Magnification Bias in Flux-Limited Shear Samples: The Slope That Decides the Sign

Lensing magnification changes which galaxies enter a flux-limited source sample, and because the change is caused by the same convergence field being measured, it feeds back into the shear statistic. The effect is governed by the logarithmic slope of the source number counts, s, through the factor five s minus two. This paper tabulates that factor and the resulting cross-term fraction at multipole 300 for slopes from 0.2 to 1.0: the fraction is -0.060 at s equal to 0.2, 0.000 at the null slope s equal to 0.40, and 0.120 at s equal to 0.8. The existence of a null slope at which magnification drops out of the selection is a design resource: samples can in principle be constructed near it. Away from the null, the correction is at the percent level and changes sign across it, so an assumed slope of the wrong sign converts a correction into an error of twice the size. All quantities are computed from stated assumptions, not measured.