  Evidence of star-planet interactions in the form of planet-modulated
chromospheric emission has been noted for a number of hot Jupiters. Magnetic
star-planet interactions involve the release of energy stored in the stellar
and planetary magnetic fields. These signals thus offer indirect detections of
exoplanetary magnetic fields. Here we report the derivation of the magnetic
field strengths of four hot Jupiter systems using the power observed in Ca II K
emission modulated by magnetic star-planet interactions. By approximating the
fractional energy released in the Ca II K line we find that the surface
magnetic field values for the hot Jupiters in our sample range from 20 G to 120
G, ~10-100 times larger than the values predicted by dynamo scaling laws for
planets with rotation periods of ~2 - 4 days. On the other hand, these value
are in agreement with scaling laws relating the magnetic field strength to the
internal heat flux in giant planets. Large planetary magnetic field strengths
may produce observable electron-cyclotron maser radio emission by preventing
the maser from being quenched by the planet's ionosphere. Intensive radio
monitoring of hot Jupiter systems will help confirm these field values and
inform on the generation mechanism of magnetic fields in this important class
of exoplanets.
