How much spin wandering can continuous gravitational wave search algorithms handle?

The canonical signal model in continuous gravitational wave searches is deterministic, and stable over the long integration times needed to separate a putative signal from the noise, e.g., with a matched filter. However, there exist plausible physical mechanisms that give rise to ``spin-wandering,'' i.e., small stochastic variations in the frequency of the gravitational wave. Stochastic variations degrade the sensitivity of matched filters which assume a deterministic frequency evolution. Suites of synthetic spin-wandering injections are performed to infer the loss in sensitivity depth ${\mathcal{D}}_{\mathrm{SW}}$ when compared to the depth for a canonical signal ${\mathcal{D}}_{\mathrm{det}}$. For a fiducial spin-wandering signal that wanders by $\ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }\text{ }\mathrm{Hz}$ per day, the depth ratio is ${\mathcal{D}}_{\mathrm{det}}/{\mathcal{D}}_{\mathrm{SW}}=4.3{9}_{\ensuremath{-}0.27}^{+0.23}$, ${1.51}_{\ensuremath{-}0.03}^{+0.02}$, ${1.75}_{\ensuremath{-}0.04}^{+0.04}$, and ${1.07}_{\ensuremath{-}0.02}^{+0.01}$ for the coherent $\mathcal{F}$-statistic, semicoherent $\mathcal{F}$-statistic, CrossCorr, and HMM-Viterbi algorithms respectively. Increasing the coherence time of the semicoherent algorithms does not necessarily increase their sensitivity to spin-wandering signals.