  We propose a reliable and efficient a posteriori error estimator for a
hybridizable discontinuous Galerkin (HDG) discretization of the Helmholtz
equation, with a first-order absorbing boundary condition, based on residual
minimization. Such a residual minimization is performed on a local and
superconvergent postprocessing scheme of the approximation of the scalar
solution provided by the HDG scheme. As a result, in addition to the super
convergent approximation for the scalar solution, a residual representative in
the Riesz sense, which is further employed to derive the a posteriori
estimators. We illustrate our theoretical findings and the behavior of the a
posteriori error estimator through two ad-hoc numerical experiments.
