Supernova resonance-scattering profiles in the presence of external illumination

We discuss a simple model for the formation of a supernova spectral line by resonance scattering in the presence of external illumination of the line-forming region by light from circumstellar interaction (toplighting). The simple model provides a clear understanding of the most conspicuous toplighting effect: a rescaling or, as we prefer, a "muting" of the line profile relative to the continuum. This effect would be present in more realistic models, but would be harder to isolate. An analytic expression for a muting factor for a P Cygni line is derived that depends on the ratio E of the toplighting specific intensity to the specific intensity from the supernova photosphere. If E < 1, the Line profile is reduced in scale or " muted." If E = 1, the line profile vanishes altogether. If E > 1, the line profile flips vertically: then having an absorption component near the observer-frame Line-center wavelength and a blueshifted emission component.