Impact of Upstream Clumpiness on Supernova Remnant Forward Shock Evolution in Molecular Cloud Environments

Supernova remnants (SNRs) are widely considered to be the primary accelerators of Galactic cosmic rays. In recent years, detailed observations have significantly progressed for young SNRs interacting with molecular clouds, a prime example being RX J1713.7−3946. When molecular clouds are clumpy, their impact can affect not only radiation properties but also shock-wave propagation. Therefore, a quantitative understanding linking observational quantities with the ambient medium structure is highly required. In this study, we perform three-dimensional hydrodynamic simulations to model a molecular cloud with an inhomogeneous density structure driven by supersonic turbulence and subsequent SNR formation. To investigate various presupernova environments, we systematically vary the medium clumpiness by replacing gas below a threshold number density with a low-density hot gas, quantifying the relationship between the forward shock velocity and the volume filling factor of the high-density clumps. As a result, we find that at an elapsed time of 1000 yr—a typical age for a young SNR—the forward shock can evolve consistently with the fast shock velocity measured in RX J1713.7−3946, provided that the clump volume filling factor is approximately 10% or less. Considering that hadronic gamma-ray emission originates exclusively from the clumpy, high-density gas, our findings suggest that the total energy of cosmic-ray protons in RX J1713.7−3946 is higher than previously estimated, amounting to at least a few percent of the typical supernova explosion energy.