  Photoacoustic tomography (PAT) is a hybrid imaging modality that intends to
construct high-resolution images of optical properties of heterogeneous media
from measured acoustic data generated by the photoacoustic effect. To date,
most of the model-based quantitative image reconstructions in PAT are performed
with either the radiative transport equation or its classical diffusion
approximation as the model of light propagation. In this work, we study
quantitative image reconstructions in PAT using the simplified $P_2$ equations
as the light propagation model. We provide numerical evidences on the
feasibility of this approach and derive some stability results as theoretical
justifications.
