  Rapidly spinning neutron stars with non-axisymmetric mass distributions are
expected to generate quasi-monochromatic continuous gravitational waves. While
many searches for unknown, isolated spinning neutron stars have been carried
out, there have been no previous searches for unknown sources in binary
systems. Since current search methods for unknown, isolated neutron stars are
already computationally limited, expanding the parameter space searched to
include binary systems is a formidable challenge. We present a new hierarchical
binary search method called TwoSpect, which exploits the periodic orbital
modulations of the continuous waves by searching for patterns in doubly
Fourier-transformed data. We will describe the TwoSpect search pipeline,
including its mitigation of detector noise variations and corrections for
Doppler frequency modulation caused by changing detector velocity. Tests on
Gaussian noise and on a set of simulated signals will be presented.
