Exploring a search for long-duration transient gravitational waves associated with magnetar bursts

Soft gamma repeaters and anomalous x-ray pulsars are thought to be magnetars, neutron stars with strong magnetic fields of order $ \newcommand{\unsim}{\mathord{\sim}} \unsim$ $ 10^{13}$ –$ \newcommand{\gauss}{{\rm gauss}} 10^{15} \gauss$ . These objects emit intermittent bursts of hard x-rays and soft gamma rays. Quasiperiodic oscillations in the x-ray tails of giant flares imply the existence of neutron star oscillation modes which could emit gravitational waves powered by the magnetar's magnetic energy reservoir. We describe a method to search for transient gravitational-wave signals associated with magnetar bursts with durations of 10 s to 1000 s of seconds. The sensitivity of this method is estimated by adding simulated waveforms to data from the sixth science run of Laser Interferometer Gravitational-wave Observatory (LIGO). We find a search sensitivity in terms of the root sum square strain amplitude of $ \newcommand{\hertz}{{\rm Hz}} \newcommand{\hrss}{h_{\rm rss}} \newcommand{\h}{\mathfrak{h}} \hrss = 1.3 \times 10^{-21}~\hertz^{-1/2}$ for a half sine-Gaussian waveform with a central frequency $f_0 = 150$ Hz and a characteristic time $\tau = 400$ s. This corresponds to a gravitational wave energy of $ \newcommand{\erg}{{\rm erg}} \newcommand{\ergs}{\erg} \newcommand{\EGW}{E_{\rm GW}} \EGW = 4.3 \times 10^{46}~{\rm \ergs}$ , the same order of magnitude as the 2004 giant flare which had an estimated electromagnetic energy of $ \newcommand{\unsim}{\mathord{\sim}} \newcommand{\erg}{{\rm erg}} \newcommand{\ergs}{\erg} \newcommand{\EEM}{E_{\rm EM}} \newcommand{\h}{\mathfrak{h}} \EEM = \unsim 1.7 \times 10^{46} (d/ 8.7~{\rm kpc}){\hspace{0pt}}^2~{\rm \ergs}$ , where d is the distance to SGR 1806-20. We present an extrapolation of these results to Advanced LIGO, estimating a sensitivity to a gravitational wave energy of $ \newcommand{\erg}{{\rm erg}} \newcommand{\ergs}{\erg} \newcommand{\EGW}{E_{\rm GW}} \newcommand{\bestUL}{4.3 \times 10^{46}} \newcommand{\bestULaLIGO}{9.0 \times 10^{44}} \newcommand{\bestULaLIGOclose}{3.2 \times 10^{43}} \EGW = \bestULaLIGOclose~{\rm \ergs}$ for a magnetar at a distance of $1.6$ kpc. These results suggest this search method can probe significantly below the energy budgets for magnetar burst emission mechanisms such as crust cracking and hydrodynamic deformation.