Pith. sign in

REVIEW 4 major objections 6 minor 1 cited by

Stellar population synthesis models with a physically varying IMF

T0 review · 4 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read If the galaxy-wide IMF varies with star formation rate, early-type galaxies of very different masses can look identical while their mass-to-light ratios differ by an order of magnitude, and massive ellipticals were $10^4$ times brighter…

desk verdict Useful SPS code paper whose headline numbers are inherited from the IGIMF calibration rather than tested; refereeing should push for sensitivity analysis and softer claims. read the letter →

arxiv 2502.03529 v1 pith:63BGB63E submitted 2025-02-05 astro-ph.GA

Akram Hasani Zonoozi , Hosein Haghi , Pavel Kroupa This is my paper · ORCID
classification astro-ph.GA
keywords stellarpopulationsynthesisgalaxy-wideinitialmassfunctionintegratedgalacticIMFmass-to-lightratioearly-typegalaxiesstarformationhistoryremnants
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper builds a stellar population synthesis model, named SPS-VarIMF, in which the galaxy-wide initial mass function is not fixed once and for all but changes with a galaxy's star formation rate and metallicity, following the integrated galactic IMF (IGIMF) theory. Using it, the authors compute how colors, luminosities, and stellar mass-to-light ratios evolve for galaxies with constant and burst-like star formation histories, under both a varying and an invariant IMF. The central result is that massive early-type galaxies built with a varying IMF can have exactly the same present-day light and colors as much lighter galaxies built with the standard IMF, while their true stellar masses and mass-to-light ratios differ by up to an order of magnitude. The paper argues that light-based mass estimates can therefore underestimate early-type galaxy masses by that factor, and that massive ellipticals would have been about $10^4$ times brighter at formation than they are today.

What carries the argument

The load-bearing object is the integrated galactic IMF (IGIMF), defined as the sum of the stellar IMFs of all embedded clusters formed in a galaxy in a 10 Myr star-formation interval: $\xi_{\rm IGIMF}(m, \psi(t)) = \int \xi_\star(m \le m_{\rm max})\, \xi_{\rm ecl}(M_{\rm ecl}, \psi(t))\, dM_{\rm ecl}$ (Eq. 10). Each embedded-cluster IMF has slopes that depend on metallicity and clump density (Eqs. 2-5), the maximum stellar mass follows from the cluster mass (Eq. 6), and the cluster mass function depends on the star formation rate (Eqs. 7-9). This varying gwIMF is then fed into conventional isochrone and spectral-library machinery (PARSEC tracks, BaSeL3.1 spectra) to build composite stellar population spectra (Eqs. 11-12). The IGIMF does the work of turning the SFR and metallicity of a galaxy into different star populations, which is what produces the predicted differences in $M/L$ ratios, colors, and remnant fractions.

What would settle it

Measure the dynamical mass-to-light ratios of the most massive quiescent ellipticals (formed mass near $10^{13}\,M_\odot$) using stellar kinematics or strong gravitational lensing. The IGIMF models with a quickly declining star formation history predict present-day $M/L_{[3.6]} \approx 4$--$6$ and $M/L_V \approx 30$--$40$, whereas the invariant canonical IMF predicts roughly 1 and 7; values close to the canonical set would falsify the IGIMF predictions. A second decisive check is deep high-redshift imaging: under the IGIMF, massive ellipticals should appear about $10^4$ times brighter during their formation burst, so the absence of such ultraluminous phases in deep surveys would falsify that prediction.

Watch

Extended reading notes

Core claim

The paper's central claim is that the integrated galactic IMF theory, in which every embedded cluster forms stars through a metallicity- and density-dependent IMF and the galaxy-wide IMF is their sum, produces observable predictions that a fixed canonical IMF cannot. The SPS-VarIMF code is the vehicle for that claim: it is the first such code, per the authors, to compute spectra, luminosities, remnant populations, and mass-to-light ratios under a gwIMF that varies with time, star formation rate, and metallicity. The decisive output is a degeneracy: a galaxy of total formed mass $10^{13}\,M_\odot$ built with the IGIMF and a galaxy of $3.5\times 10^{11}\,M_\odot$ built with the canonical IMF can reach the same present-day $[3.6]$-band and $U$-band luminosities and the same colors, while their mass-to-light ratios differ by a factor of about 30. Because light is usually the only observable, the authors conclude that adopting the wrong gwIMF can underestimate the stellar mass of an early-type galaxy by an order of magnitude; they also find that a massive elliptical with a rapidly declining star formation history would have been $10^4$ times as bright during its formation burst as it is now.

Load-bearing premise

The entire chain depends on the IGIMF input relations: that the stellar IMF inside each embedded cluster varies with metallicity and density exactly as Eqs. (2)-(5) prescribe, with $\Delta\alpha = 63$ and the adopted cluster radius relation, and that the galaxy-wide IMF is the sum over an SFR-dependent embedded-cluster mass function; if those calibrated relations are wrong, the predicted $M/L$ differences, the identical-color degeneracy, and the $10^4$ brightness peak disappear.

Editorial extensions

If this is right

  • Stellar masses of massive early-type galaxies derived from their light will be wrong by up to an order of magnitude if the canonical IMF is assumed and the IGIMF is correct.
  • A massive elliptical galaxy at the peak of its formation burst would look $10^4$ times brighter than today, so high-redshift searches should see an ultraluminous, short-lived phase.
  • For late-type galaxies with steady star formation, UV and optical colors can discriminate between a varying and an invariant galaxy-wide IMF.
  • Under the IGIMF, a galaxy's total mass affects its own mass-to-light ratio, so light-to-mass conversion is no longer a universal calibration.
  • Low-SFR galaxies form no stars above about $4\,M_\odot$, shifting the brightest phase of their light to later times compared to massive galaxies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the IGIMF is correct, the stellar mass function of massive galaxies inferred from surveys is systematically shifted upward, which would ease some tensions between observed galaxy counts and halo mass functions.
  • The predicted $10^4$ brightness peak gives a direct way to test the theory: deep UV/optical surveys at high redshift should find a population of ultraluminous, rapidly quenched ellipticals; their absence would constrain the IGIMF parameters.
  • The same SPS-VarIMF machinery could be run backwards: fitting observed $M/L$--color tracks of local early-type galaxies with measured dynamical masses would yield direct constraints on $\Delta\alpha$ and the radius relation.
  • Because the IGIMF populates massive remnants early, present-day massive ellipticals should contain a significant dark mass in stellar remnants, a prediction that gravitational-wave or gravitational-lensing mass measurements could test.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper presents SPS-VarIMF, a stellar population synthesis code that replaces the invariant canonical galaxy-wide IMF with an integrated galactic IMF (IGIMF) whose shape depends on the star formation rate and metallicity. The code combines PARSEC isochrones, the BaSeL3.1 spectral library, a metallicity- and density-dependent stellar IMF, and an SFR-dependent embedded cluster mass function. The authors compute time-evolving M/L ratios, luminosities, colors, and SEDs for SSPs and CSPs with constant and delayed-tau star formation histories, comparing canonical and IGIMF prescriptions. The headline results are that early-type galaxies with different total masses can have nearly identical luminosities and colors while having M/L ratios differing by up to an order of magnitude, that late-type galaxies can be used to identify the underlying gwIMF through UV/optical colors, and that massive present-day ellipticals would have been about 10^4 times brighter at their formation epoch under the IGIMF theory.

Significance. If the IGIMF theory is correct, the paper demonstrates a potentially large systematic effect in stellar mass inference and provides a public, reproducible tool for exploring it. The manuscript's strengths are explicit: the code is released, the ingredients are standard (PARSEC, BaSeL3.1), the equation chain is mostly transparent, and the predictions are falsifiable in principle (e.g., UV/optical colors of star-forming galaxies, M/L differences in early types). The significance is conditional, however, because the quantitative predictions are direct outputs of the adopted IGIMF calibration, whose parameters are inherited from previous work and are not independently validated or subjected to uncertainty analysis here.

major comments (4)
  1. [Sec. 2.3, Eqs. (3)-(5)] Equation (5) is not the combination of Eqs. (3) and (4). Substituting Eq. (4), with r_h = 0.1 Mecl^0.13 and Mcl = 3 Mecl, into Eq. (3) gives x = -0.14[Z] + 0.604 log10(Mecl/M_sun) - 3.11, whereas Eq. (5) expands to x = -0.14[Z] + 0.6 log10(Mecl/M_sun) - 0.78. The offset of about 2.3 in x changes alpha3 substantially; for Mecl = 10^6 M_sun, the two expressions give x ~ 0.51 and alpha3 ~ 1.73 versus x ~ 2.82 and alpha3 ~ 0.78. Since alpha3 controls the massive-star IMF, every IGIMF-based M/L, luminosity, and color result in Sections 3.1-3.3 is quantitatively affected. The authors should correct the formula, state the radius normalization actually used, and rerun the models if needed.
  2. [Sec. 2.3, Eqs. (6), (7), (9)] The 'one object above' conditions are written as integrals over ranges where the corresponding distribution has already been set to zero. Equation (1) defines xi_star only for m < mmax, yet Eq. (6) integrates xi_star from mmax to 150 M_sun; similarly, Eq. (7) sets xi_ecl = 0 for Mecl >= Mecl,max, so the integral in Eq. (9) from Mecl,max to 10^9 M_sun vanishes identically. The text should state explicitly that the untruncated power laws are used for the normalization conditions; as written, the equations are formally inconsistent. This matters because these conditions set mmax and Mecl,max, which directly shape the gwIMF.
  3. [Secs. 2.3, 3.2-3.3] The headline numbers - the order-of-magnitude M/L differences and the 10^4 peak-to-present luminosity ratio - are direct outputs of the adopted IGIMF calibration, but the paper gives no sensitivity tests or error propagation for the calibrated parameters: Delta_alpha = 63 in Eq. (2), the beta(SFR) relation in Eq. (8), the Marks-Kroupa radius relation in Eq. (4), and the dust parameters in Eq. (13). Because these are inherited from earlier work and are not anchored to independent IMF constraints in this paper, the quantitative claims need to be shown robust to plausible variations in these inputs. Please add explicit tests showing how M/L[3.6], the colors in Figures 10-14, and the peak luminosity in Figure 9 change when these parameters are varied within reasonable ranges.
  4. [Sec. 3.3, Figs. 12-14; conclusion bullet 2] The degenerate early-type pairs are constructed by selecting a canonical-IMF galaxy and an IGIMF galaxy of different total masses that happen to have the same present-day luminosities and colors. The paper does not state whether these mass pairs were tuned, nor does it quantify the range of masses, metallicities, and SFHs over which such degeneracy holds. As an existence proof the demonstration is valid, but the conclusion that adopting the wrong gwIMF can underestimate early-type masses by an order of magnitude is only supported for the chosen models. Please specify the selection procedure and explore the robustness of the degeneracy surface, especially after the Eq. (5) inconsistency is corrected.
minor comments (6)
  1. [Abstract] The sentence 'The shape of the IGIMF thus depends on the star formation rate (SFR) and metallicity' appears twice in the abstract; one occurrence should be removed.
  2. [Sec. 1 heading] The heading 'INTODUCTION' should be 'INTRODUCTION'.
  3. [Sec. 2.3, after Eq. (9)] The phrase 'The first part of Equation 10 represents...' should refer to Eq. (9), not Eq. (10).
  4. [Sec. 2.3 and Table 1] The text says 'single power-low function' and Table 1 uses 'canonicIMF'; both should read 'power-law function' and 'canonical IMF', respectively.
  5. [Figs. 12 and 15] The axis labels and captions contain rendering artifacts such as '3.5imes1011' and '3imes1012'; the multiplication signs should be typeset correctly.
  6. [References] The Weidner & Kroupa (2006) reference ends with a stray ', 2' after the page number; this appears to be a typo.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is a forward-model application of an inherited IGIMF parameterization, and its predictions are conditional outputs, not inverse fits or definitions.

full rationale

The paper does not derive the IGIMF from first principles; it explicitly adopts the IGIMF parameterization of Eqs. (2)-(10) from Yan et al. (2017, 2020, 2021), Kroupa & Weidner (2003), and Marks & Kroupa (2012). The headline results — order-of-magnitude M/L differences, the 10^4 peak luminosity, and the early-type color degeneracy — are forward-model outputs of the SPS-VarIMF code: given an assumed gwIMF and star-formation history, Eqs. (11)-(12) integrate stellar spectra and remnant masses to produce luminosities, colors, and M/L ratios. No parameter is fitted in this paper, and no observed galaxy property is used to tune the model, so the 'predictions' are not equivalent to their inputs by construction. The self-citations that supply Delta_alpha=63 and the Marks-Kroupa radius relation are empirical calibrations from earlier work, external to the present calculation; whether those calibrations are correct is a robustness or correctness concern, not a circularity. The paper also states its results conditionally, e.g. 'according to the IGIMF theory', making the assumption structure explicit. No circular step meets the required standard of an exhibited Eq. X = Eq. Y reduction or a fitted parameter renamed as a prediction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The paper takes the IGIMF theory and its calibrated parameters as inputs; the SPS machinery is standard. All quantitative outputs, M/L differences, colors, remnant fractions, and the 10^4 brightness peak, are downstream of these fitted inputs, and no independent benchmark against observed galaxies is performed.

free parameters (6)
  • Delta_alpha = 63 = 63
    Sets the metallicity dependence of the low-mass IMF slopes in Eq. (2); calibrated by Yan et al. (2020, 2021), a key driver of bottom-heavy versus top-heavy gwIMF behavior.
  • ECMF slope relation beta = -0.106 log10 psi(t) + 2 = beta = -0.106 log10(psi) + 2
    Eq. (8) sets the embedded cluster mass function slope as a function of SFR; fitted to cluster population data in prior work.
  • alpha3 slope relation coefficients = -0.41, 1.94
    Eq. (2) determines the high-mass IMF slope as a function of the density parameter x; empirically calibrated.
  • Marks-Kroupa radius relation coefficients = 0.1 pc, exponent 0.13
    Eq. (4) sets the initial half-mass radius of embedded clusters, which feeds into the density-dependent IMF slope.
  • Dust attenuation parameters tau_V and mu_D = tau_V = 1.0, mu_D = 0.33
    Eq. (13) uses these fixed values based on Charlot & Fall (2000); they affect all predicted colors and magnitude differences.
  • Remnant mass prescription coefficients = BH 0.5 m; NS 1.4 Msun; WD 0.077 m + 0.48 Msun
    Simplified metallicity-independent prescription from Renzini & Ciotti (1993) used to assign remnant masses; directly sets the remnant fractions that drive the M/L differences.
assumptions (6)
  • domain assumption All stars form in embedded clusters, and the galaxy-wide IMF is the sum of the IMFs of all embedded clusters (IGIMF theory).
    Basis of the entire model, taken from Kroupa & Weidner (2003) and prior work; the paper does not test this hypothesis.
  • domain assumption The stellar IMF within a cluster varies with metallicity and local cloud density through Eqs. (2)-(5), with the specific fitted parameters.
    The central input that determines the gwIMF; supported only by prior calibrations, not independently in this paper.
  • domain assumption The embedded cluster mass function is a single power law with SFR-dependent slope and upper cutoff determined by Eq. (9).
    Defines the integration in Eq. (10) and shapes the resulting IGIMF; the chosen functional form is assumed.
  • standard math PARSEC stellar tracks and BaSeL3.1 spectral library accurately represent stellar atmospheres and evolution across the relevant mass and metallicity range.
    Trusted external inputs; the paper relies on their accuracy without recalculating them.
  • domain assumption Galaxy metallicity is set by the mass-metallicity relation of Gallazzi et al. (2005) and is held fixed in time.
    Metallicity strongly affects colors and remnant masses; the paper states in Sec. 3.2 that it does not model chemical evolution.
  • ad hoc to paper The optimal-sampling constraints in Eqs. (6) and (9) are valid, including 'one star above mmax' and 'one cluster above Mecl,max'.
    These normalization assumptions are specific to the optimal-sampling IGIMF formulation and are not independently derived in this paper.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Stellar population synthesis models with a physically varying IMF." pith.science (2026). https://pith.science/paper/63BGB63E

@misc{pith2026250203529,
  author       = {Pith},
  title        = {Pith review of: Stellar population synthesis models with a physically varying IMF},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/63BGB63E}},
  note         = {Machine review of arXiv:2502.03529}
}
abstract

Interpreting galactic luminosity requires assumptions about the galaxy-wide initial mass function (gwIMF), often assumed invariant in most stellar population synthesis (SPS) models. If stars form in clusters with metallicity- and density-dependent \textit{stellar IMFs}, the integrated galaxy-wide IMF (IGIMF) can be calculated, with its shape depending on the star formation rate (SFR) and metallicity. The shape of the IGIMF thus depends on the star formation rate (SFR) and metallicity. We develop the \texttt{SPS-VarIMF} code which enables us for the first time to compute the spectra, luminosities, and remnant populations of galaxies in the context of the varying gwIMF with time, SFR, and an assumed metallicity. Using the \texttt{SPS-VarIMF} code one can calculate how the interpretation from the integrated galactic light may change if the underlying galaxy-wide IMF is assumed to be environmentally dependent instead of being invariant. In particular, we compare the time evolution of the galaxy color and the stellar mass-to-light ratio in different bands for the IGIMF and invariant canonical gwIMF assuming constant and delayed-$\tau$ star formation histories. We show that the underlying gwIMF can be determined by examining the colors and luminosities of late-type galaxies in UV and optical bands. On the other hand, for early-type galaxies, it is difficult to distinguish which gwIMF is valid since adopting the different gwIMFs yields almost identical colors. However, their gwIMF-dependent $M/L$ ratios differ by up to an order of magnitude. Massive present-day elliptical galaxies would have been $10^4$ times as bright as at present when they were forming.

Figures

Figures reproduced from arXiv: 2502.03529 by the authors.

Figure 1
Figure 1. Different SFR models used in this work (Sec. 2.4). The solid-gray line represents the constant SFR, while the different curves correspond to delayed-τ SFH models with e-folding time￾scales of 0.1, 1, 5, and 7 Gyr. The area under each curve is the total stellar mass formed over 13 Gyr normalized to 1 M⊙. The horizontal axis refers to the time since the onset of star formation. the initial mass, metallicity, and age o… view at source ↗
Figure 2
Figure 2. The evolution of the M/L[3.6] (upper panel) and M/LV (lower panel) ratio including remnants for single stellar population (SSP) models based on the invariant canonical gwIMF and the IGIMF. Metallicity is assigned to galaxies with different masses following the mass-metallicity relation of Gallazzi et al. (2005) such that Z = 0.03 for the Mtot = 1013M⊙ model and Z = 0.0002 for the Mtot = 105M⊙ model. The horizontal a… view at source ↗
Figure 4
Figure 4. Same as [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (8 more)
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 8
Figure 8. Figure 8: The evolution of the total bolometric luminosity of star-forming galaxies with different masses based on the invari￾ant canonical gwIMF and the IGIMF assuming a constant SFR. These are models of the late-type or disk galaxies. It is worth noting that remnant masses of …
Figure 10
Figure 10. Figure 10: The bottom panel displays the average optical to near-IR colors for galaxies with different masses and SFHs. Two SFR models are shown: solid lines for constant SFR, dashed lines for delayed-τ SFR, red lines for low-mass (metal-poor) galaxies, and black lines for massi…
Figure 11
Figure 11. Figure 11: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: Comparing the evolution of luminosity and color in different bands for two SSP galaxies in the framework of the in￾variant canonical gwIMF and the IGIMF. The horizontal axis refers to the time since the onset of star formation. material from its companion, affecting i…
Figure 14
Figure 14. Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_14.png]
Figure 15
Figure 15. Figure 15: SED of two galaxies with different masses and with the same luminosities in the [3.6] band constructed based on the invariant canonical gwIMF and the IGIMF for various SFHs at an age of 12.5 Gyr. Upper panel: SSP galaxies that have the same present-day L[3.6] and LU a…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Baryonic mass budgets in the central regions of the Bullet Cluster and their consistency with strong lensing in MOND

    astro-ph.GA 2026-06 unverdicted novelty 6.0 of 10

    MOND strong-lensing masses in the Bullet Cluster’s three BCG cores lie between lower and upper IGIMF baryonic mass estimates from JWST photometry.

Reference graph

Works this paper leans on

40 extracted references · 39 canonical work pages · cited by 1 Pith paper

  1. [1]

    J., Scott P., 2009, ARA&A, 47,

    Asplund M., Grevesse N., Sauval A. J., Scott P., 2009, ARA&A, 47,

    work page 2009

  2. [10]

    Fontanot F., De Lucia G., Hirschmann M., Bruzual G., Charlot S., Zibetti S., 2017, MNRAS, 464, 3812 Gallazzi A., Charlot S., Brinchmann J., White S. D. M., Tremonti C. A., 2005, MNRAS, 362,

    work page 2017

  3. [11]

    Yasui C., Kobayashi N., Saito M., Izumi N., Ikeda Y., 2023, ApJ, 943,

    work page 2023

  4. [37]

    Kroupa P., Gjergo E., Jerabkova T., Yan Z., 2024, arXiv, arXiv:2410.07311

    Kroupa P., Gjergo E., Asencio E., Haslbauer M., Pflamm- Altenburg J., Wittenburg N., Samaras N., et al., 2023, arXiv, arXiv:2309.11552. Kroupa P., Gjergo E., Jerabkova T., Yan Z., 2024, arXiv, arXiv:2410.07311. Lada C. J., Lada E. A., 2003, ARA&A, 41, 57 Lee, J. C., Gil de Paz, A., Tremonti, C., et al. 2009, ApJ, 706, 599-613 Lejeune T., Cuisinier F., Bus...

    arXiv 2023

  5. [41]

    M., Tumlinson, J., et al

    Geha, M., Brown, T. M., Tumlinson, J., et al. 2013, ApJ, 771, 29 Gennaro, M., Tchernyshyov, K., Brown, T. M., et al. 2018, ApJ, 855, 20 Gjergo E., Sorokin A. G., Ruth A., Spitoni E., Matteucci F., Fan X., Liang J., et al., 2023, ApJS, 264,

    work page 2013

  6. [44]

    Gunawardhana, M. L. P., Hopkins, A. M., Sharp, R. G., et al. 2011, MNRAS, 415, 1647 Habergham, S. M., Anderson, J. P., & James, P. A. 2010, ApJ, 717, 342 Haslbauer M., Kroupa P., Jerabkova T., 2023, MNRAS, 524,

    work page 2011

  7. [65]

    Mansfield S., Kroupa P., 2023, MNRAS, 525,

    work page 2023

  8. [71]

    Spera M., Mapelli M., Bressan A., 2015, MNRAS, 451,

    work page 2015

Show all 40 references
  1. [77]

    Marks, M., Kroupa, P., Dabringhausen, J., & Pawlowski, M. S. 2012, MNRAS, 422, 2246 Matteucci, F., & Brocato, E. 1990, ApJ, 365, 539 McDermid R. M., Alatalo K., Blitz L., Bournaud F., Bureau M., Cappellari M., Crocker A. F., et al., 2015, MNRAS, 448,

    2012

  2. [95]

    MNRAS 000, 1–14 (2013) SPS-IGIMF code 15 Yang Y., Liu C., Yang M., Zheng Y., Tian H., 2024, ApJ, 977,

    2013

  3. [127]

    2003, MNRAS, 344, 1000 Calura, F., Recchi, S., Matteucci, F., & Kroupa, P

    Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000 Calura, F., Recchi, S., Matteucci, F., & Kroupa, P. 2010, MNRAS, 406, 1985 Charlot S., Fall S. M., 2000, ApJ, 539,

    2003

  4. [137]

    Zhang, Q., & Fall, S. M. 1999, ApJ, 527, L81 Zhang, Z.-Y., Romano, D., Ivison, R. J., Papadopoulos, P. P., & Matteucci, F. 2018, Natur, 558, 260 Zinnkann M., Wirth H., Kroupa P., 2024, arXiv, arXiv:2402.09405. APPENDIX A: M/L VS. COLOR IN DIFFERENT BANDS FOR GALAXIES WITH TWO ...

    2013 arXiv

  5. [157]

    B., Meurer, G

    Watts, A. B., Meurer, G. R., Lagos, C. D. P., et al. 2018, MNRAS, 477, 5554 Weidner, C. & Kroupa, P. 2006, MNRAS, 365, 1333, 2 Weidner, C., Kroupa, P., Pflamm-Altenburg, J., & Vazdekis, A. 2013b, MNRAS, 436, 3309 Westera P., Lejeune T., Buser R., Cuisinier F., Bruzual G., 2002...

    2018

  6. [194]

    Marigo P., Girardi L., Bressan A., Rosenfield P., Aringer B., Chen Y., Dussin M., et al., 2017, ApJ, 835,

    2017

  7. [212]

    Bressan A., Marigo P., Girardi L., Salasnich B., Dal Cero C., Rubele S., Nanni A., 2012, MNRAS, 427,

    2012

  8. [214]

    Schombert J., McGaugh S., Lelli F., 2019, MNRAS, 483,

    2019

  9. [229]

    Lejeune T., Cuisinier F., Buser R., 1998, A&AS, 130,

    1998

  10. [243]

    Schneider, F. R. N., Sana, H., Evans, C. J., et al. 2018, Science, 359, 69 Schulz, C., Pflamm-Altenburg, J., & Kroupa, P. 2015, A&A, 582, A93 Schombert J. M., 2016, AJ, 152,

    2018

  11. [288]

    M., Driver, S

    Hopkins, A. M., Driver, S. P., Brough, S., et al. 2013, MNRAS, 430, 2047 Hopkins A. M., 2018, PASA, 35, e039. Hoversten, E. A., & Glazebrook, K. 2008, ApJ, 675, 163-187 Jeˇ r´ abkov´ a T., Hasani Zonoozi A., Kroupa P., Beccari G., Yan Z., Vazdekis A., Zhang Z.-Y., 2018, A&A, 6...

    2013

  12. [365]

    Offner, S. S. R., Clark, P. C., Hennebelle, P., et al. 2014, Proto- stars and Planets VI, 53 Pflamm-Altenburg, J., & Kroupa, P. 2008, Nature, 455, 641 Pflamm-Altenburg, J., Weidner, C., & Kroupa, P. 2011, UP2010: Have Observations Revealed a Variable Upper End of the Ini- tial...

    2014

  13. [455]

    S., 2012, LRR, 15,

    Famaey B., McGaugh S. S., 2012, LRR, 15,

    2012

  14. [481]

    Banerjee S., Kroupa P., Oh S., 2012, ApJ, 746, 15 Banik I., Zhao H., 2022, Symm, 14,

    2012

  15. [486]

    G., & Villaume, A

    Conroy, C., van Dokkum, P. G., & Villaume, A. 2017, ApJ, 837, 166 Cowie L. L., Songaila A., Hu E. M., Cohen J. G., 1996, AJ, 112,

    2017

  16. [524]

    2020, A&A, 637, A68 Yan Z., Jeˇ r´ abkov´ a T., Kroupa P., 2021, A&A, 655, A19

    Yan Z., Jerabkova T., Kroupa P., 2017, A&A, 607, A126 Yan, Z., Jerabkova, T., & Kroupa, P. 2020, A&A, 637, A68 Yan Z., Jeˇ r´ abkov´ a T., Kroupa P., 2021, A&A, 655, A19. Yan Z., Jerabkova T., Kroupa P., 2023, A&A, 670, A151. Yan Z., Li J., Kroupa P., Jerabkova T., Gjergo E., ...

    2017

  17. [673]

    ´Ubeda, L., Ma ´ ız-Apell´ aniz, J., & MacKenty, J. W. 2007, AJ, 133, 932 van Dokkum, P. G., & Conroy, C. 2011, ApJ, 735, L13 Vazdekis, A., Cenarro, A. J., Gorgas, J., Cardiel, N., & Peletier, R. F. 2003, MNRAS, 340, 1317 Vazdekis A., Ricciardelli E., Cenarro A. J., Rivero-Gon...

    2007

  18. [718]

    Conroy C., Gunn J

    MNRAS 000, 1–14 (2013) 14 Zonoozi et al. Conroy C., Gunn J. E., White M., 2009, ApJ, 699,

    2013

  19. [839]

    2012, ApJ, 747, 72 Dabringhausen J., Kroupa P., 2023, MNRAS, 526,

    Dabringhausen, J., Kroupa, P., Pflamm-Altenburg, J., & Mieske, S. 2012, ApJ, 747, 72 Dabringhausen J., Kroupa P., 2023, MNRAS, 526,

    2012

  20. [1081]

    J., Stanway E

    Eldridge J. J., Stanway E. R., Xiao L., McClelland L. A. S., Taylor G., Ng M., Greis S. M. L., et al., 2017, PASA, 34, e058. Eldridge J. J., Stanway E. R., 2022, ARA&A, 60,

    2017

  21. [1331]

    R., & Meyer, M

    Bastian, N., Covey, K. R., & Meyer, M. R. 2010, ARA&A, 48, 339 Bell E. F., de Jong R. S., 2001, ApJ, 550,

    2010

  22. [1491]

    Kroupa P., 1995, MNRAS, 277,

    1995

  23. [1496]

    Schombert J., McGaugh S., Lelli F., 2020, AJ, 160,

    2020

  24. [1507]

    2001, MNRAS, 322, 231 Kroupa, P

    Kroupa, P. 2001, MNRAS, 322, 231 Kroupa, P. 2002, Science, 295, 82 Kroupa, P., & Bouvier, J. 2003, MNRAS, 346, 369 Kroupa, P., & Weidner, C. 2003, ApJ, 598, 1076 Kroupa P., 2005, in Turon C., OFlaherty K. S., Perryman M. A. C., eds, ESA SP-576: The Three-Dimensional Universe w...

    2001

  25. [2301]

    I., 2022, A&A, 660, A61

    Dinnbier F., Kroupa P., Anderson R. I., 2022, A&A, 660, A61. Eappen R., Kroupa P., Wittenburg N., Haslbauer M., Famaey B., 2022, MNRAS, 516,

    2022

  26. [3252]

    Heger A., Fryer C

    Haslbauer M., Yan Z., Jerabkova T., Gjergo E., Kroupa P., Hasani Zonoozi A., 2024, A&A, 689, A221. Heger A., Fryer C. L., Woosley S. E., Langer N., Hartmann D. H., 2003, ApJ, 591,

    2024

  27. [3484]

    T., Gutermuth, R., Muzerolle, J., et al

    Megeath, S. T., Gutermuth, R., Muzerolle, J., et al. 2016, AJ, 151, 5 Meurer, G. R., Wong, O. I., Kim, J. H., et al. 2009, ApJ, 695, 765 Milgrom M., 1983, ApJ, 270,

    2016

  28. [4086]

    C., & Koopmans, L

    Spiniello, C., Trager, S. C., & Koopmans, L. V. E. 2015, ApJ, 803, 87 Stanway E. R., Eldridge J. J., 2019, A&A, 621, A105. Stanway E. R., Chrimes A. A., Eldridge J. J., Stevance H. F., 2020, MNRAS, 495,

    2015

  29. [4168]

    Scalo, J

    Renzini A., Ciotti L., 1993, ApJL, 416, L49. Scalo, J. M. 1986, Fundamentals Cosmic Phys., 11, 1 Scalo, J. 1998, The Stellar Initial Mass Function (38th Herstmon- ceux Conference), 142, 201 Schmidt M., 1959, ApJ, 129,

    1993

  30. [4430]

    Tinsley, B. M. 1980, Fundamentals Cosmic Phys., 5, 287 Thomas D., Maraston C., Bender R., Mendes de Oliveira C., 2005, ApJ, 621,

    1980

  31. [4605]

    R., Eldridge J

    Stanway E. R., Eldridge J. J., 2023, MNRAS, 522,

    2023

  32. [6005]

    Marigo P., 2001, A&A, 370,

    2001

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.