  Glass formation is encountered in diverse materials. Experiments have
revealed that dynamic relaxation spectra of supercooled liquids generically
become asymmetric near the glass transition temperature, $T_g$, where an
extended power law emerges at high frequencies. The microscopic origin of this
"wing" remains unknown, and was so far inaccessible to simulations. Here, we
develop a novel computational approach and study the equilibrium dynamics of
model supercooled liquids near $T_g$. We demonstrate the emergence of a power
law wing in numerical spectra, which originates from relaxation at rare,
localised regions over broadly-distributed timescales. We rationalise the
asymmetric shape of relaxation spectra by constructing an empirical model
associating heterogeneous activated dynamics with dynamic facilitation, which
are the two minimal physical ingredients revealed by our simulations. Our work
offers a glimpse of the molecular motion responsible for glass formation at
relevant experimental conditions.
