Magnetic fields of exoplanets are important in shielding the planets from cosmic rays and interplanetary plasma. Due to the interaction with the electrons from their host stars, the exoplanetary magnetospheres are predicted to have both cyclotron and synchrotron radio emissions, of which neither has been definitely identified in observations yet. As the coherent cyclotron emission has been extensively studied in literatures, here we focus on the planetary synchrotron radiation with bursty behaviors (i.e., radio flares) caused by the outbreaks of energetic electron ejections from the host star. Two key parameters of the bursty synchrotron emissions, namely the flux density and burst rate, and two key features namely the burst light curve and frequency shift, are predicted for star - hot Jupiter systems. The planetary orbital phase - burst rate relation is also considered as the signature of star-planet interactions (SPI). As examples, previous X-ray and radio observations of two well studied candidate systems, HD 189733 and V830 tau, are adopted to predict their specific burst rates and fluxes of bursty synchrotron emissions for further observational confirmations. The detectability of such emissions by current and upcoming radio telescopes shows that we are at the dawn of discoveries.
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