Determine the orbital period and long-term orbital dynamics of 3X J0042

Determine the orbital period and characterize possible long-term changes in the orbital dynamics of the M31 accreting X-ray pulsar 3X J0042 by combining XMM-Newton and NuSTAR timing observations over a longer temporal baseline, thereby resolving the ambiguity in the absolute orbital-cycle count between observations.

Background

The paper derives local orbital-epoch measurements for the five NuSTAR observations of 3X J0042 and obtains consistent projected semi-major axes from the two longest observations. However, the uncertainties in the orbital epochs prevent the authors from assigning an unambiguous number of complete orbital cycles between the NuSTAR observations. Consequently, the existing measurements cannot yet yield a sufficiently reliable combined orbital ephemeris or an improved orbital period.

The unresolved problem is to obtain a longer-baseline timing data set combining the available XMM-Newton and NuSTAR observations with additional future observations. Such data could resolve the cycle-count ambiguity, improve the orbital ephemeris, test for changes in the orbital period, and characterize the system’s long-term orbital dynamics.

References

However, these measurements cannot presently be combined into a new orbital ephemeris with sufficient confidence to improve the orbital period. In particular, the uncertainties in the measured orbital epochs do not allow the number of complete orbital cycles between the NuSTAR observations to be determined unambiguously. As a result, assigning an absolute cycle count to the individual $T_{90}$ measurements would introduce an ambiguity in the derived orbital period. A longer temporal baseline combining the available XMM-Newton and NuSTAR observations, together with additional future observations, would be valuable for resolving this ambiguity. Such a dataset could provide a sufficiently precise orbital ephemeris to investigate possible changes in the orbital period and to characterize the long-term orbital dynamics of the system.

— Detection of hard X-ray pulsations in non-ULX X-ray pulsar 3X J0042 in M31  (2609.10699 - Rikame et al., 9 Sep 2026) in Section 4.5, “Orbital ephemeris”