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We consider the issue of selecting parameters and their associated ranges forcarrying out searches for continuous gravitational waves from steadily rotatingneutron stars. We consider three different cases (i) the "classic" case of astar spinning about a principal axis; (ii) a biaxial star, not spinning about aprincipal axis; (iii) a triaxial star spinning steady, but not about aprincipal axis (as described in Jones, MNRAS vol 402, 2503 (2010)). The firstof these emits only at one frequency; the other two at a pair of harmonicallyrelated frequencies. We show that in all three cases, when written in terms ofthe original "source parameters", there exist a number of discretedegeneracies, with different parameter values giving rise to the samegravitational wave signal. We show how these can be removed by suitablyrestricting the source parameter ranges. In the case of the model as writtendown by Jones, there is also a continuous degeneracy. We show how to removethis through a suitable rewriting in terms of "waveform parameters", chosen soas to make the specialisations to the other stellar models particularly simple.We briefly consider the (non-trivial) relation between the assignment of priorprobabilities on one set of parameters verses the other. The results of thispaper will be of use when designing strategies for carrying out searches forsuch multi-harmonic gravitational wave signals, and when performing parameterestimation in the event of a detection.

Parameter choices and ranges for continuous gravitational wave searches for steadily spinning neutron stars