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We assess the detection prospects of a gravitational wave background associated with sub‐luminous gamma‐ray bursts (SL‐GRBs). We assume that the central engines of a significant proportion of these bursts are provided by newly born magnetars and consider two plausible GW emission mechanisms. First, the deformation‐induced triaxial GW emission from a newly born magnetar. Secondly, the onset of a secular bar‐mode instability, associated with the long‐lived plateau observed in the X‐ray afterglows of many gamma‐ray bursts. With regards to detectability, we find that the onset of a secular instability is the most optimistic scenario: under the hypothesis that SL‐GRBs associated with secularly unstable magnetars occur at a rate of  (48–80) Gpc −3  yr −1   or greater, cross‐correlation of data from two Einstein Telescopes (ETs) could detect the GW background associated to this signal with a signal‐to‐noise ratio of 3 or greater after 1 year of observation. Assuming neutron star spindown results purely from triaxial GW emissions, we find that rates of around  (130–350) Gpc −3  yr −1   will be required by ET to detect the resulting GW background. We show that a background signal from secular instabilities could potentially mask a primordial GW background signal in the frequency range where ET is most sensitive. Finally, we show how accounting for cosmic metallicity evolution can increase the predicted signal‐to‐noise ratio for background signals associated with SL‐GRBs.

Gravitational wave background from sub‐luminous GRBs: prospects for second‐ and third‐generation detectors