Image Details
Caption: Figure 7.
Detection rates for the χ2-based and SED-matched detection methods, as a function of the color of the star. For each color, we set the true fluxes in the g and r bands so that their quadrature-summed signal-to-noise ratio is constant (with the constant chosen so that the χ2 method produced roughly 50% detection rate), and then added independent Gaussian noise with equal variance in the two bands. The threshold for each method was set so that their false-positive rates were equal. Since the χ2 method does not care about the color of the star, its performance is constant. The ﹩{\chi }_{+}^{2}﹩ method has a slight sensitivity to the color of the star: at the color extremes where the flux is concentrated in one band, noise can scatter the star to have negative flux, which makes the ﹩{\chi }_{+}^{2}﹩ method less likely to detect it. But the largest effect is due to the ﹩{\chi }_{+}^{2}﹩ method having a lower detection threshold because ignoring negative fluxes results in a lower false-positive rate, giving it an overall greater detection rate than the χ2 method. As expected, the SED-matched methods show a “tuning” effect where they are most efficient at detecting stars of the expected colors, which in this case are, as before, “flat” (color zero), “red” (color one), and “r-band-only”; for the Bayesian methods these are weighted 49%, 49%, and 2%, respectively. The vertical dashed lines mark these “tuned” colors. As a result, very blue stars are unexpected, and their detection efficiency drops sharply, while very red stars are expected (even if at a low rate) and show a fair detection rate. Interestingly, the Bayesian method peaks at color 0.5, because these stars are acceptable to both the “flat” and “red” SEDs.
© 2026. The Author(s). Published by the American Astronomical Society.