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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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.
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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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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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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 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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DOI: https://doi.org/10.1038/s41550-022-01799-5
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