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We investigate a method to incorporate signal models that allow an additionalfrequency harmonic in searches for gravitational waves from spinning neutronstars. We assume emission is given by the general triaxial non-aligned model ofJones, whose waveform under certain conditions reduces to that of a biaxialprecessing star, or a simple rigidly rotating triaxial aligned star. Thetriaxial non-aligned and biaxial models can produce emission at both the star'srotation frequency ($f$) and $2f$, whilst the latter only emits at $2f$. Wehave studied parameter estimation for signal models using both a set ofphysical source parameters, and a set of waveform parameters that remove adegeneracy. We have assessed the signal detection efficiency, and used Bayesianmodel selection to investigate how well we can distinguish between the threemodels. We found that for signal-to-noise ratios (SNRs) $\gtrsim 6$ there is nosignificant 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 sourceswith 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 isalways favoured, but for a triaxial non-aligned source it can be hard todistinguish between the triaxial non-aligned model and the biaxial model, evenat high SNR. Finally, we apply the method to a selection of known pulsars usingdata from the LIGO fifth science run. We give the first upper limits ongravitational wave amplitude at both $f$ and $2f$ and apply the model selectioncriteria on real data.

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