limits (Section 8) on planet magnetospheric size of 1-9 planet radii, and planet magnetic fields of <0.8 G for GJ 367 (the closest-in planet at a/R∗= 3.3) to < 320 G for LHS 1678 (the most distant at a/R∗= 8). Notably, GJ 367 b’s upper limit corresponds to the circumplanetary stellar wind magnetic field strength; since planetary fields lower than this would not create an extended planetary magnetosphere, even SPI detections cannot measure planetary fields weaker than the stellar wind field.

22 Villadsen et al.
While there are many uncertainties in SPI flux density predictions, our wind model enables us to compare the relative predicted SPI power and the informativeness of upper limits across exoplanetary systems. We compare our 5 targets to 4 other slowly-rotating M dwarfs with radio SPI candidate detections (YZ Cet, Prox Cen, GJ 3323) and upper limits (GJ 486). Next to GJ 367, we find that GJ 486 provides the tightest constraint on exoplanet magnetic field, <1.5 G for our wind model. Curiously, the 3 radio-detected comparison systems have the largest orbital distances (a/R∗∼20-70) and thus relatively low predicted flux densities, although the strong stellar magnetic fields predicted for their late spectral type somewhat offset the effects of orbital distance. This disparity, of radio detections in systems with low predicted SPI power, could easily occur if the detected radio bursts are due to non-planetary stellar activity. Or, if the bursts are indeed SPI, it indicates unusually high stellar wind magnetic fields or densities that increase the SPI power or radio emission efficiency, or that later-type M dwarfs are more likely to emit up to GHz cyclotron frequencies on the star-planet flux tube, compared to the early-to-mid M slow rotators targeted in this survey. Our non-detections of targets with relatively high predicted SPI power collectively favor an approach of observing at sub-GHz frequencies to search for SPI on inactive early-to-mid M dwarfs.
10. ACKNOWLEDGMENTS JV thanks Aline Vidotto for helpful advice about stellar winds. This material is based upon work supported by the National Science Foundation under Grant No. AST-2150703 and AST-2310589 (JV, LG, EH, AW, AA) and AST-2108985 (JSP). The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Support for this work was provided by the NSF through award SOSP 19B-005 from the NRAO (CR). The Australia Telescope Compact Array is part of the Australia Telescope National Facility (grid.421683.a) which is funded by the Australian Government for operation as a National Facility managed by CSIRO. We acknowledge the Gomeroi people as the traditional owners of the Observatory site. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research made use of Astropy (http://www.astropy.org), a community-developed core Python package for Astronomy. Software: Astropy (Astropy Collaboration et al. 2013, 2018, 2022), Scipy (Virtanen et al. 2020)

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