distributions of final component masses, mass ratios, chirp masses, and delay times are found. We conclude that the predictions are, for practical purposes, robust against uncertainties in the initial conditions concerning binary parameters, with the exception of the IMF. This eliminates an important layer of the many uncertain assumptions affecting the predictions of merger detection rates with the gravitational wave detectors aLIGO/aVirgo.

IMF–METALLICITY: A TIGHT LOCAL RELATION REVEALED BY THE CALIFA SURVEY

Variations in the stellar initial mass function (IMF) have been invoked to explain the spectroscopic and dynamical properties of early-type galaxies. However, no observations have yet been able to disentangle the physical driver. We analyse here a sample of 24 early-type galaxies drawn from the CALIFA survey, deriving in a homogeneous way their stellar population and kinematic properties. We find that the local IMF is tightly related to the local metallicity, becoming more bottom-heavy towards metal-rich populations. Our result, combined with the galaxy mass-metallicity relation, naturally explains previous claims of a galaxy mass-IMF relation, derived from non-IFU spectra. If we assume that - within the star formation environment of early-type galaxies - metallicity is the main driver of IMF variations, a significant revision of the interpretation of galaxy evolution observables is necessary.

THE NON-UNIVERSALITY OF THE LOW-MASS END OF THE IMF IS ROBUST AGAINST THE CHOICE OF SSP MODEL

We perform a direct comparison of two state-of-the art single stellar population (SSP) models that have been used to demonstrate the non-universality of the low-mass end of the Initial Mass Function (IMF) slope. The two public versions of the SSP models are restricted to either solar abundance patterns or solar metallicity, too restrictive if one aims to disentangle elemental enhancements, metallicity changes and IMF variations in massive early-type galaxies (ETGs) with star formation histories different from the solar neighborhood. We define response functions (to metallicity and \alpha-abundance) to extend the parameter space of each set of models. We compare these extended models with a sample of Sloan Digital Sky Survey (SDSS) ETGs spectra with varying velocity dispersions. We measure equivalent widths of optical IMF-sensitive stellar features to examine the effect of the underlying model assumptions and ingredients, such as stellar libraries or isochrones, on the inference of the IMF slope down to ~0.1 solar masses. We demonstrate that the steepening of the low-mass end of the Initial Mass Function (IMF) based on a non-degenerate set of spectroscopic optical indicators is robust against the choice of the stellar population model. Although the models agree in a relative sense (i.e. both imply more bottom-heavy IMFs for more massive systems), we find non-negligible differences on the absolute values of the IMF slope inferred at each velocity dispersion by using the two different models. In particular, we find large inconsistency in the quantitative predictions of IMF slope variations and abundance patterns when sodium lines are used. We investigate the possible reasons for these inconsistencies.

An assessment of the evidence from ATLAS3D for a variable initial mass function

The ATLAS3D Survey has reported evidence for a non-universal stellar initial mass function (IMF) for early-type galaxies (ETGs). The IMF was constrained by comparing stellar mass measurements from kinematic data with those from spectral energy distribution (SED) fitting. Here, we investigate possible effects of scatter in the reported stellar mass measurements and their potential impact on the IMF determination. We find that a trend of the IMF mismatch parameter with the kinematic mass-to-light ratio, comparable to the trend observed by Cappellari et al., could arise if the Gaussian errors of the kinematic mass determination are typically 30 per cent. Without additional data, it is hard to separate between the option that the IMF has a true large intrinsic variation or the option that the errors in the determination are larger than anticipated. A correlation of the IMF with other properties would help to make this distinction, but no strong correlation has been found yet. The strongest correlation is with velocity dispersion. However, it has a large scatter and the correlation depends on sample selection and distance measurements. The correlation with velocity dispersion could be partly caused by the colour-dependent calibration of the surface brightness fluctuation distances of Tonry et al. We find that the K-band luminosity-limited ATLAS3D Survey is incomplete for the highest M/L galaxies below 1010.3 M⊙. There is a significant IMF–velocity dispersion trend for galaxies with SED masses above this limit, but no trend for galaxies with kinematic masses above this limit. We also find an IMF trend with distance, but no correlation between nearest neighbour ETGs, which excludes a large environmental dependence. Our findings do not rule out the reported IMF variations, but they suggest that further study is needed.

The initial mass function of early-type galaxies: no correlation with [Mg/Fe

Abstract The initial mass function (IMF) of early-type galaxies (ETGs) has been found to feature systematic variations by both dynamical and spectroscopic studies. In particular, spectral line strengths, based on gravity-sensitive features, suggest an excess of low-mass stars in massive ETGs, i.e. a bottom-heavy IMF. The physical drivers of IMF variations are currently unknown. The abundance ratio of α elements, such as [Mg/Fe], has been suggested as a possible driver of the IMF changes, although dynamical constraints do not support this claim. In this letter, we take advantage of the large Sloan Digital Sky Survey data base. Our sample comprises 24 781 high-quality spectra, covering a large range in velocity dispersion (100 < σ0 < 320 km s−1) and abundance ratio ( − 0.1 < [Mg/Fe] < +0.4). The large volume of data allows us to stack the spectra at fixed values of σ0 and [Mg/Fe]. Our analysis – based on gravity-sensitive line strengths – gives a strong correlation with central velocity dispersion and a negligible variation with [Mg/Fe] at fixed σ0. This result is robust against individual elemental abundance variations, and seems not to raise any apparent inconsistency with the alternative method based on galaxy dynamics.

GLOBULAR CLUSTER POPULATIONS: FIRST RESULTS FROM S4G EARLY-TYPE GALAXIES

Using 3.6$\mu$m images of 97 early-type galaxies, we develop and verify methodology to measure globular cluster populations from the S$^4$G survey images. We find that 1) the ratio, T$_{\rm N}$, of the number of clusters, N$_{\rm CL}$, to parent galaxy stellar mass, M$_*$, rises weakly with M$_*$ for early-type galaxies with M$_* > 10^{10}$ M$_\odot$ when we calculate galaxy masses using a universal stellar initial mass function (IMF), but that the dependence of T$_{\rm N}$ on M$_*$ is removed entirely once we correct for the recently uncovered systematic variation of IMF with M$_*$, and 2) for M$_* < 10^{10}$ M$_\odot$ there is no trend between N$_{\rm CL}$ and M$_*$, the scatter in T$_{\rm N}$ is significantly larger (approaching 2 orders of magnitude), and there is evidence to support a previous, independent suggestion of two families of galaxies. The behavior of N$_{\rm CL}$ in the lower mass systems is more difficult to measure because these systems are inherently cluster poor, but our results may add to previous evidence that large variations in cluster formation and destruction efficiencies are to be found among low mass galaxies. The average fraction of stellar mass in clusters is $\sim$ 0.0014 for M$_* > 10^{10}$ M$_\odot$ and can be as large as $\sim 0.02$ for less massive galaxies. These are the first results from the S$^4$G sample of galaxies, and will be enhanced by the sample of early-type galaxies now being added to S$^4$G and complemented by the study of later type galaxies within S$^4$G.

THE RELATION BETWEEN DYNAMICAL MASS-TO-LIGHT RATIO AND COLOR FOR MASSIVE QUIESCENT GALAXIES OUT TOz∼ 2 AND COMPARISON WITH STELLAR POPULATION SYNTHESIS MODELS

We explore the relation between the dynamical mass-to-light ratio ($M/L$) and rest-frame color of massive quiescent galaxies out to z~2. We use a galaxy sample with measured stellar velocity dispersions in combination with Hubble Space Telescope and ground-based multi-band photometry. Our sample spans a large range in $\log M_{dyn}/L_{g}$ (of 1.6~dex) and $\log M_{dyn}/L_{K}$ (of 1.3~dex). There is a strong, approximately linear correlation between the $M/L$ for different wavebands and rest-frame color. The root-mean-scatter scatter in $\log~M_{dyn}/L$ residuals implies that it is possible to estimate the $M/L$ with an accuracy of ~0.25 dex from a single rest-frame optical color. Stellar population synthesis (SPS) models with a Salpeter stellar initial mass function (IMF) can not simultaneously match $M_{dyn}/L_{g}$ vs. $(g-z)_{rest-frame}$ and $M_{dyn}/L_{K}$ vs. $(g-K)_{rest-frame}$. By changing the slope of the IMF we are still unable to explain the M/L of the bluest and reddest galaxies. We find that an IMF with a slope between $\alpha=2.35$ and $\alpha=1.35$ provides the best match. We also explore a broken IMF with a Salpeter slope at $M<1M_{\odot}$ and $M>4M_{\odot}$ and a slope $\alpha$ in the intermediate region. The data favor a slope of $\alpha=1.35$ over $\alpha=2.35$. Nonetheless, our results show that variations between different SPS models are comparable to the IMF variations. In our analysis we assume that the variation in $M/L$ and color is driven by differences in age, and that other contributions (e.g., metallicity evolution, dark matter) are small. These assumptions may be an important source of uncertainty as galaxies evolve in more complex ways.

THE STELLAR INITIAL MASS FUNCTION AT 0.9 &lt; z &lt; 1.5

We explore the stellar initial mass function (IMF) of a sample of 49 massive quiescent galaxies (MQGs) at 0.9$<$z$<$1.5. We base our analysis on intermediate resolution spectro-photometric data in the GOODS-N field taken in the near-infrared and optical with the HST/WFC3 G141 grism and the Survey for High-z Absorption Red and Dead Sources (SHARDS). To constrain the slope of the IMF, we have measured the TiO$_2$ spectral feature, whose strength depends strongly on the content of low-mass stars, as well as on stellar age. Using ultraviolet to near-infrared individual and stacked spectral energy distributions, we have independently estimated the stellar ages of our galaxies. Knowing the age of the stellar population, we interpret the strong differences in the TiO$_2$ feature as an IMF variation. In particular, for the heaviest z$\sim$1 MQGs (M$>$10$^{11}$Msun) we find an average age of 1.7$\pm$0.3 Gyr and a bottom-heavy IMF ($\Gamma_b$=3.2$\pm$0.2). Lighter MQGs (2$\times$10$^{10}$$<$M$<$10$^{11}$ Msun) at the same redshift are younger on average (1.0$\pm$0.2 Gyr) and present a shallower IMF slope ($\Gamma_b=2.7^{+0.3}_{-0.4}$). Our results are in good agreement with the findings about the IMF slope in early-type galaxies of similar mass in the present-day Universe. This suggests that the IMF, a key characteristic of the stellar populations in galaxies, is bottom-heavier for more massive galaxies and has remained unchanged in the last $\sim$8 Gyr.

VARIATIONS OF THE STELLAR INITIAL MASS FUNCTION IN THE PROGENITORS OF MASSIVE EARLY-TYPE GALAXIES AND IN EXTREME STARBURST ENVIRONMENTS

We examine variations of the stellar initial mass function (IMF) in extreme environments within the formalism derived by Hennebelle \& Chabrier. We focus on conditions encountered in progenitors of massive early type galaxies and starburst regions. We show that, when applying the concept of turbulent Jeans mass as the characteristic mass for fragmentation in a turbulent medium, instead of the standard thermal Jeans mass for purely gravitational fragmentation, the peak of the IMF in such environments is shifted towards smaller masses, leading to a bottom-heavy IMF, as suggested by various observations. In very dense and turbulent environments, we predict that the high-mass tail of the IMF can become even steeper than the standard Salpeter IMF, with a limit for the power law exponent $\alpha\simeq -2.7$, in agreement with recent observational determinations. This steepening is a direct consequence of the high densities and Mach values in such regions but also of the time dependence of the fragmentation process, as incorporated in the Hennebelle-Chabrier theory. We provide analytical parametrizations of these IMFs in such environments, to be used in galaxy evolution calculations. We also calculate the star formation rates and the mass-to-light ratios expected under such extreme conditions and show that they agree well with the values inferred in starburst environments and massive high-redshift galaxies. This reinforces the paradigm of star formation as being a universal process, i.e. the direct outcome of gravitationally unstable fluctuations in a density field initially generated by large scale shock-dominated turbulence. This globally enables us to infer the variations of the stellar IMF and related properties for atypical galactic conditions.

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.

Massive Elliptical Galaxies: BH Scouring or a Bottom-Heavy IMF?

AbstractWe present indirect constraints on the stellar initial-mass-function (IMF) in nine massive elliptical galaxies with σ ≈ 300 km/s, via a comparison of dynamical and stellar-population based stellar masses. We use adaptive-optics assisted, high resolution kinematical data from the SINFONI Search for Supermassive Black Holes that allow us to constrain the dynamical stellar mass-to-light ratio in the very centre of each galaxy. Hence we measure the IMF in a galaxy region where the stellar mass dominates over dark matter, minimising any potential degeneracy between the two mass components. In six of our galaxies – those which have depleted stellar cores – we find an IMF consistent with the one measured in the Milky-Way via direct star counts. The three remaining, power-law galaxies have instead stellar masses about a factor of two times larger than expected from a Milky-Way type IMF, indicating either a more bottom-heavy IMF (like, e.g., the Salpeter IMF) or a dark-matter distribution that is degenerate with the stellar mass down to the very centres of these galaxies. The bottom-light IMF in our core galaxies is surprising in view of previous studies that suggested a systematic IMF variation where early-type galaxies with σ ≈ 300 km/s have a Salpeter or even more dwarf-dominated IMF. Core galaxies are particularly important since their unique central orbital structure offers an independent crosscheck for the dynamical models. Our models with a bottom-light IMF are consistent with the distribution of orbits predicted by SMBH-binary core-formation models. This indicates that spatially well resolved central kinematical data are important for determining unbiased dynamical stellar mass-to-light ratios. Our results imply either that the IMF in massive galaxies varies over a wider range than previously anticipated, and is not the same in core and power-law ellipticals, or else that there are systematic variations in the distribution of dark matter among massive early-type galaxies.

Variations of the initial mass function in semi-analytical models

Deviations from a universal, MW-like, Stellar Initial Mass Function (IMF) have been reported for distant galaxies, although the physical reason behind the observed variations is still matter of ongoing debate. In this paper, we present an exploratory study to assess the impact of the proposed IMF evolution on the statistical galaxy properties, as predicted by the Semi-Analytical model of galaxy formation and evolution MORGANA. In particular, we test different dependencies for the IMF shape, as a function of both model galaxy properties (such as star formation rate, velocity dispersion or stellar mass) and environment, and compare the predicted stellar mass functions and star formation rate functions with reference runs at fixed IMF. In most cases, MORGANA predictions show deviations of the order of a few tenths of dex with respect to a run assuming an Universal Kroupa IMF. Among the proposed IMF variations, an increasing Top-Heavy IMF at increasing star formation rates has the largest impact on predicted galaxy properties, while most of the models assuming an increasing Bottom-Heavy IMF at higher masses/velocity dispersion lead to variations in galaxy properties that are of the same order as the uncertainty on the mass and star formation rate determination. By comparing the predicted galaxy stellar mass functions, we conclude that the study of the high-mass end can provide useful constraints to disentangle models assuming an increasing Top-Heavy IMF in high star forming or Bottom-Heavy IMF in massive systems.

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.