Gravitational wave background from sub-luminous GRBs: prospects for
  second and third generation detectors
  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 (Corsi & Meszaros 2009a). 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 sen- sitive. Finally,
we show how accounting for cosmic metallicity evolution can increase the
predicted signal-to-noise ratio for background signals associated with SL-GRBs.
