  Context: Accretion-powered X-ray pulsars show highly energy-dependent and
complex pulse-profile morphologies. Significant deviations from the average
pulse profile can appear, in particular close to the cyclotron line energies.
These deviations can be described as energy-dependent phase lags, that is, as
energy-dependent shifts of main features in the pulse profile. Aims: Using a
numerical study we explore the effect of cyclotron resonant scattering on
observable, energy-resolved pulse profiles. Methods: We generated the
observable emission as a function of spin phase, using Monte Carlo simulations
for cyclotron resonant scattering and a numerical ray-tracing routine
accounting for general relativistic light-bending effects on the intrinsic
emission from the accretion columns. Results: We find strong changes in the
pulse profile coincident with the cyclotron line energies. Features in the
pulse profile vary strongly with respect to the average pulse profile with the
observing geometry and shift and smear out in energy additionally when assuming
a non-static plasma. Conclusions: We demonstrate how phase lags at the
cyclotron energies arise as a consequence of the effects of angular
redistribution of X-rays by cyclotron resonance scattering in a strong magnetic
field combined with relativistic effects. We also show that phase lags are
strongly dependent on the accretion geometry. These intrinsic effects will in
principle allow us to constrain a system's accretion geometry.
