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In a recent computer study, we have shown that the combination of spatiallyheterogeneous dynamics and kinetic facilitation provides a microscopicexplanation for the emergence of excess wings in deeply supercooled liquids.Motivated by these findings, we construct a minimal empirical model to describethis physics and introduce dynamic facilitation in the trap model, which wasinitially developed to capture the thermally-activated dynamics of glassysystems. We fully characterise the relaxation dynamics of this facilitated trapmodel varying the functional form of energy distributions and the strength ofdynamic facilitation, combining numerical results and analytic arguments.Dynamic facilitation generically accelerates the relaxation of the deepesttraps, thus making relaxation spectra strongly asymmetric, with an apparent"excess" signal at high frequencies. For well-chosen values of the parameters,the obtained spectra mimic experimental results for organic liquids displayingan excess wing. Overall, our results identify the minimal physical ingredientsneeded to describe excess processes in relaxation spectra of supercooledliquids.

Excess wings and asymmetric relaxation spectra in a facilitated trap model