Parity-violating corrections to the orbital precession of binary system

TL;DR

The paper investigates gravitational parity violation using the binary pulsar PSR J1141-6545 by examining how misalignment between the white dwarf spin and the total angular momentum drives a parity-violating precession of the orbital plane, observable through the projected semi-major axis. It embeds ghost-free parity-violating gravity, including exterior and boundary contributions, in a post-Newtonian N-body framework and derives corrections to relative acceleration and to the orbital inclination, highlighting that PV effects depend on the spin projection along the total angular momentum and act perpendicular to GR. The exterior field correction is linear in the PV parameter and scales with eccentricity, while the boundary-term correction is quadratic in the parameter and exhibits oscillatory behavior; these lead to distinct observational signatures. Using the measured $\dot{x}_{obs}$ and the dominant Lense-Thirring precession in the system, the study places a conservative bound $\dot{f}_{PV} \lesssim 10^{6}$ m, with potential improvement to $\dot{f}_{PV} \lesssim 10^{2}$ m if pulsar data become available, corresponding to $M_{PV} \gtrsim 10^{-18}$–$10^{-22}$ GeV depending on the term considered. Overall, compact binary pulsar observations emerge as competitive probes of parity-violating gravity, complementary to solar-system and gravitational-wave constraints.

Abstract

In this work, we test for gravitational parity violation in the PSR J1141-6545 system by analyzing the orbital plane inclination precession induced by the misalignment between the white dwarf's spin axis and the system's total angular momentum. Using the parity-violating metric of gravity that incorporates terms from both the exterior and boundary of the field source, we calculated corrections to the relative acceleration and orbital inclination precession rates, which exhibit significant deviations from the GR prediction. The parity-violating contributions depend on the projection of the spin vector along the orbital angular momentum direction, contrasting with GR, where it depends on the projection within the orbital plane. The corrections are perpendicular to GR contribution, highlighting a fundamental distinction. The exterior field correction is linear in the theoretical parameter and coupled to eccentricity $e$, while the boundary term correction is quadratic. By comparing these corrections with GR and incorporating observational uncertainty, we derive the constraint on the theoretical parameter, yielding $ \dot{f}_{\rm PV}\lesssim 10^6~ \rm m$.

Figures (4)

• Figure 1: The oscillating black solid line represents the variation of the $\Delta\dot{x}_{\rm LT}/\dot{x}_{GR}$ ratio with respect to the parameter, where $R_2=2.1\times 10^3~\rm km$. The 13.9% verifcation of the observations (red dashed line) leads to a limit of $m_{\rm cs}\gtrsim 0.14\times 10^{-2} \rm km^{-1}$ for the parameter in the PSR J1141-6545.
• Figure 2: The oscillating black solid line represents the variation of the $\Delta\dot{x}_{\rm LT}/\dot{x}_{GR}$ ratio with respect to the parameter, where $R_2=10^4~\rm km$. The 13.9% verifcation of the observations (red dashed line) leads to a limit of $m_{\rm cs}\gtrsim 0.95\times 10^{-2} \rm km^{-1}$ for the parameter in the PSR J1141-6545.
• Figure 3: The oscillating black solid line represents the variation of the $\Delta\dot{x}_{\rm LT}/\dot{x}_{GR}$ ratio with respect to the parameter, where $R_2=5.4\times 10^3~\rm km$. The 13.9% verifcation of the observations (red dashed line) leads to a limit of $m_{\rm cs}\gtrsim 0.32\times 10^{-2} \rm km^{-1}$ for the parameter in the PSR J1141-6545.
• Figure 4: The oscillating black solid line represents the variation of the $\Delta\dot{x}_{\rm LT}/\dot{x}_{GR}$ ratio with respect to the parameter, where the radius of pulsars $R_1=20~\rm km$. The 13.9% verification of the observations (red dashed line) leads to a limit of $m_{\rm cs}\gtrsim 2.5~ \rm km^{-1}$ for the parameter in the PSR J1141-6545.