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Complex rotational dynamics of the neutron star in Hercules X-1 revealed by X-ray polarization

Abstract

In an accreting X-ray pulsar, a neutron star accretes matter from a companion star through an accretion disk. The magnetic field of the rotating neutron star disrupts the inner edge of the disk, funnelling the gas to flow onto the poles on its surface. Hercules X-1 is a prototypical persistent X-ray pulsar about 7 kpc from Earth. Its emission varies on three distinct timescales: the neutron star rotates every 1.2 s, it is eclipsed by its companion each 1.7 d, and the system exhibits a superorbital period of 35 d, which has remained stable since its discovery. Several lines of evidence point to the source of this variation as the precession of the accretion disk or that of the neutron star. Despite the many hints over the past 50 yr, the precession of the neutron star itself has yet not been confirmed or refuted. X-ray polarization measurements (probing the spin geometry of Her X-1) with the Imaging X-ray Polarimetry Explorer suggest that free precession of the neutron star crust sets the 35 d period; this has the important implication that its crust is somewhat asymmetric by a few parts per ten million.

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Fig. 1: Evolution of the observed flux, PA and PD from Her X-1.
Fig. 2: IXPE observations of Hercules X-1 as a function of spin phase.
Fig. 3: Schematic showing the geometry varying through the precession of Hercules X-1.

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Data availability

The data used for this analysis are available through High-Energy Astrophysics Science Archive Research Center under IXPE Observation IDs 01001899, 02003801 and 02004001.

Code availability

The software used for this analysis is available at https://github.com/UBC-Astrophysics/IXPE-Analysis.

References

  1. Weisskopf, M. C. et al. The Imaging X-ray Polarimetry Explorer (IXPE): pre-launch. J. Astron. Telesc. Instrum. Syst. 8, 026002 (2022).

    Article  ADS  Google Scholar 

  2. Doroshenko, V. et al. Determination of X-ray pulsar geometry with IXPE polarimetry. Nat. Astron. 6, 1433–1443 (2022).

    Article  ADS  Google Scholar 

  3. Soffitta, P. et al. The instrument of the Imaging X-ray Polarimetry Explorer. Astron. J. 162, 208 (2021).

    Article  ADS  Google Scholar 

  4. di Marco, A. et al. Handling background in IXPE polarimetric data. Astron. J. 165, 143 (2023).

    Article  ADS  Google Scholar 

  5. González-Caniulef, D., Caiazzo, I. & Heyl, J. Unbinned likelihood analysis for X-ray polarization. Mon. Not. R. Astron. Soc. 519, 5902–5912 (2023).

    Article  ADS  Google Scholar 

  6. Garg, A., Rawat, D., Bhargava, Y., Méndez, M. & Bhattacharyya, S. Flux-resolved spectropolarimetric evolution of the X-ray pulsar Hercules X-1 using IXPE. Astrophys. J. Lett. 948, l10 (2023).

    Article  ADS  Google Scholar 

  7. Scott, D. M., Leahy, D. A. & Wilson, R. B. The 35 day evolution of the Hercules X-1 pulse profile: evidence for a resolved inner disk occultation of the neutron star. Astrophys. J. 539, 392–412 (2000).

    Article  ADS  Google Scholar 

  8. Soong, Y., Gruber, D. E., Peterson, L. E. & Rothschild, R. E. Spectral behavior of Hercules X-1: its long-term variability and pulse phase spectroscopy. Astrophys. J. 348, 641 (1990).

    Article  ADS  Google Scholar 

  9. Alpar, A. & Oegelman, H. Neutron star precession and the dynamics of the superfluid interior. Astron. Astrophys. 185, 196–202 (1987).

    ADS  Google Scholar 

  10. Lipunov, V. M. & Shakura, N. I. Interaction of the accretion disk with the magnetic field of a neutron star. Sov. Astron. Lett. 6, 14–17 (1980).

    ADS  Google Scholar 

  11. Lai, D. Magnetically driven warping, precession, and resonances in accretion disks. Astrophys. J. 524, 1030–1047 (1999).

    Article  ADS  Google Scholar 

  12. Staubert, R. et al. Long-term change in the cyclotron line energy in Hercules X-1. Astron. Astrophys. 572, a119 (2014).

    Article  Google Scholar 

  13. Steiner, A. W., Gandolfi, S., Fattoyev, F. J. & Newton, W. G. Using neutron star observations to determine crust thicknesses, moments of inertia, and tidal deformabilities. Phys. Rev. C 91, 015804 (2015).

    Article  ADS  Google Scholar 

  14. Landau, L. D. & Lifshitz, E. M. Mechanics 4th edn, Vol. 1 (Butterworth-Heinemann, 1976).

  15. Shakura, N. I. et al. Observations of Her X-1 in low states during SRG/eROSITA all-sky survey. Astron. Astrophys. 648, a39 (2021).

    Article  Google Scholar 

  16. Kosec, P. et al. Vertical wind structure in an X-ray binary revealed by a precessing accretion disk. Nat. Astron. 7, 715–723 (2023).

    Article  ADS  Google Scholar 

  17. Postnov, K. et al. Variable neutron star free precession in Hercules X-1 from evolution of RXTE X-ray pulse profiles with phase of the 35-d cycle. Mon. Not. R. Astron. Soc. 435, 1147–1164 (2013).

    Article  ADS  Google Scholar 

  18. Kolesnikov, D., Shakura, N. & Postnov, K. Evidence for neutron star triaxial free precession in Her X-1 from Fermi/GBM pulse period measurements. Mon. Not. R. Astron. Soc. 513, 3359–3367 (2022).

    Article  ADS  Google Scholar 

  19. Suleimanov, V., Potekhin, A. Y. & Werner, K. Models of magnetized neutron star atmospheres: thin atmospheres and partially ionized hydrogen atmospheres with vacuum polarization. Astron. Astrophys. 500, 891–899 (2009).

    Article  ADS  Google Scholar 

  20. Staubert, R. et al. Two ~35 day clocks in Hercules X-1: evidence for neutron star free precession. Astron. Astrophys. 494, 1025–1030 (2009).

    Article  ADS  Google Scholar 

  21. Gnedin, Y. N., Pavlov, G. G. & Shibanov, Y. A. The effect of vacuum birefringence in a magnetic field on the polarization and beaming of X-ray pulsars. Sov. Astron. Lett. 4, 117–119 (1978).

    ADS  Google Scholar 

  22. Pavlov, G. G. & Shibanov, Y. A. Influence of vacuum polarization by a magnetic field on the propagation of electromagnetic waves in a plasma. Sov. J. Exp. Theor. Phys. 49, 741 (1979).

    ADS  Google Scholar 

  23. Heyl, J. S. & Shaviv, N. J. Polarization evolution in strong magnetic fields. Mon. Not. R. Astron. Soc. 311, 555–564 (2000).

    Article  ADS  Google Scholar 

  24. Heyl, J. & Caiazzo, I. Strongly magnetized sources: QED and X-ray polarization. Galaxies 6, 76 (2018).

    Article  ADS  Google Scholar 

  25. Radhakrishnan, V. & Cooke, D. J. Magnetic poles and the polarization structure of pulsar radiation. Astrophys. Lett. 3, 225 (1969).

    ADS  Google Scholar 

  26. Poutanen, J. Relativistic rotating vector model for X-ray millisecond pulsars. Astron. Astrophys. 641, a166 (2020).

    Article  ADS  Google Scholar 

  27. Leahy, D. A. & Abdallah, M. H. Hz Her: stellar radius from X-ray eclipse observations, evolutionary state, and a new distance. Astrophys. J. 793, 79 (2014).

    Article  ADS  Google Scholar 

  28. Shakura, N. I., Postnov, K. A. & Prokhorov, M. E. On some features of free precession of a triaxial body: the case of Her X-1. Astron. Astrophys. 331, l37–l40 (1998).

    ADS  Google Scholar 

Download references

Acknowledgements

IXPE is a joint US and Italian mission. The US contribution is supported by the National Aeronautics and Space Administration (NASA) and led and managed by its Marshall Space Flight Center, with industry partner Ball Aerospace (Contract NNM15AA18C). The Italian contribution is supported by the Italian Space Agency (Contract ASI-ASI-OHBI-2022-13-I.0 and Agreements ASI-INAF-2022-19-HH.0 and ASI-INFN-2017.13-H0) and its Space Science Data Center (Agreements ASI-INAF-2022-14-HH.0 and ASI-INFN 2021-43-HH.0), and by the Italian National Institute for Astrophysics and the Italian National Institute for Nuclear Physics. This research used data products provided by the IXPE Team (Marshall Space Flight Center, Space Science Data Center, Italian National Institute for Astrophysics and Italian National Institute for Nuclear Physics) and distributed with additional software tools by the High-Energy Astrophysics Science Archive Research Center at NASA’s Goddard Space Flight Center. J.H. acknowledges support from the Natural Sciences and Engineering Research Council of Canada through a discovery grant, the Canadian Space Agency through the co-investigator grant program, and computational resources and services provided by Compute Canada, Advanced Research Computing at the University of British Columbia, and the SciServer science platform (www.sciserver.org). D.G.-C. acknowledges support from a fellowship grant from the French National Centre for Space Studies. J.P. and S.S.T. were supported by the Academy of Finland (Grant Nos. 333112 and 349144) and the Väisälä Foundation. V.D. and V.F.S. thank the German Academic Exchange Service (Travel Grant No. 57525212). We used Astropy (http://www.astropy.org), a community-developed core Python package and an ecosystem of tools and resources for astronomy.

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Authors

Contributions

J.H. analysed the data and wrote the draft of the paper. J.P. led the work of the IXPE Topical Working Group on Accreting Neutron Stars and contributed to the interpretation and the text. V.D., D.G.-C., I.C., A. Mushtukov., S.S.T., D.M. and V.F.S. contributed to the interpretation of the results and writing of the text. A. Mushtukov created Fig. 3. M.B. and G.G.P. acted as internal referees of the paper and contributed to its interpretation. Other members of the IXPE collaboration contributed to the design of the mission and its science case and the planning of the observations. All authors provided input and comments on the paper.

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Correspondence to Jeremy Heyl.

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Extended data

Extended Data Fig. 1 Posteriors for the RVM for the First Main-On (2022 January).

The two-dimensional contours correspond to 68%, 95% and 99% confidence levels. The histograms show the normalized one-dimensional distributions for a given parameter derived from the posterior samples. For each parameter the median and the differences to the 16th to 84th percentiles of the posteriors are given.

Extended Data Fig. 2 Posteriors for the RVM for the First Main-On (early).

The observations from 2022 February 17 through 21 are analysed as the early portion of the first Main-On. The two- dimensional contours correspond to 68%, 95% and 99% confidence levels. The histograms show the normalized one- dimensional distributions for a given parameter derived from the posterior samples. For each parameter the median and the differences to the 16th to 84th percentiles of the posteriors are given.

Extended Data Fig. 3 Posteriors for the RVM for the First Main-On (late).

The observations from 2022 February 22 through 24 are analysed as the late portion of the First Main-On. The two- dimensional contours correspond to 68%, 95% and 99% confidence levels. The histograms show the normalized one- dimensional distributions for a given parameter derived from the posterior samples. For each parameter the median and the differences to the 16th to 84th percentiles of the posteriors are given.

Extended Data Fig. 4 Posteriors for the RVM for the Short-On (2023 January).

The two-dimensional contours correspond to 68%, 95% and 99% confidence levels. The histograms show the normalized one-dimensional distributions for a given parameter derived from the posterior samples. For each parameter the median and the differences to the 16th to 84th percentiles of the posteriors are given.

Extended Data Fig. 5 Posteriors for the RVM for the Second Main- On (2023 February).

The two-dimensional contours correspond to 68%, 95% and 99% confidence levels. The histograms show the normalized one-dimensional distributions for a given parameter derived from the posterior samples. For each parameter the median and the differences to the 16th to 84th percentiles of the posteriors are given.

Supplementary information

Supplementary Information

Supplementary Figs. 1–3.

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Heyl, J., Doroshenko, V., González-Caniulef, D. et al. Complex rotational dynamics of the neutron star in Hercules X-1 revealed by X-ray polarization. Nat Astron (2024). https://doi.org/10.1038/s41550-024-02295-8

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