Integrated Galactic Initial Mass Function Research Articles

The galaxy-wide stellar initial mass function in the presence of cluster-to-cluster IMF variations

We calculate the stellar integrated galactic initial mass function (IGIMF) in the presence of cluster-to-cluster variations of the IMF. Variations of the IMF for a population of coeval clusters that populate the initial cluster mass function (ICLMF) are taken into account in the form of Gaussian distribution functions of the IMF parameters. For the tapered power-law function used in this work, these are the slope at the high-mass end, Γ, the slope at the low-mass end, γ, and the characteristic mass Mch. The level of variations is modeled by varying the width of the Gaussian distributions. The reference values are the standard deviations of the parameters observed for the population of young clusters in the present-day Milky Way, which are σΓ = 0.6, σγ = 0.25, and σMch = 0.27 M⊙. We find that increasing the levels of dispersion for γ and Γ tends to moderately flatten the IGIMF at the low and high-mass end, respectively. The characteristic mass of the IGIMF is, however, strongly impacted by variations in Mch. Increasing the value of σMch shifts the peak of the IGIMF to lower masses, rendering the IGIMF more bottom heavy. This can provide a simple explanation for the bottom-heavy stellar mass function that is inferred for early-type galaxies since these are likely the result of a merger of disk galaxies where the physical conditions of the star-forming gas may vary significantly both in time and space in the merging system. The effect of IMF variations on the IGIMF is compared to the effects of other processes and sources of systematic variations such as those due to variations in the shape of ICLMF, the gas-phase metallicity, and the galactic star formation rate (SFR) which can potentially affect the maximum mass of stellar clusters in a galaxy and set the mean value of the characteristic mass in clusters. For the various dependencies we have explored, we found that the effect of IMF variations is a dominant factor that always affects the characteristic mass of the IGIMF. For the regimes at low metallicity where the IGIMF resembles a single power law, an increased level of IMF variations renders the IGIMF steeper and more bottom heavy, especially at low SFRs. On the other hand, variations in the IMF in the high mass regime can be easily dominated by variations in the slope of the ICLMF. We compare our results of the metallicity and SFR-dependent IGIMF to a sample of Milky Way ultra-faint dwarf (UFD) satellite galaxies that have available metallicity measurements. The present-day stellar mass function of these galaxies is a good analog to the IGIMF at the time their overall population of stars formed. We show that the slope of the stellar mass function of the UFD galaxies measured for stars in the mass range [0.4, 0.8] M⊙ can only be reproduced when IMF variations of the same order as those measured in the present-day Milky Way are included. Our results suggest that the inclusion of IMF variations in models of galaxy formation and evolution is of vital importance in order to improve our understanding of star formation and star formation feedback effects on galactic scales.

The influence of a top-heavy integrated galactic IMF and dust on the chemical evolution of high-redshift starbursts

ABSTRACT We study the effects of the integrated galactic initial mass function (IGIMF) and dust evolution on the abundance patterns of high redshift starburst galaxies. In our chemical models, the rapid collapse of gas clouds triggers an intense and rapid star formation episode, which lasts until the onset of a galactic wind, powered by the thermal energy injected by stellar winds and supernova explosions. Our models follow the evolution of several chemical elements (C, N, α-elements, and Fe) both in the gas and dust phases. We test different values of β, the slope of the embedded cluster mass function for the IGIMF, where lower β values imply a more top-heavy initial mass function (IMF). The computed abundances are compared to high-quality abundance measurements obtained in lensed galaxies and from composite spectra in large samples of star-forming galaxies in the redshift range 2 ≲ z ≲ 3. The adoption of the IGIMF causes a sensible increase of the rate of star formation with respect to a standard Salpeter IMF, with a strong impact on chemical evolution. We find that in order to reproduce the observed abundance patterns in these galaxies, either we need a very top-heavy IGIMF (β < 2) or large amounts of dust. In particular, if dust is important, the IGIMF should have β ≥ 2, which means an IMF slightly more top-heavy than the Salpeter one. The evolution of the dust mass with time for galaxies of different mass and IMF is also computed, highlighting that the dust amount increases with a top-heavier IGIMF.

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.

Chemical evolution of ultrafaint dwarf galaxies: testing the IGIMF

ABSTRACT We test the integrated galactic initial mass function (IGIMF) on the chemical evolution of 16 ultrafaint dwarf (UFD) galaxies discussing in detail the results obtained for three of them: Boötes I, Boötes II, and Canes Venatici I, taken as prototypes of the smallest and the largest UFDs. These objects have very small stellar masses (∼103–104 M⊙) and quite low metallicities ([Fe/H] < −1.0 dex). We consider four observational constraints: the present-day stellar mass, the [α/Fe] versus [Fe/H] relation, the stellar metallicity distribution function and the cumulative star formation history. Our model follows in detail the evolution of several chemical species (H, He, α-elements, and Fe). We take into account detailed nucleosynthesis and gas flows (in and out). Our results show that the IGIMF, coupled with the very low star formation rate predicted by the model for these galaxies (∼10−4–10−6 M⊙yr−1), cannot reproduce the main chemical properties, because it implies a negligible number of core-collapse SNe and even Type Ia SNe, the most important polluters of galaxies. On the other hand, a constant classical Salpeter IMF gives the best agreement with data, but we cannot exclude that other formulations of the IGIMF could reproduce the properties of these galaxies. Comparing with Galaxy data, we suggest that UFDs could not be the building blocks of the entire Galactic halo, although more data are necessary to draw firmer conclusions.

The Star Formation History and Dynamics of the Ultra-diffuse Galaxy Dragonfly 44 in MOND and MOG

Abstract The observed line-of-sight velocity dispersion σ los of the ultra-diffuse galaxy Dragonfly 44 (DF44) requires a Newtonian dynamical mass-to-light ratio of solar units. This is well outside the acceptable limits of our stellar population synthesis (SPS) models, which we construct using the integrated galactic initial mass function (IGIMF) theory. Assuming DF44 is in isolation and using Jeans analysis, we calculate σ los profiles of DF44 in Milgromian dynamics (MOND) and modified gravity (MOG) theories without invoking dark matter. Comparing with the observed kinematics, the best-fitting MOND model has and a constant orbital anisotropy of . In MOG, we first fix its two theoretical parameters α and μ based on previous fits to the observed rotation curve data of The HI Nearby Galaxy Survey (THINGS). The DF44 σ los profile is best fit with , larger than plausible SPS values. MOG produces a σ los profile for DF44 with acceptable M dyn/L I and isotropic orbits if α and μ are allowed to vary. MOND with the canonical a 0 can explain DF44 at the 2.40σ confidence level (1.66%) if considering both its observed kinematics and typical star formation histories in an IGIMF context. However, MOG is ruled out at 5.49σ (P-value of 4.07 × 10−8) if its free parameters are fixed at the highest values consistent with THINGS data.

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.

The mass–metallicity relation of tidal dwarf galaxies

Dwarf galaxies generally follow a mass-metallicity (MZ) relation, where more massive objects retain a larger fraction of heavy elements. Young tidal dwarf galaxies (TDGs), born in the tidal tails produced by interacting gas-rich galaxies, have been thought to not follow the MZ relation, because they inherit the metallicity of the more massive parent galaxies. We present chemical evolution models to investigate if TDGs that formed at very high redshifts, where the metallicity of their parent galaxy was very low, can produce the observed MZ relation. Assuming that galaxy interactions were more frequent in the denser high-redshift universe, TDGs could constitute an important contribution to the dwarf galaxy population. The survey of chemical evolution models of TDGs presented here captures for the first time an initial mass function (IMF) of stars that is dependent on both the star formation rate and the gas metallicity via the integrated galactic IMF (IGIMF) theory. As TDGs form in the tidal debris of interacting galaxies, the pre-enrichment of the gas, an underlying pre-existing stellar population, infall, and mass dependent outflows are considered. The models of young TDGs that are created in strongly pre-enriched tidal arms with a pre-existing stellar population can explain the measured abundance ratios of observed TDGs. The same chemical evolution models for TDGs, that form out of gas with initially very low metallicity, naturally build up the observed MZ relation. The modelled chemical composition of ancient TDGs is therefore consistent with the observed MZ relation of satellite galaxies.

The IGIMF and other IMFs in dSphs: the case of Sagittarius

We have studied the effects of various initial mass functions (IMFs) on the chemical evolution of the Sagittarius dwarf galaxy (Sgr). In particular, we tested the effects of the integrated galactic initial mass function (IGIMF) on various predicted abundance patterns. The IGIMF depends on the star formation rate and metallicity and predicts less massive stars in a regime of low star formation, as it is the case in dwarf spheroidals. We adopted a detailed chemical evolution model following the evolution of α-elements, Fe and Eu, and assuming the currently best set of stellar yields. We also explored different yield prescriptions for the Eu, including production from neutron star mergers. Although the uncertainties still present in the stellar yields and data prevent us from drawing firm conclusions, our results suggest that the IGIMF applied to Sgr predicts lower [α/Fe] ratios than classical IMFs and lower [hydrostatic/explosive] α-element ratios, in qualitative agreement with observations. In our model, the observed high [Eu/O] ratios in Sgr is due to reduced O production, resulting from the IGIMF mass cut-off of the massive oxygen-producing stars, as well as to the Eu yield produced in neutron star mergers, a more promising site than core-collapse supernovae, although many uncertainties are still present in the Eu nucleosynthesis. We find that a model, similar to our previous calculations, based on the late addition of iron from the Type Ia supernova time-delay (necessary to reproduce the shape of [X/Fe] versus [Fe/H] relations) but also including the reduction of massive stars due to the IGIMF, better reproduces the observed abundance ratios in Sgr than models without the IGIMF.

The chemical evolution of galaxies with a variable integrated galactic initial mass function

Standard analytical chemical evolution modelling of galaxies has been assuming the stellar initial mass function (IMF) to be invariant and fully sampled allowing fractions of massive stars to contribute even in dwarf galaxies with very low star formation rates (SFRs). Recent observations show the integrated galactic initial mass function (IGIMF) of stars, i.e. the galaxy-wide IMF, to become systematically top-heavy with increasing SFR. This has been predicted by the IGIMF theory, which is here used to develop the analytical theory of the chemical evolution of galaxies. This theory is non-linear and requires the iterative solution of implicit integral equations due to the dependence of the IGIMF on the metallicity and on the SFR. It is shown that the mass-metallicity relation of galaxies emerges naturally, although at low masses the theoretical predictions overestimate the observations by 0.3--0.4 dex. A good agreement with the observation can be obtained only if gas flows are taken into account. In particular, we are able to reproduce the mass--metallicity relation observed by Lee et al. (2006) with modest amounts of infall and with an outflow rate which decreases as a function of the galactic mass. The outflow rates required to fit the data are considerably smaller than required in models with invariant IMFs.

The [ /Fe] ratios of very metal-poor stars within the integrated galactic initial mass function theory

The aim of this paper is to quantify the amplitude of the predicted plateau in [alpha/Fe] ratios associated with the most metal-poor stars of a galaxy. We assume that the initial mass function in galaxies is steeper if the star formation rate (SFR) is low -- as per the integrated galactic initial mass function (IGIMF) theory. A variant of the theory, in which the IGIMF depends upon the metallicity of the parent galaxy, is also considered. The IGIMF theory predicts low [alpha/Fe] plateaus in dwarf galaxies, characterised by small SFRs. The [alpha/Fe] plateau is up to 0.7dex lower than the corresponding plateau of the Milky Way. For a universal IMF one should expect instead that the [alpha/Fe] plateau is the same for all the galaxies, irrespective of their masses or SFRs. Assuming a strong dependence of the IMF on the metallicity of the parent galaxy, dwarf galaxies can show values of the [alpha/Fe] plateau similar to those of the Milky Way, and almost independent on the SFR. The [Mg/Fe] ratios of the most metal-poor stars in dwarf galaxies satellites of the Milky Way can be reproduced either if we consider metallicity-dependent IMFs or if the early SFRs of these galaxies were larger than we presently think. Present and future observations of dwarf galaxies can help disentangle between these different IGIMF formulations.

STOCHASTIC STAR FORMATION AND A (NEARLY) UNIFORM STELLAR INITIAL MASS FUNCTION

Recent observations indicate a lower Halpha to FUV ratio in dwarf galaxies than in brighter systems, a trend that could be explained by a truncated and/or steeper IMF in small galaxies. However, at low star formation rates (SFRs), the Halpha to FUV ratio can vary due to stochastic sampling even for a universal IMF, a hypothesis that has, prior to this work, received limited investigation. Using SLUG, a fully stochastic code for synthetic photometry in star clusters and galaxies, we compare the Halpha and FUV luminosity in a sample of ~450 nearby galaxies with models drawn from a universal Kroupa IMF and a modified IMF, the integrated galactic initial mass function (IGIMF). Once random sampling and time evolution are included, a Kroupa IMF convolved with the cluster mass function reproduces the observed Halpha distribution at all FUV luminosities, while a truncated IMF as implemented in current IGIMF models underpredicts the Halpha luminosity by more than an order of magnitude at the lowest SFRs. We conclude that the observed luminosity is the result of the joint probability distribution function of the SFR, cluster mass function, and a universal IMF, consistent with parts of the IGIMF theory, but that a truncation in the IMF in clusters is inconsistent with the observations. Future work will examine stochastic star formation and its time dependence in detail to study whether random sampling can explain other observations that suggest a varying IMF.

Top-heavy integrated galactic stellar initial mass functions in starbursts

Star formation rates (SFR) larger than 1000 Msun/ yr are observed in extreme star bursts. This leads to the formation of star clusters with masses > 10^6 Msun in which crowding of the pre-stellar cores may lead to a change of the stellar initial mass function (IMF). Indeed, the large mass-to-light ratios of ultra-compact dwarf galaxies and recent results on globular clusters suggest the IMF to become top-heavy with increasing star-forming density. We explore the implications of top-heavy IMFs in these very massive and compact systems for the integrated galactic initial mass function (IGIMF), which is the galaxy-wide IMF, in dependence of the star-formation rate of galaxies. The resulting IGIMFs can have slopes, alpha_3, for stars more massive than about 1 Msun between 1.5 and the Salpeter slope of 2.3 for an embedded cluster mass function (ECMF) slope (beta) of 2.0, but only if the ECMF has no low-mass clusters in galaxies with major starbursts. Alternatively, beta would have to decrease with increasing SFR >10 Msun/ yr such that galaxies with major starbursts have a top-heavy ECMF. The resulting IGIMFs are within the range of observationally deduced IMF variations with redshift.

Effects of the integrated galactic IMF on the chemical evolution of the solar neighbourhood

The initial mass function determines the fraction of stars of different intial mass born per stellar generation. In this paper, we test the effects of the integrated galactic initial mass function (IGIMF) on the chemical evolution of the solar neighbourhood. The IGIMF (Weidner & Kroupa 2005) is computed from the combination of the stellar intial mass function (IMF), i.e. the mass function of single star clusters, and the embedded cluster mass function, i.e. a power law with index beta. By taking into account also the fact that the maximum achievable stellar mass is a function of the total mass of the cluster, the IGIMF becomes a time-varying IMF which depends on the star formation rate. We applied this formalism to a chemical evolution model for the solar neighbourhood and compared the results obtained by assuming three possible values for beta with the results obtained by means of a standard, well-tested, constant IMF. In general, a lower absolute value of beta implies a flatter IGIMF, hence a larger number of massive stars and larger metal ejection rates. This translates into higher type Ia and II supernova rates, higher mass ejection rates from massive stars and a larger amount of gas available for star formation, coupled with lower present-day stellar mass densities. (abridged) We also discuss the importance of the present day stellar mass function (PDMF) in providing a way to disentangle among various assumptions for beta. Our results indicate that the model adopting the IGIMF computed with beta ~2 should be considered the best since it allows us to reproduce the observed PDMF and to account for most of the chemical evolution constraints considered in this work.

The relation between the most-massive star and its parental star cluster mass

We present a thorough literature study of the most-massive star, m_max, in several young star clusters in order to assess whether or not star clusters are populated from the stellar initial mass function (IMF) by random sampling over the mass range 0.01 < m < 150 M_sol without being constrained by the cluster mass, M_ecl. The data reveal a partition of the sample into lowest mass objects (M_ecl < 10^2 M_sol), moderate mass clusters (10^2 M_sol < M_ecl < 10^3 M_sol) and rich clusters above 10^3 M_sol. Additionally, there is a plateau of a constant maximal star mass (m_max ~ 25 M_sol) for clusters with masses between 10^3 M_sol and 4 10^3 M_sol. Statistical tests of this data set reveal that the hypothesis of random sampling from the IMF between 0.01 and 150 M_sol is highly unlikely for star clusters more massive than 10^2 M_sol with a probability of p ~ 2 10^-7 for the objects with M_ecl between 10^2 M_sol and 10^3 M_sol and p ~ 3 10^-9 for the more massive star clusters. Also, the spread of m_max values at a given M_ecl is smaller than expected from random sampling. We suggest that the basic physical process able to explain this dependence of stellar inventory of a star cluster on its mass may be the interplay between stellar feedback and the binding energy of the cluster-forming molecular cloud core. Given these results, it would follow that an integrated galactic initial mass function (IGIMF) sampled from such clusters would automatically be steeper in comparison to the IMF within individual star clusters.

Population synthesis from clustered star formation

In recent years, a series of papers (Kroupa &amp; Weidner 2003, Weidner &amp; Kroupa 2004, Weidner &amp; Kroupa 2005 and Weidner &amp; Kroupa 2006, WK06 from now on) have proposed that the stellar content of an entire galaxy may not be well described by the same initial mass function (IMF) that describes the distribution of stellar masses in the star clusters, where these stars form. The reason is that star clusters also form with a cluster mass function (CMF), which is a power law with a power law index of ~−2. If the lowest mass clusters are of masses smaller than the physical upper mass limit for stars they will be deficient in high mass stars. Therefore, if the stellar content of all clusters is added together, making up the Integrated Galactic Initial Mass Function (IGIMF), the distribution of stellar masses may be steeper at the high mass end, depending on the exact shape of the CMF.

The chemical evolution of galaxies within the IGIMF theory: the [α/Fe] ratios and downsizing

The chemical evolution of galaxies is investigated within the framework of the star formation rate (SFR) dependent integrated galactic initial mass function (IGIMF). We study how the global chemical evolution of a galaxy and in particular how [alpha/Fe] abundance ratios are affected by the predicted steepening of the IGIMF with decreasing SFR. We use analytical and semi-analytical calculations to evaluate the mass-weighted and luminosity-weighted [alpha/Fe] ratios in early-type galaxies of different masses. The models with the variable IGIMF produce a [alpha/Fe] vs. velocity dispersion relation which has the same slope as the observations of massive galaxies, irrespective of the model parameters, provided that the star formation duration inversely correlates with the mass of the galaxy (downsizing). These models also produce steeper [alpha/Fe] vs. sigma relations in low-mass early-type galaxies and this trend is consistent with the observations. Constant IMF models are able to reproduce the [alpha/Fe] ratios in large elliptical galaxies as well, but they do not predict this change of slope for small galaxies. In order to obtain the best fit between our results and the observations, the downsizing effect (i.e. the shorter duration of the star formation in larger galaxies) must be milder than previously thought.

Diverging UV and Hα fluxes of star-forming galaxies predicted by the IGIMF theory

Although the stellar initial mass function (IMF) has only been directly determined in star clusters, it has been manifoldly applied on galaxy-wide scales. But taking the clustered nature of star formation into account the galaxy-wide IMF is constructed by adding all IMFs of all young star clusters leading to an integrated galactic initial mass function (IGIMF). The IGIMF is top-light compared to the canonical IMF in star clusters and steepens with decreasing total star formation rate (SFR). This discrepancy is marginal for large disc galaxies but becomes significant for Small Magellanic Cloud type galaxies and less massive ones. We here construct IGIMF-based relations between the total far- and near-ultraviolet luminosities of galaxies and the underlying SFR. We make the prediction that the Hα luminosity of star-forming dwarf galaxies decreases faster with decreasing SFR than the ultraviolet (UV) luminosity. This

Maximum stellar mass versus cluster membership number revisited

We have made a new compilation of observations of maximum stellar mass versus cluster membership number from the literature, which we analyse for consistency with the predictions of a simple random drawing hypothesis for stellar mass selection in clusters. Previously, Weidner and Kroupa have suggested that the maximum stellar mass is lower, in low-mass clusters, than would be expected on the basis of random drawing, and have pointed out that this could have important implications for steepening the integrated galactic initial mass function (IGIMF) at high masses. Our compilation demonstrates how the observed distribution in the plane of maximum stellar mass versus membership number is affected by the method of target selection; in particular, rather low n clusters with large maximum stellar masses are abundant in observational data sets that specifically seek clusters in the environs of high-mass stars. Although we do not consider our compilation to be either complete or unbiased, we discuss the method by which such data should be statistically analysed. Our very provisional conclusion is that the data are not indicating any striking deviation from the expectations of random drawing.

The influence of star clusters on galactic disks: new insights in star-formation in galaxies

AbstractStars form in embedded star clusters which play a key role in determining the properties of a galaxy's stellar population. A large fraction of newly born massive stars are shot out from dynamically unstable embedded-cluster cores spreading them to large distances before they explode. Embedded clusters blow out their gas once the feedback energy from the new stellar population overcomes its binding energy, leading to cluster expansion and in many cases dissolution into the galaxy. Galactic disks may be thickened by such processes, and some thick disks may be the result of an early epoch of vigorous star-formation. Binary stellar systems are disrupted in clusters leading to a lower fraction of binaries in the field, while long-lived clusters harden degenerate-stellar binaries such that the SNIa rate may increase by orders of magnitude in those galaxies that were able to form long-lived clusters. The stellar initial mass function of the whole galaxy must be computed by adding the IMFs in the individual clusters. The resulting integrated galactic initial mass function (IGIMF) is top-light for SFRs &lt; 10M⊙/yr, and its slope and, more importantly, its upper stellar mass limit depend on the star-formation rate (SFR), explaining naturally the mass–metallicity relation of galaxies. Based on the IGIMF theory, the re-calibrated Hα-luminosity–SFR relation implies dwarf irregular galaxies to have the same gas-depletion time-scale as major disk galaxies, implying a major change of our concept of dwarf-galaxy evolution. A galaxy transforms about 0.3 per cent of its neutral gas mass every 10 Myr into stars. The IGIMF-theory also naturally leads to the observed radial Hα cutoff in disk galaxies without a radial star-formation cutoff. It emerges that the thorough understanding of the physics and distribution of star clusters may be leading to a major paradigm shift in our understanding of galaxy evolution.