A (old) new science goal for deci-Hertz gravitational wave detectors

In the next few decades a number of space-based gravitational wave detectors sensitive in the deci-Hertz band should be operational. 

Among the main goals of such detectors are a number of "first detections" such as primordial gravitational waves, compact stellar mass inspirals and intermediate mass black hole mergers. 

Interestingly enough we find no mention of Continuous Gravitational Waves (CGWs). Such signals, which are yet to be detected, are thought to be emitted by rotating Neutron Stars (NSs) with a reasonably small degree of non-axisymmetry.

In a previous study of ours (arXiv:2303.04714) we show that, not only the frequency band currently covered by ground-based detectors is populated by less than ~ 0.5% of all NSs, but also how those sources who possess a strong magnetic field and thus are highly deformed in the scenario of a magnetically induced non-axisymmetry, all lie in the deci-Hertz band, outside the currently "visible" one.

Here we investigate on the possible role that deci-Hertz detectors can play for the cause of CGWs detection. We consider both blind and targeted searches for CGWs. 

In the former case we find that detecting unknown neutron stars will be possible if these have an almost purely toroidal magnetic field topology. This result is in line with what we find on a previous study of ours. 

In the case of known pulsars we cannot make detectability predictions, but we can explore the no-detection scenario. Already at the DECIGO pathfinder sensitivities we would be able to constrain spin-down ellipticities for ~ 300 known pulsars (currently we can do that for only ≈ 30), and of these ≈ 20 would result to have the percentage of CGW spin-down luminosity constrained down to values smaller than 0.1% (currently this is valid only for the Crab and Vela pulsars). Such estimations will increase of a factor ≈ 3 when considering DECIGO and BBO detectors.