  We present a computational study of the phonon linewidths in twisted bilayer
graphene arising from electron-phonon interactions and anharmonic effects. The
electronic structure is calculated using distance-dependent transfer integrals
based on the atomistic Slater-Koster tight-binding formalism, including
electron-electron interactions treated at the Hartree level, and the phonons
are calculated using classical force fields. These ingredients are used to
calculate the phonon linewidths arising from electron-phonon interactions.
Furthermore, anharmonic effects on the linewidths are computed using the
mode-projected velocity autocorrelation function obtained from classical
molecular dynamics. We predict a moir\'e potential induced splitting of this
mode, which arises due to contributions from high symmetry stacking regions.
Our findings show that both electron-phonon and anharmonic effects have a
significant impact on the linewidth of the Raman active G mode near the magic
angle.
