Studying the reflection of X-rays off the inner edge of the accretion disk in a neutron star low-mass X-ray binary, allows us to investigate the accretion geometry and to constrain the radius of the neutron star. We report on a NuSTAR observation of 4U 1608-52 obtained during a faint outburst in 2014 when the neutron star, which has a known spin frequency of 620 Hz, was accreting at ~1-2% of the Eddington limit. The 3-79 keV continuum emission was dominated by a Gamma~2 power law, with a ~1-2% contribution from a kTbb~0.3-0.6 keV black body component. The high-quality NuSTAR spectrum reveals the hallmarks of disk reflection; a broad iron line peaking near 7~keV and a Compton back-scattering hump around ~20-30 keV. Modeling the disk reflection spectrum points to a binary inclination of i~30-40 degrees and a small `coronal height of h<8.5 GM/c2. Furthermore, our spectral analysis suggests that the inner disk radius extended to Rin~7-10 GM/c2, close to the innermost stable circular obit. This constrains the neutron star radius to R<21 km and the redshift from the stellar surface to z>0.12, for a mass of M=1.5 Msun and a spin parameter of a=0.29.
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