  Line profiles from spatially unresolved stellar observations consist of a
superposition of local line profiles that result from observing the stellar
atmosphere under specific viewing angles. Line profile variability caused by
stellar magnetic activity or planetary transit selectively varies the weight
and/or shape of profiles at individual surface positions. The effect is usually
modeled with radiative transfer calculations because observations of spatially
resolved stellar surfaces are not available. For the Sun, we recently obtained
a broadband spectroscopic atlas of the solar center-to-limb variation (CLV). We
use the atlas to study systematic differences between largely used radiative
transfer calculations and solar observations. We concentrate on four strong
lines useful for exoplanet transmission analysis, and we investigate the impact
of CLV on transmission and Rossiter-McLaughlin (RM) curves. Solar models used
to calculate synthetic spectra tend to underestimate line core depths but
overestimate the effect of CLV. Our study shows that CLV can lead to
significant systematic offsets in transmission curves and particularly in RM
curves; transmission curves centered on individual lines are overestimated by
up to a factor of two by the models, and simulations of RM curves yield
amplitudes that are off by up to 5--10\,m\,s$^{-1}$ depending on the line. For
the interpretation of transit observations, it is crucial for model spectra
that accurately reproduce the solar CLV to become available which, for now, is
the only calibration point available.
