Radio-kinetic and radio-magnetic scaling laws and extrapolation to hot Jupiters. Panel a: radio-kinetic scaling lawrelating the overall power of the auroral radio emissions from (E)arth, (J)upiter (non-Io emissions), (S)aturn, (U)ranus, and (N)eptune (integrated over their full spectrum, beaming solid angle, and time-averaged) to the bulkkinetic energy flux from the solar wind intercepted by the corresponding magnetospheric cross-sections (black dots and labels, taken from Zarka 2007). The dotted line fit has a slope of 1 and a conversion efficiency of 10⁻⁵. The red dots and labels relate the Io-induced and Ganymede-induced radio emission powers to the bulk kinetic energy flux of (sub)corotating plasma within Jupiter’s magnetosphere. Error bars are estimated from the measured fluctuations of all displayed quantities (Kivelson et al. 2004). Panel b: radio-magnetic scaling law, relating the same radio powers as in panel a with the incident Poynting flux from the solar wind onto planetary magnetospheres or from Jupiter’s magnetosphere on Io’s ionosphere and Ganymede’s magnetosphere. The black dotted line, which fits the planetary magnetosphere points (black dots) well, has a slope of 1 and a conversion efficiency of 2 × 10⁻³ (from Zarka 2007). Including the satellites (red dots), a better fit with a slope of 1 is obtained with a constant 3 × 10⁻³ (red dotted line). The best fit with unconstrained slope has a slope of 1.15 (blue dotted line). Panel c: extrapolation of the radio-magnetic scaling laws from panel b to the parameter ranges for hot Jupiters (shaded region), where the intercepted Poynting flux can reach 10³ –10⁶ times that intercepted by Jupiter (taking into account increased magnetospheric compression and a solar-like magnetic field of ~1 Gauss). With the law of slope 1, expected radio powers are similarly 10³⁻⁶ times stronger than Jupiter’s, and one order of magnitude larger with the law of slope 1.15. Stronger stellar magnetic fields should lead to stronger radio emissions. The documented case of the magnetic binary V711τ, where the involved magnetic fields are much stronger than the Sun’s, is plotted as an orange point.