Could the stochastic gravitational wave background from newborn magnetars be detected by the advanced LIGO and Einstein Telescope?

Newborn magnetars are important gravitational wave sources due to their ultrastrong magnetic fields and fast spins, and the entire population in the Universe may significantly contribute to the stochastic gravitational wave background (SGWB). In this work, we investigate the SGWB from newborn magnetars and assess its detectability by the advanced LIGO (aLIGO) and Einstein Telescope (ET) based on three typical formation mechanisms of magnetars, i.e., the $\ensuremath{\alpha}\ensuremath{-}\mathrm{\ensuremath{\Omega}}$ dynamo, convective dynamo, and magnetic flux conservation. For the two dynamo scenarios, when calculating the SGWB, we creatively incorporate the anticorrelations between the magnetic fields and initial spin periods ${P}_{\mathrm{i}}$ with the initial dipole-field distribution of newborn magnetars. For the flux-conservation scenario, a bimodal lognormal form is adopted to describe the distribution of initial dipole fields, and all magnetars are assumed to have the same ${P}_{\mathrm{i}}$. Our results show that the SGWB from newborn magnetars may be undetectable by the aLIGO and ET if the magnetars are formed due to these mechanisms since the signal-to-noise ratio of the SGWB with respect to the ET for an observation time of one year is only 0.37 for the $\ensuremath{\alpha}\ensuremath{-}\mathrm{\ensuremath{\Omega}}$ dynamo, $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for the convective dynamo, and at most 0.21 for the flux conservation.