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The equation of state plays a critical role in the physics of the merger oftwo neutron stars. Recent numerical simulations with microphysical equation ofstate suggest the outcome of such events depends on the mass of the neutronstars. For less massive systems, simulations favor the formation of ahypermassive, quasi-stable neutron star, whose oscillations produce a short,high frequency burst of gravitational radiation. Its dominant frequency contentis tightly correlated with the radius of the neutron star, and its measurementcan be used to constrain the supranuclear equation of state. In contrast, themerger of higher mass systems results in prompt gravitational collapse to ablack hole. We have developed an algorithm which combines waveformreconstruction from a morphology-independent search for gravitational wavetransients with Bayesian model selection, to discriminate between post-mergerscenarios and accurately measure the dominant oscillation frequency. Wedemonstrate the efficacy of the method using a catalogue of simulated binarymerger signals in data from LIGO and Virgo, and we discuss the prospects forthis analysis in advanced ground-based gravitational wave detectors. From thewaveforms considered in this work and assuming an optimally oriented source, wefind that the post-merger neutron star signal may be detectable by thistechnique to $\sim 10\text{--}25$\,Mpc. We also find that we successfullydiscriminate between the post-merger scenarios with $\sim 95\%$ accuracy anddetermine the dominant oscillation frequency of surviving post-merger neutronstars to within $\sim 10$\,Hz, averaged over all detected signals. This leadsto an uncertainty in the estimated radius of a non-rotating 1.6\,M$_{\odot}$reference neutron star of $\sim 100\,$m.

Prospects For High Frequency Burst Searches Following Binary Neutron Star Coalescence With Advanced Gravitational Wave Detectors