# Maximum gravitational mass $M_{\rm TOV}=2.25^{+0.08}_{-0.07}M_\odot$ inferred at about $3\%$ precision with multimessenger data of neutron stars

**Authors:** Yi-Zhong Fan, Ming-Zhe Han, Jin-Liang Jiang, Dong-Sheng Shao, Shao-Peng Tang  
**arXiv:** [2309.12644](https://arxiv.org/abs/2309.12644)  
**Date:** 2023-09-22  
**Summary page:** https://www.summarizepaper.com/en/paper/2309.12644v1/

## Key points

- The maximal gravitational mass of nonrotating neutron stars ($M_{\rm TOV}$) is a crucial parameter in understanding compact objects.
- Precise bounds on $M_{\rm TOV}$ based on first principles alone are challenging.
- Reliable measurements of neutron star masses and/or radii are leveraged to infer $M_{\rm TOV}$ in this study.
- $M_{\rm TOV}=2.25^{+0.08}_{-0.07}~M_\odot$ with 68.3% credibility is obtained by combining the mass distribution of neutron stars with the reconstruction of the equation of state (EoS) of dense matter.
- Various data sources, including updated neutron star mass measurements, GW170817 data, and PSR J0030+0451 and PSR J0740+6620 data, are utilized.
- Theoretical information from chiral effective theory ($\chi$EFT) and perturbative quantum chromodynamics (pQCD) is incorporated at low and very high energy densities respectively.
- The narrow credible range for $M_{\rm TOV}$ is attributed to pQCD constraints and exclusion by the mass function.
- Three different EoS reconstruction methods lead to almost identical results for $M_{\rm TOV}$, ensuring robustness in the findings.
- The equation of state for neutron star matter is moderately stiff based on this precise evaluation.
- Compact objects detected by second-generation gravitational wave detectors with masses around $\sim 2.5-3 M_\odot$ are most likely lightest black holes rather than neutron stars according to the authors' proposal.
- Combining multiple data sources and theoretical considerations is important for obtaining precise inferences about the maximal gravitational mass of nonrotating neutron stars.

## Summary

The maximal gravitational mass of nonrotating neutron stars ($M_{\rm TOV}$) is a crucial parameter in understanding compact objects. However, setting precise bounds on $M_{\rm TOV}$ based on first principles alone is challenging. In this study, the authors leverage reliable measurements of neutron star masses and/or radii to robustly infer $M_{\rm TOV}$. By combining the mass distribution of these objects with the reconstruction of the equation of state (EoS) of dense matter, they achieve a precise inference of $M_{\rm TOV}=2.25^{+0.08}_{-0.07}~M_\odot$ with 68.3% credibility. To obtain this result, the authors utilize various data sources, including an updated sample of neutron star mass measurements, mass-tidal deformability data from GW170817, and mass-radius data from PSR J0030+0451 and PSR J0740+6620. They also incorporate theoretical information from chiral effective theory ($\chi$EFT) and perturbative quantum chromodynamics (pQCD) at low and very high energy densities respectively. The narrow credible range for $M_{\rm TOV}$ obtained in this study is attributed to two factors. Firstly, the high $M_{\rm TOV}$ values are suppressed by the pQCD constraint derived from theoretical considerations. Secondly, lower values of $M_{\rm TOV}$ are excluded by the mass function. To ensure robustness in their findings, three different EoS reconstruction methods are employed independently leading to almost identical results for $M_{\rm TOV}$. This precise evaluation suggests that the equation of state for neutron star matter is moderately stiff. Furthermore, based on their findings, the authors propose that compact objects detected by second-generation gravitational wave detectors with masses around $\sim 2.5-3 M_\odot$ are most likely lightest black holes rather than neutron stars. Overall this study provides a refined and detailed understanding of the maximal gravitational mass of nonrotating neutron stars highlighting the importance of combining multiple data sources and theoretical considerations to obtain precise inferences.