The Linkage between the Core Mass and the Magnetic Field of an Extrasolar Giant Planet from Future Radio Observations

Close-in gas giants are expected to have a strong magnetic field of $\sim 10-100$G. Magnetic fields in extrasolar giant planets are detectable by future radio observations in $\gtrsim 10$MHz and the spectropolarimetry of atomic lines. In contrast, the elusive interiors of exoplanets remain largely unknown. Here we consider the possibility of inferring the existence of the innermost cores of extrasolar giant planets through the detection of planetary magnetic fields. We simulated the long-term thermal evolution of close-in giant planets with masses of $0.2-10M_\mathrm{Jup}$ to estimate their magnetic field strengths. A young, massive gas giant tends to have a strong magnetic field. The magnetic field strength of a hot Jupiter is insensitive to its core mass, whereas the core strongly affects the emergence of a planetary dynamo in a hot Saturn. No dynamo-driven magnetic field is generated in a hot Saturn with no core or a small one until $\sim 10-100$Myr if metallization of hydrogen occurs at $\gtrsim 1-1.5$Mbar. The magnetic field strength of an evolved gas giant after $\sim 100\mathrm{Myr}$ is almost independent of the stellar incident flux. Detecting the magnetic field of a young, hot Saturn as a good indicator of its core may be challenging because of the weakness of radio signals and the shielding effect of plasma in the Earth's ionosphere. Hot Jupiters with $\gtrsim 0.4M_\mathrm{Jup}$ can be promising candidates for future ground-based radio observations.