First results and future prospects for dual-harmonic searches for gravitational waves from spinning neutron stars

We investigate a method to incorporate signal models that allow an additional frequency harmonic in searches for gravitational waves from spinning neutron stars. We assume emission is given by the general triaxial non-aligned model of Jones, whose waveform under certain conditions reduces to that of a biaxial precessing star, or a simple rigidly rotating triaxial aligned star. The triaxial non-aligned and biaxial models can produce emission at both the star's rotation frequency ($f$) and $2f$, whilst the latter only emits at $2f$. We have studied parameter estimation for signal models using both a set of physical source parameters, and a set of waveform parameters that remove a degeneracy. We have assessed the signal detection efficiency, and used Bayesian model selection to investigate how well we can distinguish between the three models. We found that for signal-to-noise ratios (SNRs) $\gtrsim 6$ there is no significant loss in efficiency if performing a search for a signal at $f$ and $2f$ when the source is only producing emission at $2f$. However, for sources with emission at both $f$ and $2f$ signals could be missed by a search only at $2f$. We also find that for a triaxial aligned source, the correct model is always favoured, but for a triaxial non-aligned source it can be hard to distinguish between the triaxial non-aligned model and the biaxial model, even at high SNR. Finally, we apply the method to a selection of known pulsars using data from the LIGO fifth science run. We give the first upper limits on gravitational wave amplitude at both $f$ and $2f$ and apply the model selection criteria on real data.