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Determination of the birth-mass function of neutron stars from observations

Nature Astronomy volume 9, pages 552–563 (2025)Cite this article

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Abstract

The birth-mass function of neutron stars encodes rich information about supernova explosions, double-star evolution and the properties of matter under extreme conditions. To date, it has remained poorly constrained by observations, however. Applying probabilistic corrections to account for mass accreted by recycled pulsars in binary systems to mass measurements of 90 neutron stars, we find that the birth masses of neutron stars can be described by a unimodal distribution that smoothly turns on at 1.1 M⊙ and peaks at ~1.27 M⊙, before declining as a steep power law. Such a ‘turn-on’ power-law distribution is strongly favoured against the widely adopted empirical double-Gaussian model at the 3σ level. The power-law shape may be inherited from the initial mass function of massive stars, but the relative dearth of massive neutron stars implies that single stars with initial masses greater than ~18 M⊙ do not form neutron stars, in agreement with the absence of massive red supergiant progenitors of supernovae.

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Fig. 1: Individual mass distributions of 39 recycled pulsars.
Fig. 2: Example mass models and their Bayes factors.
Fig. 3: Reconstructed birth-mass function of neutron stars based on the preferred TOP model.
Fig. 4: Posterior distributions of the TOP model parameters.

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Data availability

All the neutron-star mass measurements used in this study are listed in Extended Data Tables 1 and 2 with the original references. These mass measurements, accreted-mass corrections for recycled pulsars, posterior samples from Bayesian inference and the data behind Extended Data Tables 1 and 2 and Figs. 1–4 and Extended Data Figs. 1–4 are available via Zenodo at https://doi.org/10.5281/zenodo.14375273 (ref. 89). Source data are provided with this paper.

Code availability

The following open-source software packages were used in this paper: GalDynPsr, gwpopulation, BILBY and dynesty. The Python scripts used for data analysis and figure generation are publicly available from GitHub at https://github.com/GW-BNUZ/NSbirthMass.

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Acknowledgements

We thank Z. Li, X. Chen and Z. Han for providing data from their numerical simulations, which are plotted in Extended Data Fig. 2. We also thank I. Mandel and M. Bailes for useful discussions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 12203004 to X.Z., 12021003 and 12433001 to Z.-H.Z., 12305059 to Z.-Q.Y. and 12405056 to Z.-C.C.). X.Z. and H.G. are supported by the Fundamental Research Funds for the Central Universities. This work was supported in part by the Australian Research Council (ARC) Centre of Excellence for Gravitational Wave Discovery (Project Nos. CE170100004 and CE230100016). S.S. is a recipient of an ARC Discovery Early Career Research Award (DE220100241). This work was supported by ARC Discovery Grants DP240101786 (to B.M. and A.H.) and DP240103174 (to A.H.).

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Arts and Sciences, Beijing Normal University, Zhuhai, China

    Zhi-Qiang You, Xingjiang Zhu, Xiaojin Liu & Zu-Cheng Chen

  2. Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai, China

    Zhi-Qiang You, Xingjiang Zhu, Xiaojin Liu & Zu-Cheng Chen

  3. School of Physics and Astronomy, Beijing Normal University, Beijing, China

    Zhi-Qiang You, Xiaojin Liu, Zu-Cheng Chen, He Gao & Zong-Hong Zhu

  4. Henan Academy of Sciences, Zhengzhou, China

    Zhi-Qiang You

  5. Institute for Frontier in Astronomy and Astrophysics, Beijing Normal University, Beijing, China

    Xingjiang Zhu & He Gao

  6. School of Physics and Astronomy, Monash University, Clayton, Victoria, Australia

    Bernhard Müller, Alexander Heger, Eric Thrane, Paul Lasky & Duncan K. Galloway

  7. OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery, Hawthorn, Victoria, Australia

    Bernhard Müller, Alexander Heger, Simon Stevenson, Eric Thrane, Ling Sun, Paul Lasky & Duncan K. Galloway

  8. Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn, Victoria, Australia

    Simon Stevenson

  9. Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, China

    Zu-Cheng Chen

  10. Institute of Interdisciplinary Studies, Hunan Normal University, Changsha, China

    Zu-Cheng Chen

  11. Centre for Gravitational Astrophysics, College of Science, The Australian National University, Canberra, Australian Capital Territory, Australia

    Ling Sun

  12. Institute for Globally Distributed Open Research and Education (IGDORE), Gothenburg, Sweden

    Duncan K. Galloway

  13. Australia Telescope National Facility, CSIRO Space and Astronomy, Epping, New South Wales, Australia

    George Hobbs & Richard N. Manchester

  14. School of Physics and Technology, Wuhan University, Wuhan, China

    Zong-Hong Zhu

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  1. Zhi-Qiang You
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Contributions

X.Z. conceptualized the study, compiled the list of neutron-star mass measurements and wrote the initial draft of the paper. Z.-Q.Y. led the data curation and Bayesian inference analysis and prepared most of the figures and tables. Z.-Q.Y., X.L. and X.Z. calculated the accreted-mass corrections for recycled pulsars. B.M., A.H. and S.S. led the theoretical investigations of neutron star birth masses. E.T., Z.-C.C., L.S. and P.L. contributed to the analysis methods. D.K.G., G.H. and R.N.M. discussed the data used in the analysis. B.M., A.H., S.S., E.T., L.S., P.L., X.L. and H.G. contributed to the interpretation of the results. Z.-H.Z. contributed to supervision, funding acquisition and resources that enabled this study. All authors contributed to revisions and edits of the paper.

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Correspondence to Xingjiang Zhu or Zong-Hong Zhu.

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Extended data

Extended Data Table 1 Mass measurements of neutron stars in double neutron star and neutron star-white dwarf systems
Full size table
Extended Data Table 2 Mass measurements of neutron stars in other types of systems
Full size table

Extended Data Fig. 1 The pulsar P-\(\dot{\rm{P}}\) diagram for 39 recycled pulsars.

Black circles mark their current locations (where the error bars on the intrinsic \(\dot{\rm{P}}\) are too small to be seen except for the two globular-cluster pulsars), whereas orange and blue stars mark the minimum and plausible initial spin periods (assuming a breaking index n = 3), respectively. The solid green line is the limiting spin-up line \(\dot{\rm{P}}\) ∝ P4/3 inferred for the population of millisecond pulsars55.

Source data

Extended Data Fig. 2 The accreted mass-spin period (Δm-P) correlation used to correct for mass accreted by recycled pulsars.

The green solid line depicts a lower limit on the accreted mass19,22, while the orange solid lines and shaded band represent the mean and 90% credible region of our phenomenological model. The red dashed line is a simple scaling used in the literature25,72. The grey shaded band encompasses 90% credible region of our analytical model. Blue dots are from numerical simulations of the recycling process performed in ref. 23.

Source data

Extended Data Fig. 3 The mass probability distribution of PSR J1614–2230.

The green curve depicts the measured mass75, whereas the black curve is the birth mass deduced from detailed binary evolution calculations73, based on the original measured mass of 1.97 ± 0.04 M⊙ 6. Birth masses estimated from our analytical and phenomenological models are shown in blue and orange, respectively.

Source data

Extended Data Fig. 4 The period and luminosity distribution of pulsars with measured mass.

a, Measured mass versus spin period for 39 recycled pulsars (blue) in group A (‘Modelling the accreted masses of recycled pulsars’ in Methods) and the remaining neutron stars (orange). b, Measured mass versus luminosity at 1.4 GHz for 39 recycled pulsars, where the horizontal error bars account for uncertainties in the flux density and distance. We adopted the distance estimates from the Australia Telescope National Facility Pulsar Catalogue while assuming a 20% error. In both panels, plotted are mean values with 1σ credible errors, while the measurement uncertainty of spin periods in the upper panel is too small to be seen.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–6, Tables 1 and 2 and discussion.

Source data

Source Data Fig. 1

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Source Data Fig. 2

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Source Data Fig. 3

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Source Data Fig. 4

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Source Data Extended Data Table 1

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Source Data Extended Data Table 2

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Source Data Extended Data Fig. 1

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Source Data Extended Data Fig. 2

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Source Data Extended Data Fig. 3

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Source Data Extended Data Fig. 4

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You, ZQ., Zhu, X., Liu, X. et al. Determination of the birth-mass function of neutron stars from observations. Nat Astron 9, 552–563 (2025). https://doi.org/10.1038/s41550-025-02487-w

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