  In this work, we prove rigorous error estimates for a hybrid method
introduced in [15] for solving the time-dependent radiation transport equation
(RTE). The method relies on a splitting of the kinetic distribution function
for the radiation into uncollided and collided components. A high-resolution
method (in angle) is used to approximate the uncollided components and a
low-resolution method is used to approximate the the collided component. After
each time step, the kinetic distribution is reinitialized to be entirely
uncollided. For this analysis, we consider a mono-energetic problem on a
periodic domains, with constant material cross-sections of arbitrary size. To
focus the analysis, we assume the uncollided equation is solved exactly and the
collided part is approximated in angle via a spherical harmonic expansion
($\text{P}_N$ method). Using a non-standard set of semi-norms, we obtain
estimates of the form $C(\varepsilon,\sigma,\Delta t)N^{-s}$ where $s\geq 1$
denotes the regularity of the solution in angle, $\varepsilon$ and $\sigma$ are
scattering parameters, $\Delta t$ is the time-step before reinitialization, and
$C$ is a complicated function of $\varepsilon$, $\sigma$, and $\Delta t$. These
estimates involve analysis of the multiscale RTE that includes, but necessarily
goes beyond, usual spectral analysis. We also compute error estimates for the
monolithic $\text{P}_N$ method with the same resolution as the collided part in
the hybrid. Our results highlight the benefits of the hybrid approach over the
monolithic discretization in both highly scattering and streaming regimes.
