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 .
Firstly , 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 ) \mathrm { Gpc } ^ { -3 } \mathrm { 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 ) \mathrm { Gpc } ^ { -3 } \mathrm { 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 .