| Итог: | We consider the bias introduced by a spatially varying multiplicative shear bias (<i>m</i>-bias) on tomographic cosmic shear angular power spectra. To compute the bias in the power spectra, we estimate the mode-coupling matrix associated with an <i>m</i>-bias map using a computationally efficient pseudo-C<sub>ℓ</sub> method. This allows us to consider the effect of the <i>m</i>-bias to high ℓ. We then conduct a Fisher matrix analysis to forecast resulting biases in cosmological parameters. For a <i>Euclid</i>-like survey with a spatially varying <i>m</i>-bias, with zero mean and rms of 0.01, we find that parameter biases reach a maximum of ∼10 per cent of the expected statistical error, if multipoles up to ℓ<sub>max</sub> = 5000 are included. We conclude that the effect of the spatially varying <i>m-</i>bias may be a subdominant but potentially non-negligible contribution to the error budget in forthcoming weak lensing surveys. We also investigate the dependence of parameter biases on the amplitude and angular scale of spatial variations of the <i>m-</i>bias field, and conclude that requirements should be placed on the rms of spatial variations of the <i>m</i>-bias, in addition to any requirement on the mean value. We find that, for a <i>Euclid</i>-like survey, biases generally exceed ∼30 per cent of the statistical error for <i>m</i>-bias rms ∼0.02–0.03 and can exceed the statistical error for rms ∼0.04–0.05. This allows requirements to be set on the permissible amplitude of spatial variations of the <i>m-</i>bias that will arise due to systematics in forthcoming weak lensing measurements.
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