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Stellar population modelling of neutron stars and black holes: spatially-resolved graveyards in MaNGA/SDSS-IV galaxies

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A new initial mass–remnant mass relation, derived from hydrodynamic supernova simulations, predicts that galaxies hold fewer neutron stars and more black holes than canonical models, with remnant populations varying systematically with…

desk verdict A transparent update of the Maraston population synthesis with a new hydrodynamical initial mass-remnant mass relation and the first spatially-resolved remnant maps for 10,010 MaNGA galaxies; the quantitative claims are model-dependent, but the paper says so itself. read the letter →

arxiv 2505.15691 v1 pith:ILPCTLXU submitted 2025-05-21 astro-ph.GA

Claudia Maraston , Marco Limongi , Justus Neumann , Lorenzo Roberti , Alessandro Chieffi , Daniel Thomas , Jianhui Lian This is my paper
classification astro-ph.GA
keywords neutronstarsblackholesstellarremnantsinitialmass-remnantmassrelationcore-collapsesupernovaepopulationsynthesisMaNGAgalaxiesgravitationalwavesources
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

Using a new initial mass–remnant mass relation built from hydrodynamic supernova explosions, this paper rebuilds stellar population models to predict how many neutron stars and black holes a stellar generation leaves behind and how much mass they lock up. The central result is a redistribution of the remnant budget: fewer neutron stars (up to about 0.3 dex) and more black holes (up to 0.8 dex), with the effect strongest when massive stars rotate. The same models predict that metal-rich stellar populations store the smallest remnant mass fraction, while about half-solar metallicity yields the most massive remnants. Applied to spatially resolved star-formation histories of ~10,000 SDSS-IV/MaNGA galaxies, the models produce maps of stellar graveyards that vary with galaxy mass, star-formation history, and metallicity. If correct, the dark remnant population of galaxies is not a fixed scaling but a sensitive function of galaxy properties, with consequences for mass-to-light ratios, dark matter estimates, and gravitational-wave source forecasts.

What carries the argument

The central object is the new initial mass–remnant mass relation in Table 1, computed with the HYPERION hydrodynamic code using a thermal bomb to trigger explosions, calibrated so each ejecta has a kinetic energy of $10^{51}$ erg. The explosion follows fallback for up to roughly $10^4$ seconds, and the final mass cut separates the remnant from the ejecta; a remnant above 2 $M_\odot$ counts as a black hole. The relation depends on initial mass, metallicity, and rotation velocity, and it is embedded in the Maraston stellar population synthesis by integrating over the initial mass function, with pair-instability supernovae removing remnants for the highest masses at low metallicity. The mass-loss prescription for Wolf-Rayet stars (Nugis & Lamers 2000) is the physical input that sets CO core masses and therefore the highest remnant masses.

What would settle it

Compare the predicted NS/BH ratio and remnant mass function against a statistically significant sample of gravitational-wave compact binary mergers with known host-galaxy properties. If, for example, metal-rich galaxies are found to host many black holes above the predicted ~15–30 $M_\odot$ range at solar metallicity, the mass-loss or explosion-energy calibration is wrong; alternatively, a precise census of Milky Way neutron stars from pulsar surveys could be checked against the predicted radial neutron-star surface-density profile in a Milky Way analogue.

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Extended reading notes

Core claim

The paper's central claim is that a physically self-consistent initial mass–remnant mass relation changes what stellar population models predict about compact remnants. Instead of assuming a fixed 1.4 $M_\odot$ neutron star from 8.5 to 40 $M_\odot$ and a half-mass black hole above 40 $M_\odot$ as the older Renzini & Ciotti relation did, the new relation lets remnant type and mass fall out of hydrodynamic explosion calculations of pre-supernova models covering initial masses 13–120 $M_\odot$, metallicities [Fe/H] from −3 to +0.3, and rotation velocities 0, 150, and 300 km s$^{-1}$. The consequences are that black holes begin forming at lower initial masses (about 20 $M_\odot$ without rotation, around 13 $M_\odot$ with rotation), a wider range of remnant masses appears, and rotating massive stars at all metallicities may produce no neutron stars above 13 $M_\odot$. For single-burst populations the total number of massive remnants changes little, but the NS/BH partition shifts strongly and the mass locked in massive remnants drops from 7 per cent in metal-poor populations to 1.5 per cent in metal-rich ones. The authors then use this to map graveyards in real galaxies, finding that more massive and more metal-rich galaxies host fewer remnants and that remnant radial gradients are flat in low-mass galaxies and negative in high-mass galaxies, especially Milky Way analogues.

Load-bearing premise

The load-bearing assumption is the rate at which the most massive stars lose mass in their Wolf-Rayet phase; the paper itself notes that changing this rate moves the predicted black hole masses and the balance of neutron stars versus black holes.

Editorial extensions

If this is right

  • Galaxy mass-to-light ratios and inferred dark matter fractions shift: metal-rich galaxies have less mass in remnants, so their stellar masses are lower and dark matter fractions higher than canonical models imply.
  • Half-solar metallicity populations store the largest black hole mass fraction (about 8 per cent after 10 Myr), making them the most productive hosts for black hole merger progenitors.
  • Stellar rotation suppresses neutron star production, offering an explanation for the apparent deficit of neutron stars relative to Milky Way type IMF predictions.
  • Radial remnant gradients are flat in low-mass galaxies and negative in high-mass galaxies, predicting that gravitational-wave follow-up should find merger remnants avoiding the centres of massive galaxies.
  • Pair-instability supernovae remove remnants for the most massive, metal-poor stars, capping the maximum black hole mass near 40–50 $M_\odot$ unless binaries intervene.

Reading between the lines

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

  • The two rotation cases bracket reality; a stellar population model with a realistic rotation-velocity distribution would likely produce intermediate NS/BH ratios, a smooth extension the paper leaves implicit.
  • The models can be tested without waiting for GW statistics: for a given galaxy's star-formation history and metallicity map, the predicted remnant count per spaxel is a falsifiable map that could be compared with future high-cadence transient or neutrino searches.
  • If binary evolution is added, the assumption that most black holes remain isolated weakens; the predicted numbers are upper limits for merger rates, since binaries can alter remnant masses and create earlier neutron stars.
  • Because remnant numbers are computed from resolved star-formation histories, the same approach could be extended to estimate the dark remnant mass budget in high-redshift galaxies, where only integrated light is available.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper updates the Maraston stellar population synthesis models with a new initial mass–remnant mass (IM-RM) relation for neutron stars and black holes, computed from 1D hydrodynamical explosion simulations of Limongi & Chieffi presupernova models over a range of metallicity and rotation rates. It then computes the time evolution of remnant numbers and masses for single-burst populations and applies these models to spatially resolved star formation histories of roughly 10,000 MaNGA galaxies to produce resolved 'graveyard' maps. The headline results are that NS numbers decrease by up to 0.3 dex and BH numbers increase by up to 0.8 dex relative to the canonical Renzini & Ciotti relation, with the BH mass budget peaking at half-solar metallicity; in MaNGA galaxies, more massive and more metal-rich galaxies host fewer remnants, and radial gradients are flat in low-mass and negative in high-mass galaxies.

Significance. The paper provides a valuable, openly available update of the M05 remnant prescriptions using a much more detailed IM-RM relation, and it is the first to map remnant populations on a spaxel-by-spaxel basis in a large IFU survey. The new numbers are directly relevant for stellar mass estimation, chemical evolution, and gravitational-wave follow-up planning. Strengths include the public release of models and data on Zenodo, the explicit statement of modelling assumptions, and a careful comparison with existing IM-RM relations. However, the central quantitative claims are conditional on the adopted Wolf-Rayet mass-loss prescription and on several grid-construction choices, as detailed below.

major comments (3)
  1. [§3.3, §8, Eqs. (4)–(5)] The headline dex differences (NS lower by up to 0.3 dex, BH higher by up to 0.8 dex) are computed from the IM-RM relation in Table 1, which adopts the Nugis & Lamers (2000) Wolf-Rayet mass-loss rate. Section 3.3 states that the alternative Langer (1989) rate changes the CO core of a 60 solar-mass star from about 12 to about 4 solar masses, which would alter remnant masses for M_in of about 25 solar masses and above by factors of several, and Section 8 concedes that the absolute numbers and NS/BH fractions depend on the adopted mass-loss rate. No sensitivity test or uncertainty estimate is provided. Because a shift in the critical mass M_crit in Eqs. (4)–(5) directly changes the NS/BH number ratio, the central claims are not robust to this choice. I request a quantitative sensitivity calculation using the LA89 rate (or an equivalent uncertainty bound) and a statement of how the reported dex ranges would change.
  2. [§7.1] The MaNGA remnant maps are built on the FIREFLY star formation histories of Neumann et al. (2022), which were derived with the M11-MILES and MaStar stellar population models based on the M05 synthesis code incorporating the canonical RC93 remnant relation. The new IM-RM relation changes the remnant masses, and hence the mass-to-light ratio and the mass locked in remnants for each age and metallicity bin. The paper does not discuss whether the star formation history fit itself would change if the new remnant prescription were used. Since the remnant surface densities and absolute numbers are normalised to stellar mass, the application is not fully self-consistent. Please either recompute the SFHs with the updated remnant models or provide a quantitative estimate of the effect of the remnant prescription on the inferred stellar masses and SFH weights.
  3. [§4, Fig. 6] The half-solar metallicity model, which is the one producing the peak BH mass fraction of about 8 per cent, is obtained by interpolation between [Fe/H] = -1 and 0, and pair-instability supernovae are explicitly not considered at [Z/H] = -0.33. Since PISN already appear at [Fe/H] = -1 for the highest masses (Table 1), the absence of PISN at half-solar is a strong assumption that directly boosts the BH mass budget in this bin. Please show the sensitivity of the half-solar peak to (i) including PISN with a threshold interpolated between [Fe/H] = -1 and 0, and (ii) the interpolation method used to construct the half-solar IM-RM relation.
minor comments (5)
  1. [Abstract, §8] The phrase 'the largest number of remnants found at about half-solar metallicity' is inconsistent with the figures, which show that the total number of NS+BH remnants is nearly metallicity-independent; the half-solar feature is in the mass budget (Figures 6 and 7). Please clarify whether 'number' or 'mass fraction' is meant throughout.
  2. [Table 1] Several entries in Table 1 appear ambiguous or physically inconsistent in the typeset version, for example the [Fe/H] = -2, v_rot = 300 km/s rows for M_in = 20 and 60 solar masses, where the final masses and remnant masses are difficult to reconcile with the stated initial masses. Please verify the typesetting and ensure all entries are internally consistent.
  3. [§1, §4] There are several typographical errors, including 'sumulations' in Section 1, 'intergrals' and 'estrapolating' in Section 4, and an apparent missing closing parenthesis in Eq. (8).
  4. [§3.4] The phrase 'third observing run (O34)' likely refers to LIGO/Virgo/KAGRA O3 or O4; please correct the label.
  5. [Fig. 3 caption] The caption statement 'values larger than -2 already refer to our population model grid' is unclear; please specify which metallicities are from the new hydrodynamical calculations and which are from the M05 grid interpolation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the population-synthesis predictions are genuine integrals over a hydrodynamically computed initial mass–remnant mass relation, and the MaNGA application uses independent spectra and previously published star formation histories.

full rationale

The paper's central derivation chain starts from the new initial mass–remnant mass (IM-RM) relation in Table 1, computed for this work with the HYPERION hydrodynamical code applied to progenitor grids from Limongi & Chieffi (2018, 2020) and Roberti et al. (2024), plus new supersolar models. That relation is an input, not an output of the population-synthesis machinery. The claims that neutron-star numbers are lower by up to 0.3 dex and black-hole numbers higher by up to 0.8 dex are obtained by evaluating the integrals in Eqs. (4)–(8) with a Kroupa IMF and the adopted remnant-mass threshold of 2 M_sun; this is a genuine model computation, not a restatement of the input. The NS/BH classification threshold is an explicit, externally motivated assumption and does not itself encode the predicted dex differences. The adopted Wolf-Rayet mass-loss rate (Nugis & Lamers 2000) is a real assumption on which the massive-star remnant masses depend, and the paper both quantifies the alternative (Langer 1989) and states in Section 8 that the absolute numbers and NS/BH fractions depend on the mass-loss rate; that is a robustness caveat, not circularity, because the alternative is not used to redefine the result. The MaNGA graveyard maps are built from observed IFU spectra and independently published spatially resolved star formation histories (Neumann et al. 2022); no parameter is fitted to the remnant quantities and then renamed as a prediction. Comparisons with Fryer et al. (2012), Sukhbold et al. (2016), Spera et al. (2015), and observed WR/O ratios provide external reference points. The self-citations to Limongi & Chieffi and Neumann et al. are to code-computed stellar models and observationally fitted spectral products, respectively, so they are not load-bearing in a circular sense. Overall, the derivation is self-contained and no circular step is present.

Assumptions & free parameters 5 free parameters · 8 assumptions · 0 invented entities

The central model depends on several prior stellar evolution inputs and on calibration choices. The most consequential are the calibrated explosion energy, the 2 Msun NS/BH threshold, the adopted mass-loss rate, and the restriction to single stars. No new physical entities are introduced.

free parameters (5)
  • Calibrated explosion energy at infinity E_expl = 1e51 erg
    Set by tuning the injected thermal energy in HYPERION for every progenitor; directly sets the remnant mass via fallback. Described in Section 3.2.
  • NS/BH mass threshold = 2 Msun
    Assumed to separate neutron stars from black holes in Section 3.4; changing it redistributes NS and BH counts and masses.
  • NS mass for 8.5 to 13 Msun progenitors = 1.4 Msun
    Adopted because the new grid starts at 13 Msun; approximation stated in equation 7 as having little impact.
  • Maximum initial mass leaving a remnant = 90 Msun
    Taken from Limongi & Chieffi 2018, Figure 17, to avoid pair-instability SNe; remnant values for 90 to 100 Msun are extrapolated in log from 80 and 90 Msun, as described in Section 4.
  • Initial rotational velocities = 0 and 300 km/s
    Two extreme values only; 300 km/s is treated as maximal rotation, with no velocity distribution, and this choice strongly affects population-level NS/BH fractions.
assumptions (8)
  • domain assumption Single-star evolution only; binary interactions are ignored
    Stated in Section 6 and the Summary. Binaries can change the IM-RM relation and produce earlier neutron stars or heavier black holes, so the galaxy remnant counts are upper limits.
  • domain assumption The Limongi & Chieffi 2018 and Roberti et al. 2024 pre-supernova models are accurate
    All explosions are run on this progenitor database; errors in final masses, core masses, or mass-loss rates propagate into the remnant masses in Table 1.
  • domain assumption HYPERION with the thermal bomb and flux-limited diffusion approximates the explosion and fallback correctly
    A 1D induced-explosion scheme, not a self-consistent neutrino-driven explosion; the injected energy is calibrated to yield E_expl = 1e51 erg.
  • domain assumption The Nugis & Lamers 2000 Wolf-Rayet mass-loss rate is the correct choice
    Section 3.3 defends NL00 with WR/O number ratios, but the alternative Langer 1989 rate produces much smaller CO cores and different remnant masses above 40 Msun.
  • ad hoc to paper The 2 Msun remnant-mass threshold separates neutron stars from black holes
    Adopted in Section 3.4; the reported NS and BH counts depend directly on this boundary, and other papers use 3 Msun.
  • ad hoc to paper No pair-instability supernovae occur in the half-solar metallicity bin
    Section 4 states PISNe are not considered in the interpolated half-solar model because they usually occur at lower metallicities; this avoids zero-remnant outcomes in that bin.
  • domain assumption The Kroupa 2001 IMF is representative
    All population numbers and mass fractions are computed with this IMF; the paper notes models are available for arbitrary IMFs, but only Kroupa is shown.
  • domain assumption The MaNGA FIREFLY star formation histories are reliable
    The spatially-resolved graveyards are linear combinations of SSP remnants weighted by these SFHs; fitting systematics are not propagated.

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Pith. "Pith review of Stellar population modelling of neutron stars and black holes: spatially-resolved graveyards in MaNGA/SDSS-IV galaxies." pith.science (2026). https://pith.science/paper/ILPCTLXU

@misc{pith2026250515691,
  author       = {Pith},
  title        = {Pith review of: Stellar population modelling of neutron stars and black holes: spatially-resolved graveyards in MaNGA/SDSS-IV galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ILPCTLXU}},
  note         = {Machine review of arXiv:2505.15691}
}
read the original abstract

We update our stellar population models for the time evolution of the number and mass of massive remnants - neutron stars and black holes - with a new initial mass-remnant mass relation for core collapse supernovae. The calculations are based on hydrodynamical simulations and induced explosions of a subset of previously published pre-supernovae models spanning a wide range of stellar mass, metallicity and different values for rotation velocity. The resulting stellar population models predict lower numbers of neutron stars (by up to 0.3 dex) and higher numbers of black holes (by up to 0.8 dex), especially when stellar rotation is considered. The mass fraction locked in neutron stars and black holes is lowest in high-metallicity populations, with the largest number of remnants found at about half-solar metallicity. This mirrors the amount of available gas, ranging from 35 per cent to 45 per cent. We then apply our new models to IFU spectra for ~10,000 galaxies from the SDSS-IV/MaNGA survey for which we previously published spatially-resolved star formation histories. This allows us to probe spatially-resolved graveyards in galaxies of different types. The number and radial distribution of remnants depend on a galaxy's mass, star formation history and metal content. More massive and hence more metal-rich galaxies are found to host fewer remnants. Radial gradients in the number of remnants depend on galaxy mass mostly because of the mass-dependent profiles in mass density: the gradients are flat in low-mass galaxies, and negative in high-mass galaxies, particularly in Milky Way analogues.

Figures

Figures reproduced from arXiv: 2505.15691 by the authors.

Figure 1
Figure 1. Dependence on chemical composition (coloured labels) of the turnoff mass (y-axis) setting the evolutionary timescales (x-axis) for massive remnant production of single stellar generations. The solid line corresponds to 𝑀𝑇𝑂 = 8.5𝑀⊙, below which stars evolve into white dwarfs and the massive remnant production is halted. Dashed lines mark the time when this happens, as a function of the explored metallicity range. sta… view at source ↗
Figure 2
Figure 2. Comparison of the initial mass 𝑀in (x-axis) - remnant mass 𝑀R (y-axis) relation obtained in this paper (black line) with those by Sukhbold et al. (2016) (red line) and by Fryer et al. (2012), where the green line is for the delayed engine and the blue line for the rapid engine. developed after the core He burning, which in turn determine the post-He-burning evolution. For example, a 60 M⊙ star with solar composition… view at source ↗
Figure 3
Figure 3. Comparison of the initial mass 𝑀in (x-axis) - remnant mass 𝑀R (y-axis) relations obtained with the new calculations described in Sec. 3 (coloured lines labelled by metallicity [Z/H], where values larger than −2 already refer to our population model grid, see Sec.4) and the canonical relations (green solid line). All masses are in units of 𝑀⊙. Solid lines refer to the no-rotation case, while dashed lines to a rotatio… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Time evolution of the number of massive remnants, 𝑁𝑁𝑆 + 𝑁𝐵𝐻, calculated for 1𝑀⊙, single-burst populations characterised by a Kroupa IMF and various chemical compositions, labelled with different colours. Solid and dashed lines refer to the 𝑣rot = 0 and 𝑣rot = 300𝑘𝑚 𝑠−1…
Figure 5
Figure 5. Figure 5: Specific time evolution of BH and NS remnants (black and golden lines, respectively) of stellar population models with different chemical composition (one per panel, from the metal-rich double-solar case [𝑍/𝐻] = +0.35 to a metal-poor 1/50 𝑍⊙, i.e. [Z/H]=-1.35, from top…
Figure 6
Figure 6. Figure 6: Time evolution of the mass fraction locked in massive BH and NS remnants, 𝑀𝑁𝑆+𝐵𝐻 (normalised to 1𝑀⊙, in single-burst populations characterised by a Kroupa IMF and various chemical compositions, labelled with different colours. Solid and dashed lines refer to the 𝑣rot =…
Figure 7
Figure 7. Figure 7: Time evolution of the specific mass fractions locked in NS and BH remnants, 𝑀𝑁𝑆+𝐵𝐻 (normalised to 1𝑀⊙, in single-burst populations characterised by a Kroupa IMF and various chemical compositions, labelled with different colours. Solid and dashed lines refer to the 𝑣rot…
Figure 8
Figure 8. Figure 8: Time evolution of the gas mass fraction (normalised to 1𝑀⊙), in single-burst populations characterised by a Kroupa IMF and various chemical compositions, labelled with different colours. Solid and dashed lines refer to the 𝑣rot = 0 and 𝑣rot = 300 km s−1 cases, respecti…
Figure 9
Figure 9. Figure 9: Spatially-resolved stellar remnant distributions in galaxies, for illustrative example galaxies (Column 1) spanning a range of type and mass as in N22, [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 6
Figure 6. Figure 6: The assumption of rotation in massive stars results in a siz￾able decrease in the number of NSs in favour of BHs, as evident when comparing the bottom panels of [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 10
Figure 10. Figure 10: As in [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]
Figure 11
Figure 11. Figure 11: Effect of galaxy age and metallicity on living stars and remnants, for the case of 𝑣rot = 0 km s−1 and 𝑣rot = 300 km s−1 (left-hand and right-hand blocks of four panels, respectively). While old age boosts the relative fraction of mass locked in remnants, metallicity …
Figure 12
Figure 12. Figure 12: Left-hand panel. Radial profiles of remnants integrated over MaNGA galaxies, split in groups identified by galaxy total stellar mass, as follows: dotted lines refer to low mass galaxies, 𝑀 < 1010 𝑀⊙; dot-dashed lines refer to intermediate mass galaxies, 1010 𝑀⊙ < 𝑀 < …

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Pith tools

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