  We estimate the molecular mass around CTA 1 using data from Planck and the
Harvard CO survey. We observe that the molecular mass in the vicinity of the
complex is not enough to explain the TeV emission observed by VERITAS, even
under favorable assumptions for the cosmic-ray acceleration properties of the
supernova remnant. This supports the idea that the TeV emission comes from the
PWN. Here, we model the spectrum of the PWN at possible different stages of its
evolution, including both the dynamics of the PWN and the SNR and their
interaction via the reverse shock. We have included in the model the energy
lost via radiation by particles and the particles escape when computing the
pressure produced by the gas. This leads to an evolving energy partition, since
for the same instantaneous sharing of the injection of energy provided by the
rotational power, the field and the particles are affected differently by
radiation and losses. We present the model, and study in detail how the
spectrum of a canonical isolated PWN is affected during compression and
re-expansion and how this may impact on the CTA 1 case. By exploring the
phase-space of parameters that lead to radii in agreement with those observed,
we then analyze different situations that might represent the current stage of
the CTA 1 PWN, and discuss caveats and requirements of each one.
