Search for continuous gravitational waves from HESS~J1427-608 with a hidden Markov model

We present a search for continuous gravitational wave signals from an unidentified pulsar potentially powering HESS~J1427-608, a spatially unresolved TeV point source detected by the High Energy Stereoscopic System (HESS). The search uses a semi-coherent algorithm, which combines the maximum likelihood $\mathcal{F}$~statistic with a hidden Markov model to efficiently detect and track quasi-monochromatic signals that wander randomly in frequency. It uses data from the second observing run of the Advanced Laser Interferometer Gravitational-Wave Observatory. Multi-wavelength observations of the HESS source are combined with the proprieties of the population of TeV-bright pulsar wind nebulae to constrain the search parameters. We find no evidence of gravitational wave emission from this target. We set upper limits on the characteristic wave strain $h_0^{95\%}$ (for circularly polarized signals) at $95\%$ confidence level in sample sub-bands and interpolate it to estimate the sensitivity in the full band. We find $h_0^{95\%} = 1.3\times 10^{-25}$ near 185~Hz. The implied constraints on the ellipticity and \textit{r}-mode amplitude reach $\epsilon\leq 10^{-5}$ and $\alpha \leq 10^{-3}$ at 200~Hz, respectively.