Molecular environment, reverberation, and radiation from the pulsar wind nebula in CTA 1

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 pulsar wind nebula (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 supernova remnant 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 analyse different situations that might represent the current stage of the CTA 1 PWN, and discuss caveats and requirements of each one.