field is stronger than the planet’s field, then the planet has no extended magnetosphere. Thus, since our radio upper limits for GJ 367 were consistent with Rmag = Rp, our upper limit on GJ 367 b’s planetary magnetic field is essentially the predicted strength of the stellar wind field at that orbital distance (also seen in Figure 2, lower left). This situation is also reflected in the curve showing the reference system’s hypothetical 100-µJy upper limit on Bp as a function of orbital distance, which bends upwards left of <∼7R∗to follow Bp <= Bwind.

20 Villadsen et al.
For extremely close-in terrestrial planets, they are unlikely to have strong enough magnetic fields to carve out extended magnetospheres, and thus sub-Alfv´enic SPI can only place upper limits on their magnetic field strengths even if there were a detection.
8.9. Effects of uncertainty in modeling SPI The level of uncertainty in the SPI model depends on whether the interaction occurs at the ionosphere or in the extended magnetosphere. For the the assumption of strong ionospheric interaction (¯α = 1 and RAW = Rp), used in the baseline predictions in Figure 3 (upper panels), the uncertainty in predicted SPI power and flux density is ≈×30 due to √ρ ∼√×20 ∼×5 and Bwind ∼×6 (Section 6.7). The uncertainty in PSPI translates into an uncertainty in inferred Alfv´en Wing radius of × √
30 ≈×5 (Figure 3, lower left panel). We estimate the uncertainty in Bp assuming an extended magnetosphere. For such magnetospheric interaction, solving for upper limits on exoplanet magnetic field depends on wind conditions following
Bp ∝B−1/2 wind ρ−3/4 f −3
geo (Equations 8, 9 and 13). The extended-magnetosphere case thus reduces the impact of the uncertainty in stellar field, but introduces a strong dependence on the unknown relative orientation of the wind and planetary magnetic field ΘM through the geometric factor fgeo (Section 8.3). If we assume a random orientation of ΘM on a sphere, then there is a 68% probability that ΘM lies in the range 47◦-133◦and thus that fgeo lies between 1.1-1.7, yielding a fractional uncertainty on f −3 geo of 70%. Hence, the combined effects of wind density, field, and geometry yield an uncertainty in Bp, beyond the flux density uncertainty factored into the 3σ upper limits, of ×203/4 × 1.7 × √
6 ≈×40 (Figure 3, lower right panel). The uncertainty introduced by unknown model parameters, and by choices in modeling approach, becomes evident when comparing our results to literature models of our comparison systems. For example, our inferred exoplanet field to explain YZ Cet’s observed radio bursts is at least 20 G, higher than the ∼10 G found by Pineda & Villadsen (2023) with their analogous wind Model B. The discrepancy arises primarily because of different assumptions for fgeo (Section 8.3): we assume that the Alfv´en wing is √
2 times larger than the closed magnetosphere, reflecting perpendicular stellar wind and planet fields, whereas Pineda & Villadsen (2023) assumed the maximum (field-aligned) value of √
3, and Bp ∝f −3 geo ∼ � 2/3 −3 ∼1.8. For another comparison to literature SPI models, we ran our models with a range of wind temperatures (Section 6.7), inspired by the parameter exploration of Pe˜na-Mo˜nino et al. (2025)(PM25) for GJ 486. PM25 predicted that SPI flux density increases with wind temperature (almost proportionally), likely due to faster wind flow past the planet. In contrast, we found that a factor of 2 increase in wind temperature decreased SPI power by ×1.6 −1.25 at 3-100R∗. This relatively weak dependence occurs in our model because the uncertainty in vwind due to unknown wind temperature does not significantly affect v sin θ (which ≈vorb for close-in planets around slow rotators, Section 8.4) nor the planet’s magnetospheric size since wind magnetic pressure dominates over dynamic pressure (Section 8.8), and thus the only dependence of SPI power on wind speed is through √ρ ∼1/√vwind, where higher temperatures lead to faster vwind acceleration. These contrasting results point to different choices in modeling approach, potentially in addressing the relative orientation θ between wind velocity and magnetic field in the planet frame. With the many uncertainties involved, our calculations demonstrate the plausibility of detectable radio SPI from these systems, but observations and theoretical modeling of the magnetized stellar wind can refine predictions, as recently undertaken for YZ Cet by Pineda et al. (2026).