A Proxy for Stellar Extreme Ultraviolet Fluxes

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UV wavelength upper longer and exopl and EUV is the Furthermore, planets radiation. shaping giant (EUV) from factor escape important Atmospheric formation. an planet is escape Atmospheric date Accepted / date Received 2 1 aoaoyfrAmshrcadSaePyis nvriyo University Physics, Space and Atmospheric for Laboratory pc eerhIsiue utinAaeyo cecs Sc Sciences, of Academy e-mail: Austrian Institute, Research Space Ca ii & ie.Tesaigrltosaebsdo olcinof collection a on based are relations scaling The lines. H&K ii [email protected] lrvoe:sas–Paesadstlie:amshrs– atmospheres satellites: and Planets – stars Ultraviolet: & tla ciiyprmtr rx o stellar for proxy a parameter: activity stellar H&K .G Sreejith G. A. R HK ′ ciiyprmtrta scmol bandfo ground-b from obtained commonly is that parameter activity aucitn.main no. manuscript xrm lrvoe Fluxes Ultraviolet Extreme 1 .Fossati L. , 1 .Youngblood A. , ABSTRACT 4 K, 4; e rvnpiaiyb h tla -a n extreme-ultravio and X-ray stellar the by primarily driven c en o nern U ue rmfaue observable features from fluxes EUV inferring for means ect rdcigteEVeiso fF,G,K,adM-type and K-, G-, F-, of emission EUV the predicting r auswt nacrc faottre hc sslightly is which three, about of accuracy an with values x rdnmcly edn oms os o lsia hot classical orde the For of 10 are loss. of rates mass-loss mass HD209458b), (e.g., to Jupiters leading drodynamically, thsasalrasrto rs-eto nahydrogen- and a in emission cross-section EUV absorption the smaller than a intense has or less it an X-ray typically magnitude with is the telescopes emission of than stellar space directly X-ray few other to the a stars capabilities, are possible for adequate there not emission Although with is stellar Sun. medium EUV it facility interstellar the stars, observe and observational farther 2019) for Because an al. absorption planet. of et the (France lack irradiating capabilities flux the quanti XUV to of of necessary is amount atmo- it the rates, upper relevant mass-loss planetary infer the of and 2010; theoretically spheres 2018; conditions extract to al. physical to and/or et the Haswell observations however, estimate Désert al. the 2016), & et al. from Ehrenreich Bourrier et al. 2020) information (e.g., al. Linsky et others et Salz Cubillos many 2011; 2015; 2019; for al. 2012; et predicted Sing 2010; and 2018; al. al. et et al. Ehrenreich Mansfield et Vidal-Madjar al. al. (e.g., 2012; et et Fossati Etangs exoplanets des Lecavelier close-in few 2003; a for 2017). al. (e.g., et planets Cubillos low-gravity 2016; 2008 for al. al. or et et Lammer 2018b; 2018b), Penz for al. (e.g., al. or et stars 2020), et Kubyshkina al. Fossati active et young, (e.g., Mitani orbiting 2019; planets stars Schneider & hot Muñoz García orbiting planets for t rifrne rmhg-ult a-lrvoe (FUV) far-ultraviolet high-quality from inferences or nts p n hmsr,teeoe eed norknowledge our on depends therefore, chemistry, and ape ntpplto n ec rvsorudrtnigof understanding our drives hence and population anet meltas ,84 rz Austria Graz, 8042 6, hmiedlstrasse eosre o oesas oto h U ag is range EUV the of most stars, some for observed be ooao C 0,Budr O 00,USA 80309, CO, Boulder, 600, UCB Colorado, f aito oe ieulbimceityi h middle the in chemistry disequilibrium power radiation blte n,frtemr itn tr,t interstellar to stars, distant more the for and, abilities topei saehsbe ietyobserved directly been has escape Atmospheric measurements. 9 bu 0 erysaswt ulse log published with stars nearby 100 about 2 − .France K. , 10 lntsa neatos–Sas ciiy–Stars: – activity Stars: – interactions Planet-star s g − 1 u hycnbcm infiatylarger significantly become can they but , 2 n .Ambily S. and , sdotclosrain fthe of observations optical ased ril ubr ae1o 10 of 1 page number, Article 2 R EO2020 ©ESO HK ′ and let der fy r ; A&A proofs: manuscript no. main dominated atmosphere (e.g., Cecchi-Pestellini et al. 2009; disadvantage of forming mostly in the chromosphere, hence Sanz-Forcada et al. 2011; Tu et al. 2015), making the X- at lower temperatures compared to the typical formation ray fluxes alone inadequate to constrain upper atmospheres temperature of the EUV stellar emission. A large number of ′ and escape. studies have and continue to make use of the log RHK index, Several methods and scaling relations have been de- which has its roots in the Mount Wilson S-index (SMW), to vised to estimate stellar XUV fluxes from proxies observ- study stellar activity (e.g., Wilson 1978; Noyes et al. 1984; able at longer/shorter wavelengths, such as X-ray and Duncan et al. 1991; Baliunas et al. 1995). In this work, we obtain scaling relations enabling one to infer EUV fluxes ultraviolet (UV) fluxes (e.g., Sanz-Forcada et al. 2011; ′ Linsky et al. 2014; Chadney et al. 2015; Louden et al. for M-, K-, G-, and F-type stars directly from the log RHK 2017; France et al. 2018). For example, Linsky et al. (2014) index. This allows one to infer in a simple, direct way the derived a correlation between EUV and Lyα emission fluxes EUV emission of a large number of late-type stars without to use observations of the Lyα line to infer stellar XUV the need for high-quality space-based observations. fluxes in different bands. In their work, Linsky et al. (2014) This paper is organised as follows. Section 2 presents employed a mixture of EUV spectra measured in the past the considered sample of stars employed to derive ′ − for a few nearby stars by the EUVE satellite and solar spec- the log RHK EUV correlation. Section 3 presents the ′ − tral synthesis computations. Linsky et al. (2013) further de- log RHK EUV correlation, while we discuss the results and rived similar correlations between the fluxes of the Lyα line gather the conclusions of this work in Section 4. and several emission features in the ultraviolet (Cii, Civ, Oi, Mgii h&k lines) and optical (Ca ii H&K lines) bands. 2. Stellar sample and stellar parameters However, these scaling relations require either reconstruct- ing the Lyα line, whose core is typically heavily absorbed by We started from considering the stars comprising the sam- the interstellar medium, employing two scaling relations to ple of France et al. (2018), 104 F-, G-, K-, and M-type stars derive the stellar XUV fluxes from emission lines other than lying within about 50 pc. For each star, France et al. (2018) Lyα. More recently, France et al. (2018) followed the same estimated the EUV emission flux in the 90-360 Å wave- strategy of Linsky et al. (2014) by deriving a correlation length range on the basis of FUV observations, in particular between EUV emission fluxes in two bands (i.e., 90–360 Å of the Nv and Siiv lines, and the stellar bolometric flux at and 90–911 Å) and lines in the far-ultraviolet (Nv and Siiv) Earth (Fbol). These EUV estimates have accuracy about for which high-quality spectra had been collected with the a factor of 2 and are based on relationships between the Hubble Space Telescope. The advantage of the relation of fractional FUV emission line luminosity and the fractional France et al. (2018) over that of Linsky et al. (2013, 2014) EUV luminosity they obtained from moderate-to-high qual- is the larger sample and the use of lines forming at tem- ity EUV spectra in the 90–360Å wavelength range collected peratures closer to that of the EUV formation temperature by the EUVE satellite. range. Other works have reconstructed stellar EUV spectra For each star in the sample of France et al. (2018), we collected from the literature measurements of by scaling the solar UV spectrum to match measurements ′ of high-energy far-ultraviolet (FUV) emission lines (e.g., the log RHK activity parameter and retained only Fossati et al. 2015, 2018a). FUV and X-ray measurements the stars for which we found at least one mea- have also been combined via the differential emission measurement (Isaacson & Fischer 2010; Boro Saikia et al. sure (e.g., Louden et al. 2017) or by scaling the observed 2018; Jenkins et al. 2011, 2006; Caillault et al. 1991; XUV fluxes of nearby stars (e.g., Chadney et al. 2015). Mamajek & Hillenbrand 2008; Gray et al. 2006, 2003; Moutou et al. 2014; Arriagada 2011; Robertson et al. 2012; All of these EUV estimation methods require space- Anderson et al. 2014; Wittenmyer et al. 2009; Laws et al. based observations at FUV and/or X-ray wavelengths, 2003; Henry et al. 1996; Canto Martins et al. 2011; Pace which are not straightforward to obtain, particularly for 2013; Astudillo-Defru et al. 2017; Hinkel et al. 2017; large samples of stars. One way around this problem Ment et al. 2018; Wright et al. 2004; Hall et al. 2009; is to employ the stellar rotation rate as a proxy for ′ Morris et al. 2017). The total number of collected log RHK activity, hence XUV emission, of late-type stars (e.g., measurements is 498. The distribution of the median Johnstone et al. 2015; Tu et al. 2015), but this method is log R′ values used in this work is shown in Figure 1. The less accurate than those based on the direct measurement HK ′ distribution appears to be bimodal, with peaks at log RHK of chromospheric and/or coronal emission and it has never values of about −5.0 and −4.5, and hence it is similar to the been empirically verified, except for Sun-like stars (e.g., ′ overall distribution of log RHK values of stars in the solar Ribas et al. 2005). Furthermore, in some cases, this method neighbourhood (e.g., Vaughan & Preston 1980; Gray et al. may lead to wrong answers, such as for the planet-hosting 2003). star WASP-18, which is a fast rotator, but has an extremely ′ For each star, we identified and removed outlier log RHK low activity level that is believed to be dampened by tidal values by employing a two-step approach. First, we removed interactions with the massive close-in planet (Fossati et al. ′ all log RHK values lower than −5.1 (total of 28 removed 2018a). measurements for 17 different stars of spectral type G, K, We employ here the stellar sample of France et al. log R′ ′ and M), which is the minimum HK value (i.e., usu- (2018) to derive the correlation between the log RHK stellar ally called “basal level”) possible for main sequence late- activity index and EUV fluxes in the 90–911 Å wavelength type stars (Wright et al. 2004). However, we remark that ′ range. The log RHK index is a measure of the stellar chromo- the sample of Wright et al. (2004) was composed mostly spheric emission flux at the core of the deep Ca ii H&K ab- of F-, G-, and K-type stars and that several M dwarfs ′ sorption lines (∼3933 and ∼3968 Å), which has the advan- present log RHK values below the basal level of −5.1 (e.g., tage of lying in the optical band and therefore of being eas- Astudillo-Defru et al. 2017), which may be due to the fact ′ ily observable from the ground. However, log RHK has the that Astudillo-Defru et al. (2017) focused on planet-hosting Article number, page 2 of 10 A. G. Sreejith et al.: Ca ii H&K stellar activity parameter: a proxy for stellar Extreme Ultraviolet Fluxes stars that are typically inactive because of selection biases and/or that M-type stars may have a basal level different from that of hotter solar-like stars. Then, we excluded ′ further outliers by identifying the log RHK values deviating more than three times the median absolute deviation (MAD) from the median value. We then calculated the aver- ′ age and median from the remaining log RHK measurements (Table 2). Figure 1 presents the distribution of median ′ log RHK values obtained for each star following the removal of the outliers and compares it with the original distribution. It shows that the removal of the outliers has not significantly modified the underlying distribution, which remains bimodal. We confirmed the bimodality of the distribution by fitting it employing a double-peaked Gaussian (shown in Fig. 1) and by running a Kolmogorov-Smirnov test on the two resultant Gaussian distributions obtaining at high ′ significance that they are indeed drawn from distinct sam- Fig. 2. Standard deviation obtained from the log RHK values ples. Furthermore, because of the close distance of the stars collected from the literature following outlier removal as a func- ′ ′ tion of the median log RHK value. Black dots are for F-, G-, and in our sample, the log RHK values are not systematically depressed by interstellar medium absorption (Fossati et al. K-type stars, while blue open squares are for M-type stars. The dashed red line indicates the median standard deviation that we 2017b). This process led to a sample comprising 96 stars. ′ adopt as uncertainty on the log RHK value for stars for which ′ only one log RHK measurement is available.

Figure 3 presents the distribution of the median ′ log RHK values as a function of stellar effective temperature (Teff ) obtained from Gaia DR2 catalogue (Gaia Collaboration et al. 2018). Stellar temperature values from France et al. (2018) were retained for stars where temperature information was absent in the Gaia DR2 catalogue. This plot further shows the uncertainty and the minimum and maximum values associated with each point. As expected, following the outlier removal based on the ′ MAD, for most stars the median log RHK value lies roughly in the middle between the minimum and maximum values. The majority of the stars are G-type, but also M- and late F-type are well represented, though early and mid K-type ′ Fig. 1. Distribution of the median log RHK values for all stars stars are sparsely represented. considered in this work before (blue shaded; 99 stars, 5 stars ′ For each considered star, we updated Teff , the stellar from our initial sample had no log RHK values in the literature) distance (d), and stellar radius, hence the bolometric flux and after (hatched; 96 stars) outliers removal, namely following at Earth, using the values given in the Gaia DR2 catalogue removal of the values lying below the basal level and following (Gaia Collaboration et al. 2018). The stellar radii were up- the sigma clipping based on the MAD. The black solid line shows ′ dated using the Gaia stellar magnitudes, effective temper- the double Gaussian fit to the log RHK distribution obtained following outliers removal. atures, and distances as follows 2 Teff,sun dstar msun−mstar 5 ′ Rstar = Rsun 2 10 , (1) Figure 2 presents the standard deviation of the log RHK Teff,star dsun values for each star, following the removal of the outliers, ′ as a function of the median log RHK value. Except for one where Rstar is the stellar radius, Rsun is the solar radius, star, HD 106516, the standard deviation is smaller than 0.1 Teff,sun is the solar effective temperature (5777 K), Teff,star and the median value of the standard deviation is about is the stellar effective temperature, dstar is the distance to 0.04. Since the scatter on the standard deviation does not the star, dsun is the distance to the Sun, msun is the so- ′ increase with increasing log RHK value, the scatter is most lar apparent V -band magnitude (−26.73), and mstar is the likely driven by measurement uncertainties, rather than by apparent stellar V -band magnitude. This equation assumes stellar variability. Therefore, for each star, we took the stan- that the stellar apparent magnitude is not affected by in- dard deviation as the uncertainty on the median log R′ terstellar extinction, which we assume to be the case given HK′ value and, for the stars with only one measured log RHK the close distance to the stars in our sample. value, we considered the median value of the standard de- Our reference sample of stars is that of France et al. viation (i.e., ∼0.04) as the uncertainty on the measured (2018), which is also our source for the stellar EUV fluxes ′ ′ log RHK value. By taking the median log RHK value, we at Earth. However, for most stars, we updated both Teff mitigate the effects on the results of intrinsic stellar vari- and radius, hence bolometric fluxes at Earth. For this rea- ′ ability and non-simultaneity of the log RHK and EUV mea- son, except for the stars for which the EUV flux originates surements. from EUVE observations, we employed the scaling relations

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Table 1. Parameters of the linear correlation between stellar ′ activity index (log RHK) and EUV flux in the 90−911 Å wavelength range described by Eq. (2). Column four gives the root mean square (RMS) of the correlation, while column five gives that Pearson correlation coefficients (PCC).

Sp. Type c1 c2 RMS PCC F, G, K 1.90 ± 0.41 3.90 ± 1.96 0.40 0.8748 M 1.20 ± 0.36 2.23 ± 1.64 0.48 0.8753

3. Results Figure 5 shows the stellar EUV flux as a function of the me- ′ dian log RHK value for the stars in our sample and the best linear fit through these points. The linear fit was achieved

′ with a minimized chi-square approach accounting for the Fig. 3. Median log RHK values following outliers removal as a ′ uncertainties on both EUV fluxes and log RHK values. To function of stellar effective temperature. Black dots are for F- improve the robustness of the fits, we employed an iterative , G-, K-type stars and blue open squares are for M-type stars. ′ sigma clipping algorithm, in which we iteratively removed The red error bars indicate the standard deviation of the log RHK measurements, while the grey error bars indicate the minimum from the fit stars deviating more than 1.5 times the root ′ and maximum log RHK values collected from the literature and mean square (RMS) value. We ran separate fits for stars be- ′ longing to different spectral types obtaining that the EUV following outliers removal. For stars with a single log RHK mea- ′ surement, the standard deviation is the median value of the stan- flux vs log RHK value correlation is comparable for F-, G-, dard deviation obtained for all stars in the sample and shown and K-type stars, hence we considered all of them for the by the red dashed line in Figure 2. joint fit, but the M-type stars appear to follow a different scaling relation. However, we remark that M dwarfs later than M3.5 are fully convective and may not behave like the earlier M dwarfs in terms of chromospheric and coronal emission, but the too small sample does not allow us to identify statistically significant differences when performing separate fits. We find that the correlation between the stellar activity ′ index (log RHK) and the EUV flux in the 90−911 Å wavelength range can be described by a linear fit of the form

′ log10 (EUV (90 − 911)/Fbol)= c1 × log RHK + c2 , (2)

where the c1 and c2 coefficients are listed in Table 1. We further compute the Pearson correlation coefficients (PCC) ′ for log RHK vs log(EUV/Fbol), obtaining that the linear correlations are indeed significant (see values in Table 1). The results indicate that the correlation for F-, G-, and K-type stars is significantly steeper than that for M-type stars, which is in agreement with what has been previ- Fig. 4. The difference in EUV flux at Earth values in the 90– ously found (see e.g., Linsky et al. 2013, 2014; France et al. 360 Å wavelength range between those given by France et al. (2018) and those obtained employing the scaling relation in 2018). These results indicate also that our scaling relations France et al. (2018, Eq. (4)-(6)) provide EUV fluxes with an accuracy of about a factor of and the stellar parameters derived from the GAIA DR2 three, which is slightly higher than that of other similar catalogue. The median difference is about 2% (red dashed methods based on FUV or X-ray measurements. The scat- line). Except for stars with low EUV fluxes (below ter present in the line fits has the largest contribution to 2 × 10−14 erg cm−2 s−1) the difference is within 10%. the uncertainties in the EUV flux estimates.

4. Discussion and conclusion ′ of France et al. (2018, their Equations (4), (5), and (6)) We presented here a linear correlation between the log RHK and their Nv flux measurements to update the stellar EUV stellar activity index and the EUV flux emitted by late-type fluxes that are listed in Table 2. For the stars without a Nv stars in the 90−911 Å wavelength range, which is responsi- flux measurement, we employed the Siiv flux measurement. ble for most of the heating in upper planetary atmospheres. Figure 4 shows the difference between the EUV fluxes given This correlation enables one to convert the chromospheric by France et al. (2018) and those we obtained following the emission at the core of the Ca ii H&K lines, parameterised ′ update of the bolometric fluxes at Earth. The median dif- by the log RHK value and measurable from the ground, into ference is about 2% and, for most stars, the difference lies stellar high-energy emission that can then be used to esti- within 10%. mate for example exoplanetary atmospheric mass-loss rates.

Article number, page 4 of 10 A. G. Sreejith et al.: Ca ii H&K stellar activity parameter: a proxy for stellar Extreme Ultraviolet Fluxes

′ Fig. 5. Correlation between the stellar activity index (log RHK) and EUV flux for F-, G-, K-type stars (left; black dots) and M-type stars (right; blue open squares). The RMS on log(EUV/Fbol) after the fit for F-, G-, K-type stars and for M-type stars is 0.40 and 0.48, respectively. The stars removed as a result of the sigma clipping (see text) are indicated by the asterisks. The grey areas indicate the uncertainties on the fits.

′ ′ Fig. 6. Correlation between EUV and log RHK activity parameter following the conversion of log RHK value into Ca ii H&K chromospheric emission fluxes and the scaling relations of Linsky et al. (2013) and Linsky et al. (2014) for F- (red), G- (green), K- (blue), and M-type (magenta) stars. The black line and grey shaded area are the linear fits obtained for F-, G-, K-type stars (left) and for M-type stars (right) and shown in Figure 5. The black dots (left) and blue open squares (right) indicate the position of the stars in common between Linsky et al. (2014) and our sample where log(EUV/Fbol) are from Linsky et al. (2014). For inactive ′ stars, deriving the EUV fluxes from the log RHK values employing the scaling relations of Linsky et al. (2013) and Linsky et al. (2014) leads to overestimations of about one order of magnitude.

Before this work, one could have also combined the is the stellar radius in cm, and AU is one astronomical scaling relations published by Linsky et al. (2013) and unit in cm. The exponent p in Equation (3) is equal to Linsky et al. (2014) to convert the chromospheric emission 7.49 − 2.06 (B − V ) for main sequence stars with 0.44 ≤ at the line core into EUV fluxes, though this would have B − V < 1.28 and is equal to 6.19 − 1.04 (B − V ) for main ′ ii implied first converting the log RHK value into Ca H&K sequence stars with 1.28 ≤ B − V < 1.60 (Mittag et al. chromospheric emission and then passing through the es- 2013), while the SMW index is defined as timation of the Lyα fluxes. Therefore we compared the ′ p ′ log RHK 10 log R vs EUV fluxes obtained following that approach 10 + σT 4 HK S = eff , as well as this work’s method presented in Section 3. To MW −4 (4) ′ 1.34 × 10 Ccf this end, we first converted the log RHK values into disk- −2 −1 integrated chromospheric emission flux in erg cm s fol- where Ccf is (Rutten 1984) lowing Fossati et al. (2017b) and Sreejith et al. (2019). In 3 2 short, the disk-integrated Ca ii H&K chromospheric line log10 Ccf =0.25 (B−V ) −1.33 (B−V ) +0.43 (B−V )+0.24 . emission at a distance of 1 AU ( FHK(1 AU)) is (see Sect. 2 (5) of Fossati et al. 2017b) The parameters employed to derive FHK(1 AU) are listed 8.25−1.67 (B−V ) p 2 (SMW 10 − 10 ) R in Table 2 and the B − V values have been obtained from F (1AU)= star , (3) 1 HK AU 2 the stellar effective temperature by interpolating Table 5 of Pecaut & Mamajek (2013). where SMW is the S-index activity indicator in the Mount- 1 Wilson system (Noyes et al. 1984; Mittag et al. 2013), Rstar See also http://www.pas.rochester.edu/∼emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt .

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′ We then set an array of log RHK values, converted them to FHK(1 AU) as described above, and used the scaling relations of Linsky et al. (2013) to obtain the Lyα fluxes, which we then further converted into EUV fluxes in the 100 to 912 Å range employing the scaling relations of Linsky et al. (2014). We followed this procedure separately considering F5, G5, K5, and M0 stars. Figure 6 shows a com- ′ parison between the EUV−log RHK correlations obtained combining the scaling relations of Linsky et al. (2013) and Linsky et al. (2014) and the two linear fits derived in this work, including the uncertainties on the fits. We find that our fit for F-, G-, K-, M-type stars is significantly steeper than that obtained by combining the scaling relations of Linsky et al. (2013) and Linsky et al. (2014). For active stars, the two correlations lead to comparable results, while, as a consequence of the different slopes, difference of up to about 1.5 orders of magnitude can be observed for inactive F-, G-, K-type stars and of the order of less than one magnitude in the case of inactive M-type stars. We also followed the original formalism described by Noyes et al. ′ (1984) to compute FHK(1 AU) from the log RHK values obtaining no significant differences from the results described above. In an attempt to understand the origin of these differ- Fig. 7. Comparison between Ca ii H&K chromospheric emission ences, we took from Linsky et al. (2014) the EUV fluxes of ′ the stars that are in common with our sample and plot their flux at 1 AU calculated from log RHK employing the method described in section 4 and that used in Linsky et al. (2013). The position in Figure 6, obtaining that they follow our EUV vs ′ red dashed line represents the linear relation. We observe that log RHK fits. To further trace the origin of this difference, the method described in Section 4 over estimates the Ca ii H&K we compared the Ca ii H&K chromospheric emission flux at ′ chromospheric emission flux as compared to those provided in 1 AU calculated from log RHK using the method described Linsky et al. (2013). above and the values given by Linsky et al. (2013, their Ta- ble 4). The comparison is shown in Figure 7. Indeed, Equa- tion (3) appears to overestimate the Ca ii H&K chromospheric emission flux at 1 AU, particularly for the less active Arriagada, P. 2011, ApJ, 734, 70 stars. This further comparison suggests that the difference Astudillo-Defru, N., Delfosse, X., Bonfils, X., et al. 2017, A&A, 600, A13 may be due to the fact that Equation (3) does not account Baliunas, S. L., Donahue, R. A., Soon, W. H., et al. 1995, ApJ, 438, for the extra chromospheric emission flux falling outside 269 of the band employed to measure SMW values, and hence Boro Saikia, S., Marvin, C. J., Jeffers, S. V., et al. 2018, A&A, 616, log R′ values (Hartmann et al. 1984). In other words, the A108 HK ′ Bourrier, V., Lecavelier des Etangs, A., Ehrenreich, D., et al. 2018, wavelength bands considered for estimating the log RHK A&A, 620, A147 values and the FHK(1 AU) values employed by Linsky et al. Caillault, J.-P., Vilhu, O., & Linsky, J. L. 1991, ApJ, 383, 594 (2013) are different. Therefore deriving FHK(1 AU) from the Canto Martins, B. L., Das Chagas, M. L., Alves, S., et al. 2011, A&A, ′ 530, A73 log RHK value and then employing the Linsky et al. (2013) and Linsky et al. (2014) scaling relations may significantly Cecchi-Pestellini, C., Ciaravella, A., Micela, G., & Penz, T. 2009, A&A, 496, 863 overestimate the EUV fluxes, and hence our Equation (2) Chadney, J. M., Galand, M., Unruh, Y. C., Koskinen, T. T., & Sanz- shall be used, instead. Our results can be therefore used to Forcada, J. 2015, Icarus, 250, 357 estimate wavelength-integrated stellar EUV fluxes for stars Cubillos, P., Erkaev, N. V., Juvan, I., et al. 2017, MNRAS, 466, 1868 for which X-ray or FUV observations are either not avail- Cubillos, P. E., Fossati, L., Koskinen, T., et al. 2020, AJ, 159, 111 Duncan, D. K., Vaughan, A. H., Wilson, O. C., et al. 1991, ApJS, 76, able or not possible, hence enabling one to more accurately 383 study, for example, the upper atmospheres of planets or- Ehrenreich, D., Bourrier, V., Wheatley, P. J., et al. 2015, Nature, 522, biting late-type stars and their interaction with the host 459 star. Ehrenreich, D. & Désert, J. M. 2011, A&A, 529, A136 Fossati, L., Erkaev, N. V., Lammer, H., et al. 2017a, A&A, 598, A90 Acknowledgements. A.G.S. and L.F. acknowledge financial support Fossati, L., France, K., Koskinen, T., et al. 2015, ApJ, 815, 118 from the Austrian Forschungsförderungsgesellschaft FFG project Fossati, L., Haswell, C. 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Article number, page 7 of 10 A&A proofs: manuscript no. main ) ) are bol bol 3.47 1.23 0.97 0.89 0.90 1.01 0.99 0.96 0.96 1.00 0.91 1.01 1.04 1.02 0.98 0.99 1.03 1.01 0.97 0.90 0.87 0.90 2.98 1.12 1.06 0.99 0.98 0.99 0.95 1.03 0.99 1.22 0.95 0.89 1.03 0.95 0.94 0.99 0.96 0.96 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 2 − 911Å) log (EUV/F erg − cm 14 1 − − s EUV (90 2 − erg 10 cm 7 bol − 1 F 1.157 29.63 -5.59 0.7084.4400.5230.465 286.836.359 1015.141.7200.398 4.993.633 -4.39 8.730.999 249.42 -4.64 0.340 72.331.938 6.241.498 -6.02 586.130.363 -5.73 -5.41 49.880.246 -5.38 2.490.585 14.970.253 -5.80 -4.79 29.930.303 -5.30 6.240.208 8.730.758 -6.13 -6.11 6.244.824 -5.70 8.73 99.771.540 -5.76 132.190.251 -5.45 187.06 1067.602.676 -5.97 0.328 -5.46 -4.48 1031.040.376 -4.20 1285.210.268 -4.61 -4.66 0.685 42.40 8.73 -4.17 2.418 6.24 -3.29 0.919 13.720.636 -5.80 3.870.6160.235 -5.57 44.901.185 -5.78 27.34 -5.29 1.963 31.180.233 -6.25 224.480.209 -5.73 2.490.196 59.86 -5.53 158.38 -5.31 -4.44 4.99 8.73 -5.97 -5.30 7.48 -5.09 -5.67 -5.38 -5.42 − 197.432 5495.00 -5.56 275.053 4553.00 -5.78 10 s values, and EUV fluxes. The stellar bolometric fluxes (F ′ HK R log ′ HK R log -4.39-4.69 -4.39-4.72 -4.69-4.53 0.038 -4.71-4.89 0.083 -4.53-4.96 1 0.055 -4.88-4.66 2 0.038 -4.97-4.87 8 0.065 -4.67-4.35 1 0.053 -4.87-4.39 5 0.048 -4.35-4.88 6 0.053 -4.39-5.01 3 0.038 -4.88-4.91 4 0.187 -4.99-4.89 2 0.075 -4.91-4.92 4 0.059 -4.89-4.97 2 0.050 -4.92-4.98 7 0.060 -4.97-4.58 4 0.029 -4.98-4.42 2 0.089 -4.58-4.38 4 0.044 -4.42-4.42 8 0.038 -4.38-5.00 4 0.060 -4.42-4.34 1 0.019 -5.00-4.10 4 0.024 -4.35-4.97 4 0.029 -4.11-4.92 6 0.045 -4.98 10 -4.87 0.062 -4.95-4.78 6 0.062 -4.87-4.80 7 0.092 -4.80-5.00 6 0.044 -4.80-5.01 5 0.086 -5.00-5.00 4 0.038 -5.02-5.00 5 0.043 -5.00-4.36 5 0.039 -5.00-4.88 8 0.029 -4.36-4.99 3 0.034 -4.90 10 -4.57 0.017 -5.01-4.94 7 0.029 -4.57-5.02 5 0.028 -4.93-5.02 5 0.082 -5.02 3 0.050 -5.01 4 0.038 4 0.057 6 4 mean median stddev # d pc -type, their basic parameters, ∗ sun R eff mag mag K R SpT V B-V T F2VF5VF7V 6.48F7V 0.37F7V 0.44 4.49F9V 0.42 6.81 6502F9V 0.49 6.94 6530 1.68F9V 0.50 4.10 6310 2.15F9V 45.21 0.52 5.52 6259 1.54F9V 3.50 0.54 7.11 6148 1.14 15.60 0.55 4.71 6105 1.73 33.23 0.57 6.11 6143 1.69 51.51 0.51 5964 1.12 13.41 0.46 6227 1.11 17.34 6326 1.06 33.49 1.04 11.62 22.40 G0VG0VG0V 7.28G0V 5.39G0V 0.55 5.67G0V 0.61 7.21 5987G0V 0.58 7.63 5853 1.32G0V 0.57 6.69 5961 1.32G0V 43.67 0.58 7.60 6026 1.17G0V 17.48 0.62 7.40 6077 1.42G0V 18.28 0.64 7.81 5835 1.21 45.96 0.55 6.41 5838 1.58 48.37 0.60 4.40 6148 1.31 37.84 0.61 5965 1.30G1V 47.46 0.60 5885 1.14G1V 47.79 6028 1.06G2V 47.56 5.04 1.00G2V 22.65 7.32G2V 8.84 0.62 7.17G2V 0.63 7.54 5947G3V 0.60 6.52 5891 1.19G3V 0.59 0.01 5974 1.20G3V 13.80 0.59 5.15 6004 1.21G3V 39.00 0.71 6.20 5884 1.11 37.82 0.70 6.60 5770 0.96G4V 41.71 0.66 6.63 5805 1.21G5V 21.59 0.67 5777 1.34G5V 1.30 0.64 5.92 5765 1.13G5V 15.61 5.38 5806 1.05G5V 21.15 0.77 7.69 0.94 23.47 0.64 7.81 5586 21.77 0.65 7.88 5883 2.76 0.71 5793 0.97 42.41 0.73 5665 1.13 12.91 5676 1.05 42.21 1.07 39.43 41.92 G1.5VG1.5VG1.5V 5.95 5.64 0.64 7.61 0.62 5793 0.59 5839 1.26 5584 0.98 21.15 1.03 14.45 34.45 G4IV-V 7.68 0.67 5677 0.89 31.69 List of selected targets in order of spectral type from F- to M Name HD 28568 HD 120136 mu Ara Procyon HD 197037 HD 136118 HD 9826 HD 10647 HD 23079 HD 33262 HD 106516 HD 155358 rho CrB HD 39091 HD 187085 HD 209458 HD 114729 A HD 13931 HD 28205 HD 25825 HD 97334 HD 39587 16 Cyg A HD 72905 HD 10180 HD 117618 HD 121504 HD 199288 alpha Cen A 16 Cyg B HD 59967 HD 37124 HD 38529 HD 147513 HD 222582 HD 28185 HD 4113 HD 129333 47 UMa HD 1461 Table 2. at Earth.

Article number, page 8 of 10 A. G. Sreejith et al.: Ca ii H&K stellar activity parameter: a proxy for stellar Extreme Ultraviolet Fluxes ) ) are bol bol 0.96 0.94 0.98 0.93 1.00 7.08 1.02 1.00 0.95 0.96 0.96 0.98 1.00 1.00 0.99 0.97 0.88 0.96 0.61 0.95 0.95 0.99 0.95 0.96 0.87 0.74 0.89 0.94 0.96 0.98 1.15 0.89 1.00 0.90 0.63 0.96 0.94 0.81 0.93 0.89 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 2 − 911Å) log (EUV/F erg − cm 14 1 − − s EUV (90 2 − erg 10 cm 7 bol − 1 F 0.1820.1780.1720.0960.474 7.483.187 13.723.527 4.990.789 12.470.376 6.240.246 -5.39 62.80 -5.11 0.334 49.880.285 -5.54 37.41 -4.89 0.214 17.46 -5.88 -5.71 9.981.157 13.72 -5.85 1.157 -5.32 7.480.649 -5.33 3.740.5594.038 -5.39 19.95 -5.39 0.945 37.910.133 -5.58 259.400.436 -5.76 23.69 1303.100.371 -5.76 1.234 54.87 -5.48 0.980 -4.40 7.486.783 -5.37 7.48 -4.49 0.242 18.71 47.39 -5.24 0.263 536.25 1099.000.228 -5.25 0.730 -5.77 72.33 -5.30 0.894 -5.42 0.384 -4.26 11.22 -4.79 0.217 4.618.942 -4.52 1.251.426 261.890.270 -5.37 4.611.443 58.61 1884.002.579 -5.69 0.292 -6.77 -4.53 61.11 22.45 7482.57 -5.92 -4.57 -4.68 236.95 106.00 -5.37 -5.08 -3.29 -5.04 -4.44 11.051 148.40 -5.87 81.549 5088.15 -5.20 − 10 s values, and EUV fluxes. The stellar bolometric fluxes (F ′ HK R log ′ HK R log -4.90-4.90 -4.90-5.08 -4.90-4.65 0.034 -5.08-4.93 0.060 -4.65-4.39 2 0.038 -4.94-4.97 7 0.038 -4.39-4.45 1 0.032 -4.96-4.91 1 0.008 -4.46-4.97 8 0.037 -4.90-5.01 2 0.031 -4.95-5.02 9 0.045 -5.01-4.89 5 0.049 -5.02-4.98 5 0.041 -4.89-4.99 6 0.016 -4.98-5.03 5 0.046 -4.99-4.40 2 0.033 -5.02-4.90 9 0.004 -4.41 10 -4.32 0.041 -4.91-4.76 5 0.081 -4.32-4.80 5 0.041 -4.76-5.07 7 0.018 -4.80-4.87 5 0.019 -5.07-5.04 5 0.003 -4.86-4.38 4 0.015 -5.05-4.66 2 0.034 -4.38-4.50 6 0.035 -4.65-5.02 5 0.048 -4.50-5.01 6 0.032 -5.02-4.99 5 0.007 -5.01-4.87 4 0.043 -4.97-4.53 3 0.064 -4.85-4.84 3 0.059 -4.55-4.55 5 0.029 -4.84-4.46 5 0.042 -4.55-5.04 5 0.014 -4.47-4.87 5 0.019 -5.05-3.84 2 0.040 -4.88-4.58 4 0.029 -3.84 10 -4.45 0.024 -4.59 3 0.038 -4.45 6 0.017 2 0.048 5 4 mean median stddev # d pc -type, their basic parameters, ∗ sun R eff mag mag K R SpT V B-V T G5VG5VG5V 7.96G5V 7.98G5V 0.69 8.02G5V 0.73 8.65 5658 0.71 6.92 5596 0.87 0.01 4.85 5726 1.03G6V 35.16 0.68 5520 1.15G6V 41.02 0.67 5705 0.87G6V 49.02 7.17 5749 0.87G6V 45.95 7.63 0.92G7V 21.96 0.69 7.30G8V 9.15 0.73 7.47 5667G8V 0.69 7.78 5685 1.04G8V 0.72 3.50 5722 1.07G8V 29.30 0.66 5.95 5630 1.14G8V 37.50 0.72 5.95 5644 1.24G8V 34.69 0.79 6.58 5375 0.93G9V 39.62 0.87 6.74 5500 0.77G9V 34.23 0.76 4.59 5306 0.83G9V 3.60 0.76 6.17 5520 0.90 12.56 0.78 8.30 5540 0.87 12.59 0.77 7.01 5550 0.83K0V 17.56 0.76 5350 0.81K0V 18.29 0.80 5475 0.68 6.70 6.13 5342 0.92K1V 10.79 4.03 0.95K1V 40.47 0.75K1V 22.02 0.86 1.33 5552K1V 7.56 5407 0.82K1V 0.88 7.71 0.85 13.78 0.93 6.45 5336 5.10 0.85 6.23 5100 0.74K2V 0.75 5192 0.77K2V 1.25 0.84 5265 0.71K2V 21.08 3.73 5303 0.53K2V 21.58 5.72 0.77K2V 9.18 0.88 7.53K3V 12.28 0.91 5.71 4975 1.02 5.08 5091 0.72 0.92 7.45 4801 0.76 3.20 0.85 4833 0.77 8.80 1.00 5089 2.84 18.21 4863 0.69 29.60 0.69 5.96 16.34 G6.5VG6.5V 4.74 6.37 0.70 0.70 5915 5626 0.85 0.87 8.51 16.73 K0.5VK0.5V 7.18 5.88 0.83 0.83 5244 5280 0.70 0.83 17.00 11.14 K2.5VK2.5V 7.15 7.77 0.95 0.96 4893 4996 0.62 0.68 12.94 19.65 K0V+M4V 7.65 0.93 5015 0.72 19.78 List of selected targets in order of spectral type from F- to M Name HD 65216 HD 178911 B HD 79498 HIP 91258 HD 90156 HD 20630 HD 115617 HD 47186 HD 92788 HD 102117 HD 4208 HD 10700 HD 69830 55 Cnc HD 1237 HD 154345 HD 131156 GJ 86 HD 147018 HD 164922 HD 7924 HD 165341 HD 189733 HD 114783 HD 97658 HD 103095 HR 1925 HD 40307 HD 99492 HD 22468 HD 155886 HD 128311 HD 43162 HD 70642 HD 3651 HD 166 HD 128621 HD 192263 epsilon Eri HD 192310 Table 2. at Earth.

Article number, page 9 of 10 A&A proofs: manuscript no. main ) ) are bol bol 0.91 0.96 0.90 0.96 0.88 0.88 0.85 0.61 0.85 0.79 0.86 0.74 0.55 1.52 0.80 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 2 − 911Å) log (EUV/F erg − cm 14 1 − − s EUV (90 2 − erg 10 cm 7 bol − 1 F 0.1880.1190.0310.2420.094 37.410.023 4.990.020 7.110.098 8.600.029 59.11 -4.70 0.003 12.120.016 -5.38 28.63 1526.400.043 -4.64 0.022 -5.45 52.20 -4.20 0.010 50.52 -4.27 0.023 16.17 -3.85 -2.81 2332.00 954.00 -3.75 318.00 -2.81 180.19 -3.99 -2.27 -2.36 -2.49 -3.11 − 10 s values, and EUV fluxes. The stellar bolometric fluxes (F ′ HK R log ′ HK R log -4.75-5.01 -4.76-4.54 -5.01-4.92 0.081 -4.54-5.07 0.038 -4.93-4.66 6 0.038 -5.07-4.99 1 0.097 -4.67-3.91 1 0.038 -4.99-4.75 6 0.049 -3.88-4.86 1 0.093 -4.75-5.09 5 0.079 -4.86-3.99 2 0.043 -5.09 3 0.038 -3.99-4.29 4 0.001-5.00 1 0.007 -4.29 2 -5.00 2 0.012 0.000 2 2 -3.75 -3.75 0.038 1 mean median stddev # d pc -type, their basic parameters, ∗ sun R eff mag mag K R SpT V B-V T K3VK3VK5V 7.92K6V 8.42 0.98 9.87 1.01 7.65 4974 1.06 4832 0.67 1.18 4875 0.67 20.38 4421 0.69 24.35 0.53 50.03 11.28 M1VM1V 10.33M2V 8.63 1.51M4V 3914 1.42 12.33M4V 0.20 3992 1.17 11.21 9.52 0.36M5V 3776 10.26 9.72 1.30 0.22 1.59 10.19 29.45 3859 3742 1.56 0.13 0.10 3837 4.97 5.05 0.09 4.68 M1.5VM1.5V 8.67 10.22 1.50M2.5V 1.57 3993 3775M3.5V 9.95 0.18 0.14 4.96 1.54 10.61 7.25 M5.5V 3898 1.45 0.20 3660 11.13 9.47 0.17 1.82 9.76 3296 0.02 1.30 List of selected targets in order of spectral type from F- to M Name HD 104067 HD 156668 WASP 69 HD 85512 GJ 832 GJ 667 C LTT 2050 HD 197481 GJ 176 GJ 3470 GJ 436 AD Leo EV Lac Proxima Centauri GJ 876 Table 2. at Earth.

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