We revisit the possibility and detectability of a stochastic gravitational wave ( GW ) background produced by a cosmological population of newborn neutron stars ( NSs ) with r-mode instabilities .
The NS formation rate is derived from both observational and simulated cosmic star formation rates ( CSFRs ) .
We show that the resultant GW background is insensitive to the choice of CSFR models , but depends strongly on the evolving behavior of CSFR at low redshifts .
Nonlinear effects such as differential rotation , suggested to be an unavoidable feature which greatly influences the saturation amplitude of r-mode , are considered to account for GW emission from individual sources .
Our results show that the dimensionless energy density \Omega _ { GW } could have a peak amplitude of \simeq ( 1 - 3.5 ) \times 10 ^ { -8 } in the frequency range ( 200 - 1000 ) Hz , if the smallest amount of differential rotation corresponding to a saturation amplitude of order unity is assumed .
However , such a high mode amplitude is unrealistic as it is known that the maximum value is much smaller and at most 10 ^ { -2 } .
A realistic estimate of \Omega _ { GW } should be at least 4 orders of magnitude lower ( \sim 10 ^ { -12 } ) , which leads to a pessimistic outlook for the detection of r-mode background .
We consider different pairs of terrestrial interferometers ( IFOs ) and compare two approaches to combine multiple IFOs in order to evaluate the detectability of this GW background .
Constraints on the total emitted GW energy associated with this mechanism to produce a detectable stochastic background ( a SNR of 2.56 with 3-year cross correlation ) are \sim 10 ^ { -3 } \hskip { 2.845276 pt } M _ { \odot } c ^ { 2 } for two co-located advanced LIGO detectors , and 2 \times 10 ^ { -5 } \hskip { 2.845276 pt } M _ { \odot } c ^ { 2 } for two Einstein Telescopes .
These constraints may also be applicable to alternative GW emission mechanisms related to oscillations or instabilities in NSs depending on the frequency band where most GWs are emitted .