Piecewise frequency model for searches for long-transient gravitational waves from young neutron stars

Previous searches for a gravitational-wave signal from a possible neutron star remnant of the binary neutron star merger event GW170817 have focused on short ($<500$ s) and long duration (2.5 hr -- 8 day) signals. To date, no such post-merger signal has been detected. We introduce a new piecewise model which has the flexibility to accurately follow gravitational-wave signals which are rapidly evolving in frequency, such as those which may be emitted from young neutron stars born from binary neutron star mergers or supernovae. We investigate the sensitivity and computational cost of this piecewise model when used in a fully coherent 1800-second $\mathcal{F}$-statistic search on simulated data containing possible signals from the GW170817 remnant. The sensitivity of the search using the piecewise model is determined using simulated data, with noise consistent with the LIGO second observing run. Across a 100--2000 Hz frequency band, the model achieves a peak sensitivity of $h_{\text{rss}}^{50\%} = 4.4 \times 10^{-23} \text{Hz}^{-1/2}$ at 200 Hz, competitive with other methods. The computational cost of conducting the search, over a bank of $1.1 \times 10^{12}$ templates, is estimated at 10 days running on 100 CPU's.