High-energy galactic cosmic rays can penetrate to deep levels within Neptune's atmosphere to form a substantial ionosphere layer in the lower stratosphere and upper troposphere of the planet. Because cosmic-ray modulation in the interplanetary medium creates an inverse relationship between cosmic-ray intensity and solar activity, the ionization rate in the lower atmosphere will vary with the 11-year solar cycle in such a way that maximum ionization will occur at sunspot minimum and mininum ionization at sunspot maximum. This variable ionization may, by the process of ion-induced nucleation, regulate the formation and optical properties of an upper tropospheric haze in the atmosphere of Neptune and could thus provide a mechanism for modulating the planet's visual brightness over a solar cycle. We estimate the rates of cosmic-ray ionization at solar maximum and minimum for a range of proposed Neptune dipole magnetic field strengths; discuss the physics of formation of ion clusters and eventual aerosol particles; and, using a simple radiative transfer model, discuss the ways in which this variable aerosol formation can modulate the geometric albedo of Neptune over a solar cycle. If Voyager spacecraft observations reveal that Neptune's dipole magnetic field is about 1 Gauss or less, then our modeling indicates that variations in an aerosol layer due to differences in cosmic ray ionization may help explain some of the observed brightness variation of Neptune over a solar cycle. ¿ American Geophysical Union 1989