As of 2014 August, the Nuclear Spectroscopic Telescope Array (NuSTAR) had observed ~30 X-ray binaries either as part of the planned program, as targets of opportunity, or for instrument calibration. The main science goals for the observations include probing the inner part of the accretion disk and constraining black hole spins via reflection components, providing the first observations of hard X-ray emission from quiescent Low Mass X-ray Binaries (LMXBs), measuring cyclotron lines from accreting pulsars, and studying type I X-ray bursts from neutron stars. Here, we describe the science objectives in more depth and give an overview of the NuSTAR observations that have been carried out to achieve the objectives. These include observation of four IGR High Mass X-ray Binaries (HMXBs) discovered by INTEGRAL. We also summarize the results that have been obtained and their implications. Among the IGR HMXBs, we focus on the discovery of a cyclotron line in the spectrum of IGR J17544-2619.
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