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

## TL;DR

This study discovers that the optical depth at the iron K-edge in accretion-powered X-ray pulsars varies with pulse phase, revealing insights into the geometry and ionization state of accreting matter near neutron stars.

## Contribution

First detection of pulse phase modulating optical depths at the iron K-edge in X-ray pulsars, linking absorption features to accretion geometry and matter ionization.

## Key findings

- Significant optical depth modulation observed in Vela X-1 and GX 1+4.
- Optical depth peaks when X-ray continuum dims.
- No significant variation in iron ionization state with pulse phase.

## Abstract

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