Practical Methods for Continuous Gravitational Wave Detection using
  Pulsar Timing Data
  Gravitational Waves (GWs) are tiny ripples in the fabric of space-time
predicted by Einstein's General Relativity. Pulsar timing arrays (PTAs) are
well poised to detect low frequency ($10^{-9}$ -- $10^{-7}$ Hz) GWs in the near
future. There has been a significant amount of research into the detection of a
stochastic background of GWs from supermassive black hole binaries (SMBHBs).
Recent work has shown that single continuous sources standing out above the
background may be detectable by PTAs operating at a sensitivity sufficient to
detect the stochastic background. The most likely sources of continuous GWs in
the pulsar timing frequency band are extremely massive and/or nearby SMBHBs. In
this paper we present detection strategies including various forms of matched
filtering and power spectral summing. We determine the efficacy and
computational cost of such strategies. It is shown that it is computationally
infeasible to use an optimal matched filter including the poorly constrained
pulsar distances with a grid based method. We show that an Earth-term-matched
filter constructed using only the correlated signal terms is both
computationally viable and highly sensitive to GW signals. This technique is
only a factor of two less sensitive than the computationally unrealizable
optimal matched filter and a factor of two more sensitive than a power spectral
summing technique. We further show that a pairwise matched filter, taking the
pulsar distances into account is comparable to the optimal matched filter for
the single template case and comparable to the Earth-term-matched filter for
many search templates. Finally, using simulated data optimal quality, we place
a theoretical minimum detectable strain amplitude of $h>2\times 10^{-15}$ from
continuous GWs at frequencies on the order $\sim1/T_{\rm obs}$.
