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We report the first discovery of pulse phase modulating optical depths at theiron K-edge in accretion-powered X-ray pulsars, from Suzaku observations. Asignificant modulating optical depth of the iron K-edge is detected for VelaX-1 and GX 1+4. Similar trends are seen in GX 301-2 and OAO 1657-415, thoughwith poor statistical significance. The observed iron K-edge exhibits a maximumoptical depth, when the X-ray continuum dims, and there is no significant pulsephase variation in the ionization state of iron. The revealed changes in theoptical depth with pulse phase can be explained as being due to the accretingmatter captured by the magnetic field lines of the pulsar, which co-rotateswith the neutron star spin and is responsible for photoelectric absorption.Based on the above interpretation, we propose that the accreting matter withinthe Alfv\'en radius contains iron with an ionization state of Fe$_{\rmV\hspace{-0.1em}I-X\hspace{-0.1em}I}$ with a particle density of $10^{17}$cm$^{-3}$ and has a shape flattened along the azimuthal direction, such as anaccretion curtain.

The Modulating Optical Depth of Photoelectric Absorption Edge with Pulse Phase in Accretion-Powered X-ray Pulsars