  We performed a detailed pulse phase resolved spectroscopy of the accreting
binary X-ray pulsar Her X-1 in the energy range 3.5-75 keV and have established
pulse phase profiles for all spectral parameters. For the centroid of the
cyclotron line, the photon index and the flux of the 6.4 keV iron line, we have
studied the variation as a function of 35 d phase. We analyzed RXTE
observations of the Main-On of November 2002. Four different time intervals of
about 1 d duration were selected to provide a good coverage of a complete
Main-On. The intervals are centered at 35 d phase 0.03, 0.10, 0.15, and 0.20,
respectively. All spectral parameters show a strong modulation with pulse
phase. While the centroid energy of the cyclotron line follows roughly the
shape of the pulse profile, both the photon index and the iron line intensity
exhibit distinct minima around the peak of the X-ray pulse. With respect to
variations of the observed profiles with 35 d phase, we find that there is a
clear evolution of the shape of the pulse profiles (flux versus pulse phase), a
moderate increase of the maximum cyclotron line energy (found around pulse
phase 0.7), but no significant evolution of the shape of the pulse phase
profiles of the cyclotron line energy, the spectral power law index or the iron
line intensity. The variation of spectral parameters as a function of the pulse
phase provides important information about the system: 1. the disappearance of
the Fe line flux near the highest continuum flux may be an indication of a
hollow cone geometry of the accretion structure; ii. the apparent
non-dependence of the cyclotron line energy profiles on 35 d phase provides a
new possibility to test the model of free precession of the neutron star,
proposed to be responsible for the systematic variations in the pulse profiles.
