Direct Evidence for Stellar Initial Mass Function Variation in the Milky Way

The FUor Mass Distribution Matches the Solar Neighborhood Initial Mass Function: Evidence for a Universal Eruptive Phase

Growing evidence suggests that the stellar initial mass function (IMF) varies systematically across galaxies, deviating from the canonical Milky Way form. Such variations would modify the integrated nucleosynthetic yields and, hence, the abundance patterns used in stellar population synthesis studies. The question of how these could impact, in particular, the sodium abundance (and sodium-to-oxygen ratios) in star-forming galaxies is not fully understood. In this work, we carry out a systematically study of how high-mass IMF variations affect sodium enrichment using a one-zone galactic chemical evolution model. The model incorporates star formation histories from semi-analytic simulations and is calibrated to match the observed galaxy mass--metallicity relation. We find that varying the IMF high-mass end (and the IMF slope) could only alter the sodium abundance by less than 0.1 dex, across galaxies with stellar masses from 10^9, _⊙ to 10^ M 11 , _⊙. This result is robust under different stellar models and galaxy evolution assumptions, primarily because the sodium production is similar to that of oxygen. We conclude that sodium abundance is largely insensitive to changes in the high-mass IMF and, thus, it is unlikely to negatively impact the use of sodium indices as IMF diagnostics in stellar population studies. M

Abstract The properties of the first metal-free stars remain largely unknown, and so far, the only data-driven constraints on their initial mass function (IMF) come from near-field cosmology. Here, we interpret new observations of the C1 and C2 components of Hebe, the He II emitter near the galaxy GN-z11. Using a locally calibrated model, we robustly confirm the pristine (Population III, Pop III) nature of both components, showing that the measured upper limits on metal lines can only be reproduced by galaxies with >50% of their stellar mass in Pop III stars. We find that C1 is consistent with a purely Pop III system and adopt a simple parametric approach to infer the implications for the Pop III IMF and stellar mass. The observed He II /H γ ratio excludes steep IMFs, favoring top-heavy distributions, especially for young stellar ages (≤1 Myr). Combined with the He II luminosity, this implies a total Pop III stellar mass of 2 · 10 4 < M ⋆ / M ⊙ < 6 · 10 5 . While degeneracies between IMF, stellar mass, and age remain, adopting the lower stellar masses predicted by simulations ( M ⋆ < 10 5 M ⊙ ) strengthens the preference for top-heavy IMFs. Combining these results with near-field constraints, which instead exclude the flattest IMFs, we define a data-driven range of viable Pop III IMFs, linking characteristic mass and slope. This work demonstrates that direct observations of high- z Pop III systems can place independent constraints on the IMF of the first stars, opening a new window on their formation and properties.

The fragmentation properties of parsec-scale clumps play a fundamental role in shaping the dense gas condensations known as cores, the immediate progenitor of stars. The distribution of core masses, the so-called core mass function, is the precursor of the stellar initial mass function, which governs the distribution of stellar masses and, consequently, the evolution of galaxies. The stellar initial mass function is often described by a typical Salpeter-like slope, although deviations toward more top-heavy distributions have been reported in extreme environments, raising questions about its universality and about the physical connection between the two mass functions. To date, there are no observational constraints on the core mass function and its link to the initial mass function beyond the Milky Way.Here we present a study of the fragmentation properties and the measurement of the core mass function in an external galaxy, focusing on the 30Dor-10 region in the Large Magellanic Cloud, using high resolution observations that probe spatial scales down to 2000 au. Robust statistical analysis demonstrates that the core mass function is consistent with a Salpeter-like slope and suggests that variations in the stellar mass distribution arise from evolutionary processes rather than from initial fragmentation.

Abstract In this Letter, we report a novel discovery of unique characteristics for the tidal dwarf galaxy (candidate) Holmberg IX via a multiwavelength investigation. New observations are taken for deeply mapping H α emission and combined with archival/published data for comprehensively probing dust, gas, and stellar populations in this galaxy. We find in Holmberg IX a dearth of dust incompatible with its rich gas and metal; globally young stellar populations with prominent far-ultraviolet but deficient and marginal H α emissions, distinct from other tidal dwarf galaxies ever known. By assuming a normal initial mass function (IMF), Holmberg IX is suggested to be born ∼130 Myr ago from a bursty star formation event, which then rapidly ceased, with very few stars formed in the past ∼80 Myr that demarcates a lower age limit for the galactic mainbody; current star formation occurs only in outskirts, bringing a conundrum about the reason for the recent quenching in such a gas-rich environment. Contradicting the general expectation for tidal dwarf galaxies hosting continuous star formation, the present quiescence implies Holmberg IX currently staying in a rarely seen transient period. Without star formation continuing, Holmberg IX is likely transforming into a dwarf spheroidal galaxy, or oppositely into a(n) (ultra)diffuse system, which will probably dissolve in the end. Instead, if Holmberg IX possesses peculiar IMF and hosts low-mass, weak-H α star formation, it is able to maintain long-term survival in its current status. On whichever evolutionary pathway in reality, Holmberg IX appears as a special case updating conventional understandings of tidal dwarf galaxies and hinting potential existence of similar analogs in the Universe.

We present eight direct N-body simulations with of extremely massive, initially rotating Population III star clusters with 1.01 Nbody6++GPU 10^5 stars. Our models include primordial binaries, a continuous initial mass function, differential rotation, tidal mass loss, updated fitting formulae for extremely massive metal-poor Population III stars, and general-relativistic merger recoil kicks. We assess their impact on cluster dynamics. All runs form black holes below, within, and above the pair-instability gap, with multi-generation growth. Faster-rotating clusters core-collapse earlier; post-collapse clusters host a rotating, axisymmetric subsystem of intermediate-mass black holes (IMBHs) at the centre and an expanding halo of lower-mass objects. Pair-instability supernovae and compact-object formation at ∼2-3 Myr sharply reduce total mass and a large fraction of the cluster’s angular momentum. All Population III clusters in our simulations have the gravothermal-gravogyro catastrophe phase. We confirm two of the hypothesized formation channels of galactic nucleus seed black holes: gravitational runaway mergers of black holes and of Population III stars, which core-collapse into IMBHs thereafter. A higher initial star cluster bulk rotation correlates with earlier core collapse and, in the event counts reported here, with more coalescences and collisions, as well as lower retained (compact) binary abundances. Initial bulk rotation is a primary control parameter of cluster evolution: faster rotation accelerates early angular-momentum transport, gravothermal collapse, mass segregation, and amplifies post-collapse expansion, which also favours the formation of a compact central IMBH subsystem.

Abstract Cosmic rays (CRs) drive ionization and influence gas dynamics in molecular clouds (MCs), potentially impacting the resulting star formation outcomes. Although previous simulations of individual star formation have included methods for CR transport (CRT), none have been large enough to resolve the stellar initial mass function (IMF). We conduct numerical simulations following the collapse of a 20,000 M ⊙ MC and the subsequent star formation including CRT, both with and without CRs accelerated by winds from the young massive stars, and compare against a non-CRT simulation. We show that after the first massive stars form, the cavity produced by feedback is more pronounced in the CRT simulations because the external CRs are able to propagate inward and compress the gas into higher-density structures. This increases the subsequent star formation in the cloud; by the end of the simulation, the star formation efficiency (SFE) in the CRT simulation including stellar wind CRs is 43% higher than the non-CRT simulation. The IMF is also top-heavy in comparison, with a slope above 1 M ⊙ that is shallower by ∼20%. These effects are also present in the simulation without wind-accelerated CRs, but they are not as pronounced; the SFE is only 16% higher than the non-CRT simulation, and the IMF high-mass slope is shallower by ∼10%. These results may explain some of the observed top-heavy IMFs, which typically occur in high-CR environments such as the Galactic center.

ABSTRACT We present a strong lensing analysis of the double source plane lens J0946+1006 (colloquially ‘Jackpot’ lens) to measure the inner dark matter density profile, the stellar-to-halo mass ratio, and the stellar initial mass function normalization using a two-component stellar plus dark matter mass model. The stellar mass follows a multi-Gaussian expansion light model with a free global mass-to-light ratio and an allowed radial $M/L$ gradient, while the dark matter is described by an elliptical generalized NFW halo. The double-source-plane geometry provides additional leverage against the mass-sheet transformation and helps constrain the radial mass profile. Despite allowing both a radial stellar $M/L$ gradient and a generalized NFW halo, the data prefer an approximately constant stellar mass-to-light ratio with a Salpeter-like IMF normalization, and a dark matter halo consistent with NFW. We infer $M_{\star } = 4.4^{+0.25}_{-0.39}\times 10^{11}\, {\rm M}_{\odot }$ and an inner halo slope $\gamma _{\rm in}^{\rm halo} = 1.04^{+0.10}_{-0.14}$. The halo mass is $M_{200}^{\rm halo} = 1.11^{+0.37}_{-0.32}\times 10^{13}\, {\rm M}_{\odot }$, implying $\log _{10}(M_{200}/M_{\star })=1.41^{+0.13}_{-0.14}$. At fixed halo mass, the inferred stellar mass lies $\sim 0.1$ dex above typical literature stellar halo mass relations at similar redshift, which is comparable to the intrinsic scatter of these relations. We expect this approach to provide a practical template for future dark matter studies with the large double-source-plane lens samples from Euclid.

Ultra-compact massive galaxies (UCMGs) often exhibit elevated stellar-to-dynamical mass ratios when dynamical masses are estimated using standard virial prescriptions. This discrepancy has been interpreted as evidence for structural non-homology driven primarily by their compactness. This study investigates how the stellar-to-dynamical mass ratio depends on compactness ( ), and star formation histories. The analysis is based on a homogeneous catalogue of 482 UCMGs from the internal kinematics (σ_⋆), stellar population properties (mass-weighted age, metallicity, and Mg/Fe and surveys, extending to significantly smaller sizes than previously analysed samples. I first derive the compactness–mass relation assuming a constant virial coefficient (K=5). I then correct stellar masses for initial mass function (IMF) variations and recompute stellar-to-dynamical mass ratios using an empirical prescription in which the virial coefficient varies as a function of radius and stellar mass. Finally, I test whether the relation is modulated by stellar kinematics and population properties, including the degree of relicness (DoR), which quantifies the extremeness of the star formation history. A statistically significant anti-correlation between compactness and the IMF-corrected stellar-to-dynamical mass ratio is recovered when a constant virial coefficient is adopted, even within the relatively narrow range of , łog σ_⋆)$ space. Velocity dispersion sets the dominant axis of variation, and the corresponding plane accounts for sim62% of the variance in stellar-to-dynamical mass ratio. Including stellar age increases the explained variance to sim63%, revealing a secondary evolutionary modulation. In contrast, DoR, metallicity, and spanned by nearby UCMGs. The relation substantially flattens when a structure-dependent K is adopted, in agreement with previous literature. Beyond this one-dimensional behaviour, the data define a structural–dynamical manifold in the $(łog C Mg/Fe do not retain independent explanatory power once stellar age is included. The stellar-to-dynamical mass ratio in UCMGs is governed primarily by the depth of the gravitational potential, traced by stellar velocity dispersion, rather than by compactness alone. At fixed size, systems with higher σ_⋆ exhibit systematically lower stellar-to-dynamical mass ratio, indicating that dynamical structure regulates the apparent mass imbalance in the ultra-compact regime. Compactness largely reflects this dynamical scaling, while stellar age introduces a coherent secondary modulation linking the structural manifold to the evolutionary state of the galaxy. Non-homology in UCMGs therefore encodes coupled dynamical and assembly processes rather than purely geometric compactness.

Cosmological simulations find that pockets of star-forming gas could remain pristine up until the epoch of reionization (EoR) due to the inhomogeneous nature of metal mixing and enrichment in the early Universe. Such pristine clouds could have formed Population III stars, which could have distinct properties compared to their very high redshift ( z ≥ 20) counterparts. We investigate how Population III stars form and grow during the EoR, and whether the resulting mass distribution varies with environment or across cosmic time. We perform high-resolution (7.5 au) radiation-magnetohydrodynamics simulations of identical primordial clouds exposed to the cosmic microwave background (CMB) appropriate for z = 30 and z = 6, respectively, as part of the POPSICLE project. We also run a simulation at z = 6 with a strong external Lyman-Werner (LW) background, to span across radiative environments that could host metal-free clumps during the EoR. In the limit of no external LW radiation, we find that while the evolution of the most massive star ( M * ≈ 70M ⊙ ) is almost identical between z = 30 and z = 6, the latter exhibits less fragmentation, leading to a smaller cluster of stars with a higher median stellar mass. In the limit of high external LW radiation, we see vigorous accretion and high star formation efficiencies, leading to the formation of very massive ( M * > 100 M ⊙ ) stars. Our results suggest that Population III initial mass function (IMF) could vary with redshift simply due to the CMB, independent of the environment. We find that less massive and more compact Pop III star clusters could form during the EoR compared to z ≥ 20, with the formation of very massive and supermassive stars likely in strongly irradiated environments.

ABSTRACT The properties of high-redshift sub-millimetre galaxies (SMGs) remain controversial within hierarchical structure formation models. We revisit whether a top-heavy stellar initial mass function (IMF) in starbursts is required to reproduce both SMG observations and local galaxy properties. Using Bayesian optimization, we perform an extensive search of the 15-dimensional parameter space of the galform semi-analytical model. This efficient approach converges to optimal parameter values in fewer than 200 model evaluations, representing orders of magnitude fewer runs than traditional methods. We test whether galform can simultaneously match three key observational constraints: the $z=0$ K-band luminosity function, the SMG number counts at 850 $\mu$m, and the SMG redshift distribution. We consider two model variants: one with a universal solar neighbourhood IMF for all star formation, and another allowing the IMF slope in starbursts to vary as a free parameter. When assuming a universal Chabrier IMF, we find no parameter combination that simultaneously reproduces all three data sets. The model either matches the SMG constraints while grossly overpredicting the local K-band luminosity function, or matches the local luminosity function while severely underpredicting SMG counts by factors of 3–100. In contrast, allowing a top-heavy IMF in starbursts enables excellent simultaneous fits to all constraints. The best-fitting model prefers an IMF slope parameter $x \approx 0.7$ (where dn/dln$m \propto m^{-x}$). Our comprehensive parameter space exploration confirms that, given the implementation of galaxy formation physics within galform, a top-heavy IMF in starbursts is necessary to reconcile high-redshift dusty star-forming galaxies with local galaxy populations.

In the solar neighbourhood, the initial mass function (IMF) is canonically described by the Salpeter power-law slope for the high-mass range. As stars inherit their mass from their environment, their IMF may directly result from a core mass function (CMF) through accretion, gravitational collapse, and fragmentation. This inheritance implies that the mass of the gaseous fragments may be connected to the properties of clustered and multiple stellar systems. In these systems, mass and multiplicity are related, and this is supported by the fact that more massive primaries are observed more frequently in multiple systems. We aim to (i) quantify the influence of the hierarchical fragmentation of cores on the resulting IMF and (ii) determine the consequences of this fragmentation on the multiplicity of the stellar systems. To do so, we employed a scale-free hierarchical fragmentation model to investigate the stochastic fragmentation of the 2.5 kAU cores of the W43-MM2&MM3 molecular cloud, whose CMF is top-heavy. We also used this model to quantify the influence of deterministic mass-dependent fragmentation processes. The hierarchical fragmentation of gas clumps shifts the CMF towards a lower mass range and can modify its shape. The shift is quantified by both the number of fragments produced at each level of fragmentation and the mass the fragments inherit from their parental core. Starting from the top-heavy power-law CMF observed in W43-MM2&MM3, we show that at least four levels of hierarchical fragmentation are required to generate the turn-over peak of the canonical IMF. Within a radius of 0.2-2.5 kAU, massive stars (M > 10 M_⊙) have on average 0.9 companions, five times fewer than low-mass stars (M < 0.1 M_⊙), which are less dynamically stable and should disperse. We show that a universal IMF can emerge from mass-dependent fragmentation processes provided that more massive cores produce fewer fragments compared to lower mass cores and transfer their mass less efficiently to their fragments. Hierarchical fragmentation alone, however, cannot reconcile a universal IMF with observed stellar multiplicity. We propose that fragmentation is not scale-free but operates in two distinct regimes: a mass-dependent phase establishing the Salpeter slope and a mass-independent phase setting the turn-over. Our framework provides a way to compare core sub-fragmentation in various star-forming regions and numerical simulations.

Abstract The presence (and nature) of variations in the stellar initial mass function (IMF) at substantially subsolar masses and metallicities ( m < 0.5 M ⊙ and [M/H] ≲ −1, respectively) remains poorly constrained. Predictions from simulations vary widely, while observationally, resolved star studies of ultrafaint dwarf (UFD) galaxies suffer from small sample sizes and background galaxy contamination due to low projected stellar densities. As an alternative metal-poor target, we measure the IMF from resolved stars toward a carefully selected field in the Small Magellanic Cloud, leveraging a plethora of independent constraints on the target field stellar population including distributions of distance, age, and metallicity. We resolve >15,000 stars down to 0.16 M ⊙ within a single pointing of NIRCam on board JWST, using an observing strategy that minimizes contamination from point-source-like background galaxies. We explore three different functional forms of the IMF, forward modeling observed color–magnitude diagrams and luminosity functions. We find a best-fit single power law IMF slope of α = −1.61 − 0.03 + 0.03 , consistent with UFDs probed down to similar limiting masses. Fitting a broken power-law IMF, we find low- and high-mass slopes of α 1 = −1.44 − 0.04 + 0.04 and α 2 = −2.17 − 0.11 + 0.11 , respectively, consistent with solar neighborhood values. Assuming a lognormal IMF, we find a characteristic mass and lognormal width of m c = 0.1 2 − 0.03 + 0.03 M ⊙ and σ = 0.61 − 0.06 + 0.07 M ⊙ , respectively, allowing for characteristic masses lower than local values as seen in some simulations as well as low-metallicity Galactic clusters. Lastly, we quantify the impact of assumptions required in our analysis and discuss potential future improvements.

Abstract The stellar initial mass function (sIMF) is often treated as a stochastic probability distribution, yet such an interpretation implies Poisson noise that is inconsistent with growing observational evidence. In particular, the observed relation between the mass of the most massive star formed in an embedded cluster and the cluster’s total stellar mass supports a deterministic sampling process, known as optimal sampling. However, the physical origin of optimal sampling has not been formally established in the literature. In this work, we show that the stellar mass distribution implied by optimal sampling emerges from applying the Maximum Entropy principle to the fragmentation of star-forming clumps, whose structure is set by density- dependent cooling in the optically thin regime. Here, the maximum entropy leads to unbiased distributions. By applying calculus of variations to minimize the entropy functional obtained assuming fragmentation, we recover the power-law form of the sIMF, and we show that any distribution deviating from the sIMF violates the Maximum Entropy principle. This work provides a first-principles foundation for the deterministic nature of star formation. Thus, the sIMF is the distribution resulting from a maximally unbiased system.

Abstract Motivated by observational evidence from JWST and theoretical results from cosmological simulations, we use a simple parametric, phenomenological model to test to what extent bursty star formation (SF) with standard initial mass function, no continuous SF, no mergers, and no dust can account for the observed properties in the M UV versus M * plane of galaxies at redshifts z > 5. We find that the simplest model that fits the data has a quiescence period between bursts Δ t ∼ 100 Myr, and the stellar mass in each galaxy grows linearly as a function of time from z = 12 to z = 5 (i.e., repeated bursts in each galaxy produce approximately equal mass in stars). The distribution of burst masses across different galaxies follows a power-law d N / d M * ∝ M * α with slope α ∼ −2. At z > 9–10 the observed galaxy population typically had only one or two bursts of stars formation, hence the observed stellar masses at these redshifts (reaching M * ∼ 10 10 M ⊙ ) roughly represent the distribution of masses formed in one burst.

ABSTRACT The stellar initial mass function (IMF) is among the most fundamental distributions in astrophysics, defined as the mass spectrum of stars produced in a single star-formation event. Even in the solar neighbourhood, where measurements can be conducted via star counting, disentangling the IMF from observational effects remains challenging. In this work, we introduce a new parametrization of the stellar IMF in the 100-pc solar neighbourhood, leveraging the high-precision astrometric and photometric data from Gaia DR3: we model the colour–magnitude diagram of the field star population while accounting for observational uncertainties, Malmquist bias, Lutz–Kelker bias, variations in the mass–luminosity relation arising from metallicity differences and the effects of unresolved binaries. In particular, we synthesize the binary population with a process imitating the dynamical evolution observed in star clusters to enforce that all components are drawn from the same IMF, while simultaneously recovering the observed present-day mass-ratio distribution. We determine an averaged stellar IMF over $0.25\lt m\lt 1.0~{\rm M}_{\odot }$ that aligns with canonical IMFs but achieves significantly tighter constraints: $\alpha _1=0.75^{+0.06}_{-0.04}$, $\alpha _2=2.07^{+0.04}_{-0.03}$, and a break point at $m_{\mathrm{break}}=0.40^{+0.01}_{-0.01}$ $\mathrm{{\rm M}_{\odot }}$. Our inference also yields an averaged binary fraction over $0.25\lt m\lt 1.0~{\rm M}_{\odot }$ of approximately 26 per cent, and constrains the Gaia Data Release 3 angular resolution to $1.11^{+0.11}_{-0.08}$ arcsec. We also provide the $\xi$-parameter for our IMF, which is $0.5070_{-0.0096}^{+0.0068}$, to facilitate direct comparison with other IMF determinations.

Galactic globular clusters (GCs) were born shortly after the Big Bang. For these old stellar systems, the initial mass function (IMF) in the high-mass regime can never be observed directly, because stars more massive than about 1 M ⊙ have evolved since for a long time. However, the hydrostatic to explosive α -element ratio (HEx ratio) offers a way to bypass the lack of observable high-mass stars through the yields that massive stars released when they exploded as supernovae, which is incorporated in the stars we currently observe in GCs. The HEx ratio measures the percentage of high-mass stars over the total number of stars exploding as supernovae, and it is an efficient probe of the ephemeral first phases of the GC evolution. We exploited a recently completed survey to assemble a dataset of very homogeneous abundances of α -elements in 27 GCs from [Fe/H]~ −2.4 to~ −0.3 dex. In agreement with previous results from APOGEE, we confirm that the HEx ratio is indistinguishable for GCs that formed in situ and accreted in the Galaxy, and that this ratio decreases with increasing metallicity. However, we posit that this trend is better explained by a metallicity-dependent IMF that is deficient in the highest-mass stars at high metallicity, as corroborated by the declining [O/Mg] ratio as a function of the [Mg/H] ratio. At odds with the previous analysis based on APOGEE data, we detect an anti-correlation of HEx ratio with both present-day and initial GC masses. Finally, we hypothesise that in the analysis of APOGEE data, the stars of the GC M 54 were probably confused with stars in the core of the Sagittarius dwarf galaxy, in which the cluster is currently immersed.

Abstract Several methods for identifying Be star candidates are reviewed for observational bias with respect to system inclination, that is the angle between the stellar and disk rotation axis and the observer’s line of sight, with focus on two photometric methods that leverage narrow-band filters centred on H α and a spectroscopic method using an H α peak-finding algorithm. Tests for bias were performed using a sample of 20,000 synthetic Be stars drawn from a Salpeter initial mass function and computed libraries of spectral energy distributions and H α profiles. The spectroscopic method showed substantial bias against high inclinations ( i > 80°). Both photometric methods were biased against low inclinations, with one also biased against inclinations above 80°, resulting in a surplus in the Be star candidate detection rate for moderate inclinations (50° < i < 80°). Inclination probability distributions, including the random sin i factor, are given for the three methods that can be applied to observational samples.

Abstract We investigated the gravitational potential and mass distribution in the Galactic Center by examining the morphology and kinematics of the circumnuclear gaseous disk revealed by the molecular line data from the ALMA CMZ Exploration Survey. We obtain an estimate of the shape of the potential within the central ${\sim}20$ pc to reproduce the observed properties of the circumnuclear gas disk by simulating the motion of test particles for various axial ratios and show that the potential is approximately spherical. We construct a rotation curve by applying the terminal velocity method to the position–velocity diagrams, and calculate the mass distribution in the Galactic Center. The distribution of mass density is found to be of cusp type, approximated by $\rho _{\rm dyn}\sim 1.56\times 10^5(R/1\, \mbox{pc})^{-1.9}~M_{\odot }\, \mbox{pc}^{-3}$, where R is the distance from the nucleus. We discuss the tidal effect caused by the gravitational potential that produces the rotation curve and show that the gas disk is stable against self-gravitational contraction within a critical radius of $R_{\rm T}\sim 14 ~(\rho _{\rm gas}/10^5 {\rm H_2\, {\mbox{cm}}^{-3}})^{-1/2}\, \mbox{pc}$. This suggests suppression of star formation and a top-heavy initial mass function in the circumnuclear region.