Ultra-faint Dwarf Research Articles

Hunting for Globular Clusters in the early universe

AbstractSetting the formation of globular clusters (GCs) within a cosmological context and characterising the properties of proto-GCs at high redshift is currently a major challenge. In this work, we address that challenge by exploring a suit of high-resolution cosmological simulations from the First Billion Years (FiBY) project z at ⩾6 to investigate theoretical scenarios concerning the formation of old, low-mass stellar systems with a particular focus on GCs. Two distinct groups of objects are identified in the simulations. The first group of objects, with a high baryon fraction, we associate with proto-GCs. The second group, that exhibit a high stellar fraction, could be forming ultra-faint dwarf galaxies (UFDs). The objects with high baryon fraction are promising proto-GC candidates because they have little to no dark matter (DM), have number densities consistent with predictions from the literature, are very compact and have a high stellar density. We fit and also assess the redshift-zero globular system mass - halo mass relation and find it provides a reasonable fit to our proto-GC objects, indicating that this relation is likely set at formation.

Parameter estimation for scarce stellar populations

We present a Bayesian method to determine simultaneously the age, metallicity, distance modulus, and interstellar reddening by dust of any resolved stellar population, by comparing the observed and synthetic color magnitude diagrams on a star by star basis, with no need to bin the data into a carefully selected magnitude grid. We test the method with mock stellar populations, and show that it works correctly even for scarce stellar populations with only one or two hundred stars above the main sequence turn off. If the population is the result of two star formation bursts, we can infer the contribution of each event to the total stellar population. The code works automatically and has already been used to study massive amounts of Magellanic clouds photometric data. In this paper we analyze in detail three Large Magellanic Cloud star clusters and 6 Ultra Faint Dwarf Galaxies. For these galaxies we recover physical parameters in agreement with those quoted in the literature, age $\sim13.7$ Gyr and a very low metallicity $log\,Z\sim-4$. Searching for multiple populations in these galaxies, we find, at a very low significance level, signs of a double stellar population for Ursa Major I: a dominant old population and a younger one which contributes $\sim25$% of the stars, in agreement with independent results from other authors.

Five Gas-rich Ultrafaint Dwarf Galaxy Candidates Discovered in WIYN Imaging of ALFALFA Sources

Abstract We present results from the analysis of WIYN pODI imaging of 23 ultracompact high-velocity clouds (UCHVCs), which were identified in the ALFALFA H i survey as possible dwarf galaxies in or near the Local Group. To search for a resolved stellar population associated with the H i gas in these objects, we carried out a series of steps designed to identify stellar overdensities in our optical images. We identify five objects that are likely stellar counterparts to the UCHVCs, at distances of ∼350 kpc to ∼1.6 Mpc. Two of the counterparts were already described in Janesh et al.; the estimated distance and detection significance for one of them changed in the final analysis of the full pODI data set. At their estimated distances, the detected objects have H i masses from 2 × 104 to 3 × 106 M ⊙, M V from −1.4 to −7.1, and stellar masses from 4 × 102 to 4 × 105 M ⊙. None of the objects shows evidence of a young stellar population. Their properties would make the UCHVCs some of the most extreme objects in and around the Local Group, comparable to ultrafaint dwarf galaxies in their stellar populations, but with significant gas content. Such objects probe the extreme end of the galaxy mass function and provide a test bed for theories regarding the baryonic feedback processes that impact star formation and galaxy evolution in this low-mass regime.

RR Lyrae Stars in the Field of Sagittarius II

Abstract We present the detection of RR Lyrae variable stars in the field of the Sagittarius II (Sgr II) ultra-faint dwarf (UFD) galaxy. Using B, V time-series photometry obtained with the Korea Microlensing Telescope Network (KMTNet) 1.6 m telescope at CTIO and G-band data from Gaia Data Release 2 (DR2), we identified and characterized two ab-type and four c-type RR Lyrae variables. Five out of the six stars are clustered within three half-light radii (∼4.′8) of the galaxy indicating their association with Sgr II, while the RRab star V4 is located ∼22′ from the galaxy center. By excluding V4, the high c-type fraction (0.8) and the period of the only RRab star V3 (P V3 ≃ 0.666 days) suggest an Oosterhoff II (Oo II) classification for Sgr II. Located close to the locus of Oo II clusters in the period–amplitude diagram, V3 is similar to RRab stars in other UFDs having Oosterhoff-intermediate and Oo II properties. Sgr II is, however, more compact than usual UFDs, placed in between star clusters and dwarf galaxies in the size–luminosity plane, and therefore spectroscopic studies are eventually required to ascertain the true nature of this stellar system. We derive the metallicity ([Fe/H]RRab ≃ −2.1 ± 0.3) and heliocentric distance (∼64 ± 3 kpc) of Sgr II from the RR Lyrae stars, and estimate its age (∼12 Gyr) based on our stellar population models. The Oosterhoff properties of UFDs can be explained with the evolution effect of RR Lyrae stars in the instability strip.

Double neutron star formation: merger times, systemic velocities, and travel distances

The formation and evolution of double neutron stars (DNS) have traditionally been studied using binary population synthesis. In this work, we take an alternative approach by focusing only on the second supernova (SN) forming the DNS and the subsequent orbital decay and merger due to gravitational wave radiation. Using analytic and numerical methods, we explore how different NS natal kick velocity distributions, pre-SN orbital separations, and progenitor He-star masses affect the post-SN orbital periods, eccentricities, merger times, systemic velocities, and distances traveled by the system before merging. Comparison with the set of 17 known DNSs in the Milky Way shows that DNSs have pre-SN orbital separations ranging between 1 and 44 $R_{\odot}$. Those DNSs with pre-SN separations $\sim$1 $R_{\odot}$ have merger time distributions that peak $\sim$10-100 Myr after formation, regardless of the kick velocity received by the NS. These DNSs are typically formed with systemic velocities $\sim$10$^2$ km s$^{-1}$ and may travel $\sim$1-10 kpc before merging. Depending on progenitor mass of the second-born NS, the short merger time can account for the $r$-process enrichment observed in compact stellar systems such as ultra-faint dwarf galaxies. For Milky Way-mass galaxies only DNSs with the tightest pre-SN orbits and large kick velocities ($\gtrsim$10$^2$ km s$^{-1}$) can escape. However, those DNSs that do escape may travel as far as $\sim$Mpc before merging, which as previous studies have pointed out has implications for identifying the host galaxies to short gamma ray bursts and gravitational wave events.

Proper Motions of Milky Way Ultra-faint Satellites with Gaia DR2 × DES DR1

Abstract We present a new, probabilistic method for determining the systemic proper motions of Milky Way (MW) ultra-faint satellites in the Dark Energy Survey (DES). We utilize the superb photometry from the first public data release (DR1) of the DES to select candidate members and cross-match them with the proper motions from the Gaia DR2. We model the candidate members with a mixture model (satellite and MW) in spatial and proper motion space. This method does not require prior knowledge of satellite membership and can successfully determine the tangential motion of 13 DES satellites. With our method, we present measurements of the following satellites: Columba I, Eridanus III, Grus II, Phoenix II, Pictor I, Reticulum III, and Tucana IV. This is the first systemic proper motion measurement for several of these satellites, and the majority lack extensive spectroscopic follow-up studies. We compare these to the predictions of Large Magellanic Cloud satellites and the vast polar structure. With the high-precision DES photometry, we conclude that most of the newly identified member stars are very metal-poor ([Fe/H] ≲ −2), similar to other ultra-faint dwarf galaxies, while Reticulum III is likely more metal-rich. We also find potential members in the following satellites that might indicate their overall proper motion: Cetus II, Kim 2, and Horologium II. However, due to the small number of members in each satellite, spectroscopic follow-up observations are necessary to determine the systemic proper motion in these satellites.

Positrons and 511keV Radiation as Tracers of Recent Binary Neutron Star Mergers.

Neutron-rich material ejected from neutron star-neutron star (NS-NS) and neutron star-black-hole (NS-BH) binary mergers is heated by nuclear processes to temperatures of a few hundred keV, resulting in a population of electron-positron pairs. Some of the positrons escape from the outer layers of the ejecta. We show that the population of low-energy positrons produced by NS-NS and NS-BH mergers in the MilkyWay can account for the observed 511-keV line from the Galactic center (GC). Moreover, we suggest how positrons and the associated 511-keV emission can be used as tracers of recent mergers. Recent discovery of 511-keV emission from the ultrafaint dwarf galaxy Reticulum II, consistent with a rare NS-NS merger event, provides a smoking-gun signature of our proposal.

Dancing in the Dark: Uncertainty in Ultrafaint Dwarf Galaxy Predictions from Cosmological Simulations

Abstract The existence of ultrafaint dwarf (UFD) galaxies highlights the need to push our theoretical understanding of galaxies to extremely low mass. We examine the formation of UFDs by twice running a fully cosmological simulation of dwarf galaxies, but varying star formation. One run uses a temperature–density threshold for star formation, while the other uses an H2-based subgrid star formation model. The total number of dwarf galaxies that form is different by a factor of 2 between the two runs, but most of these are satellites, leading to a factor of 5 difference in the number of luminous UFD companions around more massive, isolated dwarfs. The first run yields a 47% chance of finding a satellite around an M halo ∼ 1010 M ⊙ host, while the H2 run predicts only a 16% chance. Metallicity is the primary physical parameter that creates this difference. As metallicity decreases, the formation of H2 is slowed and relegated to higher-density material. Thus, our H2 run is unable to form many (and often, any) stars before reionization removes gas. These results emphasize that predictions for UFD properties made using hydrodynamic simulations, in particular regarding the frequency of satellites around dwarf galaxies, the slope of the stellar mass function at low masses, and the properties of ultrafaint galaxies occupying the smallest halos, are extremely sensitive to the subgrid physics of star formation contained within the simulation. However, upcoming discoveries of UFDs will provide invaluable constraining power on the physics of the first star formation.

A MegaCam Survey of Outer Halo Satellites. VII. A Single Sérsic Index versus Effective Radius Relation for Milky Way Outer Halo Satellites* †

Abstract In this work, we use structural properties of the Milky Way’s outer halo (R G > 25 kpc) satellites (dwarf spheroidal galaxies, ultra-faint dwarf (UFD) galaxies and globular clusters (GCs)) derived from deep, wide-field, and homogeneous data to present evidence of a correlation in the Sérsic index versus effective radius plane followed by a large fraction of outer halo GCs and satellite dwarf galaxies. We show that this correlation can be entirely reproduced by fitting empirical relations in the central surface brightness versus absolute magnitude and Sérsic index versus absolute magnitude parameter spaces, and by assuming the existence of two types of outer halo GCs: one of high surface brightness (HSB group), with properties similar to those of inner halo clusters; and another of low surface brightness (LSB group), which share characteristics with dwarf spheroidal and UFD galaxies. Given the similarities of LSB clusters with dwarf spheroidal and UFD galaxies, we discuss the possibility that outer halo clusters also originated inside dark matter halos and that tidal forces from different host galaxy potentials are responsible for the different properties between HSB and LSB clusters.

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

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

R-process Enrichment of the Ultra-faint Dwarf Galaxies by Fast-merging Double-neutron Stars

Abstract The recent aLIGO/aVirgo discovery of gravitational waves from the neutron star merger (NSM) GW170817 and the follow-up kilonova observations have shown that NSMs produce copious amounts of r-process material. However, it is difficult to reconcile the large natal kicks and long average merging times of double-neutron stars (DNSs) with the levels of r-process enrichment seen in ultra-faint dwarf (UFD) galaxies such as Reticulum II and Tucana III. Assuming that such dwarf systems have lost a significant fraction of their stellar mass through tidal stripping, we conclude that contrary to most current models, it is the DNSs with rather large natal kicks but very short merging timescales that can enrich UFD-type galaxies. These binaries are either on highly eccentric orbits or form with very short separations due to an additional mass transfer between the first-born neutron star and a naked helium star, the progenitor of the second neutron star. These DNSs are born with a frequency that agrees with the statistics of the r-process UFDs, and merge well within the virial radius of their host halos, therefore contributing significantly to their r-process enrichment.

The Origin of r-process Enhanced Metal-poor Halo Stars In Now-destroyed Ultra-faint Dwarf Galaxies

Abstract The highly r-process-enhanced (r-II) metal-poor halo stars we observe today could play a key role in understanding early ultra-faint dwarf galaxies (UFDs), the smallest building blocks of the Milky Way. If a significant fraction of metal-poor r-II halo stars originated in the UFDs that merged to help form the Milky Way, observations of r-II stars could help us study these now-destroyed systems and probe the formation history of our Galaxy. To conduct our initial investigation into this possible connection, we use high-resolution cosmological simulations of Milky Way-mass galaxies from the Caterpillar suite in combination with a simple, empirically motivated treatment of r-process enrichment. We determine the fraction of metal-poor halo stars that could have formed from highly r-process-enhanced gas in now-destroyed low-mass UFDs, the simulated r-II fraction, and compare it to the “as observed” r-II fraction. We find that the simulated fraction, f r−II,sim ∼ 1%–2%, can account for around half of the “as observed” fraction, f r−II,obs ∼ 2%–4%. The “as observed” fraction likely overrepresents the fraction of r-II stars due to incomplete sampling, though, meaning f r−II,sim likely accounts for more than half of the true f r−II,obs. Further considering some parameter variations and scatter between individual simulations, the simulated fraction can account for around 20%–80% of the “as observed” fraction.

Gaia Data Release 2

Context. The Gaia second Data Release (DR2) presents a first mapping of full-sky RR Lyrae stars and Cepheids observed by the spacecraft during the initial 22 months of science operations. Aims. The Specific Objects Study (SOS) pipeline, developed to validate and fully characterise Cepheids and RR Lyrae stars (SOS Cep&RRL) observed by Gaia, has been presented in the documentation and papers accompanying the Gaia first Data Release. Here we describe how the SOS pipeline was modified to allow for processing the Gaia multi-band (G, GBP, and GRP) time-series photometry of all-sky candidate variables and produce specific results for confirmed RR Lyrae stars and Cepheids that are published in the DR2 catalogue. Methods. The SOS Cep&RRL processing uses tools such as the period–amplitude and the period–luminosity relations in the G band. For the analysis of the Gaia DR2 candidates we also used tools based on the GBP and GRP photometry, such as the period–Wesenheit relation in (G, GRP). Results. Multi-band time-series photometry and characterisation by the SOS Cep&RRL pipeline are published in Gaia DR2 for 150 359 such variables (9575 classified as Cepheids and 140 784 as RR Lyrae stars) distributed throughout the sky. The sample includes variables in 87 globular clusters and 14 dwarf galaxies (the Magellanic Clouds, 5 classical and 7 ultra-faint dwarfs). To the best of our knowledge, as of 25 April 2018, the variability of 50 570 of these sources (350 Cepheids and 50 220 RR Lyrae stars) has not been reported before in the literature, therefore they are likely new discoveries by Gaia. An estimate of the interstellar absorption is published for 54 272 fundamental-mode RR Lyrae stars from a relation based on the G-band amplitude and the pulsation period. Metallicities derived from the Fourier parameters of the light curves are also released for 64 932 RR Lyrae stars and 3738 fundamental-mode classical Cepheids with periods shorter than 6.3 days.

Extreme chemical abundance ratio suggesting an exotic origin for an ultradiffuse galaxy

Ultradiffuse galaxies (UDGs) are a population of extended galaxies but with relatively low luminosities. The origin of these objects remains unclear, largely due to the observational challenges of the low surface brightness Universe. We present here a detailed stellar population analysis of a relatively isolated UDG, DGSAT I, based on spectroscopic data from the Keck Cosmic Web Imager integral field unit. The star formation history of DGSAT I seems to be extended, with a mean luminosity-weighted age of ∼3 Gyr, in agreement with previous photometric studies. However, we find a very high [Mg/Fe] abundance ratio, which is extreme even in the context of the highly alpha-enhanced massive ellipticals and ultrafaint dwarfs. The [Mg/Fe] enhancement of DGSAT I appears to be 10 times higher than the most magnesium-enhanced stellar systems discovered to date, and suggests that the chemical enrichment of this object was dominated by core-collapse supernovae. Intriguingly, this breaks the canonical relation between [Mg/Fe] and star formation time-scale. With a measured velocity dispersion of 56 ± 10 km s−1, DGSAT I also shows a high-mass-to-light ratio, which indicates that it is highly dark matter dominated. The metal-poor conditions of DGSAT I may have enhanced the formation of massive stars, while at the same time, additional mechanisms are needed to prevent iron-rich yields from being recycled into stars. These results suggest that some UDGs could have experienced chemical enrichment episodes similar to the first building blocks of galaxies.

Chemical Abundances in the Ultra-faint Dwarf Galaxies Grus I and Triangulum II: Neutron-capture Elements as a Defining Feature of the Faintest Dwarfs*

Abstract We present high-resolution spectroscopy of four stars in two candidate ultra-faint dwarf galaxies (UFDs), Grus I (Gru I) and Triangulum II (Tri II). Neither object currently has a clearly determined velocity dispersion, placing them in an ambiguous region of parameter space between dwarf galaxies and globular clusters (GCs). No significant metallicity difference is found for the two Gru I stars, but both stars are deficient in neutron-capture elements. We verify previous results that Tri II displays significant spreads in metallicity and [α/Fe]. Neutron-capture elements are not detected in our Tri II data, but we place upper limits at the lower envelope of Galactic halo stars, consistent with previous very low detections. Stars with similarly low neutron-capture element abundances are common in UFDs but rare in other environments. This signature of low neutron-capture element abundances traces chemical enrichment in the least massive star-forming dark matter halos and further shows that the dominant sources of neutron-capture elements in metal-poor stars are rare. In contrast, all known GCs have similar ratios of neutron-capture elements to those of halo stars, suggesting that GCs do not form at the centers of their own dark matter halos. The low neutron-capture element abundances may be the strongest evidence that Gru I and Tri II are (or once were) galaxies rather than GCs, and we expect future observations of these systems to robustly find nonzero velocity dispersions or signs of tidal disruption. However, the nucleosynthetic origin of this low neutron-capture element floor remains unknown.

Latest results on dark matter searches with H.E.S.S

The nature of Dark Matter (DM) is one of the most debated questions of contemporary physics. Ground-based arrays of Cherenkov telescopes such as the High Energy Spectroscopic System (H.E.S.S.) search for DM signatures through the detection of Very-High-Energy (VHE, E > 100 GeV) gamma-rays. DM particles could selfannihilate in dense environments producing VHE γ-rays in the final states that could be eventually detected by H.E.S.S.. The H.E.S.S. observation strategy for DM search focuses towards the Galactic Centre (GC) region and nearby dwarf galaxy satellites of the Milky Way. The GC dataset provides the most stringent constraints on the DM annihilation cross section in the mass range 300 GeV - 70 TeV. Searches have been carried out towards classical and ultra-faint dwarf galaxies to test specific heavy DM models. The latest results towards the GC and dwarf galaxies are shown.

Warm FIRE: simulating galaxy formation with resonant sterile neutrino dark matter

We study the impact of a warm dark matter (WDM) cosmology on dwarf galaxy formation through a suite of cosmological hydrodynamical zoom-in simulations of $M_{\rm halo} \approx10^{10}\,M_{\odot}$ dark matter halos as part of the Feedback in Realistic Environments (FIRE) project. A main focus of this paper is to evaluate the combined effects of dark matter physics and stellar feedback on the well-known small-scale issues found in cold dark matter (CDM) models. We find that the $z=0$ stellar mass of a galaxy is strongly correlated with the central density of its host dark matter halo at the time of formation, $z_{\rm f}$, in both CDM and WDM models. WDM halos follow the same $M_{\star}(z=0)-V_{\rm max}(z_{\rm f})$ relation as in CDM, but they form later, are less centrally dense, and therefore contain galaxies that are less massive than their CDM counterparts. As a result, the impact of baryonic effects on the central gravitational potential is typically diminished relative to CDM. However, the combination of delayed formation in WDM and energy input from stellar feedback results in dark matter profiles with lower overall densities. The WDM galaxies studied here have a wider diversity of star formation histories (SFHs) than the same systems simulated in CDM, and the two lowest $M_{\star}$ WDM galaxies form all of their stars at late times. The discovery of young ultra-faint dwarf galaxies with no ancient star formation -- which do not exist in our CDM simulations -- would therefore provide evidence in support of WDM.

The suppression of star formation on the smallest scales: what role does environment play?

The predominantly ancient stellar populations observed in the lowest-mass galaxies (i.e. ultra-faint dwarfs) suggest that their star formation was suppressed by reionization. Most of the well-studied ultra-faint dwarfs, however, are within the central half of the Milky Way dark matter halo, such that they are consistent with a population that was accreted at early times and thus potentially quenched via environmental processes. To study the potential role of environment in suppressing star formation on the smallest scales, we utilize the Exploring the Local Volume in Simulations (ELVIS) suite of $N$-body simulations to constrain the distribution of infall times for low-mass subhalos likely to host the ultra-faint population. For the ultra-faint satellites of the Milky Way with star-formation histories inferred from $Hubble~Space~Telescope$ imaging, we find that environment is highly unlikely to play a dominant role in quenching their star formation. Even when including the potential effects of pre-processing, there is a $\lesssim 0.1\%$ probability that environmental processes quenched all of the known ultra-faint dwarfs early enough to explain their observed star-formation histories. Instead, we argue for a mass floor in the effectiveness of satellite quenching at roughly $M_{\star} \sim 10^{5}~M_{\odot}$, below which star formation in surviving galaxies is globally suppressed by reionization. We predict a large population of quenched ultra-faint dwarfs in the Local Field ($1 < R/R_{\rm{vir}} < 2$), with as many as $\sim250$ to be discovered by future wide-field imaging surveys.

With and without spectroscopy: Gaia DR2 proper motions of seven ultra-faint dwarf galaxies

Aims. We present mean absolute proper motion measurements for seven ultra-faint dwarf galaxies orbiting the Milky Way, namely Boötes III, Carina II, Grus II, Reticulum II, Sagittarius II, Segue 2, and Tucana IV. For four of these dwarfs our proper motion estimate is the first ever provided. Methods. The adopted astrometric data come from the second data release of the Gaia mission. We determine the mean proper motion for each galaxy starting from an initial guess of likely members, based either on radial velocity measurements or using stars on the horizontal branch identified in the Gaia (GBP – GRP, G) colour-magnitude diagram in the field of view towards the UFD. We then refine their membership iteratively using both astrometry and photometry. We take into account the full covariance matrix among the astrometric parameters when deriving the mean proper motions for these systems. Results. Our procedure provides mean proper motions with typical uncertainties of ∼0.1 mas yr−1, even for galaxies without prior spectroscopic information. In the case of Segue 2 we find that using radial velocity members only leads to biased results, presumably because of the small number of stars with measured radial velocities. Conclusions. Our procedure allows the number of member stars per galaxy to be maximized regardless of the existence of prior spectroscopic information, and can therefore be applied to any faint or distant stellar system within reach of Gaia.

Impact of metallicity and star formation rate on the time-dependent, galaxy-wide stellar initial mass function

The stellar initial mass function (IMF) is commonly assumed to be an invariant probability density distribution function of initial stellar masses. These initial stellar masses are generally represented by the canonical IMF, which is defined as the result of one star formation event in an embedded cluster. As a consequence, the galaxy-wide IMF (gwIMF) should also be invariant and of the same form as the canonical IMF; gwIMF is defined as the sum of the IMFs of all star-forming regions in which embedded clusters form and spawn the galactic field population of the galaxy. Recent observational and theoretical results challenge the hypothesis that the gwIMF is invariant. In order to study the possible reasons for this variation, it is useful to relate the observed IMF to the gwIMF. Starting with the IMF determined in resolved star clusters, we apply the IGIMF-theory to calculate a comprehensive grid of gwIMF models for metallicities, [Fe/H] ∈ (−3, 1), and galaxy-wide star formation rates (SFRs), SFR ∈ (10−5, 105) M⊙ yr−1. For a galaxy with metallicity [Fe/H] &lt; 0 and SFR &gt; 1 M⊙ yr−1, which is a common condition in the early Universe, we find that the gwIMF is both bottom light (relatively fewer low-mass stars) and top heavy (more massive stars), when compared to the canonical IMF. For a SFR &lt; 1 M⊙ yr−1 the gwIMF becomes top light regardless of the metallicity. For metallicities [Fe/H] &gt; 0 the gwIMF can become bottom heavy regardless of the SFR. The IGIMF models predict that massive elliptical galaxies should have formed with a gwIMF that is top heavy within the first few hundred Myr of the life of the galaxy and that it evolves into a bottom heavy gwIMF in the metal-enriched galactic centre. Using the gwIMF grids, we study the SFR−Hα relation and its dependency on metallicity and the SFR. We also study the correction factors to the Kennicutt SFRK − Hα relation and provide new fitting functions. Late-type dwarf galaxies show significantly higher SFRs with respect to Kennicutt SFRs, while star-forming massive galaxies have significantly lower SFRs than hitherto thought. This has implications for gas-consumption timescales and for the main sequence of galaxies. We explicitly discuss Leo P and ultra-faint dwarf galaxies.