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The FAST Galactic Plane Pulsar Snapshot Survey. IX. Timing Three Binary Pulsars with Wide Orbits and Low Orbital Eccentricities

Z. L. Yang, J. L. Han, W. Q. Su, C. Wang, J. P. Yuan, T. Wang, Yi Yan, J. Xu, W. C. Jing, P. F. Wang, N. N. Cai, D. J. Zhou, X. J. Chen, D. Zhao

Abstract

Current pulsar timing models face challenges when applied to binary pulsars with wide orbits and low orbital eccentricities. The conventional \texttt{DD} model accurately characterizes the orbits of such systems, but it suffers from strong correlations between the time of periastron passage ($T_0$) and the longitude of periastron ($ω$). The ELL1 model avoids these parameter correlations, yet fails due to the limitations of its first-order low-eccentricity approximation. Recent enhancements to the ELL1 model (dubbed ELL1+ model) have incorporated higher-order terms but retain the low-eccentricity approximation. In this study, we propose a further improved model, ELL1R, which eliminates reliance on the low-eccentricity approximation through rigorous calculation of the Römer delay. This modification can avoid strong parameter correlations in the DD model, and it can be used in systems with mild eccentricity $0.01\lesssim e\lesssim0.1$ where the ELL1+ model can not. Using the ELL1R model, we present the first phase-coherent timing solutions for three binary pulsars: PSR~J1851--0108 (orbital period: 228 days), PSR~J1910+0423 (886 days), and PSR~J1923+2022 (777 days). Validation against the DD and ELL1+ models confirms that ELL1R yields consistent timing results while integrating the advantages of the two models. Our analysis further indicates that all three pulsars are mildly recycled. The companions of PSRs J1910+0423 and J1923+2022 are likely white dwarfs, whereas the nature of PSR J1851--0108's companion remains unknown.

The FAST Galactic Plane Pulsar Snapshot Survey. IX. Timing Three Binary Pulsars with Wide Orbits and Low Orbital Eccentricities

Abstract

Current pulsar timing models face challenges when applied to binary pulsars with wide orbits and low orbital eccentricities. The conventional \texttt{DD} model accurately characterizes the orbits of such systems, but it suffers from strong correlations between the time of periastron passage () and the longitude of periastron (). The ELL1 model avoids these parameter correlations, yet fails due to the limitations of its first-order low-eccentricity approximation. Recent enhancements to the ELL1 model (dubbed ELL1+ model) have incorporated higher-order terms but retain the low-eccentricity approximation. In this study, we propose a further improved model, ELL1R, which eliminates reliance on the low-eccentricity approximation through rigorous calculation of the Römer delay. This modification can avoid strong parameter correlations in the DD model, and it can be used in systems with mild eccentricity where the ELL1+ model can not. Using the ELL1R model, we present the first phase-coherent timing solutions for three binary pulsars: PSR~J1851--0108 (orbital period: 228 days), PSR~J1910+0423 (886 days), and PSR~J1923+2022 (777 days). Validation against the DD and ELL1+ models confirms that ELL1R yields consistent timing results while integrating the advantages of the two models. Our analysis further indicates that all three pulsars are mildly recycled. The companions of PSRs J1910+0423 and J1923+2022 are likely white dwarfs, whereas the nature of PSR J1851--0108's companion remains unknown.
Paper Structure (9 sections, 8 equations, 3 figures, 2 tables)

This paper contains 9 sections, 8 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Observations and Data Reduction
  3. FAST Observations
  4. Pulsar timing procedure and ELL1R timing model
  5. Timing results and discussion
  6. PSR J1851--0108
  7. PSR J1910+0423
  8. PSR J1923+2022
  9. Summary and discussion

Figures (3)

  • Figure 1: Timing residuals of PSRs J1851--0108, J1910+0423 and J1923+2022 as as a function of epoch or orbital phase. The error bars show the $1\sigma$ uncertainties of the measured TOAs taken with the $L$-band 19-beam receiver of FAST. No systematic trends are visible. Their weighted root-mean-square of timing residuals $\sigma_{\rm res}$ are shown in each subpanel.
  • Figure 2: The polarization profiles of PSRs J1851--0108, J1910+0423, and J1923+2022 obtained by adding data from all available FAST tracking observations with a beam offset less than 1.0$'$ offset from the pulsar position, with integration times of 2.3, 1.4, and 0.4 hours, respectively. The total intensity profile (black line), linear (blue dashed line), and circular (red dotted line, positive for the left-hand sense) polarization profiles are plotted in the lower sub-panel, with a scale-box indicating the 1-bin width and the $\pm2\sigma$ of flux density. The linear polarization angles (PA) are plotted in the upper sub-panel with the error bar represented for $\pm1\sigma$.
  • Figure 3: The distribution of projected semi-major axis $x$ and orbital eccentricity $e$ for binary pulsars. Data from the ATNF pulsar catalog v2.7.0 Manchester+2005AJ....129.1993M are shown, with the three GPPS binary pulsars presented in this work highlighted as red stars.