Since 2009, several rapid and bright flares have been observed at high energies (>100 MeV) from the direction of the Crab Nebula. Several hypotheses have been put forward to explain this phenomenon, but the origin is still unclear. The detection of counterparts at higher energies with the next generation of Cherenkov telescopes will be determinant to constrain the underlying emission mechanisms. We aim at studying the capability of the Cherenkov Telescope Array (CTA) to explore the physics behind the flares, by performing simulations of the Crab Nebula spectral energy distribution, both in flaring and steady state, for different parameters related to the physical conditions in the nebula. In particular, we explore the data recorded by Fermi during two particular flares that occurred in 2011 and 2013. The expected GeV and TeV gamma-ray emission is derived using different radiation models. The resulting emission is convoluted with the CTA response and tested for detection, obtaining an exclusion region for the space of parameters that rule the different flare emission models. Our simulations show different scenarios that may be favourable for achieving the detection of the flares in Crab with CTA, in different regimes of energy. In particular, we find that observations with low sub-100 GeV energy threshold telescopes could provide the most model-constraining results.
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