  Direct observations of solar wind are mostly limited to the vicinity of the
ecliptic plane. Retrieving the latitudinal structure of solar wind indirectly
based on observations of the backscatter glow of interstellar neutral hydrogen
is complex and requires support from theoretical models. The GLOWS instrument,
to operate on the planned IMAP mission, will scan the helioglow along
circumsolar rings with an angular distance of ~75 degrees. Its objective is to
retrieve the latitudinal structure of the ionization rate of interstellar
hydrogen and with this, the structure of the solar wind. In preparation for
future analysis, we studied the sensitivity of the light curves to temporal and
latitudinal variation of the ionization rate of interstellar hydrogen and the
solar Lyman-alpha illumination. Based on carefully planned numerical
experiments, we analyze the time delay and relaxation time of the system for
variations of the ionization rate and solar illumination in heliolatitude and
with time. We found that variations in the solar illumination are reflected in
the helioglow without delay, but relaxation takes longer than the variation
rise time. By contrast, variations in the ionization rate are anti-correlated
with the helioglow brightness with a delay of several months. We also found
that the helioglow is not sensitive to variations in the ionization rate at the
solar poles, so retrieving the ionization rate and solar wind at the poles
requires an approximation of the ionization rate profiles with appropriate
parametric functions.
