wind speed and density predictions in the near-star regions relevant for sub-Alfv´enic SPI. In an Alfv´en-wave-driven model of TRAPPIST-1’s stellar wind, R´eville et al. (2024) find that the possible range of slow and fast stellar wind speeds spans a factor of 2 depending on unknown parameters, consistent with our assumed wind speed uncertainty. 4) Wind density near planet. Our wind density predictions have two main uncertainties: wind temperature and mass loss rate. For mass loss rate, the uncertainty in rotation period and X-ray
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luminosity is a small effect compared to the observed scatter of ± × 10 in the Wood et al. (2021) relationship, as noted for the SPI wind modeling of R´eville et al. (2024). We note that one of our comparison systems, GJ 486, has an X-ray-based predicted mass loss rate of 0.05 ˙M⊙, compared to a spindown-based law (Johnstone et al. 2015) predicting 1.4 ˙M⊙(Pe˜na-Mo˜nino et al. 2025). This wide discrepancy underscores the need for further observations and modeling of winds of slowly-rotating M dwarfs. We estimate a net uncertainty in density of ×20 (Figure 2, upper left panel): ×2 from temperature and ×10 in mass loss rate.
7. POSSIBLE CAUSES OF NON-DETECTIONS There are multiple possible causes of a non-detection of radio SPI: 1) super-Alfv´enic interaction, 2) timing and geometry, 3) frequency limits, and 4) flux density below detection limit. In this section, we rule out #1 as unlikely and consider options #2 and #3, while we discuss #4 in Section 8.
7.1. Super-Alfv´enic interaction SPI cannot power stellar radio emission if the interaction is super-Alfv´enic, i.e. the stellar wind speed relative to the planet exceeds the local Alfv´en speed. We used our wind model to calculate the Alfv´en speed for our targets, predicting MA ≲0.1 for our 5 targets (Figure 2). We also predict that all of our comparison sample are sub-Alfv´enic, including Prox Cen b with MA ∼0.5, but in a more sophisticated 3D model of Prox Cen’s wind, Kavanagh et al. (2021) find that the wind should become super-Alfv´enic at ∼40−70R∗for a wide range of stellar mass loss rates. The difference may arise because of our use of magnetic field correlations instead of observed quantities. Our 5 primary targets are so close to the star that even considerably lower stellar magnetic fields than predicted would not make them super-Alfv´enic.
7.2. Timing & geometry The timing of observations, and the geometry of the system, could cause non-detections due to either angular beaming or luminosity changes due to stellar wind variability. Kavanagh & Vedantham (2023) predict that angular beaming will cause transiting systems to be visible 4% of the time, and only 49% of transiting systems will ever direct their emission towards Earth. As a caveat, this study assumes a uniform distribution for the unknown stellar inclination and magnetic obliquity whereas if these are preferentially nearly aligned with the orbital axis the detection rate may be higher. To account for the 4% problem, we observed almost a full orbital period for all of our targets (Table 2). ZDI observations could enable tailored simulations to help address whether individual systems are in the ever-observable 49%.
7.3. Footpoint conditions & observing frequency The magnetic flux tube connecting planet and star ends at a stellar footpoint, producing radio emission at the cyclotron frequency at a range of heights along the flux tube, up to a maximum surface cyclotron frequency if not absorbed by the stellar wind. Pe˜na-Mo˜nino et al. (2025) and Pe˜na-Mo˜nino & P´erez-Torres (2025) considered the possibility of free-free absorption of an ECM signal on GJ 367 and YZ Cet, respectively. They found that for coronal temperatures around 2 MK, absorption is negligible for mass loss rates < 10 ˙M⊙(GJ 486) and < 2 ˙M⊙(YZ Cet), well above our targets’ predicted mass loss rates (Table 3). However, an emission cutoff below our observed frequency band may explain the observed non-detections.