Impact of Stellar Superflares on Planetary Habitability

Our analysis is based on the application of stellar flare and star spot data derived mostly from the Kepler mission (Notsu et al. 2013, 2015a, 2015b, 2019; Maehara et al. 2015, 2017), in the ExoKyoto exoplanetary database (Y. A. Yamashiki et al. 2019, in preparation). Our method utilizes star spot data derived from optical light curves to be used in parametric studies of the thickness of hypothetical exoplanetary atmospheres as the major attenuation factor of the incident radiation (see Table 1). These data are used as input for the PHITS (Sato et al. 2018) Monte Carlo simulation model that is used for simulations of surface dose for terrestrial-type exoplanets.

The following equations derive an assumed stellar flare magnitude from observed stellar spot size data. For the estimation of spot size, we used the same method as Maehara et al. (2017). Figures 1 and 2 illustrate flare frequency versus flare energy for solar flares. The solid line and dotted line represent the estimated scaling low calculated using Equation (1) as a different star spot area derived from Maehara et al. (2017).

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Using the results of the above study, we derived the flare frequency distribution over its energy in the optical band as a function of the stellar spot size as follows:

$$\begin{eqnarray}&&\displaystyle \frac{{dN}}{{dE}}={C}_{0}\left[{\mathrm{yr}}^{-1}\,{\mathrm{erg}}^{-1}\right]{\left[\displaystyle \frac{{A}_{\mathrm{spot}}}{{10}^{-2.75}{A}_{\mathrm{phot}}}\right]}^{1.05}{\left[\displaystyle \frac{{E}_{\mathrm{flare}}}{{10}^{31}\mathrm{erg}}\right]}^{-1.99},\end{eqnarray} \tag{ 1 }$$

in which N is the flare frequency (yr⁻¹), A_spot is the total area of star spots, A_phot is the total visible area of the stellar surface, E_flare is the total expected stellar flare energy (erg), and C₀ is the flare frequency constant (10^29.4).

Here we define E₀ = 10³¹ erg and set N as 1; we then may determine annual maximum flare energy as follows:

$$\begin{eqnarray}&&{E}_{\mathrm{AMF}}={C}_{0}^{-\tfrac{1}{1+a}}{\left[\displaystyle \frac{{A}_{0}}{A}\right]}^{\tfrac{b}{1+a}}{E}_{0}^{\displaystyle \frac{a}{1+a}},\end{eqnarray} \tag{ 2 }$$

in which E_AMF is the annual maximum flare energy, that is, the total expected stellar flare energy per year (erg yr⁻¹), a = −1.99, b = 1.05.

The spot maximum flare, that is, the maximum flare energy under a determined star spot area, can be illustrated as

$$\begin{eqnarray}&&{E}_{\mathrm{SMF}}=7\times {10}^{32}(\mathrm{erg})\left(\displaystyle \frac{f}{0.1}\right){\left(\displaystyle \frac{{B}_{0}}{{10}^{3}{\rm{G}}}\right)}^{2}{\left[\displaystyle \frac{{A}_{\mathrm{spot}}/(2\pi {R}_{\odot }^{2})}{0.001}\right]}^{3/2},\end{eqnarray} \tag{ 3 }$$

in which f is the fraction of magnetic energy that can be released as flare energy, B is the magnetic field strength, E_SMF is the spot maximum flare energy, that is, the theoretical maximum flare energy with a determined star spot area (erg), and R_⊙ is the solar radius (7 × 10¹⁰ cm).

Possible maximum flare energy in this study was determined in the following way: (1) Evaluate maximum star spot coverage of the star through observation of stellar light curves. In this study, we observed a 20% coverage of star spot on Proxima Centauri (Davenport 2016; Wargelin et al. 2017); accordingly we determined the maximum star spot coverage as 20%. Then, (2) calculate maximum energy induced by the star spot area by Shibata et al. (2013).

The outline of the estimation method is as follows:

Step 1. Derive the magnitude and frequency of stellar proton events from each star (1) by using direct observation of a stellar flare as a proxy for SPE energy and (2) by applying the star spot area and/or rotational period correlation methodology. The conversion equation is presented and discussed in the next section. We use the above information to extract representative star spot areas, which can be applied to the conversion equations for flare energy expressed in the following section. Accordingly we obtain (a) annual maximum flare (see Equation (2)), spot maximum flare (see Equation (3)) (Shibata et al. 2013; Aschwanden et al. 2017), and (c) possible maximum flare, calculated assuming that the target star surface is covered with star spots under the maximum percentage of observed star spot area (set as 20% of half the spherical area).

Step 2. After the above procedure is completed for each star system, the possible quantitative exposures are assumed by the following procedure: (4) estimating the fluence of each stellar proton event at the TOA using Equation (7).

As for the atmospheric compositions of exoplanets, three types of atmospheres for typical extrasolar planets are considered (explained in detail in the following section). For those typical atmospheric compositions, the potential doses for life on extrasolar planets are determined through the following procedure.

Step 3. (5) Calculate the possible dose rate from the Monte Carlo simulations using PHITS (Sato et al. 2018) for three typical atmospheric compositions as extrasolar planetary atmospheres, (6) normalize the dose by determining the Earth equivalent ratio, which was previously normalized by using (6a) the Carrington-class event, assuming that the event has X45 class, or by (6b) the deepest observed flare event GLE43, which occurred in 1989, as X13 class (Xapsos et al. 2000). (7) Calculate conversion coefficients for each exoplanet by comparing the values calculated in (4) and (6). (8) Convert the reference dose value calculated in (6) into each extrasolar planet case using conversion coefficients.

When high-energy SEPs precipitate into the planetary atmosphere, they induce extensive air shower (EAS) by producing various secondary particles, such as neutrons and muons. We conducted a three-dimensional EAS simulation by using the PHITS (Sato et al. 2018), which is a general purpose Monte Carlo code for analyzing the propagation of radiation in any materials. PHITS version 2.88 with the recommended setting for cosmic-ray transport simulation (Sato et al. 2014) was used in this survey. In our simulations we assume the size and the mass of the modeled planets to be the same as that of the Earth.

The impact of stellar proton events on a planet depends upon its atmospheric composition. We consider three: Earth-like (N₂+ O₂ rich), Mars-like or Venus-like (CO₂ rich), and a young Earth-sized or super-Earth planet with a primary H₂-rich atmosphere. We assume that the Earth-type atmosphere is the standard land-ocean planetary atmosphere composed mostly of nitrogen and oxygen (N₂+ O₂). A Venusian-like atmosphere is represented as a CO₂-rich atmosphere resulting from the runaway greenhouse effect and subsequent outgassing of CO₂ from carbonates. The Mars-like atmosphere is an example of a low gravity–low pressure planetary CO₂-rich atmosphere that has experienced severe atmospheric escape driven by strong stellar ionizing radiation flux. We also model a young Earth-sized H₂-rich atmosphere, because such an atmosphere is assumed for large super-Earth planets, whose gravitational pull might be sufficiently large to retain substantial atmospheric H₂. Hydrogen-rich atmospheres of Earth-sized exoplanets can be formed due to capture of hydrogen from protoplanetary atmospheres and/or during the accretion period (Elkins-Tanton & Seager 2008; Lammer et al. 2018). Thus, here we refer to young Earth-sized exoplanets.

The composition of the atmosphere for the above three typical atmospheric types was set to 78% nitrogen, 21% oxygen, and 1% argon for the Earth-like (N₂+ O₂) atmosphere, 100% carbon dioxide for the Martian/Venusian-type (CO₂), and 100% hydrogen for the young-Earth-type (H₂). During the Monte Carlo simulation using PHITS, we assume the composition of the planet interior to be covered with sufficient liquid water for the terrestrial type, while the same gas was continuously filled in the planet interior for the other cases. In our simulation of all model atmospheres (young Earth-type [H₂], Earth-like [N₂+ O₂], Martian and Venusian-type [CO₂]) cases we assume the exoplanet radius and mass to be 1 R_Earth and 1 M_Earth, respectively. Numerical simulation of super-Earths will be performed in the upcoming studies.

We assume that stellar accelerated protons are isotropically distributed in space as they precipitate into the atmospheres of the modeled planets and have two different energy spectra represented by the SPE spectra derived for the Carrington-class event in 1859 (Townsend et al. 2006) and the 43rd ground-level enhancement (GLE) in 1989 (Xapsos et al. 2000), respectively.

The Carrington-class event is considered to be the largest eruptive event recorded in modern human history. However, according to Smart et al. (2006), proton energy spectra associated with the Carrington-class event were rather soft in comparison with other solar flares that produce GLEs. Thus, the radiation dose at the ground level during the event is expected to be not significantly high, because only a small fraction of the high-energy protons (with energies over 3 GeV for an 1 bar atmosphere) and their secondary particles can penetrate into the deep atmosphere.

To estimate the maximum impact on the ground level, we therefore calculated the radiation dose during the solar flare in association with a harder proton spectrum, GLE43, which is one of the most significant GLEs that has occurred after satellite observations were started in the late 20th century. It should be noted that GLE43 was selected as a typical SPE associated with a hard proton spectrum to estimate the maximum impact of SPE exposure at deeper locations in the atmosphere, although its flare class was not extremely high (X13). GLE5 (1956 February 23) -type spectra were also considered as a relevant event for the survey.

Figure 3 illustrates event-integrated spectra of the GLE43 and the Carrington flare.

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We have simulated four scenarios of exoplanetary dipole magnetic moments: (1) B = 0 (unmagnetized planet), (2) 0.1 × B_Earth, (3) 1 × B_Earth (Earth-like magnetic moment), and (4) 10 × B_Earth. The impact of the planetary magnetic field on the surface dose was modeled via the magnetospheric filter functions for the above four different magnetic moments, 0, 0.1, 1, and 10 B_Earth, evaluated by Grießmeier et al. (2015).

The fluence of protons, neutrons, positive and negative muons, electrons, positrons, and photons was scored as a function of the atmospheric depth. They were then converted to the absorbed dose in grays and the effective dose in Sieverts (Sv) using the stopping power and the fluence to the dose conversion coefficients for the isotropic irradiation (International Commission on Radiological Protection, 2010), respectively. It should be mentioned that the effective dose is defined only for the purpose of radiological protection. However, we evaluated it for discussing the possible exposure effects on human-like life-forms because there is no alternative quantity that can be used for this discussion. More detailed descriptions of the simulation procedures as well as their verification results for the solar energetic particle and galactic cosmic-ray simulation in the terrestrial atmosphere were given in our previous papers (Sato 2015; Sato et al. 2018b).

The impacts of all components produced by cosmic-ray interactions with the different atmospheric types in different layers were also individually evaluated and finally integrated to produce a final ground-level dose value for each simulated scenario. By examining all these different parameters together (atmospheric composition, geomagnetic field strength, and simulated cosmic-ray interactions), we have evaluated the atmospheric barrier needed for life on each of the target planets to survive a stellar flare event. This approach assumes that the potential life is as similarly radiation tolerant as that present on Earth.

Our goal is to study the effect of high ionizing particle fluxes caused by stellar activity on habitability of close-in Earth-sized and super-Earth exoplanets located within habitable zones. CHZs around low-luminosity M dwarfs are located within 0.05 au, which suggests that many of them orbit their host stars within sub-Alfvenic distance and are subject to direct irradiation via high particle fluxes. To study the resulting surface dose we selected four exoplanets around active M dwarfs, one exoplanet around K dwarfs with detected superflare, and one exoplanet around a G dwarf with higher stellar activity than our Sun. We selected the target stars for this survey according to the following procedure: (1) Select host star with exoplanet in habitable zone with direct superflare observation through Kepler observation (Kepler-283). (2) Select Kepler stars whose flare frequency and magnitude can be estimated from their activities (Kepler-1634). (3) Select well-documented host star for well-documented exoplanets (GJ699 (Barnards Star), Proxima Centauri, Ross-128, TRAPPIST-I). Stellar activities for all stars are estimated using their light curves.

Shibata et al. (2013) estimated the maximum value (upper limit) of flare energy, which is determined by the star spot area and magnetic field strength. We used this methodology to calculate the theoretical maximum flare energy for six host stars using their star spot areas: 1.15 × 10³² erg for GJ 699 (Barnard's star), 2.13 × 10³³ erg for Kepler-283, 1.18 × 10³⁴ erg for Kepler-1634, 5.55 × 10³³ erg for Proxima Centauri, 7.72 × 10³¹ erg for Ross 128, and 9.09 × 10³² erg for TRAPPIST-1.

With this method, the current observed star spot area in each star restricts the maximum flare energy. However, it is unclear whether the observed period represents the maximum or minimum activity of the star. Accordingly, we also evaluated the potential maximum energy of the stellar flare by the following method.

For those stars whose stellar temperature is above 4000 K, we estimated maximum flare energy based on the relationship between Kepler stars by comparing their maximum observed energy and stellar temperature as well as their associated radii (H. Maehara 2019, private communication).

For those stars whose stellar temperature is below 4000 K, we assumed, in the extreme situation, that 20% of the stellar surface is covered by a star spot. Considering the extreme condition, we calculated the maximum energy using Shibata et al. (2013).

By introducing flare energy as the input for considerable maximum energy of the superflares for their planetary systems, we may theoretically calculate the possible maximum dose for their host planets.

Figure 4 shows the vertical profile of radiation dose on Earth and Mars caused by SPEs with the hard proton spectrum (imitating GLE43) (a and b), and soft spectrum (imitating Carrington) (c and d), penetrating N₂+ O₂–rich (terrestrial-type) atmosphere Earth with 10³⁰ erg (black triangle), 10³² erg (red circle), 10³⁴ erg (blue square), and 10³⁶ erg (red cross) in grays (a and c) and Sieverts (b and d). This figure shows that the radiation dose at the tropopose (around 170 g cm⁻² atmospheric depth) becomes 0.5 mSv, which mostly agrees with the aerial observation, when the solar flare energy is scaled to E₀ = 10³². Note that this normalization has been made for an idealized series of flares, considering the horizontal angle of the SPE injection as 90°; in other words, the probability of reaching Earth is one in four.

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Figures 5 and 6 show vertical profile of radiation dose in grays and Sieverts, respectively, on Earth and Mars for possible flares on several different scales, caused by hard proton spectrum (imitating GLE43) (a and c) and soft spectrum (imitating Carrington reproduced by Townsend et al. 2006) (b and d) penetrating N₂+ O₂–rich (terrestrial-type) atmosphere for Earth (a and b) and CO₂-rich (Martian type) atmosphere for Mars (c and d), with flares every one-tenth of a year (36 days, corresponding to 7.2 × 10³¹ erg), one year (corresponding to 7.2 × 10³² erg), spot maximum flare (corresponding to 3.6 × 10³³ erg), and possible maximum flare (corresponding to 1.6 × 10³⁶ erg). In these scenarios, the spot maximum flare is the maximum possible flare observed within decades in the target stellar system (in this case our solar system) estimated based on star spot area of the target star. According to the calculation shown in these figures, the SPEs under the above scenarios do not induce a critical dose at ground level when we have sufficient atmospheric depth such as Earth, even under the possible maximum flare (1.6 × 10³⁶ erg) scenario, whereas it becomes a nearly critical dose on the Martian surface with thinner atmospheric depth when the spot maximum flare (3.6 × 10³³ erg) event occurs.

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The estimated doses under the annual maximum flare and under the spot maximum flare are shown in Tables 2 and 3, respectively. The estimated doses at the TOA on GJ 699 b, Proxima Centauri b, Ross-128 b, and TRAPPIST-1 e under the spot maximum flare (Shibata et al. 2013) become 1.60 × 10² Gy (7.25 Sv), 5.36 × 10⁵ Gy (2.43 × 10⁴ Sv), 7.13 ×10³ Gy (3.23 × 10² Sv), and 2.60 × 10⁵ Gy (1.18 × 10⁴ Sv), respectively.

Figures 7 and 8 illustrate the vertical radiation dose in grays and Sieverts, respectively, for major documented planetary systems, including Proxima Centauri b, Ross-128 b, TRAPPIST-1 e, and Kepler-283 c (the only habitable planet in the Kepler field with observed flares) for possible flares on several different scales, caused by hard proton spectrum (imitating GLE43) penetrating N₂+ O₂–rich (terrestrial type) atmosphere for Earth with flares every one-tenth of a year (36 days), one year (annual), spot maximum, and possible maximum flare. In these scenarios, the spot maximum flare is the maximum possible flare to be observed within decades in the target stellar system. On these planets, the SPE does not reach critical levels with sufficient atmospheric depth (equal to that of the Earth) even for the possible maximum flare scenario, having 1.42 × 10⁻⁴ Gy (1.6 × 10⁻³ Sv) for Proxima Centauri b and 3.70 × 10⁻⁴ Gy (4.14 × 10⁻³ Sv) for Ross-128 b. Proxima Centauri b shows a smaller difference between the possible maximum flare dose and spot maximum flare dose, whereas a larger difference can be found on Ross-128 b, showing that Ross-128b is relatively calm in the range of the same temperature class.

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However, when considering the possible maximum flare, calculated assuming that the whole star is covered by the maximum percentage of star spot (20%, observed from Proxima Centauri's light-curve survey), the estimated radiation dose at the terrestrial lowest atmospheric thickness measured at the summit of Everest (at AD 365 g cm⁻² set in this study) applied to Proxima Centauri b, Ross-128 b, TRAPPIST-1 e, and Kepler-283 c, reaches a fatal dose of 0.36 Gy (3.64 Sv), 0.93 Gy (9.45 Sv), 3.03 Gy (30.8 Sv), and 0.68 Gy (6.89 Sv), respectively.

We calculated the vertical profile of the radiation dose, caused by the proton spectrum similar to the one reconstructed for the GLE43 and Carrington-class events for each planet (GJ-699b, Kepler-283 c, Kepler-1634 b, Proxima Centauri b, Proxima Centauri b, Ross 128 b, TRAPPIST-1 e), with terrestrial-type atmospheric compositions under annual maximum flare and spot maximum flare events, by comparing that of Earth and Mars (see Figures 9 and 10).

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For the evaluation at different atmospheric depths we employed the following four typical atmospheric depth reference layers: TOA is equivalent to ≈0 g cm⁻²; Martian surface atmospheric pressure (MS) is equivalent to 9 g cm⁻²; terrestrial minimum atmospheric pressure, observed at the summit of the Himalayas, is equivalent to 365 g cm⁻² in this study; and (Earth's) ground-level atmospheric pressure is equivalent to 1037 g cm⁻². Possible exoplanetary surface was estimated as one-tenth of the terrestrial surface, equivalent to 103.7 g cm⁻². Note that the value is not identical to the real observation data but to the nearest value employed in the Monte Carlo numerical simulation.

According to these calculations, we can specify the critical dose for each planet, which is presumed in this study to be 10 Sv per annual event (see Section A.1. of the Appendix). Using this threshold, we may determine the minimum requirement of the atmospheric depth for terrestrial-type life-form evolution. According to our analysis, the critical atmospheric depths required to secure terrestrial-type life-form evolution on the surface of each modeled exoplanet exposed by annual severe flare events are 2.77 g cm⁻² for GJ 699 b (Barnard's Star b) (0.267% of terrestrial atmospheric depth), 3.27 × 10² g cm⁻² for Proxima Centauri b (31.6% of terrestrial atmospheric depth), 7.59 × 10 g cm⁻² (7.31%) for Ross 128 b, and 3.06 × 10² g cm⁻² for TRAPPIST-1 e (29.5%) (Figures 9 and 10). We note that without sufficient atmospheric depth, the surface primitive life-forms on those planets suffer from severe radiation doses, even for relatively small-scale flares.

We also performed calculations of the radiation doses for CO₂-rich and H₂-rich atmospheres for each planet (see Figures 11–14). The difference between each atmospheric composition does not become significant especially when compared with the N₂+ O₂– and CO₂-rich types. However, it is evident that H₂-rich atmosphere dissipates higher energetic particles more significantly.

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The presence of a geomagnetic dipole shield around a planet and its relative strength will influence its efficacy for reducing the irradiation effect of any solar flares on surface life-forms. First, we recalculated the surface dose (grays and Sieverts) assuming that all exoplanets (GJ-699 b, Kepler-283 c, Kepler-1634 b, Proxima Centauri b, Ross-128 b, TRAPPIST-1 e in comparison with Earth and Mars) have the same amount of magnetic shield as the Earth (B = B_Earth) (see Figures 15 and 16). Then we evaluated the scenarios with the planetary dipole magnetic field (uniform over the whole planet surface) of (1) 0 (no magnetosphere), (2) 0.1 × B_Earth, (3) 1 × B_Earth (Earth level), and (4) 10 × B_Earth for four documented exoplanets (Proxima Centauri b, Ross-128b, and TRAPPIST-1 e, and Kepler-283 c) (see Figure 17).

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XUV radiation caused by stellar superflares does not significantly increase the annual planetary surface UV flux on the exoplanets modeled unless high stellar magnetically driven events (flares and CMEs) severely damage their atmospheric thickness and impact their chemistry. However, since stellar quiescent XUV radiation induces atmospheric escape from a terrestrial-type planet, a more critical situation may be predicted, that is, the atmospheric depth of those exoplanets can easily reach at least one-tenth of terrestrial atmospheric thickness. The atmospheric escape rate of O⁺/N⁺ ions from Proxima Centauri b, TRAPPIST-1 e, Ross-128b, and Kepler-283 c are, respectively, 76.2, 53.5, 7.92, and 6.82 times stronger than that of the Earth due to higher stellar XUV fluxes incident on the planetary atmospheres caused by closer proximity to their respective host stars according to the equation proposed by Airapetian et al. (2017a).

In such a scenario, the radiation dose at Proxima Centauri b and TRAPPIST-1 e reaches nearly fatal levels for complex life-forms even through the modest annual flares, reaching 1.32 Gy (8.09 Sv) and 1.09 Gy (6.68 Sv), respectively (see Figure 8).

The stellar proton event impact onto different exoplanets has been evaluated assuming three major types of atmosphere (N₂ + O₂, CO₂, H₂). In general, H₂-rich atmosphere, which may be present on either younger Earth-sized exoplanets or super-Earths with relatively larger masses, has a maximum absorption ratio compared with the other two atmospheres. This might be because of the lower molecular weight of hydrogen, which enables larger molecular numbers under the same atmospheric pressure. Under the other two major types of atmosphere (N₂ + O₂, CO₂), there are still significant reduction effects when atmospheric pressure is sufficient as that of the Earth. For TRAPPIST-1 e and Proxima Centauri b, even for annual maximum flare events, the dose becomes relatively large but not at the level that may affect complex life-forms. However, with reduced atmospheric pressure to the level at the top of the terrestrial surface (352 g cm⁻²), observed at the summit of the Himalayas, the dose becomes significantly high. The dose with higher atmospheric depth than the Martian surface, especially in units of Sieverts, has been evaluated to be higher than in previous papers calculated by different approaches with hypothetical stellar flare magnitude (Atri 2017). This may be induced by the difference in definitions of the effective doses, as well as precise numerical evaluation using PHITS (Sato et al. 2018b). This relatively higher dose in Sieverts compared with the unit in grays, calculated at the higher atmospheric depth than Martian surface, is mainly induced by the neutron particle, generated as a secondary cosmic-ray when SEP reaches the atmosphere, as shown in Figures 18 and 19.

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Our conclusion is that, with relevant thickness of atmospheric depth for each type of atmosphere, there will be no significant damage to surface life-forms, except for some critical planets located very close to their stars.

Projected stellar proton events with harder spectra using GLE43 have a deeper penetration of intensive protons toward the terrestrial atmospheric depth, whereas projected stellar proton events with softer spectra using the Carrington flare have a sudden reduction of the dose at the mid altitude of the atmosphere (atmospheric depth between 10¹ and 10² g cm^–2).

By taking a look at Figure 16, most of the critical dose only applies for Proxima Centauri b and TRAPPIST-1 e when the atmospheric depth was lower than that of Martian surface when all exoplanets have the same amount of magnetic shield as Earth (B = B_Earth), except for the scenario with spot maximum flare with proton spectrum imitating GLE43 (b). Each value of the magnetic field may result in a significant dose reduction at the TOA, from (1) 9.37 × 10⁴ Gy (4.24 × 10³ Sv) with no magnetosphere to (3) 1.40 × 10² Gy (2.7 × 10¹ Sv) with Earth-level magnetosphere (1 × B_Earth) almost 1/700 of the dose in grays (1/160 in Sv) that would be received with no protective magnetic field. Also at the ground level, the dose was reduced from (1) 2.49 × 10⁻⁵ Gy (2.79 × 10⁻⁵ Sv) with no magnetosphere, to (3) 3.23 × 10⁻⁶ Gy (3.19 × 10⁻⁵ Sv) with Earth-level magnetosphere (1 × B_Earth) on Proxima Centauri b, almost one-tenth of the dose that would be received with no protective magnetic field. We may consider that, with the presence of magnetic shields, those listed planets all become habitable at least when the minimum amount of atmospheric depth is present.

We also evaluated XUV flux values from stellar flares as follows (see Section A.4. in the Appendix). Here we assume that the UV energy portion is up to 10% of the total flare energy and estimate XUV dose by annual maximum flare. As a result, annual XUV dose values due to stellar flares at the TOA of the target exoplanets are 10⁵ ∼ 10⁶ J m⁻² (see Table 2). They are all smaller than 0.001% of the terrestrial annual UV dose at the TOA (∼4.3 × 10⁹ J m⁻²).

In addition to estimating the flare XUV values, we also roughly evaluate the quiescent component of XUV fluxes from stellar temperature (spectral class) and spot size (see Section A.4. of the Appendix). As a result, the annual total flux of the whole XUV and UV wavelength range (10–4000 Å) at the TOA of all our target exoplanets is smaller than the annual total of the Earth. For example, in the most severe case, Kepler-1634b shows 56% of the Earth values. The impulsive UV doses from annual maximum flares are not significant when compared with the annual dose from steady components. In contrast, the XUV (1–1200 Å) fluxes at the TOA of the target exoplanets have much higher values compared with those at Earth. For example, Proxima Centauri experiences ∼76 times larger annual XUV flux at its TOA compared with Earth's value, while TRAPPIST-1 e has ∼65 times larger flux values. This is because the XUV contribution in the overall UV emission from cool M dwarfs is larger than that for the Sun (Ribas et al. 2017).

Since coronal XUV radiation induces atmospheric escape via photoionization, we can estimate the atmospheric escape rate on Proxima Centauri b, TRAPPIST-1 e, Ross-128b, and Kepler-283 c using the proposed XUV flux escape rate scaling by Airapetian et al. (2017a). In order to estimate these values, we needed to obtain or synthesize the possible XUV flux for those hoststars. In this study, we calculated all XUV fluxes according to the method illustrated in the Appendix. After obtaining the XUV fluxes, we compared them with the atmospheric escape rate from the Earth. The atmospheric escape rates via quiescent XUV emission from Proxima Centauri b, TRAPPIST-1 e, Ross-128b, and Kepler-283 c are, respectively, 76.2, 53.5, 7.92, and 6.82 times stronger than that of the Earth due to the higher XUV fluxes incident on close-in exoplanetary atmospheres. If not enough outgassing for these planets is expected, the assumed atmospheric depths especially for Proxima Centauri b and TRAPPIST-1 e may reach ≤1/10 of the atmospheric pressure on Earth. In such a scenario, the radiation dose on Proxima Centauri b and TRAPPIST-1 e reach nearly fatal levels even through annual flares, reaching 1.32 Gy (8.09 Sv) and 1.09 Gy (6.68 Sv), respectively (see Figures 7 and 8).

The following items are not well characterized in the presented models: (1) the MUSCLES survey provides stellar spectra ranging from XUV to IR based on observed (Chandra and XMM and HST) and empirical estimates. However, the MUSCLES study includes stars earlier than M4 dwarfs (T_eff > 3000 K), and thus there are no relevant data for cooler stars, such as TRAPPIST-1, whose T_eff is almost 2500 K. Our models based on these assumptions should be updated with new observations to be performed in the near future (Airapetian et al. 2019). (2) The correlation between XUV fluxes and star spot sizes, assumed from previous solar observations, is currently only at a hypothetical stage, especially for cool M dwarfs. The specific relationship should be investigated in detail in accordance with photospheric temperature and wavelength. In short, we have to investigate each stellar temperature (spectral class) and planetary body in more detail to clarify those relationships. (3) In general, there are no sufficient observational results about stellar activities especially for active M dwarfs, which should be the focus of future observations. (4) We need to deepen the survey for active M dwarfs when collecting more UV-EUV data, as most stellar objects determined by the MUSCLES survey are not active M dwarfs, except for Proxima Centauri. Moreover, as for Proxima Centauri (Wargelin et al. 2017), the stellar activity may change in accordance with the stellar cycle. (5) We made the first assumption of the ratio for XUV and EUV in this survey, which should be supported and adopted through sufficient observational results. The Mega-MUSCLES project (Froning et al. 2018) will also focus on a survey for TRAPPIST-1, with which we can check the validity of our assumption.

As mentioned above, two types of radiation doses, the absorbed dose in grays and the effective dose in Sieverts, were deduced from the simulation. In general, the absorbed doses are higher than the effective doses at the TOA because lower energy protons, which have a small impact on the human body due to their shorter range, predominantly contribute to the dose at the location. In contrast, the relation is reversed at the ground level because of the contribution of neutrons, which have a more significant impact on the human body and become very important in such deeper locations.

In this study, we need to presume the critical dose for discussing the habitability of a planet. In general, mortality due to radiation exposure is discussed with respect to the absorbed dose throughout the whole body; for example, the whole-body absorbed dose that is lethal for half of the exposed individuals, LD₅₀, is around 4 Gy for photon exposure (International Commission on Radiological Protection, 2007). However, LD₅₀ is expected to be different for cosmic-ray exposure due to higher relative biological effectiveness. In addition, the whole-body absorbed dose depends on the size of the creature; the radiological sensitivities significantly vary with species. Thus, we decided to select the effective dose as an index for discussing habitability because it is the most well-known radiological protection quantity and set the critical dose to 10 Sv per annually occurring stellar proton event.

A single flare event occurs on the stellar surface, and the energy via electromagnetic wave radiates in all directions, whereas during a proton event, the energy has clear directionality. For the SPEs, the release angle of the proton may be limited within a certain angle from the solar equator. We consider that the total area that may be affected by the SPEs can be expressed as

$$\begin{eqnarray}&&{A}_{\mathrm{SPE}}=2\pi {R}_{{\rm{e}}}\times {T}_{{\rm{D}}}\times {H}_{\mathrm{SPE}},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{T}_{{\rm{D}}}=2{R}_{{\rm{e}}}\sin {\theta }_{{\rm{V}}},\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{H}_{\mathrm{SPE}}=\displaystyle \frac{{\theta }_{{\rm{H}}}}{360},\end{eqnarray} \tag{ 6 }$$

in which A_SPE is the total flare affected area in 1 au distance, R_e is Earth's semimajor axis, H_SPE is the ratio of SPE horizontal release angle over the entire orbital circle, θ_V is the vertical release angle of SPEs, and θ_H is the horizontal release angle of SPE (in this study we assume that θ_V and θ_H are equal to 15° and 90°, respectively).

Thus, the expected SPE energy per unit area received at Earth's TOA during a determined period (1 yr) can be expressed as

$$\begin{eqnarray}&&{E}_{{\mathrm{SPE}}_{\mathrm{Earth}}}=\displaystyle \frac{{E}_{\mathrm{flare}}\times {H}_{{\rm{P}}}\times {R}_{\mathrm{SPE}}}{{A}_{\mathrm{SPE}}},\end{eqnarray} \tag{ 7 }$$

in which H_P = θ_H/180 is the horizontal exposure probability (we employ 0.5) and R_SPE is the fraction of SPE energy in total flare energy per year. In this study, we employed 0.25 (Aschwanden et al. 2017).

From the above equation, we may calculate fluence on any exoplanet using the relative proportion to the fluence at Earth's TOA.

In order to apply this comparison with stellar flares, we employed a normalized value based on the GOES X-ray class of the flare events. We can safely assume that total energy of flares can be estimated from the GOES X-ray class (Namekata et al. 2017). Accordingly, we assumed that the total energy of the Carrington-class event (estimated as X45 class) was 4.5 × 10²⁵ Joules and GLE43 (estimated as X13 class) was 1.3 × 10²⁵ Joules.

To integrate the above reference of SPEs, applicable for stellar proton events, the following constants are determined as

$$\begin{eqnarray}&&{E}_{{\mathrm{PE}}_{\mathrm{GLE}43}}=\displaystyle \frac{{E}_{\mathrm{GLE}43}\times {R}_{\mathrm{SPE}}}{{A}_{\mathrm{SPE}}},\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&{E}_{{\mathrm{PE}}_{\mathrm{Car}}}=\displaystyle \frac{{E}_{\mathrm{Car}}\times {R}_{\mathrm{SPE}}}{{A}_{\mathrm{SPE}}},\end{eqnarray} \tag{ 9 }$$

in which E_GLE43 is the total energy of GLE43 (estimated as 1.3 × 10³² [erg] = 1. 3 × 10²⁵ [Joule]) and E_Car is the total energy of a Carrington-class event (estimated as 4.5 × 10³² [erg] = 1. 3 × 10²⁵ [Joule]). Note that coefficient H_P has not been multiplied as it is obvious that those events released SEP toward the Earth.

XUV radiation is considered one type of harmful radiation released from a single stellar flare event. The proportion of XUV radiation in a single flare event has not been fully determined. However, according to Aschwanden et al. (2017), the energetic portion of the UV continuum (with the sum of the ranges 200–228, 370–504, 504–912, 1464–1609, and 1600–1740 Å) is 3.96 × 10²⁹ erg, equivalent to 1.8% of estimated total flare energy (X2.2 class event 2.2 × 10³¹ erg) in a solar flare. In this study, since there are no related studies about the proportion of UV radiation as a function of stellar temperature, diameter, and other factors, we use solar flare results (Aschwanden et al. 2017) as a reference and roughly assume that the UV portion of 10% of total flare energy is the most extreme case. To determine the portion of XUV in the total UV dose of the flare as one extreme case, we assume that 50% of the total UV energy emitted during stellar flare is XUV energy.

When determining normal UV irradiation for each of the exoplanets, since there are no direct observations for most of the target stars, we synthesize the spectra using the published spectra curve from the MUSCLES project (France et al. 2016; Loyd et al. 2016; Youngblood et al. 2016) (using dapt-const-res-sed SED in version 2.2 data set) and applied a similar spectral on the basis of temperature, trying to create an extreme UV case of a similar type to the star. We used the MUSCLES-observed spectra for 13 stars (GJ1214, GJ551 [Proxima Cen], GJ876, GJ436, GJ581, GJ667C, GJ176, GJ832, HD 85512, HD 40307, HD 97658, eps Eridanis, and the Sun) and synthesized the spectra for the target stars (TRAPPIST-1, Ross-128, Kepler-283, Kepler-1634). In the synthesizing process we divide the whole spectra into two, (1) one that is mostly related to the photospheric temperature, applied for IR, VR, and UVA and UVB, in particular for wavelengths longer than 1200 Å; and (2) one that is mostly related to the magnetic activity mainly in the chromosphere, applied for XUV, in particular for the wavelength from 1 to 1200 Å. For (2) we made the hypothesis that the intensity of XUV is in proportion to the star spot area, based on the hypothesis that the star spot area represents the average magnetic field strength of the target star, thus the chromospheric activity level. In this study, because our aim is to evaluate extreme cases under different star systems, we introduce a ratio to specify the weight of each effect. Currently, we set two extreme cases when synthesizing the spectra of the XUV portion, as (1) 100% of the total magnetic flux-related (magnetic) term, generated from observed XUV (GJ551) calculated using the relative portion of the star spot area, and (2) 60% of the magnetic term + 40% of the photosphere temperature-related (photospheric) term. We set 20% of the magnetic term + 80% of the photospheric term when synthesizing the spectra of the EUV portion, while applying the following equation to synthesized fluxes in each wavelength:

$$\begin{eqnarray}&&{F}_{{\rm{I}}}={R}_{{A}_{\mathrm{spotUV}}}\times {F}_{{A}_{\mathrm{spot}}}+(1-{R}_{{A}_{\mathrm{spotUV}}}){F}_{{T}_{\mathrm{eff}}},\end{eqnarray} \tag{ 10 }$$

in which F_I is the UV flux for target stars, ${R}_{{A}_{\mathrm{spotUV}}}$ is the impact ratio of star spot in UV (same for XUV), ${F}_{{A}_{\mathrm{spot}}}$ is the flux calculated from the relative size of the star spot area, normalized by the observed GJ551 (Proxima Cen) star spot area and its UV (XUV) spectra, and ${F}_{{T}_{\mathrm{eff}}}$ is the flux calculated from the photospheric temperature of the star.

For example, when synthesizing a portion of IR, VR, far-FUV, middle-UV, and near-UV for TRAPPIST-1 (2550 K), for the VR, IR region, we employed the spectra of GJ1214 (2935 K) as a proxy for a lower temperature star. The spectra of Ross-128 (3192 K) were computed with GJ876 (3062 K) and GJ436 (3281 K). The spectra of Kepler-283 (4351 K) were calculated using HD 85512 (4305 K) and HD 40307 (4783 K), and the spectra of Kepler-1634 (5474 K) were synthesized with that of eps Eridanis and our Sun. For the chromospheric component (XUV), we synthesized spectra mainly from Proxima Centauri and eps Eridanis, whose XUV components were much higher than that of other stars.

Then we calculated the portion of UV (including XUV and others) and set its value as the radiation boundary from the central star. Irradiance at the top of the atmosphere of each planet can be calculated using normal radiation propagation. Estimating UV energy from stellar flares, we applied the statistical occurrence probability and possible total energy of the flare from each central star. Applying this UV energy ratio and projected planetary position, we calculated the energy at the TOA of each planet. Using the above hypotheses, the most intensive UV and XUV at the TOA induced by annual maximum flares, assuming this portion, were observed on Ross-128 b, reaching 8.75 × 10⁵ J m⁻² for total UV and 4.38 × 10⁵ J m⁻² for XUV (1–1200 Å), followed by Kepler-1634 b with 4.60 × 10⁴ J m⁻², Proxima Centauri b with 1.57 × 10⁴ J m⁻², and TRAPPIST-1 e with 8.24 × 10³ J m⁻², as shown in Table 4. Although all values are largely compared with terrestrial impact values, they are all below 0.001% of the terrestrial annual UV dose at the TOA (estimated as 4.31 × 10⁹ J m⁻², shown in Table 4. Also, by comparing the total dose during annual irradiation, the total value is far below the annual dose for the terrestrial case. The total annual UV (10–4000 Å) dose does not reach the terrestrial level for all of the exoplanets, with the maximum value 0.53 in the terrestrial case of Kepler-1634 b.

At the same time, limiting the dose of XUV (1–1200 Å), most habitable exoplanets have a higher value compared with that of Earth, reaching up to 76 times the value at Proxima Centauri b, followed by TRAPPIST-1 e with 65 times in the (2) calculation, since the XUV portion in the normal irradiation of the Sun is smaller than the observed M dwarf and thus it reflects an annual dose. On TRAPPIST-1 b, c, and d, the XUV portion reaches a significant value of 418, 223, and 112, respectively (as shown in Table 4). When applying the most extreme cases (1), TRAPPIST-1 e becomes the highest, reaching 100 times the value compared with Earth. On TRAPPIST-1 b, c, and d for the (1) calculation, the XUV portion reaches significant values of 644, 344, and 173 times, respectively (as shown in Table 5). They are, however, generally considered as nonhabitable planets in the system. Having relevant atmospheric depth and an ion layer, equivalent to that of the Earth—where most of XUV is absorbed by a factor of 10⁻¹⁵–10⁻²², the irradiation may be absorbed before reaching the planetary surface. The flare impact on the UV dose only becomes important when superflares induce a significant reduction of the ozone layer (Segura et al. 2010) or when they accelerate significant atmospheric escape (Airapetian et al. 2016). Accordingly the atmospheric protection becomes more important for those planets due to higher ratio of normal irradiation of XUV.

Table 4.  UV Energy from Annual Maximum Flare at TOA in Each Planet

Exoplanet	${E}_{\mathrm{UV}}^{\mathrm{flare}}$ a	$\tfrac{{E}_{\mathrm{UV}}^{\mathrm{flare}}}{{E}_{\mathrm{UV},\mathrm{Earth}}^{\mathrm{flare}}}$ b	$\tfrac{{E}_{\mathrm{UV}}^{\mathrm{flare}}}{{E}_{\mathrm{UV},\mathrm{Earth}}^{\mathrm{flux}}}$ c	${E}_{\mathrm{XUV}}^{\mathrm{flare}}$ d	$\tfrac{{E}_{\mathrm{XUV}}^{\mathrm{flare}}}{{E}_{\mathrm{XUV},\mathrm{Earth}}^{\mathrm{flare}}}$ e	$\tfrac{{E}_{\mathrm{XUV}}^{\mathrm{flare}}}{{E}_{\mathrm{XUV},\mathrm{Earth}}^{\mathrm{flux}}}$ f	${E}_{\mathrm{XUV}}^{\mathrm{normal}}$ g
Name	(J m−2)		(%)	(J m−2)		(%)	(J m−2)
GJ 699 b	8.74E+03	7.27E+04	2.59E−06	4.37E+03	7.27E+04	2.51E−02	2.35E+04
Kepler-283 c	4.43E+02	3.69E+03	1.31E−07	2.22E+02	3.69E+03	1.27E−03	1.19E+06
Kepler-1634 b	4.60E+04	3.83E+05	1.37E−05	2.30E+04	3.83E+05	1.32E−01	6.67E+05
Proxima Centauri b	1.57E+04	1.31E+05	4.66E−06	7.86E+03	1.31E+05	4.51E−02	1.33E+07
Ross-128 b	8.75E+04	7.28E+05	2.60E−05	4.38E+04	7.28E+05	2.51E−01	1.38E+06
TRAPPIST-1 b	5.30E+04	4.41E+05	1.57E−05	2.65E+04	4.41E+05	1.52E−01	5.99E+07
TRAPPIST-1 c	2.82E+04	2.35E+05	8.39E−06	1.41E+04	2.35E+05	8.11E−02	3.20E+07
TRAPPIST-1 d	1.42E+04	1.18E+05	4.22E−06	7.12E+03	1.18E+05	4.08E−02	1.61E+07
TRAPPIST-1 e	8.24E+03	6.86E+04	2.45E−06	4.12E+03	6.86E+04	2.37E−02	9.32E+06
TRAPPIST-1 f	4.75E+03	3.96E+04	1.41E−06	2.38E+03	3.96E+04	1.36E−02	5.38E+06
TRAPPIST-1 g	3.22E+03	2.68E+04	9.54E−07	1.61E+03	2.68E+04	9.23E−03	3.64E+06
TRAPPIST-1 h	1.65E+03	1.37E+04	4.89E−07	8.24E+02	1.37E+04	4.73E−03	1.86E+06
Sol d (Earth)	3.70E−01	3.08E+00	1.10E−10	1.85E−01	3.08E+00	1.06E−06	1.74E+05
Sol e (Mars)	1.59E−01	1.33E+00	4.72E−11	7.96E−02	1.33E+00	4.57E−07	7.51E+04
Exoplanet	${E}_{\mathrm{UV}}^{\mathrm{normal}}$ h	${E}_{\mathrm{Visible}}^{\mathrm{normal}}$ i	${E}_{\mathrm{IR}}^{\mathrm{normal}}$ j	${E}_{\mathrm{XUV}}^{\mathrm{flare}+\mathrm{quiescent}}$ k	$\tfrac{{E}_{\mathrm{XUV}}^{\mathrm{flare}+\mathrm{quiescent}}}{{E}_{\mathrm{XUV},\mathrm{Earth}}^{\mathrm{flare}+\mathrm{quiescent}}}$ l	${E}_{\mathrm{UV}}^{\mathrm{flare}+\mathrm{quiescent}}$ m	$\tfrac{{E}_{\mathrm{UV}}^{\mathrm{flare}+\mathrm{quiescent}}}{{E}_{\mathrm{UV},\mathrm{Earth}}^{\mathrm{flare}+\mathrm{quiescent}}}$ n
Name	(J m−2)	(J m−2)	(J m−2)	(J m−2)		(J m−2)l
GJ 699 b	1.65E+06	8.68E+07	7.79E+08	2.79E+04	0.16	1.66E+06	0.00
Kepler-283 c	4.25E+08	1.14E+10	2.83E+10	1.19E+06	6.82	4.25E+08	0.13
Kepler-1634 b	1.79E+09	1.14E+10	1.33E+10	6.90E+05	3.96	1.79E+0.9	0.53
Proxima Centauri b	2.44E+07	8.78E+08	2.74E+10	1.33E+07	76.21	2.44E+07	0.01
Ross-128 b	9.25E+07	5.01E+09	5.81E+10	1.50E+06	8.61	9.25E+07	0.03
TRAPPIST-1 b	2.13E+08	8.97E+09	1.72E+11	7.29E+07	418.36	2.13E+08	0.06
TRAPPIST-1 c	1.14E+08	4.79E+09	9.19E+10	3.89E+07	223.21	1.14E+08	0.03
TRAPPIST-1 d	5.73E+07	2.41E+09	4.63E+10	1.96E+07	112.34	5.73E+07	0.02
TRAPPIST-1 e	3.32E+07	1.40E+09	2.68E+10	1.13E+07	65.07	3.32E+07	0.01
TRAPPIST-1 f	1.91E+07	8.05E+08	1.54E+10	6.54E+06	37.52	1.91E+07	0.01
TRAPPIST-1 g	1.30E+07	5.44E+08	1.05E+10	4.42E+06	25.39	1.30E+07	0.00
TRAPPIST-1 h	6.64E+06	2.79E+08	5.36E+09	2.27E+06	13.01	6.64E+06	0.00
Sol d (Earth)	3.37E+09	1.93E+10	2.04E+10	1.74E+05	1.00	3.37E+09	1.00
Sol e (Mars)	1.45E+09	8.32E+09	8.81E+09	7.51E+04	0.43	1.45E+09	0.43

Notes. TOA ≈ 0 g cm⁻².

^aUV energy by annual maximum flare at TOA. ^bRatio to Earth's annual maximum flare. ^cRatio to Earth's annual UV flux at TOA. ^dXUV energy by annual maximum flare at TOA. ^eRatio to Earth's annual maximum flare. ^fRatio to Earth's annual UV flux at TOA. ^gAnnual XUV energy by normal stellar radiation at TOA. ^hAnnual UV energy by normal stellar radiation at TOA. ⁱAnnual visible ray energy by normal stellar radiation at TOA. ^jAnnual IR energy by normal stellar radiation at TOA. ^kAnnual total (flare + quiescent) XUV energy at TOA. ^lRatio to Earth/annual total (flare + quiescent) XUV energy at TOA. ^mAnnual total (flare + quiescent) UV energy at TOA. ⁿRatio to Earth/annual total (flare + quiescent) UV energy at TOA.

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Table 5.  UV Energy at TOA, with Synthesized Spectra Assuming 100% of the Impact Ratio of Star Spot in Equation (10)

Exoplanet	${E}_{\mathrm{UV}}^{\mathrm{flare}}$ a	$\tfrac{{E}_{\mathrm{UV}}^{\mathrm{flare}}}{{E}_{\mathrm{UV},\mathrm{Earth}}^{\mathrm{flare}}}$ b	$\tfrac{{E}_{\mathrm{UV}}^{\mathrm{flare}}}{{E}_{\mathrm{UV},\mathrm{Earth}}^{\mathrm{flux}}}$ c	${E}_{\mathrm{XUV}}^{\mathrm{flare}}$ d	$\tfrac{{E}_{\mathrm{XUV}}^{\mathrm{flare}}}{{E}_{\mathrm{XUV},\mathrm{Earth}}^{\mathrm{flare}}}$ e	$\tfrac{{E}_{\mathrm{XUV}}^{\mathrm{flare}}}{{E}_{\mathrm{XUV},\mathrm{Earth}}^{\mathrm{flux}}}$ f	${E}_{\mathrm{XUV}}^{\mathrm{normal}}$ g
Name	(J m−2)		(%)	(J m−2)		(%)	(J m−2)
Kepler-283 c	8.24E+03	6.85E+04	2.44E−06	4.12E+03	6.85E+04	2.36E−02	1.01E+05
Kepler-1634 b	4.60E+04	3.83E+05	1.37E−05	2.30E+04	3.83E+05	1.32E−01	7.07E+05
Proxima Centauri b	1.57E+04	1.31E+05	4.66E−06	7.86E+04	1.31E+05	4.51E−02	1.33E+07
Ross-128 b	8.75E+04	7.28E+05	2.60E−05	4.38E+04	7.28E+05	2.51E−01	1.38E+06
TRAPPIST-1 b	5.30E+04	4.41E+05	1.57E−05	2.65E+04	4.41E+05	1.52E−01	1.12E+08
TRAPPIST-1 c	2.83E+04	2.35E+05	8.39E−06	1.41E+04	2.35E+05	8.11E−02	5.99E+07
TRAPPIST-1 d	1.42E+04	1.18E+05	4.22E−06	7.12E+03	1.18E+05	4.08E−02	3.01E+07
TRAPPIST-1 e	8.24E+03	6.86E+04	2.45E−06	4.12E+03	6.86E+04	2.37E−02	1.75E+07
TRAPPIST-1 f	4.75E+03	3.96E+04	1.41E−06	2.38E+03	3.96E+04	1.36E−02	1.01E+07
TRAPPIST-1 g	3.22E+03	2.68E+04	9.54E−07	1.61E+03	2.68E+04	9.23E−03	6.81E+06
TRAPPIST-1 h	1.65E+03	1.37E+04	4.89E−07	8.24E+02	1.37E+04	4.73E−03	3.49E+06
Sol d (Earth)	3.70E−01	3.08E+00	1.10E−10	1.85E−01	3.08E+00	1.06E−06	1.74E+05
Sol e (Mars)	1.60E−01	1.33E+00	4.72E−11	7.96E−02	1.33E+00	4.57E−07	7.51E+04
Exoplanet	${E}_{\mathrm{UV}}^{\mathrm{normal}}$ h	${E}_{\mathrm{Visible}}^{\mathrm{normal}}$ i	${E}_{\mathrm{IR}}^{\mathrm{normal}}$ j	${E}_{\mathrm{XUV}}^{\mathrm{flare}+\mathrm{quiescent}}$ k	$\tfrac{{E}_{\mathrm{XUV}}^{\mathrm{flare}+\mathrm{quiescent}}}{{E}_{\mathrm{XUV},\mathrm{Earth}}^{\mathrm{flare}+\mathrm{quiescent}}}$ l	${E}_{\mathrm{UV}}^{\mathrm{flare}+\mathrm{quiescent}}$ m	$\tfrac{{E}_{\mathrm{UV}}^{\mathrm{flare}+\mathrm{quiescent}}}{{E}_{\mathrm{UV},\mathrm{Earth}}^{\mathrm{flare}+\mathrm{quiescent}}}$ n
Name	(J m−2)	(J m−2)	(J m−2)	(J m−2)		(J m−2)
Kepler-283 c	1.96E+09	1.12E+10	1.19E+10	1.05E+05	0.60	1.96E+09	0.58
Kepler-1634 b	1.90E+09	1.21E+10	1.41E+10	7.30E+03	4.19	1.90E+0.9	0.56
Proxima Centauri b	2.44E+07	8.78E+08	2.74E+10	1.33E+07	76.21	2.44E+07	0.01
Ross-128 b	9.24E+07	5.01E+09	5.81E+10	1.42E+06	8.17	9.25E+07	0.03
TRAPPIST-1 b	2.53E+08	8.97E+09	1.72E+11	1.12E+08	644.10	2.53E+08	0.07
TRAPPIST-1 c	1.35E+08	4.79E+09	9.19E+10	5.99E+07	343.66	1.35E+08	0.04
TRAPPIST-1 d	6.79E+07	2.41E+09	4.63E+10	3.01E+07	172.95	6.79E+07	0.02
TRAPPIST-1 e	3.93E+07	1.40E+09	2.68E+10	1.75E+07	100.19	3.97E+07	0.01
TRAPPIST-1 f	2.27E+07	8.04E+08	1.54E+10	1.01E+07	57.76	2.27E+07	0.01
TRAPPIST-1 g	1.53E+07	5.44E+08	1.05E+10	6.81E+06	39.09	1.53E+07	0.00
TRAPPIST-1 h	7.86E+06	2.79E+08	5.36E+09	3.49E+06	20.03	7.86E+06	0.00
Sol d (Earth)	3.37E+09	1.93E+10	2.04E+10	1.74E+05	1.00	3.37E+09	1.00
Sol e (Mars)	1.45E+09	8.32E+09	8.81E+09	750E+04	0.43	1.45E+09	0.43

Notes. TOA ≈ 0 g cm⁻².

^aUV energy by annual maximum flare at TOA. ^bRatio to Earth's annual maximum flare. ^cRatio to Earth's annual UV flux at TOA. ^dXUV energy by annual maximum flare at TOA. ^eRatio to Earth's annual maximum flare. ^fRatio to Earth's annual UV flux at TOA. ^gAnnual XUV energy by normal stellar radiation at TOA. ^hAnnual UV energy by normal stellar radiation at TOA. ⁱAnnual visible ray energy by normal stellar radiation at TOA. ^jAnnual IR energy by normal stellar radiation at TOA. ^kAnnual total (flare + quiescent) XUV energy at TOA. ^lRatio to Earth/annual total (flare + quiescent) XUV energy at TOA. ^mAnnual total (flare + quiescent) UV energy at TOA. ⁿRatio to Earth of annual total (flare + quiescent) UV energy at TOA.

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