2026ApJ..1000..155Y

Current pulsar timing models face challenges when applied to binary pulsars with wide orbits and low orbital eccentricities. The conventional Damour-Deruelle (DD) model accurately characterizes the orbits of such systems, but it suffers from strong correlations between the time of periastron passage (T₀) 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 ≲ e ≲ 0.1, where the ELL1+ model cannot be used. 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.