Hidden Markov model tracking of continuous gravitational waves from young supernova remnants

Searches for persistent gravitational radiation from nonpulsating neutron stars in young supernova remnants (SNRs) are computationally challenging because of rapid stellar braking. We describe a practical, efficient, semi-coherent search based on a hidden Markov model (HMM) tracking scheme, solved by the Viterbi algorithm, combined with a maximum likelihood matched filter, the $\mathcal{F}$-statistic. The scheme is well suited to analyzing data from advanced detectors like the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). It can track rapid phase evolution from secular stellar braking and stochastic timing noise torques simultaneously without searching second- and higher-order derivatives of the signal frequency, providing an economical alternative to stack-slide-based semi-coherent algorithms. One implementation tracks the signal frequency alone. A second implementation tracks the signal frequency and its first time derivative. It improves the sensitivity by a factor of a few upon the first implementation, but the cost increases by two to three orders of magnitude.