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

Abstract

We consider the issue of selecting parameters and their associated ranges for carrying out searches for continuous gravitational waves from steadily rotating neutron stars. We consider three different cases (i) the 'classic' case of a star spinning about a principal axis; (ii) a biaxial star, not spinning about a principal axis; (iii) a triaxial star spinning steady, but not about a principal axis (as described in Jones, MNRAS 402, 2503 (2010)). The first of these emits only at one frequency; the other two at a pair of harmonically related frequencies. We show that in all three cases, when written in terms of the original 'source parameters', there exist a number of discrete degeneracies, with different parameter values giving rise to the same gravitational wave signal. We show how these can be removed by suitably restricting the source parameter ranges. In the case of the model as written down by Jones, there is also a continuous degeneracy. We show how to remove this through a suitable rewriting in terms of 'waveform parameters', chosen so as to make the specialisations to the other stellar models particularly simple. We briefly consider the (non-trivial) relation between the assignment of prior probabilities on one set of parameters verses the other. The results of this paper will be of use when designing strategies for carrying out searches for such multi-harmonic gravitational wave signals, and when performing parameter estimation in the event of a detection.

First Search for Gravitational Waves from Known Pulsars with Advanced LIGO

“…In cases where the search requires the recalculation of f D ( ) t when evaluating the likelihood, this can be computationally 166 The analysis code actually works with a signal parameterized in terms of the "waveform" model defined in Jones (2015) and Pitkin et al (2015), where = -h C 2 0 2 2 and f = F C 0 22 .…”

“…For the parameters f 0 , i cos , and ψ, we generally have no prior knowledge of their values, and so use flat priors within their allowed ranges: These ranges do not necessarily span the full physically allowable range of source values, but are a degenerate range that will contain all possible observable signal waveforms (Jones 2015;Pitkin et al 2015). In some cases, there is information about the inclination and/or polarization angle of the source (see Appendix B).…”

“…When these restricted priors were used in the previous analyses of Aasi et al (2014), there has been an implicit (and at the time unrealized) assumption about the rotation of the star. As noted in Jones (2015), constraining ι and ψ to particular values implicitly forces a rotation direction on the signal, while the PWN observations (or indeed the electromagnetic timing observations) give us no knowledge of the actual rotation direction. To incorporate this unknown rotation direction in the search, while maintaining the convenient minimal range in ψ of p 2 radians, there must be a bimodal distribution on ι with the additional mode at p i -radians.…”

Tracking continuous gravitational waves from a neutron star at once and twice the spin frequency with a hidden Markov model

“…The components of the gravitational-wave signal are in a more complicated form [43] h 2+ = 1 2 (1 + cos 2 ι){[h 0 (sin 2 ψ − cos 2 ψ cos 2 θ) −h 0 sin 2 θ] cos 2Φ + h 0 sin 2ψ cos θ sin 2Φ}, (20)…”

“…V, because Φ 0 and θ are degenerate. We have 0 ≤ θ ≤ π/2 and 0 ≤ Φ 0 ≤ 2π, or 0 ≤ θ ≤ π and 0 ≤ Φ 0 ≤ π[43].…”