Multi-messenger detectability of continuous gravitational waves from the near future to next generation detectors

TL;DR

This paper investigates the multi-messenger detectability of continuous gravitational waves from spinning, deformed neutron stars, synthesizing theoretical models with electromagnetic observations and projecting detectability across current and future detectors. It analyzes two main GW-source classes—known pulsars (targeted, directed) and non-pulsing neutron stars (Cas A–type and Sco X-1–type)—and introduces sensitivity formalisms, including the dependence of upper limits on the noise power spectral density $S_h$, the depth parameter ${\mathcal D}$, and network configurations. The authors update prior estimates, presenting detailed curves and target-by-target expectations (e.g., MSPs with $\epsilon\sim10^{-9}$, Crab/Vela with $\epsilon\sim10^{-6}$, and LMXBs under torque balance) and arguing that first detections are likely in the near term, with many signals anticipated for next-generation instruments like Cosmic Explorer and the Einstein Telescope. A lack of detections in the coming years would challenge standard theories of millisecond pulsar formation and spin regulation by gravitational waves, while a positive detection would provide transformative insights into neutron star interiors, magnetic fields, and the physics of dense matter.

Abstract

Continuous gravitational waves have the potential to transform gravitational wave astronomy and yield fresh insights into astrophysics, nuclear and particle physics, and condensed matter physics. We evaluate their detectability by combining various theoretical and observational arguments from the literature and systematically applying those arguments to known astronomical objects and future gravitational wave detectors. We detail and update previous estimates made in support of Cosmic Explorer [M. Evans et al., arXiv:2306.13745; I. Gupta et al., Class. Quantum Grav. 41, 245001 (2024)]. It is commonly argued that the spins of accreting neutron stars are regulated by gravitational wave emission and that millisecond pulsars contain a young pulsar's magnetic field buried under accreted material. If either of these arguments holds, the first detection of continuous gravitational waves is likely with near future upgrades of current detectors, and many detections are likely with next generation detectors such as Cosmic Explorer and the Einstein Telescope. A lack of detections in the next several years would begin to raise serious doubts about current theories of millisecond pulsar formation.

Figures (6)

• Figure 1: Strain noise power spectral densities as functions of frequency for a variety of planned detectors, plus a recent (O4) noise curve from the LIGO Livingston Observatory (LLO) Capote for reference.
• Figure 2: Millisecond pulsars that should be detected by various networks. Pink diamonds show intrinsic strain for known pulsars assuming an ellipticity of $10^{-9}$, except for rare cases where the spin-down limit is slightly lower and is shown instead. Filled diamonds indicate pulsars for which the spin-down is known. Hollow diamonds indicate pulsars for which it is not known, and therefore the strain plotted may be too high. Solid curves show sensitivities for various interferometer networks assuming a sensitivity depth of 500 Hz$^{-1/2}.$ The two dashed curves assume a sensitivity depth of 1000 Hz$^{-1/2},$ which is achievable with long, stable runs and good pulsar timing.
• Figure 3: Young pulsars that could be detected by various networks. Pink diamonds are as in the previous Figure, but assuming an ellipticity of $10^{-6}.$ Here we plot only pulsars whose spin-downs are known and consistent with that ellipticity and whose characteristic ages are less than $10^7$ yr. Solid and dashed curves have sensitivity depths as in the previous Figure.
• Figure 4: Pulsars that could be detectable via $r$-mode GW emission. Pink diamonds are as the previous two figures, but assuming an $r$-mode with GW emission at 1.5 times the spin frequency and amplitude $\alpha$ of $10^{-3}$ or the spin-down limit, whichever is lower.
• Figure 5: Detectable ellipticity (left side) and $r$-mode amplitude (right side) for a tricky target (SNR 1987A) and an easier target (IC 443) for a modestly improved network (HLV operating in O5) and for a greatly improved network (4020ET). The variation between targets is greater than the variation between networks. For standard theoretical predictions of maximum ellipticity and $r$-mode amplitude, an easy target is detectable above tens of Hz and a tricky target is detectable above hundreds of Hz.