Residuals (black) from the subtraction of noiseless, spotted transit light curves from noise-added, spotted light curves for four combinations of stellar radius, planetary radius, and stellar apparent magnitude. Red curves represent the residuals after three-point smoothing. Horizontal blue lines are the 3 × σ_75s noise level, while vertical green lines mark the umbra-penumbra boundaries. Detectable penumbral have residuals above 3 × σ_{75 s}.