Axion Oscillations in Binary Systems: Angle-action Surgery
Vincent Desjacques, Evgeni Grishin, Yonadav Barry Ginat · 2020 · 8 citationsRead the paper
Abstract Scalar, tensor waves induce oscillatory perturbations in Keplerian systems that can be probed with measurements of pulsar timing residuals. In this paper, we consider the imprint of coherent oscillations produced by ultralight axion dark matter on the Roemer time delay. We use the angle-action formalism to calculate the time evolution of the observed signal and its dependence on the orbital parameters and the axion phase. We derive exact analytical expressions for arbitrary binary pulsar mass ratio and eccentricity, alleviating the need for long numerical integrations. We emphasize the similarity of the expected signal-to-noise ratio with the response of a harmonic oscillator to an external oscillatory driving. We validate our theoretical predictions with numerical simulations. Our results furnish a useful benchmark for numerical codes and analysis procedures and, hopefully, will motivate the search for such imprints in real data.
What the full text shows
Theory or simulation- Derived exact analytical expressions for the imprint of ultralight axion dark matter oscillations on the Roemer time delay for arbitrary binary pulsar mass ratios and eccentricities. (0 ≤ e < 1)
- The relative amplitude of the effect on the Roemer time delay is proportional to the dark matter density and the square of the orbital frequency. — ∑ ∝ GρDM Ω² (Resonant region Ω ≈ ma)
- Theoretical predictions for instantaneous variations in the Roemer time delay showed excellent agreement with numerical simulations. (0 ≤ e < 1)
- Setup
- Numerical validation used a binary pulsar system with total mass M = 2 M⊙, dark matter density ρDM = 5 × 10³ M pc⁻³, and axion mass ma = 10⁻³⁰ GeV.
- How
- The authors used the angle-action formalism to solve equations of motion at first order in perturbations to calculate the time evolution of the binary separation. These analytical results were validated using the REBOUND framework with the IAS15 high-order integrator.
- Limitations
- Ignored the orientation of the orbital plane relative to the observer's line of sight. · Did not consistently include the back-reaction of the binary system (e.g., gravitational wave emission).
Summarized by Gemma 4 from the open-access full text · 8 Oct 2026. Read it