In X-ray binaries, rapid variability in X-ray flux of greater than an order of magnitude on time-scales of a day or less appears to be a signature of wind accretion from a supergiant companion. When the variability takes the form of rare, brief, bright outbursts with only faint emission between them, the systems are called Supergiant Fast X-ray Transients (SFXTs). We present data from twice-weekly scans of the Galactic bulge by the Rossi X-ray Timing Explorer (RXTE) that allow us to compare the behaviour of known SFXTs and possible SFXT candidates with the persistently bright supergiant X-ray binary 4U 1700-377. We independently confirm the orbital periods reported by other groups for SFXTs SAX J1818.6-1703 and IGR J17544-2619. The new data do not independently reproduce the orbital period reported for XTE J1739-302, but slightly improve the significance of the original result when the data are combined. The bulge source XTE J1743-363 shows a combination of fast variability and a long-term decline in activity, the latter behaviour not being characteristic of supergiant X-ray binaries. A far-red spectrum of the companion suggests that it is a symbiotic neutron star binary rather than a high-mass binary, and the reddest known of this class: the spectral type is approximately M8 III.
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