Prospects of GRB observations for CTA from a phenomenological model

Very high energy (VHE, i.e. $\gtrsim 10$ GeV) photons from Gamma-Ray Bursts (GRBs), as high as 90 GeV in rest frame energy, have been detected by the $Fermi$ Large Area Telescope (LAT). This provides hope for a high statistics GRB detection by a ground-based instrument in the VHE domain. We here report on our estimates of the expected GRB detection rate and $\gamma$-ray rate (in case of detection) for the next generation ground-based Imaging Air Cherenkov Telescopes (IACTs): the Cherenkov Telescope Array (CTA). Moreover, we investigated the effect critical design parameters of CTA have on our predictions and we compare the performance of various observing strategies for the array pointing. Our estimations are based on a phenomenological model which uses temporal and spectral information from GRBs detected by $Fermi$-LAT as well as other instruments operating at lower energy. While detection of VHE emission from GRBs has eluded ground-based instruments thus far, our results suggest it should be within reach of CTA with a rate between 0.35 and 1.6 GRBs/year depending on the characteristics of the true GRB population and the performance that CTA will eventually achieve.