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Long-term variations of X-ray pulse profiles for the Crab pulsar: data analysis and modeling

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Abstract

The pulse profiles of the Crab pulsar (as well as some other pulsars) vary with time. They can lead to a major source of intrinsic timing noise, which lacks a detailed physical model. The phase separation Δ between the first left peak (P1) and the second right peak (P2) is a key parameter that shows the variations of pulse profiles for the Crab pulsar. It was found that the evolution of A has a tendency with increasing rates of 0.82° ± 0.25°, 0.80° ± 0.54°, and 0.77° ± 0.28° per century for the 2–6, 6–15, and 15–60 keV bands, respectively. Furthermore, the flux ratios (P2/P1) of X-ray pulse profiles in the three bands were calculated, and the derived flux ratios were consistent with the radio and X-ray measurements of the Insight-HXMT. In addition to discovering the physical origin of the pulse changes, the high-SNR X-ray pulse profiles were simulated in the annular gap model, and two model parameters (e.g., the maximum emission heights of the two peaks) were observed to slightly affect the variations of peak separation. We fitted the long-term variations of emission heights of the two peaks and discovered that the emission heights showed increasing tendencies with time. Variations of these emission heights induced a characteristic period derivative, and a complete formula for both the magnetic dipole radiation and wind-particle-induced variations of the moment of inertia was used for the pulsar’s spin-down to obtain the variation rate ά of the magnetic inclination angle, which was −1.60° per century. Intrinsic timing noise is observed to be mainly induced by the variations of pulse profiles, which might correlate with a characteristic spin period derivative arising from the fluctuations of the emission regions. This work will lay a foundation for understanding the origin of intrinsic timing noise and making high-precision timing models in the future.

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Authors and Affiliations

  1. School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    LunHua Shang, XiangQun Cui, Hua Shen & RiHong Zhu

  2. Qian Xuesen Laboratory of Space Technology, Beijing, 100094, China

    LunHua Shang, YuanJie Du, LiangWei Huang, XinYuan Zhang, XiaoMin Bei & QingQing Lin

  3. Nanjing Institute of Astronomical Optics and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Nanjing, 210042, China

    XiangQun Cui

  4. XinJiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi, 830011, China

    ShiJun Dang

  5. University of Chinese Academy of Sciences, Beijing, 100049, China

    ShiJun Dang, YouLi Tuo & LinLi Yan

  6. CAS Key Laboratory of FAST, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100101, China

    JiGuang Lu

  7. Guizhou Radio Astronomy Observatory, Chinese Academy of Sciences, Guiyang, 550025, China

    JiGuang Lu

  8. School of Physics and Electronic Science, Guizhou Normal University, Guiyang, 550001, China

    JunTao Bai & QiJun Zhi

  9. Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guizhou Normal University, Guiyang, 550001, China

    JunTao Bai & QiJun Zhi

  10. Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China

    YouLi Tuo & LinLi Yan

  11. School of Physics, Peking University, Beijing, 100871, China

    GuoJun Qiao

  12. Key Laboratory of Advanced Solid Laser, Nanjing University of Science and Technology, Nanjing, 210094, China

    Hua Shen & RiHong Zhu

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Shang, L., Du, Y., Cui, X. et al. Long-term variations of X-ray pulse profiles for the Crab pulsar: data analysis and modeling. Sci. China Phys. Mech. Astron. 63, 109511 (2020). https://doi.org/10.1007/s11433-019-1505-8

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