  Accreting supermassive binary black holes (SMBBHs) are potential
multi-messenger sources because they emit both gravitational wave and
electromagnetic (EM) radiation. Past work has shown that their EM output may be
periodically modulated by an asymmetric density distribution in the
circumbinary disk, often called an "overdensity" or "lump;" this modulation
could possibly be used to identify a source as a binary. We explore the
sensitivity of the overdensity to SMBBH mass ratio and magnetic flux through
the accretion disk. We find that the relative amplitude of the overdensity and
its associated EM periodic signal both degrade with diminishing mass ratio,
vanishing altogether somewhere between 1:2 and 1:5. Greater magnetization also
weakens the lump and any modulation of the light output. We develop a model to
describe how lump formation results from internal stress degrading faster in
the lump region than it can be rejuvenated through accretion inflow, and
predicts a threshold value in specific internal stress below which lump
formation should occur and which all our lump-forming simulations satisfy.
Thus, detection of such a modulation would provide a constraint on both
mass-ratio and magnetic flux piercing the accretion flow.
