562 78 1580 221 1940 271 | 0.47 6.4×1026 2 7.95 0.21 0.68 6.3×1025 3 0.43 0.050 0.62 1.7×1027 4 19.4 0.42 0.80 1.9×1027 5 30.1 0.43 |
| Reference | 301 42 | 1.23 1.1×1026 * 0.82 0.073 |

10 Villadsen et al.
where β = −2.7 and (LX/Lbol)sat = 10−3.13 give C = (LX/Lbol)satRo−β sat = 5.26 × 10−16. We predict mass loss per area similar to solar values for our targets (0.3-2 times solar; Table 3), due to their observed/expected weak coronal activity.
6.3. Wind base conditions: Temperature We model the stellar wind as an isothermal Parker wind. To do so, we estimate the wind temperature from X-ray coronal temperatures. GJ 367, our only X-ray-detected target, has a coronal temperature of 1.82 MK (Poppenhaeger et al. 2024). Brown et al. (2023) [B23] found that the coronal temperature for dozens of M dwarfs (mostly slow rotators) was in the range 2-6 MK, with many stars clustered around 3 MK, suggesting that the typical coronal temperature of our targets may be around 3 MK. However, many of B23’s X-ray data could only be fit with a single temperature component, which is dominated by dense, hot active regions, and which may thus overestimate the wind temperature in open-field regions. For example, ´O Fionnag´ain & Vidotto (2018) [OV18] find that the relation between rotation and average X-ray coronal temperature from Johnstone et al. (2015) predicts a coronal temperature for the Sun that is 1.36 times higher than the basal solar wind temperature of 1.5 MK needed for their polytropic model to match the solar wind. To mitigate the risk of overestimating wind temperatures based on an average coronal temperature, we can also look at the lower temperature component in multi-temperature fits to M dwarf coronal X-ray observations. This approach is consistent with Sun-as-a-star X-ray observations, which have a dominant coronal emission component at 1 MK (Peres et al. 2000), agreeing with a 1.1-MK isothermal fit to the slow solar wind (Sheeley et al. 1997). For the 5 of 23 stars in B23 that have a 2 or 3-temperature fit to the X-ray while in a quiescent or low state, the low-temperature component ranges from 1.4-1.7 MK. We choose a wind temperature that lies between (3 MK)/1.36 (based on the OV18 scale factor and typical coronal temperatures from B23) and 1.5 MK (based on a typical low-temperature component in B23), and thus we assume a typical wind temperature of 2 MK for our targets. Since the average coronal temperatures in B23 vary from 2-6 MK, roughly a factor of 2 around the typical value of 3 MK, we also assume a factor of 2 uncertainty in wind temperature due to the variation between stars.
6.4. Wind magnitude at planet: Stellar magnetic field The wind magnetic field strength at the planet depends on whether the stellar field is open or closed at that distance. Vidotto et al. (2014a) performed ZDI-grounded MHD wind simulations of 6 active early M dwarfs, and found that the “effective source surface,” where the field is almost entirely radial and open, occurs at 2.8-4.6R∗. An open stellar field at ≳3R∗should thus be a reasonable approximation for all targets, even GJ 367 b at 3.3R∗. Since our stars are slow rotators, we also assume the field is purely radial with no azimuthal component, so B(˜r) = Bopen˜r−2, where we define ˜r = r/R∗. How does the large-scale surface field BZDI relate to the stellar surface-averaged open radial field Bopen? Lehmann et al. (2024) produced ZDI maps of six slowly-rotating M dwarfs, typically detecting only the poloidal field, which is dominated by a radial component but also has a weaker meridional component (50% or less of the radial component). Since the magnetic field components add in quadrature, the radial component of the ZDI magnetic field matches the overall magnitude to within ∼10%. We thus assume that our predicted BZDI is purely radial and contributes to the magnetic flux. In Vidotto et al. (2014a)’s six wind models, the unsigned open magnetic flux at a large distance |  | 367 2 8 |  |  |  |