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The magnetic fields of the solar system planets provide valuable insightsinto the planets' interiors and can have dramatic consequences for theevolution of their atmospheres and interaction with the solar wind. However, wehave little direct knowledge of magnetic fields in exoplanets. Here we presenta method for detecting magnetic fields in the atmospheres of close-inexoplanets based on spectropolarimetric transit observations at the wavelengthof the helium line at 1083 nm. This methodology has been successfully appliedbefore for exploring magnetic fields in solar coronal filaments. Strongabsorption signatures (transit depths on the order of a few percent) in the1083 nm line have recently been observed for several close-in exoplanets. Weshow that in the conditions in these escaping atmospheres, metastable heliumatoms should be optically pumped by the starlight and, for field strengths morethan a few $\times 10^{-4}$ G, should align with the magnetic field. Thisresults in linearly polarized absorption at 1083 nm that traces the fielddirection (the Hanle effect), which we explore by both analytic computation andwith the Hazel numerical code. The linear polarization $\sqrt{Q^2+U^2}/I$ranges from $\sim 10^{-3}$ in optimistic cases down to a few $\times 10^{-5}$for particularly unfavorable cases, with very weak dependence on fieldstrength. The line-of-sight component of the field results in a slight circularpolarization (the Zeeman effect), also reaching $V/I\sim {\rm few}\times10^{-5}(B_\parallel/10\,{\rm G})$. We discuss the detectability of thesesignals with current (SPIRou) and future (extremely large telescope)high-resolution infrared spectropolarimeters, and we briefly comment onpossible sources of astrophysical contamination.

Detecting Magnetic Fields in Exoplanets with Spectropolarimetry of the Helium Line at 1083 nm