Cumulative probability distributions for our fiducial synthetic R = 13 km data, but using in the analysis a model for the synthetic background that differs from the correct background by a factor that is the same at all energies: 0.97 (left blue dotted line), 0.99 (left black dashed line), 1.01 (right black dashed line), or 1.03 (right blue dotted line). The solid red line shows the previous fit, which uses the best estimate of the background derived from 0.1 Ms of synthesized off-source data. Deviations of more than ∼3% from the true background produce poor fits that would be detectable in the analysis; for example, a background that is 10% too small (large) gives a ﹩{\chi }^{2}﹩ that is 90 (143) larger than the ﹩{\chi }^{2}﹩ for the true background. This figure shows that systematic errors introduced by incorrect background estimates are modest (a few tenths of a kilometer) if the fit is good. Note that for a given fractional deviation from the true background level, an incorrectly high background is easier to detect than an incorrectly low background, because for a given frms in the data added background strongly worsens the fit whereas a deficit in the background can be accommodated by making the star smaller. This bias, if it exists, is therefore more likely to lead to an underestimate than to an overestimate of the radius.