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tokens: given the age determined by Burgasser Mamajek ( 2017 ), the activity index described in Section 3.2 , and the XUV fluxes that have been measured for the star (Bolmont et al. 2017 ; Bourrier et al. 2017 ; Wheatley et al. 2017 ). As noted earlier, the combination of these stellar attributes ensures that the TRAPPIST-1 planets will have been subjected to extended periods of activity-related atmospheric erosion. As such, the possible atmospheric erosion effects will need to be accounted for in consideration of the habitability potential of the planets. We calculated the incident flux and escape velocities for the TRAPPIST-1 planets based on the planetary and stellar properties provided by Gillon et al. ( 2017 ), where the bolometric luminosity is the result of spectral energy distribution analysis by Filippazzo et al. ( 2015 ). These calculated values are shown in Table 1 , and are depicted in Figure 5 along with the incident flux and escape velocities for various solar system objects. The cosmic shoreline based upon the estimates by Zahnle Catling ( 2017 ) is shown as a solid line, where the solar system objects to the left of the line tend to not have atmospheres and objects to the right tend to have (albeit sometimes tenuous) atmospheres. Note that the incident flux shown in the plot represents the total (bolometric) flux received at the distance of the planets from the host star. The derivation of the cosmic shoreline power law by Zahnle Catling ( 2017 ) utilized the scaling relationships of Lammer et al. ( 2009 ) that related extreme ultraviolet (EUV) and XUV excess to stellar age and spectral type. Thus, our adoption of the bolometric flux includes the atmospheric erosion effects of the intrinsic EUV and XUV radiation as a subset of the total flux. The XUV flux related to magnetic activity, as described in this paper, will add an additional component to the atmospheric eroding flux effects. Increasing the XUV component has the effect of down-weighting the influence of the escape velocity for retaining the atmosphere. This means that low-mass stars with a higher relative rate of XUV emission will have a substantially greater atmospheric erosion effect on their hosted planets. In Figure 5 , we include two additional lines for the cosmic shoreline that reduce the escape velocity effect by factors of 2 (dashed) and 4 (dotted). These lines thus represent stars for which the XUV flux is 16 and 256 times higher than the solar flux. In the case of the former, this indicates that only the g planet has a reasonable chance of retaining a planetary atmosphere, whereas in the case of the latter, all of the planets are likely to be barren. These shifts of the cosmic shoreline are consistent with the XUV flux measurements conducted by Wheatley et al. ( 2017 ) of TRAPPIST-1, which indicated that the incident flux received by the planets may be several orders of magnitude larger than that received by the Earth. Such incident flux would result in atmosphere