  Linear polarization in X- and gamma-rays is an important diagnostic of many
astrophysical sources, foremost giving information about their geometry,
magnetic fields, and radiation mechanisms. However, very few X-ray polarization
measurements have been made, and then only mono-energetic detections, whilst
several objects are assumed to have energy dependent polarization signatures.
In this paper we investigate whether detection of energy dependent polarization
from cosmic sources is possible using the Compton technique, in particular with
the proposed PoGOLite balloon-experiment, in the 25-100 keV range. We use
Geant4 simulations of a PoGOLite model and input photon spectra based on Cygnus
X-1 and accreting magnetic pulsars (100 mCrab). Effective observing times of 6
and 35 hours were simulated, corresponding to a standard and a long duration
flight respectively. Both smooth and sharp energy variations of the
polarization are investigated and compared to constant polarization signals
using chi-square statistics. We can reject constant polarization, with energy,
for the Cygnus X-1 spectrum (in the hard state), if the reflected component is
assumed to be completely polarized, whereas the distinction cannot be made for
weaker polarization. For the accreting pulsar, constant polarization can be
rejected in the case of polarization in a narrow energy band with at least 50%
polarization, and similarly for a negative step distribution from 30% to 0%
polarization.
