  Since the k correction depends on the spectral energy distribution (SED) of a
galaxy, any high-z galaxy with a spatially non-homogeneous SED will experience
a spatially varying relative dimming or brightening in addition to the pure
distance effect. The morphology of galaxies will therefore change with z. For
instance, an early spiral galaxy observed in the V band would show a prominent
bulge at z=0, whereas, if at z=1, the V filter probes the rest-frame near-UV
where the bulge is faint and the disk relatively brighter, thus the galaxy may
appear as bulgeless. For galaxies with strong nebular emission, an additional
effect is that the shifting of strong nebular features in or out of filters
will result in a non-monotonous color evolution with z. Hence, unlike the
effects of distance, cosmological surface brightness dimming, and gravitational
lensing, which are all achromatic, the fact that most galaxies have a spatially
varying SED leads to a chromatic surface brightness modulation (CMOD) with z.
While the CMOD effects are in principle easy to grasp, they affect the
characterization of galaxies in a complex fashion. Properties such as the
bulge-to-disk ratio, Sersic exponent, effective radius, radial color gradients,
and stellar mass determinations from SED fitting will depend on z, the filters
employed, and the rest-frame 2D SED patterns in a galaxy, and will bias results
inferred on galaxy evolution across cosmic time (e.g., the evolution of the
mass-size, bulge-SMBH, and Tully-Fisher relation), if these effects are not
properly taken into account. In this article we quantify the CMOD effects for
idealized galaxies built from spectral synthesis models and from galaxies with
observed integral field spectroscopy, and we show that they are significant and
should be taken into account in studies of resolved galaxy properties and their
evolution with z. (abridged)
