The impact of galaxy colour gradients on cosmic shear measurement
  Cosmic shear has been identified as the method with the most potential to
constrain dark energy. To capitalise on this potential it is necessary to
measure galaxy shapes with great accuracy, which in turn requires a detailed
model for the image blurring, the Point Spread Function (PSF). In general the
PSF varies with wavelength and therefore the PSF integrated over an observing
filter depends on the spectrum of the object. For a typical galaxy the spectrum
varies across the galaxy image, thus the PSF depends on the position within the
image. We estimate the bias on the shear due to such colour gradients by
modelling galaxies using two co-centered, co-elliptical Sersic profiles, each
with a different spectrum. We estimate the effect of ignoring colour gradients
and find the shear bias from a single galaxy can be very large depending on the
properties of the galaxy. We find that halving the filter width reduces the
shear bias by a factor of about 5. We show that, to first order, tomographic
cosmic shear two point statistics depend on the mean shear bias over the galaxy
population at a given redshift. For a single broad filter, and averaging over a
small galaxy catalogue, we find a mean shear bias which is subdominant to the
predicted statistical errors for future cosmic shear surveys. However, the true
mean shear bias may exceed the statistical errors, depending on how accurately
the catalogue represents the observed distribution of galaxies in the cosmic
shear survey. We then investigate the bias on the shear for two-filter imaging
and find that the bias is reduced by at least an order of magnitude. Lastly, we
find that it is possible to calibrate galaxies for which colour gradients were
ignored using two-filter imaging of a fair sample of noisy galaxies, if the
galaxy model is known. For a S/N of 25 the number of galaxies required in each
tomographic redshift bin is of order 1e4.
