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Determination of X-ray pulsar geometry with IXPE polarimetry

Abstract

Using observations of X-ray pulsar Hercules X-1 by the Imaging X-ray Polarimetry Explorer we report a highly significant (>17σ) detection of the polarization signal from an accreting neutron star. The observed degree of linear polarization of ~10% is far below theoretical expectations for this object, and stays low throughout the spin cycle of the pulsar. Both the degree and angle of polarization exhibit variability with the pulse phase, allowing us to measure the pulsar spin position angle 57(2) deg and the magnetic obliquity 12(4) deg, which is an essential step towards detailed modelling of the intrinsic emission of X-ray pulsars. Combining our results with the optical polarimetric data, we find that the spin axis of the neutron star and the angular momentum of the binary orbit are misaligned by at least ~20 deg, which is a strong argument in support of the models explaining the stability of the observed superorbital variability with the precession of the neutron star.

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Fig. 1: Overview and evolution of polarization properties of Her X-1 over the period of observation.
Fig. 2: Energy dependence of the polarization of Her X-1.
Fig. 3: Pulse-phase dependence of the polarization properties of Her X-1.
Fig. 4: Geometry of the system from the observer’s perspective.
Fig. 5: Posterior distribution corner plot for the RVM fit of the PA phase dependence.

Data availability

IXPE data and analysis tools are publicly available from the HEASARC data archive (https://heasarc.gsfc.nasa.gov). Optical polarimetry data used in the paper are published in ref. 29.

References

  1. Tananbaum, H. et al. Discovery of a periodic pulsating binary X-ray source in Hercules from UHURU. Astrophys. J. Lett. 174, L143 (1972).

    Article  ADS  Google Scholar 

  2. Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M. & Andrae, R. Estimating distances from parallaxes. V. Geometric and photogeometric distances to 1.47 billion stars in Gaia Early Data Release 3. Astron. J. 161, 147 (2021).

    Article  ADS  Google Scholar 

  3. Middleditch, J. & Nelson, J. Studies of optical pulsations from HZ Herculis/Hercules X-1: a determination of the mass of the neutron star. Astrophys. J. 208, 567–586 (1976).

    Article  ADS  Google Scholar 

  4. Truemper, J. et al. Evidence for strong cyclotron line emission in the hard X-ray spectrum of Hercules X-1. Astrophys. J. Lett. 219, L105–L110 (1978).

    Article  ADS  Google Scholar 

  5. Giacconi, R. et al. Further X-ray observations of Hercules X-1 from Uhuru. Astrophys. J. 184, 227 (1973).

    Article  ADS  Google Scholar 

  6. Truemper, J., Kahabka, P., Oegelman, H., Pietsch, W. & Voges, W. EXOSAT observations of the 35 day cycle of Hercules X-1: evidence for neutron star precession. Astrophys. J. Lett. 300, L63 (1986).

    Article  ADS  Google Scholar 

  7. 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 

  8. 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 

  9. Caiazzo, I. & Heyl, J. Polarization of accreting X-ray pulsars - II. Hercules X-1. Mon. Not. R. Astron. Soc. 501, 129–136 (2021).

    Article  ADS  Google Scholar 

  10. Leahy, D. A. Modelling the extreme ultraviolet emission during the low state of Hercules X-1. Mon. Not. R. Astron. Soc. 342, 446–452 (2003).

    Article  ADS  Google Scholar 

  11. Klochkov, D. K. et al. Observational manifestations of the change in the tilt of the accretion disc to the orbital plane in Her X-1/HZ Her with phase of its 35-day period. Astron. Lett. 32, 804–815 (2006).

    Article  ADS  Google Scholar 

  12. Leahy, D. & Wang, Y. The 35-day cycle of Hercules X-1 in multiple energy bands from MAXI and Swift/BAT monitoring. Universe 7, 160 (2021).

    Article  ADS  Google Scholar 

  13. Igna, C. D. & Leahy, D. A. Light-curve dip production through accretion stream-accretion disc impact in the HZ Her/Her X-1 binary star system. Mon. Not. R. Astron. Soc. 425, 8–20 (2012).

    Article  ADS  Google Scholar 

  14. Shakura, N. I., Prokhorov, M. E., Postnov, K. A. & Ketsaris, N. A. On the origin of X-ray dips in Her X-1. Astron. Astrophys. 348, 917–923 (1999).

    ADS  Google Scholar 

  15. Kislat, F., Beilicke, M., Guo, Q., Zajczyk, A. & Krawczynski, H. An unfolding method for X-ray spectro-polarimetry. Astropart. Phys. 64, 40–48 (2015).

    Article  ADS  Google Scholar 

  16. Strohmayer, T. E. X-ray spectro-polarimetry with photoelectric polarimeters. Astrophys. J. 838, 72 (2017).

    Article  ADS  Google Scholar 

  17. 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 

  18. 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, 741–749 (1979).

    ADS  Google Scholar 

  19. 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 

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

    Article  ADS  Google Scholar 

  21. Radhakrishnan, V. & Cooke, D. J. Magnetic poles and the polarization structure of pulsar radiation. Astrophys. Lett. 3, 225–229 (1969).

    ADS  Google Scholar 

  22. Poutanen, J. Relativistic rotating vector model for X-ray millisecond pulsars. Astron. Astrophys. 641, A166 (2020).

    Article  ADS  Google Scholar 

  23. Buchner, J. et al. X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue. Astron. Astrophys. 564, A125 (2014).

    Article  Google Scholar 

  24. Blum, S. & Kraus, U. Analyzing X-ray pulsar profiles: geometry and beam pattern of Hercules X-1. Astrophys. J. 529, 968–977 (2000).

    Article  ADS  Google Scholar 

  25. Drissen, L., Lamontagne, R., Moffat, A. F. J., Bastien, P. & Seguin, M. Spectroscopic and polarimetric parameters of the runaway WN7 binary system HD 197406: is the secondary an X-ray–quiet black hole? Astrophys. J. 304, 188 (1986).

    Article  ADS  Google Scholar 

  26. Reynolds, A. P. et al. A new mass estimate for Hercules X-1. Mon. Not. R. Astron. Soc. 288, 43–52 (1997).

    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. 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 

  29. Egonsson, J. & Hakala, P. Discovery of variable optical polarization in Her X-1. Astron. Astrophys. 244, L41–L42 (1991).

    ADS  Google Scholar 

  30. 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 

  31. Brown, J. C., McLean, I. S. & Emslie, A. G. Polarisation by Thomson scattering in optically thin stellar envelopes. II. Binary and multiple star envelopes and the determination of binary inclinations. Astron. Astrophys. 68, 415–427 (1978).

    ADS  Google Scholar 

  32. Kravtsov, V. et al. Orbital variability of the optical linear polarization of the γ-ray binary LS I +61° 303 and new constraints on the orbital parameters. Astron. Astrophys. 643, A170 (2020).

    Article  Google Scholar 

  33. Petterson, J. A., Rothschild, R. E. & Gruber, D. E. A model for the 35 day variations in the pulse profile of Hercules X-1. Astrophys. J. 378, 696 (1991).

    Article  ADS  Google Scholar 

  34. Biryukov, A. & Abolmasov, P. Magnetic angle evolution in accreting neutron stars. Mon. Not. R. Astron. Soc. 505, 1775–1786 (2021).

    Article  ADS  Google Scholar 

  35. Caiazzo, I. & Heyl, J. Polarization of accreting X-ray pulsars. I. A new model. Mon. Not. R. Astron. Soc. 501, 109–128 (2021).

    Article  ADS  Google Scholar 

  36. Mönkkönen, J. et al. Constraints on the magnetic field structure in accreting compact objects from aperiodic variability. Mon. Not. R. Astron. Soc. 515, 571–580 (2022).

    Article  ADS  Google Scholar 

  37. 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 

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

    Article  ADS  Google Scholar 

  39. Baldini, L. et al. Design, construction, and test of the gas pixel detectors for the IXPE mission. Astropart. Phys. 133, 102628 (2021).

    Article  Google Scholar 

  40. Kislat, F., Clark, B., Beilicke, M. & Krawczynski, H. Analyzing the data from X-ray polarimeters with Stokes parameters. Astropart. Phys. 68, 45–51 (2015).

    Article  ADS  Google Scholar 

  41. Baldini, L. et al. ixpeobssim: a simulation and analysis framework for the Imaging X-ray Polarimetry Explorer. SoftwareX 19, 101194 (2022) https://doi.org/10.1016/j.softx.2022.101194

  42. Arnaud, K. A. XSPEC: the first ten years. In Astronomical Data Analysis Software and Systems V Conference Series Vol. 101 (eds Jacoby, G. H. & Barnes, J.) 17-20 (Astronomical Society of the Pacific, 1996).

  43. Rankin, J. et al. An algorithm to calibrate and correct the response to unpolarized radiation of the X-ray polarimeter onboard IXPE. Astron. J. 163, 39 (2022).

    Article  ADS  Google Scholar 

  44. Di Marco, A. et al. A weighted analysis to improve the X-ray polarization sensitivity of the Imaging X-ray Polarimetry Explorer. Astron. J. 163, 170 (2022).

    Article  ADS  Google Scholar 

  45. Życki, P. T., Done, C. & Smith, D. A. The 1989 May outburst of the soft X-ray transient GS 2023+338 (V404 Cyg). Mon. Not. R. Astron. Soc. 309, 561–575 (1999).

    Article  ADS  Google Scholar 

  46. Wit, E., van den Heuvel, E. & Romeijn, J.-W. ‘All models are wrong…’: an introduction to model uncertainty. Stat. Neerl. 66, 217–236 (2012).

    Article  MathSciNet  Google Scholar 

  47. Staubert, R., Klochkov, D. & Wilms, J. Updating the orbital ephemeris of Hercules X-1; rate of decay and eccentricity of the orbit. Astron. Astrophys. 500, 883–889 (2009).

    Article  ADS  Google Scholar 

  48. Lomb, N. R. Least-squares frequency analysis of unequally spaced data. Astrophys. Space Sci. 39, 447–462 (1976).

    Article  ADS  Google Scholar 

  49. Scargle, J. D. Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. Astrophys. J. 263, 835–853 (1982).

    Article  ADS  Google Scholar 

  50. Kuster, M. et al. in Exploring the Gamma-Ray Universe Special Publication Vol. 459 (eds Gimenez, A. et al.) 309–312 (ESA, 2001).

  51. Wolff, M. T. et al. The NuSTAR X-ray spectrum of Hercules X-1: a radiation-dominated radiative shock. Astrophys. J. 831, 194 (2016).

    Article  ADS  Google Scholar 

  52. Mushtukov, A. A., Suleimanov, V. F., Tsygankov, S. S. & Poutanen, J. The critical accretion luminosity for magnetized neutron stars. Mon. Not. R. Astron. Soc. 447, 1847–1856 (2015).

    Article  ADS  Google Scholar 

  53. Staubert, R. et al. Discovery of a flux-related change of the cyclotron line energy in Hercules X-1. Astron. Astrophys. 465, L25–L28 (2007).

    Article  ADS  Google Scholar 

  54. Zel’dovich, Y. B. & Shakura, N. I. X-ray emission accompanying the accretion of gas by a neutron star. Sov. Astron. 13, 175–183 (1969).

    ADS  Google Scholar 

  55. Suleimanov, V. F., Poutanen, J. & Werner, K. Accretion heated atmospheres of X-ray bursting neutron stars. Astron. Astrophys. 619, A114 (2018).

    Article  ADS  Google Scholar 

  56. González-Caniulef, D., Zane, S., Turolla, R. & Wu, K. Atmosphere of strongly magnetized neutron stars heated by particle bombardment. Mon. Not. R. Astron. Soc. 483, 599–613 (2019).

    Article  ADS  Google Scholar 

  57. Mushtukov, A. A., Suleimanov, V. F., Tsygankov, S. S. & Portegies Zwart, S. Spectrum formation in X-ray pulsars at very low mass accretion rate: Monte Carlo approach. Mon. Not. R. Astron. Soc. 503, 5193–5203 (2021).

    Article  ADS  Google Scholar 

  58. van Adelsberg, M. & Lai, D. Atmosphere models of magnetized neutron stars: QED effects, radiation spectra and polarization signals. Mon. Not. R. Astron. Soc. 373, 1495–1522 (2006).

    Article  ADS  Google Scholar 

  59. 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 

  60. Pavlov, G. G. & Zavlin, V. E. Polarization of thermal X-rays from isolated neutron stars. Astrophys. J. 529, 1011–1018 (2000).

    Article  ADS  Google Scholar 

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Acknowledgements

This Article is based on observations made by IXPE, a joint US and Italian mission. This research used data products provided by the IXPE Team (MSFC, SSDC, INAF and INFN) and distributed with additional software tools by the High-Energy Astrophysics Science Archive Research Center (HEASARC), at the NASA Goddard Space Flight Center (GSFC). The US contribution is supported by NASA and led and managed by its Marshall Space Flight Center (MSFC), with industry partner Ball Aerospace (contract number NNM15AA18C). The Italian contribution is supported by the Italian Space Agency (Agenzia Spaziale Italiana, ASI) through contract number ASI-OHBI-2017-12-I.0, agreement numbers ASI-INAF-2017-12-H0 and ASI-INFN-2017.13-H0, and its Space Science Data Center (SSDC) and by the Istituto Nazionale di Astrofisica (INAF) and the Istituto Nazionale di Fisica Nucleare (INFN) in Italy. V.D. and V.F.S. acknowledge support from the German Academic Exchange Service (DAAD) under travel grant number 57525212. J.P. and S.S.T. thank the Russian Science Foundation for support under grant number 20-12-00364 and the Academy of Finland for support under grant numbers 333112, 349144, 349373 and 349906. V.F.S. thanks the German Research Foundation (DFG) for grant number WE 1312/53-1. I.C. is a Sherman Fairchild Fellow at Caltech and thanks the Burke Institute at Caltech for supporting her research. A.A.M. acknowledges support from the Netherlands Organization for Scientific Research Veni Fellowship.

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Authors

Contributions

V.D. analysed the data and wrote the draft of the manuscript. J.P. led the work of the IXPE Topical Working Group on Accreting Neutron Stars and contributed to modelling the geometrical parameters, the interpretation and the text. S.S.T. produced an independent analysis of the data. V.F.S. led modelling of the polarization from heated atmospheres. A.D.M., F.L.M., F.M. and J.R. provided quick-look analysis of the data and energy scale correction calculation. I.C., J.H., A.A.M., S.Z., R.S. and A.S. contributed to interpretation of the results and writing of the text. M.B. and G.G.P. acted as internal referees of the paper and contributed to interpretation. Other members of the IXPE collaboration contributed to the design of the mission and its science case and planning of the observations. All authors provided input and comments on the manuscript.

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Correspondence to Victor Doroshenko or Juri Poutanen.

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Nature Astronomy thanks Hua Feng and Konstantin Postnov for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Observed Stokes spectra of Her X-1.

The top row shows spectra of the three Stokes parameters I, Q, and U, while the bottom row shows the residuals to the best-fitting model NTHCOMP for intensity and polconst for Q and U). The results for the three detector units are colour-coded, the black points in the first panel show the estimated background level for each detector.

Extended Data Fig. 2 Probability distribution function for the misalignment angle.

The distribution normalized to the peak value is shown for the misalignment angle between the pulsar and the orbital angular momenta. The red hatched region corresponds to the 68% confidence interval (that is between 16th and 84th percentiles of the posterior probability distribution). Four panels correspond to four different cases for the choice of χp: (A)χp = χp,* = 56.9°±1.6°; (B)χp = χp,* +180°; (C)χp = χp,* +90°; (D)χp = χp,* −90°.Here we take χorb = χorb,* = 28.9°±5.9°.

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Supplementary Information

Supplementary Figs. 1–3 and Tables 1–5.

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Doroshenko, V., Poutanen, J., Tsygankov, S.S. et al. Determination of X-ray pulsar geometry with IXPE polarimetry. Nat Astron 6, 1433–1443 (2022). https://doi.org/10.1038/s41550-022-01799-5

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