Stellar IMF Research Articles

The stellar initial mass function, core mass function and the last-crossing distribution

Hennebelle & Chabrier 2008 (HC08) attempted to derive the stellar IMF as a consequence of turbulent density fluctuations, using an argument similar to Press & Schechter 1974 for Gaussian random fields. Like that example, however, this solution does not resolve the 'cloud in cloud' problem; it also does not extend to large scales that dominate the velocity/density fluctuations. In principle, these can change the results at the order-of-magnitude level. Here, we use the results from Hopkins 2011 (H11) to generalize the excursion set formalism and derive the exact solution in this regime. We argue that the stellar IMF and core mass function (CMF) should be associated with the last-crossing distribution, i.e. the mass spectrum of bound objects defined on the smallest scale on which they are self-gravitating. This differs from the first-crossing distribution (mass function on the largest self-gravitating scale) which is defined cosmologically and which H11 show corresponds to the GMC mass function in disks. We derive an analytic equation for the last-crossing distribution that can be used for an arbitrary collapse threshold in ISM and cosmological studies. With this, we show that the same model that predicts the GMC mass function and large-scale structure of galaxy disks also predicts the CMF (and by extrapolation IMF) in good agreement with observations. The only adjustable parameter in the model is the turbulent velocity power spectrum, which in the range p~5/3-2 gives similar results. We also use this to justify why the approximate solution in HC08 is reasonable (up to a normalization) over the CMF/IMF mass range; however there are significant corrections at intermediate and high masses. We discuss how the exact solutions here can be embedded into time-dependent models that follow density fluctuations, fragmentation, successive generations of star formation.

ON THE AVERAGE DENSITY PROFILE OF DARK-MATTER HALOS IN THE INNER REGIONS OF MASSIVE EARLY-TYPE GALAXIES

We study a sample of 39 massive early-type lens galaxies at redshift z < 0.3 to determine the slope of the average dark-matter density profile in the innermost regions. We keep the strong lensing and stellar population synthesis modeling as simple as possible to measure the galaxy total and luminous masses. By rescaling the values of the Einstein radius and dark-matter projected mass with the values of the luminous effective radius and mass, we combine all the data of the galaxies in the sample. We find that between 0.3 and 0.9 times the value of the effective radius the average logarithmic slope of the dark-matter projected density profile is -1.0 +/- 0.2 (i.e., approximately isothermal) or -0.7 +/- 0.5 (i.e., shallower than isothermal), if, respectively, a constant Chabrier or heavier, Salpeter-like stellar IMF is adopted. These results provide positive evidence of the influence of the baryonic component on the contraction of the galaxy dark-matter halos, compared to the predictions of dark matter-only cosmological simulations, and open a new way to test models of structure formation and evolution within the standard LCDM cosmological scenario.

The Galactic initial mass function: origin in the combined mass distribution functions of dust grains and gas clouds

We present here a theoretical model to account for the stellar IMF as a result of the composite behaviour of the gas and dust distribution functions. Each of these has previously been modelled and the models tested against observations. The model presented here implies a relation between the characteristic size of the dust grains and the characteristic final mass of the stars formed within the clouds containing the grains, folded with the relation between the mass of a gas cloud and the characteristic mass of the stars formed within it. The physical effects of dust grain size are due to equilibrium relations between the efficiency of grains in cooling the clouds, which is a falling function of grain size, and the efficiency of grains in catalyzing the production of molecular hydrogen, which is a rising function of grain size. We show that folding in the effects of grain distribution can yield a reasonable quantitative account of the IMF, while gas cloud mass function alone cannot do so.

RADIATION-HYDRODYNAMIC SIMULATIONS OF THE FORMATION OF ORION-LIKE STAR CLUSTERS. I. IMPLICATIONS FOR THE ORIGIN OF THE INITIAL MASS FUNCTION

One model for the origin of typical galactic star clusters such as the Orion Nebula Cluster (ONC) is that they form via the rapid, efficient collapse of a bound gas clump within a larger, gravitationally-unbound giant molecular cloud. However, simulations in support of this scenario have thus far have not included the radiation feedback produced by the stars; radiative simulations have been limited to significantly smaller or lower density regions. Here we use the ORION adaptive mesh refinement code to conduct the first ever radiation-hydrodynamic simulations of the global collapse scenario for the formation of an ONC-like cluster. We show that radiative feedback has a dramatic effect on the evolution: once the first ~10-20% of the gas mass is incorporated into stars, their radiative feedback raises the gas temperature high enough to suppress any further fragmentation. However, gas continues to accrete onto existing stars, and, as a result, the stellar mass distribution becomes increasingly top-heavy, eventually rendering it incompatible with the observed IMF. Systematic variation in the location of the IMF peak as star formation proceeds is incompatible with the observed invariance of the IMF between star clusters, unless some unknown mechanism synchronizes the IMFs in different clusters by ensuring that star formation is always truncated when the IMF peak reaches a particular value. We therefore conclude that the global collapse scenario, at least in its simplest form, is not compatible with the observed stellar IMF. We speculate that processes that slow down star formation, and thus reduce the accretion luminosity, may be able to resolve the problem.

THE BOLOCAM GALACTIC PLANE SURVEY. V. HCO + AND N 2 H + SPECTROSCOPY OF 1.1 mm DUST CONTINUUM SOURCES

We present the results of observations of 1882 sources in the Bolocam Galactic Plane Survey (BGPS) at 1.1 mm with the 10m Heinrich Hertz Telescope simultaneously in HCO+ J=3-2 and N2H+ J=3-2. We detect 77% of these sources in HCO^+ and 51% in N2H+ at greater than 3$\sigma$. We find a strong correlation between the integrated intensity of both dense gas tracers and the 1.1 mm dust emission of BGPS sources. We determine kinematic distances for 529 sources (440 in the first quadrant breaking the distance ambiguity and 89 in the second quadrant) We derive the size, mass, and average density for this subset of clumps. The median size of BGPS clumps is 0.75 pc with a median mass of 330 M$_{\odot}$ (assuming T_{Dust}=20 K). The median HCO+ linewidth is 2.9 km s$^{-1}$ indicating that BGPS clumps are dominated by supersonic turbulence or unresolved kinematic motions. We find no evidence for a size-linewidth relationship for BGPS clumps. We analyze the effects of the assumed dust temperature on the derived clump properties with a Monte Carlo simulation and we find that changing the temperature distribution will change the median source properties (mass, volume-averaged number density, surface density) by factors of a few. The observed differential mass distribution has a power-law slope that is intermediate between that observed for diffuse CO clouds and the stellar IMF. BGPS clumps represent a wide range of objects (from dense cores to more diffuse clumps) and are typically characterized by larger sizes and lower densities than previously published surveys of high-mass star-forming regions. This collection of objects is a less-biased sample of star-forming regions in the Milky Way that likely span a wide range of evolutionary states.

The effect of variations in the input physics on the cosmic distribution of metals predicted by simulations

[Abridged] We investigate how a range of physical processes affect the cosmic metal distribution using a suite of cosmological, hydrodynamical simulations. Focusing on z = 0 and 2, we study the metallicities and metal mass fractions for stars as well as for the ISM, and several more diffuse gas phases. We vary the cooling rates, star formation law, structure of the ISM, galactic winds, feedback from AGN, reionization history, stellar IMF, and cosmology. In all models stars and the warm-hot IGM (WHIM) constitute the dominant repository of metals, while for z > 2 the ISM is also important. In models with galactic winds, predictions for the metallicities of the various phases vary at the factor of two level and are broadly consistent with observations. The exception is the cold-warm IGM, whose metallicity varies at the order of magnitude level if the prescription for galactic winds is varied, even for a fixed wind energy per unit stellar mass formed, and falls far below the observed values if winds are not included. At the other extreme, the metallicity of the intracluster medium (ICM) is largely insensitive to the presence of galactic winds, indicating that its enrichment is regulated by other processes. The mean metallicities of stars (~ Z_sun), the ICM (~ 0.1 Z_sun), and the WHIM (~ 0.1 Z_sun) evolve only slowly, while those of the cold halo gas and the IGM increase by more than an order of magnitude from z = 5 to 0. Higher velocity outflows are more efficient at transporting metals to low densities, but actually predict lower metallicities for the cold-warm IGM since the winds shock-heat the gas to high temperatures, thereby increasing the fraction of the metals residing in, but not the metallicity of, the WHIM. Besides galactic winds driven by feedback from star formation, the metal distribution is most sensitive to the inclusion of metal-line cooling and feedback from AGN.

THE DARK ENERGY SURVEY: PROSPECTS FOR RESOLVED STELLAR POPULATIONS

Wide angle and deep surveys, regardless of their primary purpose, always sample a large number of stars in the Galaxy and in its satellite system. We here make a forecast of the expected stellar sample resulting from the Dark Energy Survey and the perspectives that it will open for studies of Galactic structure and resolved stellar populations in general. An estimated 1.2x10^8 stars will be sampled in DES grizY filters. This roughly corresponds to 20% of all DES sources. Most of these stars belong to the stellar thick disk and halo of the Galaxy. DES will probe low-mass stellar and sub-stellar objects at depths from 3 to 8 times larger than SDSS. The faint end of the main-sequence will be densely sampled beyond 10 kpc. The slope of the low mass end of the stellar IMF will be constrained to within a few hundredth dex, even in the thick disk and halo. In the sub-stellar mass regime, the IMF slope will be potentially constrained to within dlog \phi(m) / dlog m ~ 0.1$. About 3x10^4 brown dwarf and at least 7.6x10^5 white dwarf candidates will be selected, the latter embedded into the thick disk and halo. The stellar halo flattening will also be constrained to within a few percent. DES will probe the main sequence of new Milky Way satellites and halo clusters for distances out to ~ 120 kpc, therefore yielding stellar surface density contrasts 1.6-1.7 times larger than those attainable with SDSS. It will also allow detection of these objects in the far reaches of the stellar halo, substantially increasing the number and quality of probes to the Galactic potential. Combined with northern samples, such as the SDSS, the DES stellar sample will yield constraints on the structure and stellar populations of Galactic components in unprecedented detail. In particular, the combined sample from both hemispheres will allow detailed studies of halo and thick disk asymmetries and triaxiality.

The star cluster – field star connection in nearby spiral galaxies

Recent studies have started to cast doubt on the assumption that most stars are formed in clusters. Observational studies of field stars and star cluster systems in nearby galaxies can lead to better constraints on the fraction of stars forming in clusters. We aim to constrain the amount of star formation happening in long-lived clusters for four galaxies through the homogeneous study of field stars and star clusters. Using HST/ACS-WFPC2 images of the galaxies NGC45, NGC1313, NGC5236 and NGC7793, we estimate star formation histories by means of the synthetic CMD method. Masses and ages of star clusters are estimated using simple stellar population model fitting. Comparing observed and modeled luminosity functions we estimate cluster formation rates. By randomly sampling the stellar IMF, we construct artificial star clusters and quantify how stochastic effects influence cluster detection, integrated colors and age estimates. Star formation rates appear to be constant over the past 10-100 Myr. The number of clusters identified per galaxy varies, with few massive (>10^5Msun) and few old (>1Gyr) clusters. The galaxies NGC5236 and NGC1313 show high star and cluster formation rates compare to NGC7793 and NGC45. Stochastic sampling of the SIMF has a strong impact on estimation of ages, colors and completeness for clusters with masses <10^4Msun, while for high masses the effect is less pronounced. Stochasticity also makes size measurements highly uncertain at young ages, making it difficult to distinguish between clusters and stars based on sizes. The ratio of star formation happening in clusters compared to the global star formation ($\Gamma$) appears to vary for different galaxies. We find no obvious relation between $\Gamma$ and the star formation rate density within the range probed here. The $\Gamma$ values do, however, appear to correlate with the specific U-band luminosity (T_L (U)).

THE EFFECT OF DUST COOLING ON LOW-METALLICITY STAR-FORMING CLOUDS

The theory for the formation of the first population of stars (Pop III) predicts a IMF composed predominantly of high-mass stars, in contrast to the present-day IMF, which tends to yield stars with masses less than 1 M_Solar. The leading theory for the transition in the characteristic stellar mass predicts that the cause is the extra cooling provided by increasing metallicity and in particular the cooling provided at high densities by dust. The aim of this work is to test whether dust cooling can lead to fragmentation and be responsible for this transition. To investigate this, we make use of high-resolution hydrodynamic simulations. We follow the thermodynamic evolution of the gas by solving the full thermal energy equation, and also track the evolution of the dust temperature and the chemical evolution of the gas. We model clouds with different metallicities, and determine the properties of the cloud at the point at which it undergoes gravitational fragmentation. We follow the further collapse to scales of an AU when we replace very dense, gravitationally bound, and collapsing regions by a simple and nongaseous object, a sink particle. Our results suggest that for metallicities as small as 10^{-5}Z_Solar, dust cooling produces low-mass fragments and hence can potentially enable the formation of low mass stars. We conclude that dust cooling affects the fragmentation of low-metallicity gas clouds and plays an important role in shaping the stellar IMF even at these very low metallicities. We find that the characteristic fragment mass increases with decreasing metallicity, but find no evidence for a sudden transition in the behaviour of the IMF within the range of metallicites examined in our present study.

DISSECTING THE RED SEQUENCE. III. MASS-TO-LIGHT VARIATIONS IN THREE-DIMENSIONAL FUNDAMENTAL PLANE SPACE

The Fundamental Plane has finite thickness and is tilted from the virial relation, indicating that dynamical mass-to-light ratios (Mdyn/L) vary among early type galaxies. We use a sample of 16,000 quiescent galaxies from the Sloan Digital Sky Survey to map out variations in Mdyn/L through the 3D Fundamental Plane space defined by velocity dispersion (sigma), effective radius (R_e), and effective surface brightness. We consider contributions to Mdyn/L variation due to stellar population effects, IMF variations, and variations in the dark matter fraction within one R_e. Along the FP, we find that the stellar population contribution scales as M*/L ~ f(sigma), while the dark matter and/or IMF contribution scales as Mdyn/M* ~ g(Mdyn). The two contributions to the tilt of the FP rotate the plane around different axes in the 3D space, with dark matter/IMF variations likely dominating. Through the thickness of the FP, we find that Mdyn/L variations must be dominated either by IMF variations or by real differences in dark matter fraction with R_e. Thus the finite thickness of the FP is due to variations in the stellar mass surface density within R_e, not the fading of passive stellar populations. These structural variations are correlated with galaxy star formation histories such that galaxies with higher Mdyn/M* at a given sigma have higher [Mg/Fe], lower metallicities, and older mean stellar ages. It is difficult to explain the observed correlations by allowing the IMF to vary, suggesting difference in dark matter fraction dominate. These can be produced by variations in the "conversion efficiency" of baryons into stars or by the redistribution of stars and dark matter through dissipational merging. A model in which some galaxies experience low conversion efficiencies due to premature truncation of star formation provides a natural explanation for the observed trends.

The universality hypothesis: binary and stellar populations in star clusters and galaxies

AbstractIt is possible to extract, from the observations, distribution functions of the birth dynamical properties of a stellar population, and to also infer that these are quite invariant to the physical conditions of star formation. The most famous example is the stellar IMF, and the initial binary population (IBP) seems to follow suit. A compact mathematical formulation of the IBP can be derived from the data. It has three broad parts: the IBP of the dominant stellar population (0.08–2M⊙), the IBP of the more-massive stars and the IBP of brown dwarfs. These three mass regimes correspond to different physical regimes of star formation but not to structure in the IMF. With this formulation of the IBP it becomes possible to synthesize the stellar-population of whole galaxies.

THE GALAXY LUMINOSITY FUNCTION DURING THE REIONIZATION EPOCH

The new Wide Field Camera 3/IR observations on the Hubble Ultra-Deep Field started investigating the properties of galaxies during the reionization epoch. To interpret these observations, we present a novel approach inspired by the conditional luminosity function method. We calibrate our model to observations at z=6 and assume a non-evolving galaxy luminosity versus halo mass relation. We first compare model predictions against the luminosity function measured at z=5 and z=4. We then predict the luminosity function at z>=7 under the sole assumption of evolution in the underlying dark-matter halo mass function. Our model is consistent with the observed z>6.5 galaxy number counts in the HUDF survey and suggests a possible steepening of the faint-end slope of the luminosity function: alpha(z>8)< -1.9 compared to alpha=-1.74 at z=6. Although we currently see only the brightest galaxies, a hidden population of lower luminosity objects (L/L_{*}> 10^{-4}) might provide >75% of the total reionizing flux. Assuming escape fraction f_{esc}~0.2, clumping factor C~5, top heavy-IMF and low metallicity, galaxies below the detection limit produce complete reionization at z>8. For solar metallicity and normal stellar IMF, reionization finishes at z>6, but a smaller C/f_{esc} is required for an optical depth consistent with the WMAP measurement. Our model highlights that the star formation rate in sub-L_* galaxies has a quasi-linear relation to dark-matter halo mass, suggesting that radiative and mechanical feedback were less effective at z>6 than today.

GALAXY FORMATION WITH COLD GAS ACCRETION AND EVOLVING STELLAR INITIAL MASS FUNCTION

The evolution of the galaxy stellar mass function is especially useful to test the current model of galaxy formation. Observational data have revealed a few inconsistencies with predictions from the $\Lambda {\rm CDM}$ model. For example, most massive galaxies have already been observed at very high redshifts, and they have experienced only mild evolution since then. In conflict with this, semi-analytical models of galaxy formation predict an insufficient number of massive galaxies at high redshift and a rapid evolution between redshift 1 and 0 . In addition, there is a strong correlation between star formation rate and stellar mass for star-forming galaxies, which can be roughly reproduced with the model, but with a normalization that is too low at high redshift. Furthermore, the stellar mass density obtained from the integral of the cosmic star formation history is higher than the measured one by a factor of 2. In this paper, we study these issues using a semi-analytical model that includes: 1) cold gas accretion in massive halos at high redshift; 2) tidal stripping of stellar mass from satellite galaxies; and 3) an evolving stellar initial mass function (bottom-light) with a higher gas recycle fraction. Our results show that the combined effects from 1) and 2) can predict sufficiently massive galaxies at high redshifts and reproduce their mild evolution at low redshift, While the combined effects of 1) and 3) can reproduce the correlation between star formation rate and stellar mass for star-forming galaxies across wide range of redshifts. A bottom-light/top-heavy stellar IMF could partly resolve the conflict between the stellar mass density and cosmic star formation history.

On the nature of star formation at large galactic radii

We have compared far-ultraviolet (FUV), near-ultraviolet (NUV), and Halpha measurements for star forming regions in 21 galaxies, in order to characterise the properties of their discs at radii beyond the main optical radius (R25). In our representative sample of extended and non-extended UV discs we find that half of the extended UV discs also exhibit extended Halpha emission. We find that extended UV discs fall into two categories, those with a sharp truncation in the Halpha disc close to the optical edge (R25), and those with extended emission in Halpha as well as in the ultraviolet. Although most galaxies with strong Halpha truncations near R25 show a significant corresponding falloff in UV emission (factor 10--100), the transition tends to be much smoother than in Halpha, and significant UV emission often extends well beyond this radius, confirming earlier results by Thilker et al. (2007) and others. After correcting for dust attenuation the median fraction of total FUV emission from regions outside of R25 is 1.7%, but it can be as high as 35% in the most extreme cases. The corresponding fractions of Halpha emission are approximately half as large on average. This difference reflects both a slightly lower ratio of Halpha to UV emission in the HII regions in the outer discs, as well as a lower fraction of star clusters showing HII regions. Most HII regions in the extended disc have fluxes consistent with small numbers of ionising O-type stars, and this poor sampling of the upper initial mass function in small clusters can probably account for the differences in the emission properties, consistent with earlier conclusions by Zaritsky & Christlein (2007), without needing to invoke a significant change in the stellar IMF itself. Consistent Ha/FUV ratios and brightest HII region to total Halpha fluxes in the inner and extended discs across our whole galaxy sample demonstrate no evidence for a change in the cluster luminosity function or the IMF in the low gas density outer disc.

Galactic consequences of clustered star formation

AbstractIf all stars form in clusters and both stars and clusters follow a power-law distribution which favours the creation of low-mass objects, the numerous low-mass clusters will be deficient in high-mass stars. Therefore, the stellar mass function integrated over the entire galaxy (the integrated galactic initial mass function; IGIMF) will be steeper at the high-mass end than the underlying stellar IMF. We show how the steepness of the IGIMF depends on the sampling method and on the assumptions made regarding the star cluster mass function. We also investigate the O-star content, integrated photometry and chemical enrichment of galaxies that result from several IGIMFs compared to more standard IMFs.

DENSE CORES IN THE PIPE NEBULA: AN IMPROVED CORE MASS FUNCTION

In this paper we derive an improved core mass function (CMF) for the Pipe Nebula from a detailed comparison between measurements of visual extinction and molecular-line emission. We have compiled a refined sample of 201 dense cores toward the Pipe Nebula using a 2-dimensional threshold identification algorithm informed by recent simulations of dense core populations. Measurements of radial velocities using complimentary C18O (1-0) observations enable us to cull out from this sample those 43 extinction peaks that are either not associated with dense gas or are not physically associated with the Pipe Nebula. Moreover, we use the derived C18O, central velocities to differentiate between single cores with internal structure and blends of two or more physically distinct cores, superposed along the same line-of-sight. We then are able to produce a more robust dense core sample for future follow-up studies and a more reliable CMF than was possible previously. We confirm earlier indications that the CMF for the Pipe Nebula departs from a single power-law like form with a break or knee at M ~ 2.7 +/- 1.3 Msun. Moreover, we also confirm that the CMF exhibits a similar shape to the stellar IMF, but is scaled to higher masses by a factor of ~4.5. We interpret this difference in scaling to be a measure of the star formation efficiency (22 +/- 8%). This supports earlier suggestions that the stellar IMF may originate more or less directly from the CMF.

Fragmentation in molecular clouds and its connection to the IMF

We present an analysis of star-forming gas cores in an SPH simulation of a Giant Molecular Cloud. We identify cores using their deep potential wells. This yields a smoother distribution with clearer boundaries than density. Additionally, this gives an indication of future collapse, as bound potential cores (p-cores) represent the earliest stages of fragmentation in molecular clouds. We find that the mass function of the p-cores resembles the stellar IMF and the observed clump mass function, although p-core masses (~0.7 Msol) are smaller than typical density clumps. The bound p-cores are generally subsonic, have internal substructure, and are only quasi-spherical. We see no evidence of massive bound cores supported by turbulence. We trace the evolution of the p-cores forward in time, and investigate the connection between the original p-core mass and the stellar mass that formed from it. We find that there is a poor correlation, with considerable scatter suggesting accretion onto the core is dependent on more factors than just the initial core mass. During the accretion process the p-cores accrete from beyond the region first bound, highlighting the importance of the core environment to its subsequent evolution.

The cluster birthline in M 33

We test the reliability of infrared (IR) emission to trace star formation in individual star-forming sites of M33, and outline a new method for testing the distribution function of massive stars in newly formed clusters. We select IR sources from the Spitzer survey of M33 and show that the IR and Halpha luminosities are not correlated. Complementing the infrared photometry with GALEX-UV data, we estimate the source bolometric luminosities. For a given stellar IMF we simulate a theoretical curve for the expected bolometric-to-Halpha luminosity ratio, along which stellar clusters are born. We call this the cluster birthline in the Lbol--Lbol/LHal plane. The birthline is flat for Lbol>3x10^{39}erg/s because all clusters fully sample the IMF and it increases toward lower luminosities as the upper end of the IMF becomes incompletely sampled. The observations of M33 show that young isolated clusters lie close to the theoretical birthline for a wide range of Lbol. The luminosity is not proportional to Halpha emission for low mass clusters and aging moves clusters above the birthline. The best fit to the birthline is for a randomly sampled IMF, in which the mass of most massive star in a cluster is not strictly limited by the cluster's mass. We also find that the IR luminosity of young stellar clusters in M33 is not proportional to their bolometric luminosity. This irregularity could be the result of low and patchy dust abundance in M33.

Rescuing the Initial Mass Function for Arp 78

We present deep R and narrowband H α images of Arp 78 obtained with the WIYN 3.5 m telescope on Kitt Peak. GALEX observations had shown a very extended UV structure for this system, reaching beyond the optical radius of Arp 78 and also beyond its previously known Hα radius. Our new H α data now show agreement not only with the spatial extent of the near- and far-UV maps, but also in terms of structural details. Star formation rates derived from L(Hα) and L(FUV) are in reasonable agreement, indicating that in this case the upper stellar IMF in the UV-bright outer arm is relatively normal. The star-forming sites in the outer arms are younger than ~15 Myr and massive enough to properly sample the IMF up to high masses; their low optical visibility evidently is a property of their youth.

Insights into the Origin of the Galaxy Mass-Metallicity Relation

AbstractWe examine mass–metallicity relations for nearby (D &lt; 2 Mpc) gas-rich and gas-poor dwarf galaxies. We derived stellar and baryonic masses using photometric data and used average stellar iron abundances as the metallicity indicator. With the inclusion of available data for massive galaxies, we find a continuous mass–metallicity relation for galaxies spanning nine orders of magnitude in mass, and that the mass–metallicity relations are the same for both gas-rich and gas-poor dwarf galaxies. We derive stellar effective yields from the stellar abundances, finding that gas-poor dwarf galaxies form a single sequence with mass, whereas gas-rich dwarf galaxies have higher yields at comparable mass. Simple chemical evolution models show that a mass-dependent star-formation efficiency can simultaneously account for the correlations between metallicity, gas fraction, and stellar effective yield with mass. In agreement with recent and independent results, we conclude that a key driver of the mass-metallicity relation is the variation of star-formation efficiency with galaxy mass, modulated by galaxy mass-dependent outflows and/or stellar IMF variations, and coupled with environmental gas-removal processes.