  In the past five years, approximately one third of the 65 pulsars discovered
by radio observations of Fermi unassociated sources are black widow pulsars
(BWPs). BWPs are binary millisecond pulsars with companion masses ranging from
0.01-0.1 solar masses which often exhibit radio eclipses. The bloated
companions in BWP systems exert small torques on the system causing the orbit
to change on small but measurable time scales. Because adding parameters to a
timing model reduces sensitivity to a gravitational wave (GW) signal, the need
to fit many orbital frequency derivatives to the timing data is potentially
problematic for using BWPs to detect GWs with pulsar timing arrays. Using
simulated data with up to four orbital frequency derivatives, we show that
fitting for orbital frequency derivatives absorbs less than 5% of the low
frequency spectrum expected from a stochastic gravitational wave background
signal. Furthermore, this result does not change with orbital period.
Therefore, we suggest that if timing systematics can be accounted for by
modeling orbital frequency derivatives and is not caused by spin frequency
noise, pulsar timing array experiments should include BWPs in their arrays.
