In this paper we present the results of searches for periodic neutrino emission from a catalog of binary systems. Such modulation, observed in the photon flux, would be caused by the geometry of these systems. In the analysis, the period is fixed by these photon observations, while the phase and duration of the neutrino emission are treated as free parameters to be fit with the data. If the emission occurs during ~20% or less of the total period, this analysis achieves better sensitivity than a time-integrated analysis. We use the IceCube data taken from May 31, 2007 to April 5, 2008 with its 22-string configuration, and from April 5, 2008 to May 20, 2009 with its 40-string configuration. No evidence for neutrino emission is found, with the strongest excess occurring for Cygnus X-3 at 2.1 sigma significance after accounting for trials. Neutrino flux upper limits for both periodic and time-integrated emission are provided.
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