The number of confirmed exoplanets has crested 4000 with more being added to the pile every day. A large number of these planets have measured masses and radii which allows the bulk density to be known. A much smaller number have had their atmospheric structure and composition characterized. There is a fundamental property of exoplanets, however, that remains an empirical mystery: magnetic field strengths. Magnetic fields likely play an important role in a planet's mass loss history, which can fundamentally alter the planet's atmosphere across evolutionary timescales.
Despite their importance, exoplanet magnetic fields have not yet been detected. Radio searches for emission generated by electrons in exoplanet magnetic fields go back to the 1970's but none have so far been successful. More recent iterations are underway (see the work done by the Low Frequency Array, or LOFAR) but no detections have been announced. Additionally, indirect effects of exoplanet magnetic fields on transit signatures have been reported but the interpretations of the data remain ambiguous.
In our recent work (https://www.nature.com/articles/s41550-019-0840-x) we took a novel approach to estimating the magnetic fields for a small number of hot Jupiters. Planets with very short orbital periods are expected to interact magnetically with the large scale magnetic fields of their host stars. These star-planet interactions can generate enhanced emission in spectral lines that are formed in the star's upper atmosphere, i.e., the chromosphere. In order to estimate the field strengths of the hot Jupiters in our sample, we took previously published signals of star-planet magnetic interactions and applied an accurate flux calibration method to them so we could estimate the total amount of energy released in the emission lines. Then, applying an analytic theory of how the planet and star's magnetic fields interact, we calculated what the necessary planetary magnetic field strengths would be to create the observed signal. Our results are the first semi-empirical estimates of exoplanet magnetic field strengths.
The field strengths we calculate for our hot Jupiters are large, 20 G to 120 G, larger than expected if only the planet's rotation period is considered. Instead, our results support the idea that a planet's field strength is set by how much heat is moving through the interior, i.e., the internal heat flux. Scaling laws for magnetic field strength have been developed using the idea of internal heat flux and do a good job of describing field strengths for objects of planetary mass all the way up to rapidly rotating main sequence stars. The extra heat that enhances the field strengths in our sample comes from their close proximity to their stars, hence their classification as hot Jupiters. These results have important implications for more direct detection of exoplanet magnetic fields (e.g., via electron-cyclotron emission with radio telescopes) and our understanding of how dynamos generate magnetic fields in planets.