A non-secular perturbative treatment of binary orbits shows that resonant gravitational waves and ultra-light dark matter drive quadratic growth of the true anomaly perturbation, substantially boosting projected detection sensitivities.
Bayesian sensitivity of binary pulsars to ultra-light dark matter
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abstract
Ultra-light dark matter perturbs the orbital motion of binary pulsars, in particular by causing peculiar time variations of a binary's orbital parameters, which then induce variations in the pulses' times-of-arrival. Binary pulsars have therefore been shown to be promising detectors of ultra-light dark matter. To date, the sensitivity of binary pulsars to ultra-light dark matter has only been studied for dark matter masses in a narrow resonance band around a multiple of the binary pulsar orbital frequency. In this study we devise a two-step, bayesian method that enables us to compute semi-analytically the sensitivity for all masses, also away from the resonance, and to combine several observed binaries into one global sensitivity curve. We then apply our method to the case of a universal, linearly-coupled, scalar ultra-light dark matter. We find that with next-generation radio observatories the sensitivity to the ultra-light dark matter coupling will surpass that of solar-system constraints for a decade in mass around $m\sim10^{-21}$ $\text{eV}$, even beyond resonance.
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Prospects for gravitational wave and ultra-light dark matter detection with binary resonances beyond the secular approximation
A non-secular perturbative treatment of binary orbits shows that resonant gravitational waves and ultra-light dark matter drive quadratic growth of the true anomaly perturbation, substantially boosting projected detection sensitivities.