An Integrated Picture of Star Formation, Metallicity Evolution, and Galactic Stellar Mass Assembly

We report the stellar mass functions obtained from 20 radiation hydrodynamical simulations of star cluster formation in 500 M$_\odot$ molecular clouds with metallicities of 3, 1, 1/10, and 1/100 of the solar value, with the clouds subjected to levels of the cosmic microwave background radiation that are appropriate for star formation at redshifts $z=0, 3, 5, 7,$ and 10. The calculations include a thermochemical model of the diffuse interstellar medium and treat dust and gas temperatures separately. We find that the stellar mass distributions obtained become increasingly bottom light as the redshift and/or metallicity are increased. Mass functions that are similar to a typical Galactic initial mass function are obtained for present-day star formation ($z=0$) independent of metallicity, and also for the lowest-metallicity (1/100 solar) at all redshifts up to $z=10$, but for higher metallicities, there is a larger deficit of brown dwarfs and low-mass stars as the metallicity and redshift are increased. These effects are a result of metal-rich gas being unable to cool to as lower temperatures at higher redshift due to the warmer cosmic microwave background radiation. Based on the numerical results, we provide a parametrization that may be used to vary the stellar initial mass function with redshift and metallicity; this could be used in simulations of galaxy formation. For example, a bottom-light mass function reduces the mass-to-light ratio compared to a typical Galactic stellar initial mass function, which may reduce the estimated masses of high-redshift galaxies.

The evolution of the galaxy stellar mass--star formation rate relationship (M*-SFR) provides key constraints on the stellar mass assembly histories of galaxies. For star-forming galaxies, M*-SFR is observed to be fairly tight with a slope close to unity from z~0-2. Simulations of galaxy formation reproduce these trends owing to the generic dominance of smooth and steady cold accretion in these systems. In contrast, the amplitude of the M*-SFR relation evolves markedly differently than in models. Stated in terms of a star formation activity parameter alpha=(M*/SFR)/(t_H-1 Gyr), models predict a constant alpha~1 out to redshifts z=4+, while the observed M*-SFR relation indicates that alpha increases by X3 from z~2 until today. The low alpha at high-z not only conflicts with models, but is also difficult to reconcile with other observations of high-z galaxies. Systematic biases could significantly affect measurements of M* and SFR, but detailed considerations suggest that none are obvious candidates to reconcile the discrepancy. A speculative solution is considered in which the stellar initial mass function (IMF) evolves towards more high-mass star formation at earlier epochs. Following Larson, a model is investigated in which the characteristic mass Mhat where the IMF turns over increases with redshift. The observed and predicted M*-SFR evolution may be brought into agreement if Mhat=0.5(1+z)^2 Mo out to z~2. Such evolution broadly matches recent observations of cosmic stellar mass growth, and the resulting z=0 cumulative IMF is similar to the paunchy IMF favored by Fardal et al to reconcile the observed cosmic star formation history with present-day fossil light measures. [abridged]

We present a comparison between simulation results and X-ray observational data on the evolution of the metallicity of the intracluster medium (ICM). The simulations of galaxy clusters have been carried out using a version of the TREE PM-smoothed particle hydrodynamics (SPH) GADGET-2 code that includes a detailed model of chemical evolution by assuming three different shapes for the stellar initial mass function (IMF). Besides the Salpeter IMF, we also used the IMF proposed by Kroupa and the top-heavier IMF by Arimoto and Yoshii. We find that simulations predict significant radial gradients of the Iron abundance, Z Fe , which extend over the whole cluster virialized region. Using the Salpeter IMF, the profiles of Z Fe have an amplitude which is in a reasonable agreement with Chandra observations within 0.2R 500 . At larger radii, we do not detect any flattening of the metallicity profiles. As for the evolution of the ICM metal abundance out to z = 1, it turns out that the results based on the Salpeter IMF agree with observations. We find that the evolution of Z Fe in simulations is determined by the combined action of (i) the sinking of already enriched gas, (ii) the ongoing metal production in galaxies and (iii) the locking of ICM metals in newborn stars. As a result, rather than suppressing the metallicity evolution, stopping star formation at z = 1 has the effect of producing an even too fast evolution of the emission-weighted ICM metallicity, with too high values of Z Fe at low redshift within 0.2R 200 . Finally, we compare simulations with the observed rate of Type Ia supernovae per unit B-band luminosity (SnU B ). We find that our simulated clusters do not reproduce the decreasing trend of SnU B at low redshift, unless star formation is truncated at z = 1.

We use the full VIPERS redshift survey in combination with SDSS-DR7 to explore the relationships between star-formation history (using d4000), stellar mass and galaxy structure, and how these relationships have evolved since z~1. We trace the extents and evolutions of both the blue cloud and red sequence, by fitting double Gaussians to the d4000 distribution of galaxies in narrow stellar mass bins, for four redshift intervals over 0<z<1. This reveals downsizing in star formation, as the high-mass limit of the blue cloud retreats steadily with time from M*~10^11.2 M_sun at z~0.9 to M*~10^10.7 M_sun by the present day. The number density of massive blue-cloud galaxies (M*>10^11 M_sun, d4000<1.55) drops sharply by a factor five between z~0.8 and z~0.5. These galaxies are becoming quiescent at a rate that largely matches the increase in the numbers of massive passive galaxies seen over this period. We examine the size-mass relation of blue cloud galaxies, finding that its high-mass boundary runs along lines of constant M*/r_e or equivalently inferred velocity dispersion. Larger galaxies can continue to form stars to higher stellar masses than smaller galaxies. As blue cloud galaxies approach this high-mass limit, they start to be quenched, their d4000 values increasing to push them towards the green valley. In parallel, their structures change, showing higher Sersic indices and central stellar mass densities. For these galaxies, bulge growth is necessary for them to reach the high-mass limit of the blue cloud and be quenched by internal mechanisms. The blue cloud galaxies that are being quenched at z~0.8 lie along the same size-mass relation as present day quiescent galaxies, and seem the likely progenitors of today's S0s.

Context. Between the blue cloud and the red sequence peaks on the galaxy colour–magnitude diagram there is a region sparsely populated by galaxies called the green valley. In a framework where galaxies mostly migrate on the colour–magnitude diagram from star forming to quiescent, the green valley is considered a transitional galaxy stage. The details of the processes that drive galaxies from star-forming to passive systems still remain unknown. Aims. We aim to measure the transitional timescales of nearby galaxies across the green valley, through the analysis of Galaxy Evolution Explorer and Javalambre Photometric of Local Universe Survey photometric data. Specifically, we seek to study the impact of bars on the quenching timescales. Methods. We developed a method that estimates empirically the star formation quenching timescales of green valley galaxies, assuming an exponential decay model of the star formation histories and through a combination of narrow and broad bands from the Javalambre Photometric of Local Universe Survey and Galaxy Evolution Explorer. We correlated these quenching timescales with the presence of bars. Results. We find that the Javalambre Photometric of Local Universe Survey colours F0395 −g and F0410 −g are sensitive to different star formation histories, showing, consequently, a clear correlation with the Dn(4000) and Hδ, A spectral indices. We measured quenching timescales based on these colours and we find that quenching timescales obtained with our new approach are in agreement with those determined using spectral indices. We also compared the quenching timescales of green valley disc galaxies as a function of the probability of hosting a bar. We find that galaxies with high bar probability tend to quench their star formation slowly. Conclusions. We conclude that: (1) Javalambre Photometric of Local Universe Survey filters can be used to measure quenching timescales in nearby green valley galaxies; and (2) the resulting star formation quenching timescales are longer for barred green valley galaxies. Considering that the presence of a bar indicates that more violent processes (e.g. major mergers) are absent in host galaxies, we conclude that the presence of a bar can be used as a morphological signature for slow star formation quenching.

Stars do not form continuously distributed over star-forming galaxies. They form in star clusters of different masses. This nature of clustered star formation is taken into account in the theory of the integrated galactic stellar initial mass function (IGIMF) in which the galaxy-wide initial mass function (IMF) on galaxy-wide scales is calculated by adding all IMFs of young star clusters. For massive stars, the IGIMF is steeper than the universal IMF in star clusters and steepens with decreasing star formation rate (SFR) which is called the IGIMF effect. The current SFR and the total Hα luminosity of galaxies therefore scale nonlinearly in the IGIMF theory compared to the classical case in which the galaxy-wide IMF is assumed to be constant and identical to the IMF in star clusters. Here we apply for the first time the revised SFR–LHα relation on a sample of local volume star-forming galaxies with measured Hα luminosities. The fundamental results are: (1) the SFRs of galaxies scale linearly with the total galaxy neutral gas mass, (2) the gas depletion timescales of dwarf irregular and large disk galaxies are about 3 Gyr, implying that dwarf galaxies do not have lower star formation efficiencies than large disk galaxies, and (3) the stellar-mass buildup times of dwarf and large galaxies are only in agreement with downsizing in the IGIMF context, but contradict downsizing within the traditional framework that assumes a constant galaxy-wide IMF.

We present new griffin project hydrodynamical simulations that model the formation of galactic star cluster populations in low-metallicity (Z = 0.00021) dwarf galaxies, including radiation, supernova, and stellar wind feedback of individual massive stars. In the simulations, stars are sampled from the stellar initial mass function (IMF) down to the hydrogen-burning limit of 0.08 M⊙. Mass conservation is enforced within a radius of 1 pc for the formation of massive stars. We find that massive stars are preferentially found in star clusters and follow a correlation set at birth between the highest initial stellar mass and the star cluster mass that differs from pure stochastic IMF sampling. With a fully sampled IMF, star clusters lose mass in the galactic tidal field according to mass-loss rates observed in nearby galaxies. Of the released stellar feedback, 60 per cent of the supernova material and up to 35 per cent of the wind material reside either in the hot interstellar medium (ISM) or in gaseous, metal-enriched outflows. While stellar winds (instantaneously) and supernovae (delayed) start enriching the ISM right after the first massive stars form, the formation of supernova-enriched stars and star clusters is significantly delayed (by &amp;gt;50 Myr) compared to the formation of stars and star clusters enriched by stellar winds. Overall, supernova ejecta dominate the enrichment by mass, while the number of enriched stars is determined by continuous stellar winds. These results present a concept for the formation of chemically distinct populations of stars in bound star clusters, reminiscent of multiple populations in globular clusters.

We investigate the star formation histories (SFHs) of 983 early-type dwarf galaxies classified into five morphological subtypes-dS0, dE, dEbc, dSph, and dEbl-across six environments ranging from the field to rich clusters such as Ursa Major and Virgo. Using full spectral fitting of SDSS spectra with the starlight code, we derive detailed SFHs and chemical enrichment patterns. We find that SFHs are primarily shaped by morphology, with environment playing a secondary but non-negligible role. Red early-type dwarfs (dS0, dE, dSph) typically formed most of their stars early and quenched rapidly, whereas blue early-type dwarfs (dEbc, dEbl) exhibit extended or ongoing star formation and host extremely metal-poor stars, suggesting continued pristine gas accretion. Environmental dependence is clearest in low-mass systems: field galaxies often show prolonged SFHs and delayed enrichment, while Virgo Cluster galaxies tend to quench earlier and enrich more rapidly. Cumulative SFHs reinforce these trends, with dSph galaxies showing the earliest quenching and least environmental dependence, indicating a likely primordial origin. Metallicity evolution also varies with mass and environment, progressing most slowly in low-mass field galaxies and most rapidly in high-mass cluster galaxies. Our results highlight the combined influence of morphology, stellar mass, and environment on the evolutionary diversity of early-type dwarfs, and suggest that both internal processes (nature) and external conditions (nurture) are intricately linked in shaping their star formation and chemical enrichment histories.

Recent studies proposed that cosmic rays (CR) are a key ingredient in setting the conditions for star formation, thanks to their ability to alter the thermal and chemical state of dense gas in the UV-shielded cores of molecular clouds. In this paper, we explore their role as regulators of the stellar initial mass function (IMF) variations, using the semi-analytic model for GAlaxy Evolution and Assembly (GAEA). The new model confirms our previous results obtained using the integrated galaxy-wide IMF (IGIMF) theory: both variable IMF models reproduce the observed increase of $\alpha$-enhancement as a function of stellar mass and the measured $z=0$ excess of dynamical mass-to-light ratios with respect to photometric estimates assuming a universal IMF. We focus here on the mismatch between the photometrically-derived ($M^{\rm app}_{\star}$) and intrinsic ($M_{\star}$) stellar masses, by analysing in detail the evolution of model galaxies with different values of $M_{\star}/M^{\rm app}_{\star}$. We find that galaxies with small deviations (i.e. formally consistent with a universal IMF hypothesis) are characterized by more extended star formation histories and live in less massive haloes with respect to the bulk of the galaxy population. While the IGIMF theory does not change significantly the mean evolution of model galaxies with respect to the reference model, a CR-regulated IMF implies shorter star formation histories and higher peaks of star formation for objects more massive than $10^{10.5} M_\odot$. However, we also show that it is difficult to unveil this behaviour from observations, as the key physical quantities are typically derived assuming a universal IMF.

We present catalogues of stellar masses, star formation rates (SFRs), and ancillary stellar population parameters for galaxies spanning 0 &amp;lt; z &amp;lt; 9 from the Deep Extragalactic VIsible Legacy Survey (DEVILS). DEVILS is a deep spectroscopic redshift survey with very high completeness, covering several premier deep fields including COSMOS (D10). Our stellar mass and SFR estimates are self-consistently derived using the spectral energy distribution (SED) modelling code ProSpect, using well-motivated parametrizations for dust attenuation, star formation histories, and metallicity evolution. We show how these improvements, and especially our physically motivated assumptions about metallicity evolution, have an appreciable systematic effect on the inferred stellar masses, at the level of ∼0.2 dex. To illustrate the scientific value of these data, we map the evolving galaxy stellar mass function (SMF) and the SFR–M⋆ relation for 0 &amp;lt; z &amp;lt; 4.25. In agreement with past studies, we find that most of the evolution in the SMF is driven by the characteristic density parameter, with little evolution in the characteristic mass and low-mass slopes. Where the SFR–M⋆ relation is indistinguishable from a power law at z &amp;gt; 2.6, we see evidence of a bend in the relation at low redshifts (z &amp;lt; 0.45). This suggests evolution in both the normalization and shape of the SFR–M⋆ relation since cosmic noon. It is significant that we only clearly see this bend when combining our new DEVILS measurements with consistently derived values for lower redshift galaxies from the Galaxy And Mass Assembly (GAMA) survey: this shows the power of having consistent treatment for galaxies at all redshifts.

The rest-frame intrinsic UV luminosity is often used as an indicator of the instantaneous star formation rate (SFR) in a galaxy. While it is in general a robust indicator of the ongoing star formation activity, the precise value of the calibration relating the UV luminosity to the SFR (Bν) is sensitive to various physical properties, such as the recent star formation and metal enrichment histories, along with the choice of stellar initial mass function (IMF). The distribution of these properties for the star-forming galaxy population then suggests that the adoption of a single calibration is not appropriate unless properly qualified with the uncertainties on the calibration. We investigate, with the aid of the GALFORM semi-analytic model of galaxy formation, the distribution of UV-SFR calibrations obtained using realistic star formation and metal enrichment histories. At z = 0, we find that when the IMF is fixed (to the Kennicutt IMF), the median calibration is Bfuv = 0.9 where SFR/[M⊙ yr−1] = Bν × 10−28 × Lν/[erg s−1 Hz−1]. However, the width of the distribution Bfuv suggests that for a single object there is around a 20 per cent intrinsic uncertainty (at z = 0, rising to ≃30 per cent at z = 6) on the SFR inferred from the FUV luminosity without additional constraints on the star formation history or metallicity. We also find that the median value of the calibration Bfuv is correlated with the SFR and redshift (at z &gt; 3) raising implications for the correct determination of the SFR from the UV.

ABSTRACTWe review recent determinations of the present‐day mass function (PDMF) and initial mass function (IMF) in various components of the Galaxy—disk, spheroid, young, and globular clusters—and in conditions characteristic of early star formation. As a general feature, the IMF is found to depend weakly on the environment and to be well described by a power‐law form for m≳1 M⊙ and a lognormal form below, except possibly for early star formation conditions. The disk IMF for single objects has a characteristic mass around mc ∼ 0.08 M⊙ and a variance in logarithmic mass σ ∼ 0.7, whereas the IMF for multiple systems has mc ∼ 0.2 M⊙ and σ ∼ 0.6. The extension of the single MF into the brown dwarf regime is in good agreement with present estimates of L‐ and T‐dwarf densities and yields a disk brown dwarf number density comparable to the stellar one, nBD ∼ n* ∼ 0.1 pc−3. The IMF of young clusters is found to be consistent with the disk field IMF, providing the same correction for unresolved binaries, confirming the fact that young star clusters and disk field stars represent the same stellar population. Dynamical effects, yielding depletion of the lowest mass objects, are found to become consequential for ages ≳130 Myr. The spheroid IMF relies on much less robust grounds. The large metallicity spread in the local subdwarf photometric sample, in particular, remains puzzling. Recent observations suggest that there is a continuous kinematic shear between the thick‐disk population, present in local samples, and the genuine spheroid one. This enables us to derive only an upper limit for the spheroid mass density and IMF. Within all the uncertainties, the latter is found to be similar to the one derived for globular clusters and is well represented also by a lognormal form with a characteristic mass slightly larger than for the disk, mc ∼ 0.2–0.3 M⊙, excluding a significant population of brown dwarfs in globular clusters and in the spheroid. The IMF characteristic of early star formation at large redshift remains undetermined, but different observational constraints suggest that it does not extend below ∼1 M⊙. These results suggest a characteristic mass for star formation that decreases with time, from conditions prevailing at large redshift to conditions characteristic of the spheroid (or thick disk) to present‐day conditions. These conclusions, however, remain speculative, given the large uncertainties in the spheroid and early star IMF determinations.These IMFs allow a reasonably robust determination of the Galactic present‐day and initial stellar and brown dwarf contents. They also have important galactic implications beyond the Milky Way in yielding more accurate mass‐to‐light ratio determinations. The mass‐to‐light ratios obtained with the disk and the spheroid IMF yield values 1.8–1.4 times smaller than for a Salpeter IMF, respectively, in agreement with various recent dynamical determinations. This general IMF determination is examined in the context of star formation theory. None of the theories based on a Jeans‐type mechanism, where fragmentation is due only to gravity, can fulfill all the observational constraints on star formation and predict a large number of substellar objects. On the other hand, recent numerical simulations of compressible turbulence, in particular in super‐Alfvénic conditions, seem to reproduce both qualitatively and quantitatively the stellar and substellar IMF and thus provide an appealing theoretical foundation. In this picture, star formation is induced by the dissipation of large‐scale turbulence to smaller scales through radiative MHD shocks, producing filamentary structures. These shocks produce local nonequilibrium structures with large density contrasts, which collapse eventually in gravitationally bound objects under the combined influence of turbulence and gravity. The concept of a single Jeans mass is replaced by a distribution of local Jeans masses, representative of the lognormal probability density function of the turbulent gas. Objects below the mean thermal Jeans mass still have a possibility to collapse, although with a decreasing probability.

Peaks and lulls in the star formation rate (SFR) over the history of the Galaxy produce plateaux and declines in the present day mass function (PDMF) where the main-sequence lifetime overlaps the age and duration of the SFR variation. These PDMF features can be misinterpreted as the form of the intrinsic stellar initial mass function (IMF) if the star formation rate is assumed to be constant or slowly varying with time. This effect applies to all regions that have formed stars for longer than the age of the most massive stars, including OB associations, star complexes, and especially galactic field stars. Related problems may apply to embedded clusters. Evidence is summarized for temporal SFR variations from parsec scales to entire galaxies, all of which should contribute to inferred IMF distortions. We give examples of various star formation histories to demonstrate the types of false IMF structures that might be seen. These include short-duration bursts, stochastic histories with log-normal amplitude distributions, and oscillating histories with various periods and phases. The inferred IMF should appear steeper than the intrinsic IMF over mass ranges where the stellar lifetimes correspond to times of decreasing SFRs; shallow portions of the inferred IMF correspond to times of increasing SFRs. If field regions are populated by dispersed clusters and defined by their low current SFRs, then they should have steeper inferred IMFs than the clusters. The SFRs required to give the steep field IMFs in the LMC and SMC are determined. Structure observed in several determinations of the Milky Way field star IMF can be accounted for by a stochastic and bursty star formation history.

We present a compilation of measurements of the stellar mass density as a function of redshift. Using this stellar mass history we obtain a star formation history and compare it to the instantaneous star formation history. For z &lt; 0.7 there is good agreement between the two star formation histories. At higher redshifts the instantaneous indicators suggest star formation rates larger than that implied by the evolution of the stellar mass density. This discrepancy peaks at z= 3 where instantaneous indicators suggest a star formation rate around 0.6 dex higher than those of the best fit to the stellar mass history. We discuss a variety of explanations for this inconsistency, such as inaccurate dust extinction corrections, incorrect measurements of stellar masses and a possible evolution of the stellar initial mass function.

Observational studies are showing that the galaxy-wide stellar initial mass function are top-heavy in galaxies with high star-formation rates (SFRs). Calculating the integrated galactic stellar initial mass function (IGIMF) as a function of the SFR of a galaxy, it follows that galaxies which have or which formed with SFRs > 10 Msol yr^-1 would have a top-heavy IGIMF in excellent consistency with the observations. Consequently and in agreement with observations, elliptical galaxies would have higher M/L ratios as a result of the overabundance of stellar remnants compared to a stellar population that formed with an invariant canonical stellar initial mass function (IMF). For the Milky Way, the IGIMF yields very good agreement with the disk- and the bulge-IMF determinations. Our conclusions are that purely stochastic descriptions of star formation on the scales of a pc and above are falsified. Instead, star formation follows the laws, stated here as axioms, which define the IGIMF theory. We also find evidence that the power-law index beta of the embedded cluster mass function decreases with increasing SFR. We propose further tests of the IGIMF theory through counting massive stars in dwarf galaxies.