(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).

SPI Radio Search 21 9. CONCLUSIONS We conducted GHz radio observations of 5 slowly-rotating M dwarfs with close-in exoplanets to search for stellar radio bursts induced by sub-Alfv´enic SPI: LTT 3780 at 2-4 GHz with the VLA, and LHS 3844, GJ 367, LHS 1678, and GJ 1252 at 1.1-3.1 GHz with ATCA. We observed each target for most or all of an orbital period. In time series with 5-minute time binning, we did not detect any radio bursts in Stokes I or V, with Stokes V 3σ upper limits of 75 µJy (VLA) and 300-600 µJy (ATCA). In images of the full observation, we detected quiescent Stokes I emission from LHS 3844 at 63±12 µJy and tentatively detected quiescent Stokes V emission from LHS 1678 at -70±9 µJy, although poor source coherence in the latter case makes the detection tentative. Lack of temporal variability means that neither of these signals are consistent with the minutes-to-hours long bursts expected as angularly-beamed emission from a planet-connected flux tube sweeps past the viewer, but they could be consistent with active regions on the slowly-rotating stellar surface. LHS 1678’s early-M type and low photometric variability (Kar et al. 2024) make its polarized radio emission particularly surprising. Quiescent emission from exoplanetary hosts provides background illumination that can enable exoplanet radio transit observations, if these targets are confirmed as quiescent emitters in multiple epochs. The radio transit profile should be modified by exoplanet magnetospheres, but for uniform stellar emission, a small fractional transit depth would require next-generation radio facilities (Hazra et al. 2022). However, with luck, current facilities could detect high transit depths due to the concentration of stellar radio emission in small active regions (Pope et al. 2019). To interpret the non-detection of SPI radio bursts, we constructed a stellar wind model for our targets (Section 6). We used a radial 1D isothermal Parker wind, and a radial open magnetic field whose strength is scaled down to account for most of the surface field not connecting to open field lines. Since our targets did not have magnetic or stellar wind measurements, we adopt prescriptions for predicting these values from literature rotation-based correlations. While the uncertainties in mass loss rate and stellar magnetic field lead to ∼×30 uncertainty in the predicted SPI radio flux density, these rotation-based wind predictions enable population studies and strategic target selection for cases where it is not feasible to perform detailed magnetic/wind observations and modeling for every target. The radio SPI non-detection may be caused by unlucky geometry with beamed emission never directed towards Earth, or an observing frequency above the maximum cyclotron frequency on the star-planet magnetic flux tube, or an SPI flux density too low to detect. We predict that all of our targets are sub-Alfv´enic and thus can transfer energy to radiate near the star; the predicted stellar large-scale surface fields correspond to cyclotron frequencies of 20-250 MHz, but small-scale surface fields may boost local cyclotron frequencies into the GHz range. If the non-detections are due to low flux density, our stellar wind model implies upper 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.