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.

SPI Radio Search 15 M dwarfs, including slow rotators such as YZ Cet (Pineda & Villadsen 2023) and GJ 3323 (Ortiz Ceballos et al. 2024), are known to emit polarized emission (likely ECM) at GHz frequencies, and polarized bursts on active M dwarfs such as AD Leo may connect to large-scale magnetic structures (Zarka et al. 2025). Motivated by such past detections of GHz coherent bursts on M dwarfs, we observed at 1-4 GHz in order to tap into the high sensitivity of GHz radio facilities. However, GHz bursts could also originate from small-scale closed magnetic loops that do not connect magnetically to the stellar wind, as seen for solar ECM bursts by Yu et al. (2024). Table 3 predicts magnetic fields for our targets, with average surface fields (including small-scale flux) of 130-560 G, and large-scale fields of 8-80 G, with an estimated uncertainty of order ×5. These predicted fields are lower than those of our comparison sample because our current targets are mostly earlier spectral type. If the planet field lines connect to weakly magnetized coronal holes, similar to the fast solar wind, then the average large-scale field may provide a good estimate of the ECM cutoff frequency, which would be of order 20-250 MHz for our targets. However, if the planet field lines connect to coronal streamers, like the slow solar wind, then the footpoints may land near active regions with enhanced field and thus reach cyclotron frequencies of 0.4-1.6 GHz. With the significant uncertainty in the predicted stellar magnetic fields, it is plausible that our targets may have SPIdriven ECM above 1 GHz, but the ECM cutoff frequency also provides a reasonable explanation for all of the non-detections. Stellar magnetic field observations of close-in exoplanet hosts can help select appropriate observing frequencies to optimize sensitivity in the search for radio SPI.
While geometry and observing frequency are plausible explanations for our non-detections, another possible explanation is flux density too low to detect, a case that would give constraints on exoplanet magnetospheric size and field strength, as we discuss in the following sections.
8. UPPER LIMITS ON EXOPLANET MAGNETOSPHERE Our goal is to translate between observed radio flux density (upper limits) and exoplanet magnetic field strength, which determines the interaction cross-section and thus the SPI power. First, we generate “minimum” SPI power predictions for a planet-sized magnetosphere. Then, we compare these predictions to observations to place upper limits on the target planets’ magnetospheric size and field strength.
8.1. Alfv´en wing model for SPI power Callingham et al. (2024) review various models for predicting SPI power. Here we adopt the widelyused Alfv´en wing model (Saur et al. 2013, S13), which has been benchmarked against solar-system observations and numerical simulations. We wrote independent code for this project, but we note that the Alfv´en-wing model has recently become available in the SPI modeling code SIRIO (Pe˜na-Mo˜nino & P´erez-Torres 2025). In the Alfv´en wing model, the SPI power is the integrated Poynting flux leaving the planet and traveling back towards the star in one of two Alfv´en wings, since in an open stellar field the other wing does not connect to the star. Saur et al. (2013)’s Equation 55 for SPI power, which we denote PSPI, is valid for low Alfv´en Mach number MA. The underlying approximation that (1 −1/M2
A)−1/2 ≈MA
(Callingham et al. 2024) is accurate to within 20% for MA < 0.8. Pineda & Hallinan (2018) reframe this equation in cgs to show the dependence of MA on wind density:
PSPI = 1
� 4πρ . (8)
2 ¯α2R2 AWv2B sin2 θ 16 Villadsen et al.