# Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar

## Abstract

Despite its importance to our understanding of physics at supranuclear densities, the equation of state (EoS) of matter deep within neutron stars remains poorly understood. Millisecond pulsars (MSPs) are among the most useful astrophysical objects in the Universe for testing fundamental physics, and place some of the most stringent constraints on this high-density EoS. Pulsar timing—the process of accounting for every rotation of a pulsar over long time periods—can precisely measure a wide variety of physical phenomena, including those that allow the measurement of the masses of the components of a pulsar binary system1. One of these, called relativistic Shapiro delay2, can yield precise masses for both an MSP and its companion; however, it is only easily observed in a small subset of high-precision, highly inclined (nearly edge-on) binary pulsar systems. By combining data from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 12.5-yr data set with recent orbital-phase-specific observations using the Green Bank Telescope, we have measured the mass of the MSP J0740+6620 to be $${\mathbf{2}}{\mathbf{.14}}_{ - {\mathbf{0}}{\mathbf{.09}}}^{ + {\mathbf{0}}{\mathbf{.10}}}$$M (68.3% credibility interval; the 95.4% credibility interval is $${\mathbf{2}}{\mathbf{.14}}_{ - {\mathbf{0}}{\mathbf{.18}}}^{ + {\mathbf{0}}{\mathbf{.20}}}$$M). It is highly likely to be the most massive neutron star yet observed, and serves as a strong constraint on the neutron star interior EoS.

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## Data availability

PSR J0740+6620 TOAs from both the 12.5-yr data set and from the two supplemental GBT observations will be available at https://data.nanograv.org on publication of this manuscript.

## Code availability

All code mentioned in this work is open source and available at the links provided in the manuscript.

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## Acknowledgements

The NANOGrav Project receives support from NSF Physics Frontiers Center award no. 1430284. Pulsar research at UBC is supported by an NSERC Discovery Grant and by the Canadian Institute for Advanced Research (CIFAR). The National Radio Astronomy Observatory and the Green Bank Observatory are facilities of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. S.M.R is a CIFAR Senior Fellow. W.W.Z. is supported by the CAS Pioneer Hundred Talents Program, the Strategic Priority Research Program of the Chinese Academy of Sciences grant no. XDB23000000 and the National Natural Science Foundation of China grant nos. 11690024, 11743002 and 11873067. Supplementary Green Bank conjunction-phase observing project codes were 18B-289 and 18B-372 (DDT).

## Author information

Authors

### Contributions

The creation of the NANOGrav 12.5-yr data set was made possible through extensive observations and pulsar-timing activities conducted by all the authors. H.T.C. was responsible for the NANOGrav-adjacent concentrated observing campaigns and the majority of this manuscript’s contents. H.T.C., E.F., S.M.R. and P.B.D. were responsible for the extended J0740+6620 data analysis (the merging of NANOGrav and conjunction-phase observations) and modelling effort. E.F. was responsible for much of the initial work on J0740+6620 that informed the supplementary observing proposals, and for the development of the gridding code that yielded both the mass and inclination credibility intervals and Fig. 2.

### Corresponding author

Correspondence to H. T. Cromartie.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Astronomy thanks John Antoniadis and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Reprints and Permissions

Cromartie, H.T., Fonseca, E., Ransom, S.M. et al. Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar. Nat Astron 4, 72–76 (2020). https://doi.org/10.1038/s41550-019-0880-2

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