  We study the parameter estimation bias induced by intrinsic alignments on a
Euclid-like weak lensing survey. For the intrinsic alignment signal we assume a
composite alignment model for elliptical and spiral galaxies using tidal
shearing and tidal torquing as the alignment generating mechanism,
respectively. The parameter estimation bias is carried out analytically with a
Gaussian bias model and through running Monte-Carlo-Markov-chains on synthetic
data including the alignment signal with a likelihood only including the cosmic
shear signal. In particular, we study the impact of $II$ and $GI$ alignment
terms individually as well as the more realistic situation where both types of
alignment are present, and investigate the scaling of the estimation biases
with varying strength of the alignment signal. Our results show that intrinsic
alignments can cause substantial biases in cosmological parameters even if the
coupling of galaxies to the ambient large is small. Especially
$GI$-contributions strongly bias key cosmological parameters such as the dark
energy equation of state. We also correct the analytic expression for the
Gaussian bias model and find that the biases induced by intrinsic alignments
are not accurately recovered by the simple analytic model.
