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A&A
Volume 693, January 2025
Article Number A285
Number of page(s) 22
Section Planets, planetary systems, and small bodies
DOI https://doi.org/10.1051/0004-6361/202451680
Published online 24 January 2025

© The Authors 2025

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

The detection of atmospheric features in transiting exoplanets has become the best approach to understanding the composition and evolution of their atmospheres. The earliest detection reports were made for Na I (Charbonneau et al. 2002) and H I Lyman α (Vidal-Madjar et al. 2003), both in HD 209458 b. A number of atomic and molecular species have been detected since then (e.g., Madhusudhan 2019, and references therein). It is remarkable that helium, the second most abundant element in stars and in Solar System planets such as Jupiter or Saturn, was not detected until 2018. Theoretical works (Seager & Sasselov 2000) have predicted the possibility to detect the He I infrared triplet at 10 830 Å in the atmosphere of transiting exoplanets. An attempt to detect this feature was made by Sasselov & Sanz-Forcada in 2000 and 2001, using the NASA Infrared Telescope Facility (IRTF), but no feature was detected due to bad weather conditions in both campaigns combined with insufficient instrument sensitivity. Moutou et al. (2003) used VLT/ISAAC to search for the same feature, but no detection was made either. During the following years the search for atmospheric features focused on other species. The idea of observing exoplanet atmospheres using the He I 10 830 line was resurrected by Oklopčić & Hirata (2018). The line was soon detected independently by three different groups (Spake et al. 2018; Nortmann et al. 2018; Allart et al. 2018), and two more detections were reported in the same year (Mansfield et al. 2018; Salz et al. 2018). Nortmann et al. (2018) also identified, as proposed by Seager & Sasselov (2000), that in exoplanet atmospheres the line formation is directly related to the incoming stellar irradiation in the XUV band at λλ ~ 5–504 Å, with 504 Å being the wavelength corresponding to the first ionization energy of He.

The neutral helium atom possesses two types of configurations, namely, orthohelium, and parahelium, corresponding to different sets of energy levels. In orthohelium, the most conspicuous line is actually a triplet, at 10 830 Å1. This triplet is associated with a less intense optical triplet at 5876 Å. The formation of these triplets has long been studied in both massive or low-mass stars. Two mechanisms have been proposed to explain the formation of the triplets: (i) collisional excitation from the singlet (parahelium) levels may populate the ground level of the triplet (orthohelium), allowing for the formation of the triplet lines at 10830 and 5876 Å. A high temperature (≳20 000 K) is required for this mechanism to operate. Alternatively, in a colder environment, (ii) the He I atom can be radiatively ionized with EUV photons (λ < 504 Å) that would soon recombine into neutral atoms, some of them populating the triplet lower levels in a de-excitation cascade (photoionization-recombination mechanism). Examples of the first mechanism are present in stellar winds observed in the G21 supergiant α Aqr (Dupree et al. 1992). The second mechanism is thought to be responsible for the formation of the line in stellar chromospheres of late-type stars (e.g., Zarro & Zirin 1986), which receive EUV photons from their coronae. In this case, a balance of the two mechanisms could occur in dwarfs because of the high temperatures and density reached in their chromospheres (Andretta & Giampapa 1995; Sanz-Forcada & Dupree 2008).

In the case of planet atmospheres, the photoionization-recombination mechanism is likely responsible for producing this line, given their cold environment. Hence, we would expect to see a relation between the ionizing XUV irradiation of the planets and the observed He I triplet in their atmospheres. A small sample of five objects reported by Nortmann et al. (2018) seems to follow this trend, but a recent compilation of all published data on He I 10830 in exoplanets (Fossati et al. 2022) could not find such relation. Fossati et al. (2022) used the (Hionizing) radiation in the range 5–920 Å (XUVH) as a proxy of the He-ionizing radiation. Similar non-conclusive results were found by Kirk et al. (2022), Fossati et al. (2023), and Allart et al. (2023). A further study was carried out by Zhang et al. (2023a), using a relationship between planetary mass-loss rates estimated from observations and the theoretical energy-limited mass-loss rates. These authors were able to find a rather good correlation between the XUV flux in the same range and the observed He I triplet absorption.

In this paper, we attempt to probe the correlation between ionizing stellar XUVHe (in the range 5–504 Å) irradiation and the He I triplet in exoplanets. Since high-energy photons are easily absorbed by the interstellar medium (ISM), no direct observations of spectra in the range 400–504 Å are available for stars other than the Sun and most stars do not have reliable data in the 100–400 Å range either. A coronal model is needed to estimate the stellar spectral energy distribution (SED) in the range not covered by the actual data. It is thus necessary to calculate accurate coronal models of the exoplanet host stars and to calibrate a relation allowing us to easily calculate the broadband XUVHe stellar flux. Details of the X-ray and UV observations used to prepare these models, as well as on the method employed, are described in Sects. 2 and 3. The results obtained for the objects in the sample are given in Sect. 4, together with a new scaling law to easily calculate the broadband EUV emission in the H- and He-ionizing ranges, provided that the X-ray flux is available. The different parametrizations to relate the XUVHe flux and the He I line are explored, too. In Sect. 5, we discuss the results as compared with actual He I detections observed in exoplanet atmospheres, along with the implications that they have for research on the planet atmospheres. The conclusions are given in Sect. 6. We then provide appendices to further discuss the comparison with other XUV scaling laws (Appendix A) and the relation between the He I 10 830 equivalent width and the XUVHe flux (Appendix B). Tables with the observing logs and main results are found in Appendix C. In Appendix D (online), we include the tables with X-rays and UV line fluxes, along with the figures and tables providing results of the coronal models.

2 Observations

We were granted XMM-Newton Director Discretionary Time (DDT, prop. IDs #101704 and #106917, PI Sanz-Forcada), and Guest Observer time (prop. ID #092312, PI Sanz-Forcada) to observe a sample of planet-hosting stars suitable for a search of the He 1 10 830 triplet with the Calar Alto high-Resolution search for M dwarfs with Exoearths with Near-infrared and optical Echelle Spectrographs (CARMENES; Quirrenbach et al. 2014). XMM-Newton simultaneously operates two high-spectral resolution detectors (RGS, λλ ~6–38 Å, λ/Δλ ~ 100–500, den Herder et al. 2001) and three European Photon Imaging Camera (EPIC-PN and EPIC-MOS) detectors (sensitivity range 0.1–15 keV and 0.2–10 keV, respectively, E/ΔE ~ 20–50, Turner et al. 2001; Strüder et al. 2001). XMM-Newton also includes an optical monitor (OM). We did not use the OM data in this work because the light in its UV filters is severely contaminated with stellar photospheric emission (Orell-Miquel et al. 2023). The data were reduced using the XMM-Newton Science Analysis Software (SAS) v20.0, and analyzed following standard procedures within the Interactive Spectral Interpretation System (ISIS, Houck & Denicola 2000) package. Most targets did not have enough statistics to use RGS, so EPIC data were used to obtain a discrete (one to three temperatures) fit to the spectra.

Some objects were also observed with the Chandra X-ray observatory (Weisskopf et al. 2002). The High Energy Transmission Grating Spectrograph (HETGS) contains two gratings, HEG (High Energy Grating, λλ ~ 1.5–15 Å, λ/Δλ – 120–1200), and MEG (Medium Energy Grating λλ ~ 3–30 Å, λ/Δλ ~ 60–1200), which operate simultaneously, permitting the further analysis of the data with different spectral resolutions. The Low Energy Transmission Grating Spectrograph (LETGS, λλ ~ 3–175 Å, λ/Δλ ~ 60–1000) was used in combination with the High Resolution Camera (HRC-S). The positive and negative orders were summed for the flux measurements. Lines formed in the first dispersion order, but contaminated with contribution from higher dispersion orders, were not employed in the analysis. We also used the Advanced CCD Imaging Spectrometer (ACIS, E/ΔE ~ 20–50) with no grating. Standard reduction tasks present in the CIAO v4.14 package were employed in the reduction of data retrieved from the Chandra archive and the extraction of the HEG and MEG spectra. All objects observed in X-rays are listed in Table C.1. We complemented our sample with the objects in the database X-exoplanets2 (Sanz-Forcada et al. 2011, hereafter SF11), which were reanalyzed for this work as explained in Sect. 3. New XMM-Newton observations were included for a few targets of the X-exoplanets original sample (Table C.1): GJ 436, GJ 674, HD 27442, HD 75289, HD 108147, HD 189733, and HD 190360. In targets with more than one XMM-Newton observation, we combined all the data to improve the quality of the EPIC spectra used in the fitting. Two objects formerly detected only with ROSAT, or with lower quality Chandra spectra, have now XMM-Newton observations (GJ 832, and υ And). In the case of ι Hor we used the coronal model from Sanz-Forcada et al. (2019). A few more targets were added to the sample, either because they are interesting M stars hosting exoplanets (e.g., TRAPPIST-1) because they have been surveyed searching for the He I 10 830 triplet or because they can be used to establish a better relation between X-rays and EUV, such as V1298 Tau (Maggio et al. 2023).

Five special cases of M dwarfs, Proxima Cen, AU Mic, AD Leo, Lalande 21185 (GJ 411, HD 95735), and GJ 674, were analyzed in detail using high-resolution X-ray spectra from the XMM-Newton or the Chandra archives. The use of information from individual spectral lines greatly improves the quality of the coronal models, as shown by Sanz-Forcada et al. (2003b). In these cases, we also included UV spectra (see below). Although the light curves of these targets indicate the possible presence of stellar flares, we preferred to use the combined data of quiescent and flaring states, as we understand that this reflects better the average activity of the star. In the case of Proxima Cen, it was necessary to correct for the radial velocity of the different datasets to co-add the RGS spectra3. Besides these five stars, a few targets for which we have only low-resolution XMM-Newton/EPIC or Chandra/ACIS spectra were analyzed including high-resolution UV spectra from: Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS, Kimble et al. 1998)4 or Cosmic Origins Spectrograph (COS, Osterman et al. 2011)5; Far Ultraviolet Spectroscopic Explorer (FUSE, 905–1187 Å, λ/Δλ ~ 15000–20000, Moos et al. 2000); and Extreme Ultraviolet Explorer (EUVE, 70–750 Å, λ/Δλ ~ 200–400, Haisch et al. 1993), as listed in Table C.2. Extracted spectra from HST and FUSE were obtained through the Mikulski Archive for Space Telescopes (MAST), while EUVE spectra were reduced from the raw data to improve data quality, using the Image Reduction and Analysis Facility (IRAF) EUV standard tools. We also add to this list the X-ray measurements from τ Boo (Maggio et al. 2011), now complemented with HST/STIS line fluxes, to extend the coronal model to transition region temperatures (down to T ~ 104 K).

The HD 209458 and HD 189733 data were reanalyzed since Sanz-Forcada et al. (2010) to improve the results. In both cases, all the available XMM-Newton/EPIC data are combined. In the case of HD 209458 the data analysis was limited to the spectral range 0.3–8 keV to improve the statistics of the spectral fitting, which is now characterized by S/N=3.2. The data of both stars were complemented with HST/COS, as detailed by Lampón et al. (2020, 2021). In the latter case, we also fixed a software bug that led us to overestimate the flux in the EUV range and further made a more accurate analysis of the abundance pattern in the entire temperature range. New updated values of broadband EUV fluxes are made available in Table C.3. All these new fluxes supersede measurements formerly reported in CARMENES papers (e.g., Nortmann et al. 2018; Lampón et al. 2021; Lampón et al. 2023) or in Chadney et al. (2015) for the cases of AU Mic and AD Leo.

3 Methodology

We made use of coronal models to produce synthetic XUV spectra. To do so, we first calculated the volume emission measure (EM) at different coronal temperatures using the X-ray spectra, with EM = ∫ Ne NH dV as defined by Brickhouse & Dupree (1998), where Ne and NH are electron and hydrogen densities, respectively. The ISIS package and the Astrophysics Plasma Emission Database (APED, Smith et al. 2001) were used to fit the low resolution spectra, and to measure spectral line fluxes in high resolution spectra. We reanalyzed all the X-ray spectra included in SF11 to account for the updated stellar distances provided by Gaia DR3 (Gaia Collaboration 2023) and used ATOMDB v3.0.9 in the spectral fitting and further coronal modeling. The flux of the C III multiplet at −1176 Å is measured as one line, and its theoretical flux is evaluated using Raymond (1988) atomic data instead of ATOMDB6. The X-ray luminosity was calculated in the 0.12–2.48 keV band (~5–100 Å), similar to the ROSAT/PSPC standard band, by global fitting of the XMM-Newton/EPIC or Chandra/ACIS low resolution spectra. The spectral fit was used to calculate a coronal model (Table D.1). The interstellar medium (ISM) hydrogen column density was fixed, using values from ISMTool7 adapted to the stellar distances. The X-ray to bolometric luminosities ratio gives an indication of the activity level of the star (e.g., Pizzolato et al. 2003; Wright et al. 2011). The bolometric luminosity of the stars was calculated using the calibration by Pecaut & Mamajek (2013) based on G and Ks magnitudes8, for stars with spectral types earlier than K5. The calibration from Cifuentes et al. (2020) was used for later spectral types, based on the G and J magnitudes.

In cases with X-ray high-resolution spectra, individual line fluxes were measured considering the point spread function (PSF) of the instrument, as described by Sanz-Forcada et al. (2003b). The EUVE line fluxes were measured using standard IRAF software. The X-ray or EUV line fluxes were used to build the coronal model – namely, the emission measure distribution (EMD) – in the range of log T (K)~5.8–7.4, while the UV line fluxes are employed for the transition region range, log T (K)~4–5.7, including a few cases in which coronal lines were measured in the UV. The spectral line fluxes measured in the spectra and the observed-to-predicted line fluxes ratio with the resulting EMD are listed in Tables D.2–D.11. The EMDs are listed in Tables D.12 and D.13 and shown in Figs. 1–2 and D.1–D.8. In cases where no UV spectra are available, the coronal model is extended to the transition region assuming larger error bars for this temperature range, following SF11. The technique employed to build the EMD is described in detail by Sanz-Forcada et al. (2003b) and references therein. The basic idea is that an initial EMD is proposed, with emission measure values at each temperature in a grid of 0.1 dex in the log T (K) ~ 4.0–7.5 range, and an initial set of atomic abundances; the EM is convolved with the emissivity function of each observed spectral line. The same operation is performed for any eventual blends that the observed line could have. The predicted line fluxes are then compared to the observed line fluxes and from this comparison, we changed the EMD to better match the observations in an iterative process. The abundances are calculated by doing this process for the lines of only one element (frequently, Fe) and incorporating the lines of other elements trying to partially overlap the temperature range covered by the new element and the former ones. The solution found through this process is then probed with a Monte Carlo method and modified when needed, to calculate the error bars associated with the EM at each temperature, letting the observed fluxes vary by up to 1σ in a large number of iterations.

We considered stellar abundances in the corona and transition region in the preparation of the coronal models (Tables D.1, D.14, D.15). In stars with low statistics X-ray spectra, solar photospheric abundances were used by default, except for the stellar photospheric [Fe/H] when available. In the case of abundances obtained from the global fit and the EMD, we used Fe from the global fit, and the other elements from the EMD. The level of the EMD was then based on either C or Si. In the case of HD 189733, there is a Fe III line formed at transition region temperatures that could be used to fix the EMD level with coronal Fe abundance. As we were not confident in the quality of this line, instead we used the coronal abundances of Si, Ne, and O to fix the level of the EMD. Finally, we made use of coronal models to produce synthetic XUV SED, as detailed by SF11, using the ISIS software. These SEDs in the 1–2800 Å range are made available in the X-exoplanets database, and in Table 1 as described in Sect. 6. Although some individual line fluxes may not be correct given the actual level of accuracy of ATOMDB, we are confident on the overall correctness of these SEDs in the range covered; namely, 5-920 Å. The extension to longer wavelengths should be done with care because ATOMDB has not been sufficiently tested for some of the lines at these wavelengths (e.g., the multiplet of C III at 1176 Å). An additional difficulty may arise for stars with substantial photospheric contribution in the UV, which becomes more important for F and G stars. Emission from plasma with photospheric temperatures is not generally covered by ATOMDB.

thumbnail Fig. 1

Coronal models of Proxima Cen (left) and AU Mic (right), combining data from XMM-Newton, EUVE, HST/STIS, and FUSE. Upper panels: emission measure distributions (EMDs, thick line). The thin lines represent the contribution function for each ion (the emissivity function multiplied by the EMD at each point). The small numbers indicate the ionization stages of the species. Lower panels: observed-to-predicted line flux ratios for the ion stages in the upper panels. The dashed lines denote a factor of 2.
thumbnail Fig. 2

Same as in Fig. 1, but for AD Leo (GJ 388, left) and Lalande 21185 (right), combining data from Chandra, EUVE, and HST/STIS (AD Leo), and XMM-Newton and HST/STIS (Lalande 21185).

4 Results

We calculated the broadband stellar luminosity in two different EUV bands, affecting the H ionization (EUVH. ~ 100–920 Å) and He ionization (EUVHe, ~ 100–504 Å), as listed in Table C.3. The summed flux in the XUV bands; namely, X-rays (5–100 Å) as well as EUVH and EUVHe, were calculated at the planet orbital separation. We also calculated as a reference the mass loss rates, multiplied by the planet density (ρṀp), assuming the energy-limited approach and ignoring effects related to the mass transfer through the Roche lobe: M˙XUV~3FXUV,H4Gρp,${\dot M_{{\rm{XUV}}}}\~{{3{F_{{\rm{XUV}},{\rm{H}}}}} \over {4{\rm{G}}{\rho _{\rm{p}}}}},$(1)

where FXUV,H stands for the flux density in the 5–912 Å spectral range, G is the gravitational constant, and ρp is the planet bulk density, following SF11 and references therein. Table C.3 includes both the stars in the sample of Table C.1 and those available in X-exoplanets as listed by SF11. The latest were updated using new Gaia distances, as well as the new ATOMDB atomic models, as described above.

Details on some individual targets are provided, and the newly calibrated relation between X-rays and EUV flux is described next. We also explored the relation between XUVHe stellar irradiation onto the planet atmosphere and the observation of the helium infrared triplet (see Sect. 4.4).

4.1 Notes on individual targets

The sample studied in this work pays special attention to M dwarfs, the main focus of the CARMENES survey. We included some of the brightest M stars in X-rays, such as AU Mic, Proxima Cen, and AD Leo, to obtain the best possible coronal models, so that they can be widely employed in planet atmospheric modeling. The brightest objects have plenty of lines to perform an adequate coronal model and calculate the coronal abundances. Some targets are faint in X-rays and their coronal abundance analysis is more complicated, introducing some uncertainty in the balance between the EM at lower (transition region) and higher (coronal) temperatures. Some details to be considered in individual cases are discussed here. In a few stars (WASP-77, GJ 357, GJ 486, HD 149026, and TOI-836), due to the scarcity of bright spectral lines in the COS and STIS ranges, we had to include lines with S/N < 3 to prepare the transition region model. We included the candidate planets AD Leo b and Barnard’s star b (Tuomi et al. 2018; Ribas et al. 2018) in the sample, although their detection has been questioned afterwards (Carleo et al. 2020; Lubin et al. 2021; Kossakowski et al. 2022).

The Barnard’s star (GJ 699) coronal model, in its high temperature component, is based on the Chandra/ACIS spectral fit, rather than on the two coronal lines measured with HST/STIS. Ne and N abundances are uncertain because we could not disentangle them from the EM values within the temperature range of line formation. Also, no relative abundances relative to Fe were calculated. Thus, the actual level of the EM in the transition region could be different. However, the observed coronal Fe lines are in agreement with the 1 − T fit to the Chandra value, supporting an Fe abundance that should not deviate substantially from solar photospheric values. The problem of uncertain abundances affects also GJ 1214 in N and O, in a similar temperature range.

Some of the X-ray fluxes calculated in this paper differ from former publications (e.g., Louden et al. 2017; King et al. 2018). Sometimes this is due to the assumption of a different ISM absorption or coronal metallicity. We also avoid the fit of X-ray spectra below 0.3 keV, used in the mentioned work, to avoid instrumental problems such as noise in the low-energy end of EPIC spectra. Our EMD results can also be compared with those by Duvvuri et al. (2021), based on a technique that uses smooth polynomials and solar photospheric abundances to fit a differential emission measure (DEM). Their results are discrepant with ours, as discussed in Appendix A. The use of global fits to get the DEM (or EMD) from high-resolution spectra was argued against the analysis of similar data from EUVE spectra (Bowyer et al. 2000; Favata & Micela 2003; Güdel 2004) because it tended to produce artificial features not supported by observed line fluxes or continuum (e.g., Fig. 13 of Schrijver et al. 1995). This is a variant of the technique used by Duvvuri et al. (2021). A similar approach was adopted by Louden et al. (2017). The use of smooth polynomials imposes constrains to the DEM shape, which may not correspond to the actual DEM of the star. Another discrepancy arises when the XMM-Newton/OM UV signal is used to scale the SED modeled at UV wavelengths (Zhang et al. 2023b): the UV filters of this instrument are contaminated by stellar photospheric emission from longer wavelengths. Therefore, they cannot be used to set the UV level of emission of late-type main sequence stars (King et al. 2018; Orell-Miquel et al. 2023).

4.2 X-exoplanets 1.1: New calibration

Although it is generally advisable to calculate an individual coronal model for each stellar target, the use of scaling laws is being extensively used in the literature as a first order approach to the problem of planet photoevaporation. We thus consider it important to update the relation of X-exoplanets (SF11) with a better coverage of the different stellar activity regimes.

We calculated a new relation for the EUVH and EUVHe against X-ray flux. This relation allows for a fast and reliable calculation of the flux in the EUV spectral ranges, where real data are not available. The first relation of this kind was provided by SF11, who fitted a linear relation between log LX and log LEUV,H, with some deviation from the linear fit at higher values. Such deviation is more evident for higher activity stars (Maggio et al. 2023). When applying a similar linear fit to out current sample, this behavior is confirmed, yielding some data dispersion. The resulting linear fits are: logLeuvH=(0.821±0.041)CX+(28.16±0.05)$\log {L_{{\rm{euvH}}}} = (0.821 \pm 0.041){C_{\rm{X}}} + (28.16 \pm 0.05)$(2) logLeuvHe=(0.874±0.031)CX+(27.74±0.04),$\log {L_{{\rm{euvHe}}}} = (0.874 \pm 0.031){C_{\rm{X}}} + (27.74 \pm 0.04),$(3)

where CX = log LX − 27.44, and they are valid in the range log LX ~ 25.5–30.5. These fits have a Pearson’s correlation factor r = 0.920 and 0.957, and a standard deviation of the residuals (RMS) of 0.406 and 0.309, respectively.

The X-ray or EUV luminosities depend on the stellar activity, as well as on the stellar size. To remove the latter dependence, we may use the stellar surface flux, with the associated uncertainties of the stellar radius (Appendix A). Instead, we fit a relation between log LX/Lbol and log LEUV/Lbol (Fig. 3). The use of Lbol removes the effect of the stellar size. Linear fits to these data have r = 0.923 and 0.960, and RMS=0.380 and 0.281, respectively. A substantial bremsstrahlung continuum contribution has an increasing importance with stellar activity, and this continuum is more relevant in X-rays than at EUV wavelengths. A linear fit does not account for the dependence of broadband fluxes on this continuum. Thus a better result is found when applying a quadratic fit: logLEUV,HLbol=(−0.062±0.016)(UX)2                       +(0.763±0.037)UX+(−4.792±0.051),$\eqalign{ & \log {{{L_{{\rm{EUV}},{\rm{H}}}}} \over {{L_{{\rm{bol}}}}}} = ( - 0.062 \pm 0.016){\left( {{U_{\rm{X}}}} \right)^2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + (0.763 \pm 0.037){U_{\rm{X}}} + ( - 4.792 \pm 0.051), \cr} $(4) logLEUV,HeLbol=(−0.022±0.016)(UX)2                        +(0.824±0.029)UX+(−5.268±0.039),$\eqalign{ & \log {{{L_{{\rm{EUV}},{\rm{He}}}}} \over {{L_{{\rm{bol}}}}}} = ( - 0.022 \pm 0.016){\left( {{U_{\rm{X}}}} \right)^2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + (0.824 \pm 0.029){U_{\rm{X}}} + ( - 5.268 \pm 0.039), \cr} $(5)

where UX = log(LX/Lbol) + 5.60. These results are valid for log LX/Lbol ~ −3.1 to −8.8, although the application of the equation for values lower than ~−7.2 should be done with caution. Although some dispersion still exists, this approach shows a better fit (RMS=0.359 and 0.277, respectively). The remaining data dispersion might be related to deficiencies in the coronal models, such as a lack of high-resolution spectral data or problems in the calculations of stellar abundances in the corona and transition region temperature range. These problems can be mitigated by using only stars with good high-resolution spectra, both in the X-ray and UV bands. This will be subject of a future work. An intrinsic problem is also the presence of coronal activity cycles, with an X-ray amplitude that can range from a factor of ~2 to a factor of ~50, depending on stellar activity levels. The two extreme cases observed to date are: ι Hor (log LX/Lbol ~ −4.9; Sanz-Forcada et al. 2019) and the solar cycle (log LX/Lbol ~ −5.9 to −7.6; Orlando et al. 2001). The problem of stellar cycles can only be solved by using the average value of an already known cycle, which is the case in very few stars. The problem is also mitigated if the UV data are taken contemporaneously to the X-ray data.

thumbnail Fig. 3

EUV vs X-ray luminosities in two different EUV ranges for the H (100–920 Å) and He ionization (100–504 Å). There are different scales for the two EUV luminosity ranges. Left: linear fit over EUV against X-ray luminosity. Right: quadratic fit over the luminosity ratios with the bolometric luminosity.

4.3 Equivalent widths of the He I 10830 detections

To carry out a homogeneous analysis, we needed to revise some of the equivalent widths (EWs) of the previously published He detected planets with CARMENES. However, these changes were marginal. The EWs of planets HD 209458 b, HD 189733 b, GJ 3470 b, GJ 1214 b, WASP-69 b, and HAT-P-32 b were not changed and, thus, they were taken from Table 3 of Lampón et al. (2023). The EWs were integrated in the range 10831.0–10834.5 Å (wavelengths in vacuum). For the EW of WASP-76 b, the upper limit of 21.3 mÅ reported by Casasayas-Barris et al. (2021) was adopted instead of the value of 12.4 mÅ reported by Lampón et al. (2023). The latter value was obtained by integrating in a wider range, 10831.0–10835.5 Å, as the signal of this planet was significantly broadened and red-shifted. Except as noted, the same procedure was used for the planets with detected signal.

For WASP-52 b, the EW was calculated from the model fit to the data performed by Kirk et al. (2022). That fit shows an offset of 0.1%, which was subtracted. Kirk et al. (2022) also detected a small and rather noisy signal of WASP-177 b and used it to fit their model. The EW for the measured spectrum integrated in their spectral range is 5.8 mÅ, while that for the model is 7.5 mÅ. We took the mean value of 6.65 mÅ. For HAT-P-18 b, the EW was obtained from the absorption depth of 0.46% reported by Paragas et al. (2021) integrated over their bandpass of 6.35 Å. The EW of HD 235088 b (TOI-1430b) was reported by Orell-Miquel et al. (2023) with a value of 9.5±1.1 mÅ, while our value obtained by integrating over the usual 10831.0–10834.5 Å spectral range is slightly larger, 11.1 mÅ. Zhang et al. (2023b) reported a value of 6.6±0.5 mÅ in a different observation.

Zhang et al. (2022a) reported a value for the EW of 8.6±0.6 mÅ in HD 73583 b (TOI 560 b). From their figures, by integrating over the spectral range described above, we obtained 7.43 mÅ. In the case of TOI-1268 b, we faced a similar problem. The EW by Orell-Miquel et al. (2024) is 19.1 mÅ. The value obtained with the method described above is 17.7 mÅ. We note that in this case the upper limit of the integration was slightly smaller, 10834.2 Å, due to a lack of data. Thesame remarks apply to TOI-2018 b, where we calculated 6.8 mÅ instead of the value of 7.8 mÅ from Orell-Miquel et al. (2024).

HAT-P-67 b seems to show a rather variable He(23S) absorption (see, e.g., Bello-Arufe et al. 2023 and Gully-Santiago et al. 2024). The CARMENES measurement, reported by Bello-Arufe et al. (2023) in their Fig. 6b, seems to have a problem as the absorption profile shows an unrealistic emission-like feature at wavelengths shorter than 10832.5 Å. That feature was likely caused by their lack of a realistic out-of-transit baseline, which prevented them from making an appropriate normalization. That is, it could be due to an increased He I absorption at bluer wavelengths towards the end of the transit. This planet was observed with a longer baseline by Gully-Santiago et al. (2024). Hence, we decided to include these measurements in our analysis. By using our method for calculating the EW, we derived from their measurements shown in Fig. 13 (the in-transit mean taken in the visit of May 2020) a value of 147 mÅ. In this case, we consider the larger value of 25 mÅ that covers the significant variability shown by the planet as “error” of the EW and not the real measured uncertainty (see the mid-transit values in Fig. 9 of the work cited above). It is worth noting that Gully-Santiago et al. (2024) measured a rather large EW of ~330 mÅ at the mid transit, as well as a significant pre-transit absorption of ~200 mÅ (see their Fig. 9). They stated, however, that “only a small fraction of the He I excess signal would be expected to trace the planet’s motion.” Here we focus on the absorption of the He(23S) that is being ejected from the atmosphere, not in the He(23S) that has already been ejected and forms the cloud around the planet. Then, we can estimate this absorption by taking the difference of the EW at the mid transit, from that of the material already expelled (pre-transit). This results in an absorption of ~130 mÅ, which is very close to the adopted value of 147 mÅ for the mid-transit measured in May 2020.

For HAT-P-26 b, the EW was obtained from the absorption depth of 0.31% reported by Vissapragada et al. (2022) integrated over their full width half maximum (FWHM) bandpass of 6.35 Å. We obtained a value of 19.7±6.4 mÅ. The warm super-puffy TOI-1420b planet was observed by Vissapragada et al. (2024), who obtained a high (8.5σ) He triplet signal, with an absorption depth of 0.671%±0.079%. With those values and taking the bandwidth of their filter of 6.4 Å, we obtained an EW of 42.9±5.1 mÅ.

4.4 The relation between He 110830 and XUV ionizing irradiation

It is expected that the formation of the He I 10 830 triplet in an exoplanet atmosphere is related to the stellar irradiation on the planet by photons capable of ionizing the neutral helium atoms; namely, those with λ ≲ 504 Å. The actual process of formation of these lines requires also that electrons are available in the plasma for the recombination of He atoms after the radiative ionization, and the main origin of these electrons is the radiative ionization of H atoms by photons with λ ≲ 912 Å (we used 920 Å as ionization edge in our model to cover a slightly wider range). Furthermore, the stellar irradiation in this wavelength range also affects the He triplet concentration through the total density. As that radiation is responsible for the ionization of the H atmosphere, it changes the mean molecular weight and, hence, through the hydrodynamic equations, it affects the density. The stellar irradiation also affects the state of the upper atmosphere through the cooling and heating processes, which, in turn, affect the temperature and hence the hydrodynamic and the density. In addition, a third variable must be considered: the ionization of the ground level of orthohelium atoms, which takes place for λ ≲ 2600 Å (Kramida et al. 2023) and thus depends on the photospheric emission of the star. Although a combination of these three stellar fluxes should be considered, the right balance between the effects of the fluxes in the three bands is difficult to establish in a general way for all stars. Thus, we took the flux in the XUV range up to 504 Å (XUVHe) as a proxy of these three processes, as it is expected to be the dominant term and, in a large number of stars, this flux is well correlated with XUVH. Some attempts to derive such dependence have been undertaken9.

To further test this hypothesis, we collected information on the detections of the He I 10 830 triplet reported to date (see below) to compare them with the XUVHe flux (Table C.4). However, not all the targets in the list have a complete coronal model to calculate the XUV contribution. For those cases we calculated the flux by indirect means. The quality of the XUVHe fluxes calculated decreases in this order (as noted in Fig. 4): (1) cases with both X-ray and UV spectra, resulting in a complete coronal model; (2) targets with X-ray spectra, but no UV spectra (the coronal model with lower temperature section is extrapolated); (3) X-ray bulk flux available, such as ROSAT fluxes, and the XUVHe flux is calculated using the scaling law in Eq. (5); (4) X-ray flux determined from the rotation period and the X-ray vs. rotation relation by Wright et al. (2011), with subsequent calculation of XUVHe flux; and (5) calculation of the XUVHe flux based on blackbody emission of the stellar photosphere, for a star with unlikely or negligible coronal emission (KELT-9)10. We also included upper limits for both the He detection and XUV flux. In case (2) the low temperature part of the coronal model is extrapolated from the high temperature section (SF11); upper and lower boundaries are considered during this extrapolation; thus, the XUV upper limits are based on the upper boundary coronal model, rather than on the central value used to evaluate the SED in different contexts, such as the case of WASP-12 of Czesla et al. (2024). The separate fits for the positive detections in the groups (1), (2), and (4) show consistency within the error bars with the general fit. In addition to the expected dependence of the He absorption on the stellar XUV irradiation as discussed above, we also empirically evaluated its dependence on other star-planet system parameters. The detailed discussion is found in Appendix B. Here, we include a summary of that formulation and the results.

The first point is that we choose as a proxy of the He(23 S) absorption the EW of the absorption profile, instead of the depth (peak) of such profile, as chosen in some previous studies. The reason is that we are interested in relating the bulk He(23S) absorption by the planet atmosphere, and the EW is a better proxy since it is independent of the width of the absorption profile; namely, it is independent of its potential broadening by Doppler temperature and by the radial outflows of the escaping atmosphere.

The second aspect is the star’s surface. The transmission (or, equivalently, the EW) is measured as a ratio of the equivalent He(23 S) absorbing area of the planet atmosphere (usually expressed as the surface of a ring) and the area of the stellar disk (R*2)$\left( {R_*^2} \right)$. If we are interested in the properties of the He(23S) absorption of a given planet atmosphere independently of the size of its host star, it seems reasonable to de-scale the measured EW by the stellar disk area; that is, to consider EW⋅R*2$EW \cdot R_*^2$ instead of just EW.

An additional parameter that we considered is the planet gravitational potential, Φρ, as suggested by, for instance, the theoretical model of Salz et al. (2016) and the analysis of the He(23S) absorption in diverse planets carried out by Lampón et al. (2023). According to those studies the EW is expected to be inversely proportional to the gravitational field because for a planet with a weaker gravitational potential, the atmosphere is escaping more easily, leading to a more extended atmosphere and, hence, a larger absorption.

A further parameter that we considered is a geometric factor related to the planet size (see Appendix B), included in a general way with Rpγ$R_{\rm{p}}^\gamma $, where γ is likely to vary between 1 and 3 depending on the star-planet system. For planets with very compressed atmospheres as, for example, the case of HD 189733 b (Salz et al. 2018; Lampón et al. 2023), the EW is expected to be proportional to Rp (γ=1). However, for those with very extended and flat He(23S) distributions, for instance, GJ 1214 b (Lampón et al. 2023), the exponent γ could be larger than 2. Thus, the relationship that we considered generally takes the form (see Eq. (B.13)): EW⋅R⋆2≈FXUVRpγΦp.$EW \cdot R_ \star ^2 \approx {{{F_{{\rm{XUV}}}}R_{\rm{p}}^\gamma } \over {{\Phi _{\rm{p}}}}}.$(6)

We performed several tests for different relationships between EW and XUV fluxes, as well as for Eq. (6), using different values of the exponent γ of Rpγ$R_{\rm{p}}^\gamma $ (Table B.1). The EW values collected for all planets with detected He(23 S) signal and the XUVHe fluxes and other parameters listed in Table C.4 were used. The stellar spectral type is also listed in the Table to alert for the possible photospheric contribution at wavelengths below 2600 Å.

The results for the simple relationship between EW and FXUV (see Fig. B.2) yields a decent Pearson’s correlation coefficient of r = 0.579, but clearly inferior to other tests described below. The correlation coefficient of the fit largely improves to a value of r = 0.782 when scaling the EW by the area of the star’s disk (see Fig. B.3). A further test was performed by using Eq. (6) with a value of γ = 1, namely, EW proportional to Rp (see Fig. B.3). The correlation coefficient obtained in this case is even better, reaching the value of r = 0.891. A subsequent test was performed by considering γ = 2, namely, EW proportional to Rp2$R_{\rm{p}}^2$ (see Fig. 4), yielding a slightly better correlation than in the previous case, r = 0.898. We then proceeded to use the latter fit, which resulted in an empirical equation, excluding upper limits, of log(EW⋅R*2)=α⋅(log(FXUV,He⋅Rp2ϕp)−0.96)+β,$\log \left( {EW \cdot R_*^2} \right) = \alpha \cdot \left( {\log \left( {{{{F_{{\rm{XUV}},{\rm{He}}}} \cdot R_{\rm{p}}^2} \over {{\phi _{\rm{p}}}}}} \right) - 0.96} \right) + \beta ,$(7)

where α = 0.480 ± 0.054 and β = 1.052 ± 0.066. The EW is given in mÅ, the stellar radius, R*, in R⊙ units, FXUV,He in W/m2, and Rp2/Φp$R_{\rm{p}}^2/{\Phi _{\rm{p}}}$, which is equivalent to the inverse planet density, ρp−1$\rho _{\rm{p}}^{ - 1}$, in Jovian units. Error bars include the uncertainties in all of these quantities.

thumbnail Fig. 4

He I 10 830 triplet equivalent width, multiplied by the stellar area, plotted against FXUV,He, weighted by ϕp/Rp2${\phi _{\rm{p}}}/R_{\rm{p}}^2$, i.e., by the planet density. The 1σ error bands to the fit, calculated only with positive detections (filled symbols), are displayed in light blue. Different colors indicate the method used to calculate the XUV flux in the 5–504 Å range (see Sect. 4.4). Half-filled symbols are used for the equivalent width upper limits calculated by our team, while those calculated by other authors are shown in open symbols.

5 Discussion

The effects of high-energy stellar irradiation on the exoplanet atmospheres has been subject of increasing interest in recent years. The effects on the planet atmospheres are not limited to the formation of lines such as the He I 10 830 triplet, but they also affect large scale phenomena such as atmospheric mass loss (atmospheric escape). The actual mass loss rate of a planet depends also on other variables different from stellar irradiation, such as atmospheric composition, stellar winds, or presence of planetary magnetic fields, and it requires an individualized approach to every case (e.g., Kubyshkina et al. 2018). However Eq. (1) is widely used to roughly compare the expected planet evolution of different cases. Since atmospheric photoevaporation should lead to atmospheric instability, a planet with a current high mass loss rate is unlikely to be habitable. The approach in Eq. (1) assumes that the atmosphere is based mainly on H, which can be appropriate for Jovian-like planets, but it may not be applicable in the case of rocky planets such as Teegarden’s star b or TRAPPIST-1 b. In any case, modeling or analyzing planet atmospheres requires (as accurate as possible) knowledge of XUV stellar irradiation. With this work, we are providing new XUV synthetic SEDs for planet-hosting stars, which represents an improvement with respect to the X-exoplanets first release (SF11) by updating the stellar coronal models and the atomic data used to model the emission from corona and transition region. However, the number of planets hosting stars that have accurate X-ray spectra is quite limited. For those cases that do not, we include new XUV scaling laws that can be easily applied even in absence of an X-ray detection (e.g., by using the rotation period of the star, as explained in Sect. 4). For more in-depth studies, we advise users to select a star with a similar stellar spectral type and log LX/Lbol as a proxy. A more detailed work providing a grid of models of this kind will be released in the near future.

5.1 XUV scaling laws

Early works dealing with the planet photoevaporation problem assumed that the XUV emission from exoplanet host stars would be similar to the solar spectrum, scaled by the size of the star (Lecavelier Des Etangs 2007). Alternatively, they have made use of the UV flux from the Sun and a young star for their calculations (Murray-Clay et al. 2009). A slight variation was applied by Linsky et al. (2014), France et al. (2016), and Sreejith et al. (2020), who used the solar EUV SED scaled by the overall emission in X-rays and UV of the stars. Their models were subsequently used, for instance, in Vissapragada et al. (2022), but their XUV fluxes are discrepant with ours by up to a factor of six. This approach is deficient, given that EUV spectra of active stars can be very different from those of quiet stars like the Sun (e.g., Sanz-Forcada et al. 2003a). Namekata et al. (2023) used the stellar magnetic flux and the solar spectra to extrapolate the XUV flux in active solar-like stars. The relation is calibrated mainly based on solar data, with some data coming from more active stars, along with additional uncertainties as the stellar magnetic flux is required.

A different approach was introduced by SF11, including coronal models built with X-rays and UV data to create synthetic SEDs in the non-observed EUV spectral range. A relation between the transition region and the corona was calibrated using coronal models based on EUVE and International Ultraviolet Explorer (IUE) data, then used to complement the coronal models of stars with no UV data available. One of the results of this approach was a scaling law between X-rays and EUV luminosity that could be applied for cases where only a broadband X-ray flux is known. Chadney et al. (2015) tried to apply a more physical relation between X-rays and EUV emission by considering the activity level of the star (using the surface stellar flux, FX and FEUV) in six stars, one of them based on actual solar data. King et al. (2018) followed a similar approach (without defining the FX used) using the same stellar data from three stars, along with solar data with some corrections applied with respect to Chadney et al. (2015). In both cases the sample was small, with most information taken from the Sun and a few very active stars. In addition, the use of stellar radius introduces further uncertainties to the problem. Johnstone et al. (2021) calibrated a relation between X-rays (5–124 Å) and the EUV surface flux in the range 100–360 Å in a sample dominated by active stars, where a new set of solar data was included. The stellar data in this case came from EUVE spectra, but with some spectra having a low quality above 180 Å (Sanz-Forcada et al. 2003a), and being usually contaminated by geocoronal emission around the He II λ304 Å line. As in the other cases, this calibration also propagates the uncertainties of the stellar radii. For the rest of the EUV range, 360–920 Å, Johnstone et al. (2021) extrapolated the ratio between these two EUV bands in the Sun to the entire range of stellar activity. While plasma in X-rays and in the EUV 100–360 Å range is mainly made of spectral lines (and continuum) formed above 106 K, the 360–920 Å flux has a substantial contribution of lines formed at lower temperatures. Thus, it is not evident that the solar spectrum paradigm can be used for the active stars. The range of activity levels explored by Johnstone et al. (2021) included only a few low-activity stars, which are, nonetheless, still more active than some of our stars. Further comparison with these three relations is shown in Appendix A. More recently Krishnamurthy & Cowan (2024) made use of the relation between age and X-ray luminosity applied by SF11 to calculate the accumulated XUV flux over time on a planet atmosphere. While the X-ray luminosity can be used, in general terms, to estimate an approximate stellar age, the opposite is not advisable. Obtaining an accurate measurement of a stellar age is a difficult task in astrophysics; thus, using a poorly determined stellar age to calculate the X-ray and EUV fluxes may end up accumulating large uncertainties. We prefer to calculate the X-rays flux from stellar rotation if no actual measurement is available.

The new scaling law that we provide in Eq. (4) and Fig. 3 solves the limitations of past works by using coronal models for the calibration of the relation. It also uses variables that also depend on the stellar activity level to sample better the different ranges of activity. This new relation overcomes the observed problems with high activity stars (Maggio et al. 2023) and covers a wide range of activity levels. We also calculated a new relation in the range that affects the neutral helium ionization, namely, λ < 504 Å (Eq. (5)). This allows us to better estimate the impact of the stellar high-energy irradiation on the line formation of the planetary He I 10 830 triplet. Further comparisons with other recent works in the literature are provided in Appendix A.

5.2 The empirical relation between XUV and He I 10 830

Earlier attempts to find an empirical relation between He I 10 830 equivalent width and XUV (either at the H or the He ionization edges) have only indicated a trend, but not a clear relation (Nortmann et al. 2018; Fossati et al. 2022; Kirk et al. 2022; Allart et al. 2023). To evaluate the relation, these authors used δRp/Heq, which is the amplitude of excess helium absorption observed, in units of the planets’ atmospheric scale heights, against the XUV stellar flux at the planet. A further study by Zhang et al. (2023a) used a different approach. They did not use the atmospheric scale height, which strictly speaking, corresponds to hydrostatic but not to hydrodynamic conditions. Instead, they plotted the mass-loss rate estimated from observations versus the theoretical energy-limited mass-loss rate (i.e., assuming a heating efficiency of 1), where the former were assumed proportional to Rstar · EW and the latter to FXUV,H/ρXUV, where ρXUV is the density of the planet calculated with the planet radius of XUV absorption (RXUV). In that way, they reached a rather good correlation.

To reduce the data dispersion in those relationships, we sought alternative parametrizations. The He I 10 830 equivalent width and the XUVHe irradiation cannot directly be related with each other, as this relation neglects the impact of the stellar radius on the depth of any absorption signals measured, and the impact of the planet radius on the irradiation energy received by the planet. We therefore used the EW multiplied by stellar area, and the XUVHe flux multiplied by the planetary disk area and divided by the planetary gravitational potential (equivalent to a division by the planet density; see Sect. 4.4, Fig. 4, and Table C.4).

Although the observed empirical trend is clear, some dispersion is still present in the data. One reason could be the contribution of photospheric flux with λ < 2600 Å, which ionizes the ground level of the He triplet, diminishing the expected absorption of the line. However, no deviation related to the spectral type is evident. Other relevant factors are likely related to the atmospheric composition, whether there is a primordial atmosphere, mainly composed of H and He, or the current He content is lower. Some outliers (the TRAPPIST-1 planets, 55 Cnc e, TOI- 1807 b, GJ 486 b, GJ 9827 b) lie below the He level that would be expected for their XUV irradiation: because of their Earth- and super-Earth size and high densities (Fig. 5, Table C.4), they may be fully rocky without an atmosphere or they may have an atmosphere that is rather tenuous; otherwise, it may be thick, but with a high mean molecular weight. Some upper limits correspond to sub-Neptunian planets (GJ 9827 d, GJ 436 b, HD 97658 b, K2- 100 b), which might have atmospheric conditions and chemical compositions that complicate the helium detection with current instrumentation. From Figs. 4 and 5, we identify that among planets with density lower than 2 g cm−3, 15 out of 28 planets were detected (54 ± 4%). Yet another physical reason that could explain the dispersion observed is stellar variability. The ionization levels of He I depend on the stellar XUV emission, which is highly variable, especially during flares. However, the XUV level is based on X-ray observations that are not simultaneous to the He I 10 830 observations. An issue that is more related to the data acquisition and analysis is the difficulties in the measurements of exoplanets orbiting distant (i.e., faint) stars. In the particular case of WASP-177 b, Kirk et al. (2022) had some problems with systematics in the measurement of the He triplet. Another source of dispersion could be the actual dependence on the planet radius or surface, as explained in Appendix B.

thumbnail Fig. 5

He I 10 830 triplet equivalent width, multiplied by the stellar area, plotted against planet density 1σ error bars are indicated. Same colors and symbols to Fig. 4 apply for an easier identification. Labels are included for some planets detected as upper limits (see Sect. 5.2).

6 Conclusions

Planet atmospheric photoevaporation takes place due to XUV (λ ≲ 920Å) stellar irradiation. The He I 10 830 Å triplet is used to study this phenomenon. The formation of the line in a planet atmospheric environment follows a process of ionization by photons with λ < 504 Å, followed by a recombination with electrons that are mainly the result of hydrogen ionization (by photons with λ < 912 Å). The main problem to evaluate the stellar flux at those wavelengths is the absorption of these photons by the ISM. To overcome this problem, we constructed coronal (and transition region) models of the star. We then calculated a synthetic SED in the whole XUV range (λλ ~ 5-920 Å).

We analyzed new XMM-Newton, Chandra, and EUV spectra of 50 stars, either from proprietary or archival observations. We also used high-resolution spectra to measure individual lines formed at these temperatures in 5 stars. In the case of 26 stars, we extended the analysis to the transition region temperatures by measuring UV lines in high-resolution spectra from HST and FUSE. We built detailed emission measure distributions (EMDs) for this group. We also updated the analysis of the spectra in X-exoplanets (SF11) using the latest Gaia distances, and the latest version of ATOMDB. The overall sample includes 100 stars hosting 163 planets, of which 75 stars have S/N > 3, and the rest are considered upper limits. The whole sample, excluding upper limits, was then used to calculate new scaling laws for an easier calculation of the broadband fluxes that matter for the He and H ionization. A new approach to the problem was introduced by using the X-ray and EUV luminosity weighted by the bolometric luminosity. This allows us to remove effects related to stellar size, while closely considering the behavior of the scaling laws with the stellar activity. Future improvements will include more coronal high quality EMDs to reduce the dispersion observed in the data when the low-resolution X-ray spectra alone are used to model the coronae.

The newly calculated scaling laws are then used to evaluate the stellar He-ionizing irradiation in 48 exoplanets for which the He I 10 830 Å triplet has been measured, including upper limits. In the cases with no X-rays measurements, we used an X-ray luminosity based on the stellar rotation period. We then checked the expected trend of the formation of this line in exoplanet atmospheres with the XUVHe stellar irradiation. A clear relation is observed, once the planet gravitational potential, along with the stellar and planetary surface are included. The remaining dispersion observed in the data can be attributed to the He content in the planet atmospheres. Some outliers, such as the TRAPPIST- 1 b, e, and f planets, as well as 55 Cnc e, could be explained by the lack of planetary gaseous atmospheres. The stellar variability and the difficulties to measure the He I 10 830 Å triplet in the transmission spectrum of the planet also contribute to the data dispersion. The observed relation can be used to predict the detectability of the He I 10 830 Å triplet in a transiting planet.

Data availability

The SEDs modeled listed in Table 1, are available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/693/A285. The X-ray spectral fits, line fluxes and remaining emission measure distributions (Tables D.1–D.15 and Figs. D.1–D.8) are available at https://zenodo.org/records/14500302.

Acknowledgements

We thank the anonymous referee for the useful comments that helped improve the manuscript. We acknowledge financial support from the Agencia Estatal de Investigación (AEI/10.13039/501100011033) of the Ministerio de Ciencia e Innovación and the ERDF “A way of making Europe” through projects PID2022-137241NB-C4[1:4], PID2022-141216NB- I00, PID2021-125627OB-C31, and the Centre of Excellence “Severo Ochoa” and “María de Maeztu” awards to the Instituto de Astrofísica de Canarias (CEX2019- 000920-S), Instituto de Astrofísica de Andalucía (CEX2021-001131-S) and Institut de Ciències de l’Espai (CEX2020-001058-M). We also acknowledge the support of the DFG priority program SPP 1992 “Exploring the Diversity of Extrasolar Planets” (CZ 222/5-1). We acknowledge Norbert Schartel for the observations granted as XMM-Newton Director Discretionary Time (DDT). This research has made use of the NASA’s High Energy Astrophysics Science Archive Research Center (HEASARC), and it is based on observations made with HST, FUSE, EUVE, XMM-Newton and Chandra, and obtained from the MAST data archive at the Space Telescope Science Institute, and the public archives of XMM- Newton and Chandra. CARMENES is an instrument at the Centro Astronómico Hispano en Andalucía (CAHA) at Calar Alto (Almería, Spain), operated jointly by the Junta de Andalucía and the Instituto de Astrofísica de Andalucía (CSIC). CARMENES was funded by the Max-Planck-Gesellschaft (MPG), the Consejo Superior de Investigaciones Científicas (CSIC), the Ministerio de Economía y Competitividad (MINECO) and the European Regional Development Fund (ERDF) through projects FICTS-2011-02, ICTS-2017-07-CAHA-4, and CAHA16-CE-3978, and the members of the CARMENES Consortium (Max-Planck-Institut für Astronomie, Instituto de Astrofísica de Andalucía, Lan- dessternwarte Königstuhl, Institut de Ciències de l’Espai, Institut für Astrophysik Göttingen, Universidad Complutense de Madrid, Thüringer Landessternwarte Tautenburg, Instituto de Astrofísica de Canarias, Hamburger Sternwarte, Centro de Astrobiología and Centro Astronómico Hispano-Alemán), with additional contributions by the MINECO, the Deutsche Forschungsgemeinschaft (DFG) through the Major Research Instrumentation Programme and Research Unit FOR2544 “Blue Planets around Red Stars”, the Klaus Tschira Stiftung, the states of Baden-Württemberg and Niedersachsen, and by the Junta de Andalucía.

Appendix A Comparison with other XUV determination approaches

In this section, we show further comparisons between our XUV modeling approach and others employed in the literature, as outlined in Sect. 4. Here, we also discuss in more detail the use of DEM polynomial fits as an alternative technique to our EMD. The results from our scaling laws are also compared against other works in the literature.

A.1. Comparison with polynomial fits of the differential emission measure

Some recent publications have developed a technique to calculate the DEM of a star by fitting smooth polynomials functions (Louden et al. 2017; Duvvuri et al. 2021, hereafter LOU17 and DUV21 respectively). Here we compare our results with those of LOU17 and DUV21. G. Duvvuri kindly provided the DEM solutions for three targets in common with ours: AU Mic, Barnard’s Star, and Trappist-1. A similar approach was applied by LOU17 to determine the DEM of HD 209458. To transform their DEM into volume DEM at the distances (d′) used in our work, we corrected by the stellar radius (R) and distance (d) used by them. Although the basic concept of DEM and EMD are similar, there are differences in the way they relate to the temperature. Therefore we needed to transform the DEM into EMD. The definition of the DEM and EMD and formulae needed to transform them were given by, e.g., Bowyer et al. (2000), and Del Zanna et al. (2002) and references therein. We use the definition of the volume emission measure, evaluated in a temperature interval 2δ around Ta as in Brickhouse & Dupree (1998), namely, EM=∫Ta−δTa+δNeNH  dV$\int_{{T_a} - \delta }^{{T_a} + \delta } {{N_{\rm{e}}}} {N_{\rm{H}}}\,\,{\rm{d}}V$. The DEM is defined as DEM=NeNHdV dT$DEM = {N_{\rm{e}}}{N_{\rm{H}}}{{{\rm{d}}V} \over {{\rm{d}}T}}$. We included another term to account for the temperature grid in a log T scale: d(logT)dT=1ln(10)T${{{\rm{d}}(\log T)} \over {{\rm{d}}T}} = {1 \over {\ln (10)T}}$. We integrated the DEM in a temperature interval Δ(log T) around a temperature Ta, assuming that the emission measure is constant in that interval. Then the emission measure (in the EMD definition) relates to DEM as EM=DEM⋅4π(Rd′d)2⋅Ta⋅ln10⋅Δ(logT),$EM = DEM \cdot 4\pi {\left( {{{R{d^\prime }} \over d}} \right)^2} \cdot {T_a} \cdot \ln 10 \cdot \Delta (\log T),$(A.1)

where Δ(log T) (K) = 0.1 is the temperature resolution of the ATOMDB models used in our work. Once the DEMs were transformed into EMDs (Fig. A.1), we calculated the predicted line fluxes using the solar coronal abundances assumed in LO17 and DUV21 to test how good are the models provided by those authors. The results of this comparison are shown in Fig. A.2.

The smooth shape imposed by polynomial fits yields large differences with our results, in special in the temperature ranges with fewer spectral lines, such as the regions with log T (K)< 4.5, and ∼5.2–6.0. DUV21 used solar coronal abundances in all cases, which might explain some of the discrepancies, as acknowledged by DUV21. While this assumption could be a good approximation for a solar-like quiet corona, like that of HD 209458, it is inadequate for a very active star like AU Mic11, as shown in Fig. A.2 (see e.g., Sanz-Forcada et al. 2003b). In the case of Barnard’s star, DUV21 made a different DEM for flaring and quiescent stages, while we used only one overall EMD. However none of the DUV21 functions match the minimum of the EMD as sampled by us. Finally, TRAPPIST-1 model also over-interprets the information available in the X-rays spectra by providing a continuous DEM along the high temperature range.

thumbnail Fig. A.1

EMD calculated in our work, with shaded 1σ error bands, as compared with those of LOU17 and DUV21. Dashed lines indicate an uncertain EMD despite formal error bands. The results from our global fit to the X-ray spectra are indicated with error bars.
Table A.1

Comparison of modeled EUV broadband luminositiesa .

In all cases, there are obvious discrepancies, of up to three orders of magnitude, between predicted and observed line fluxes when the EMDs of DUV21 and LOU17 are employed. Their EUV broadband fluxes differ by up to ∼1 dex from ours (Table A.1).

A.2 Comparison with other scaling laws

In this section, we compare the results from our scaling law described in Sect. 4.2 and other works in the literature. Our X-ray vs. EUVH luminosity linear fit has an RMS=0.406. Figure A.3 includes a comparison with the SF11 linear fit (RMS=0.411 with the current dataset) to LX and LEUV,H. The addition of UV high- spectral resolution data and values with larger X-ray luminosity seems to lower the EUV modeled luminosity, but both fits are consistent.

Scaling laws based on the surface stellar flux are shown in Fig. A.4 together with our own fit to the data. Our fit is logFEUV,H=(0.784±0.044)CX+(5.54±0.05),$\log {F_{{\rm{EUV}},{\rm{H}}}} = (0.784 \pm 0.044){C_{\rm{X}}} + (5.54 \pm 0.05),$(A.2)

where CX = log FX − 4.88, all in c.g.s units. The plot includes only the stars of our sample with a stellar radius available in the Extrasolar Planet Encyclopaedia12 database, 65 stars. Our linear fit to the data shows a Pearson’s correlation factor r = 0.911, and an RMS of 0.386. The Johnstone et al. (2021) relation has an RMS of 0.405 with this dataset, Chadney et al. (2015) an RMS=0.445, and King et al. (2018) an RMS=0.462. The literature fits have a worse RMS than our linear fit between log LX and log LEUV,H (Fig. 3). They also have a dependence on the stellar radius, introducing a new source of uncertainty. We display the literature fits extrapolated to cover our range of values. Although all of the fits are roughly consistent with ours, discrepancies arise for the most active stars, and especially for the least active stars.

thumbnail Fig. A.2

EMDs calculated from the DEM published in LOU17 and DUV21, using our line fluxes measurements to test the quality of the fit. Symbols and lines as in Fig. 1. In the lower panels the axis range has been adapted to show all available line fluxes ratios. An offset of one order of magnitude is indicated with dotted lines.

Poppenhaeger (2022) calculated the EUV flux in the range 200–504 Å based on EUVE observations in a number of targets. This is a spectral range severely affected by ISM absorption (see, e.g., Sanz-Forcada et al. 2003a) and the spectra are contaminated by geocoronal emission around the He II 304 Å line, as those in Johnstone et al. (2021). Since Poppenhaeger (2022) calculated the absorption based on two lines that are absent in most of the spectra, there may be systematic under- or over-estimation in this calculation. Moreover, most lines above ∼370 Å are absent in EUVE spectra, and some of the observed lines are actually the second order of stronger bluewards lines. An example is the EUVE spectrum of AD Leo (Sanz-Forcada & Micela 2002), a star at only ∼5 pc from us. The low quality spectrum of AD Leo shown in Fig. 9 of Poppenhaeger (2022) came from an automatic reduction available in HEASARC, quite below the quality level that can be achieved by a customized data reduction, which would anyway be insufficient to accurately calculate the flux in the 200–504 Å spectral range. In Fig. A.5 we show the fit that we did to our calculated EUV fluxes in this range, as compared with the Poppenhaeger (2022) fits (their relation was also applied by Fossati et al. 2023). They are obviously discrepant. Our linear fit is logLEUV,200−504Å=(0.855±0.033)CX+(27.66±0.04),$\log {L_{{\rm{EUV}},200 - 504{\AA}}} = (0.855 \pm 0.033){C_{\rm{X}}} + (27.66 \pm 0.04),$(A.3)

where CX = log LX − 27.44 in c.g.s. units. This is valid in the range log LX ~ 25.5 − 30.5. This fit has a Pearson’s correlation factor r = 0.951 and an RMS=0.326. The spectral range used to calculate LX by Poppenhaeger (2022) was 0.2–5 keV, instead of our 0.12–2.4 keV range. We tested the impact of this difference by measuring the flux in an active (AD Leo) star and a more quiet (GJ 357) star. The flux in the 0.2–5 keV range is ~ 4% lower for AD Leo, and ~0.3 dex lower for GJ 357, thus increasing the differences between the two relations.

thumbnail Fig. A.3

EUV vs. X-ray flux with our data and the fitby SF11. 1σ error bands to both fits, and their original datasets, are displayed in light gray and red respectively.
thumbnail Fig. A.4

EUV vs. X-ray surface flux with our data and some literature fits. 1σ error bands to our fit is displayed in light gray.
thumbnail Fig. A.5

X-ray vs. EUV (in the range 200–504 Å) luminosity with our data and the fits calculated by Poppenhaeger (2022). 1σ error bands to our fit are displayed in light gray.

Appendix B Relations between He I λ10 830 Å equivalent width and XUV flux

In this section, we seek an empirical relationship between the stellar XUV irradiation, measured in the 5–504 Å range, and the equivalent width (EW) of the He I λ10 830 Å line in the planet atmosphere. The equivalent width, EW, of an absorbing line over the frequency interval Δν in a planetary atmosphere during the primary transit is given by EW≃∫Δν𝓐 ν dνπR⋆2,$EW \simeq {{\int_{\Delta v} {{_{\,v}}} {\rm{d}}v} \over {\pi R_ \star ^2}},$(B.1)

where ν is the frequency, 𝒜ν is the absorption of the entire planetary atmosphere, R⋆ is the stellar radius, and we assume that R⋆2≫Rp2.$R_ \star ^2 \gg R_p^2.$. The absorption 𝒜ν is obtained by integrating the partial absorption of the areas covered by infinitesimal spherical rings over all impact parameter b values (see, e.g., Sect. 3.3 in Lampón et al. 2020 and Fig. B.1) as: 𝓐ν=2π∫RpR*b[ 1−Tν(b) ]db,${_v} = 2\pi \int_{{R_p}}^{{{\rm{R}}_*}} b \left[ {1 - {{\cal T}_v}(b)} \right]{\rm{d}}b,$(B.2)

where we assume spherical symmetry, Rp is the radius of the planet, TOA is the top of the atmosphere in front of the star, and the transmission 𝒯ν is given by Tν(b)=exp[ −∫−TOATOAkν(x)n(x)dx ],${{\cal T}_v}(b) = \exp \left[ { - \int_{ - {\rm{TOA}}}^{{\rm{TOA}}} {{k_v}} (x)n(x){\rm{d}}x} \right],$(B.3)

where kν is the absorption coefficient (also denoted by σν(x), the absorption cross section) of the He(23S) lines and n(x) is the He(23 S) concentration.

To estimate the dependence of EW on the different parameters, we considered the two extreme conditions of (a) optically thick, where the transmission near the line center, 𝒯ν=He I(b), is close to zero, and (b) optically thin, where 𝒯ν=He I (b) is close to unity. This approach in two extreme situations seems reasonable as we know that most gas giant atmospheres have, in general, a narrow (compressed) region at low altitudes with large He(23S) concentrations, and an extended and slowly decreasing He(23S) concentration at medium to larger radii (see, e.g., Fig. A.1 in Lampón et al. 2023). The first region can be considered in optically thick conditions while the latter in the optically thin regime.

B.1 Optically thick

In this case, 𝒯 (b) ≃ 0, the EW is given by that produced by an opaque ring of height HHe,0. From Eqs. B.1 and B.2, with 𝒯 (b) ≃ 0, we obtain EWthick ∝2RpHHe,0R⋆2.$E{W_{{\rm{thick }}}} \propto {{2{R_{\rm{p}}}{H_{{\rm{He}},0}}} \over {R_ \star ^2}}.$(B.4)

thumbnail Fig. B.1

He(23S) column along the line of sight, x, at the impact parameter, b, and distance from the center of the planet, r.

To estimate the extension of the opaque region, HHe,0, it is reasonable to assume that it is proportional to the irradiating XUV flux FXUV, as this flux controls the He(23S) concentration that enters into Eq. B.3. In fact, the planets with larger XUV fluxes have larger peaks of He(23S) concentrations (see Fig. A.1 in Lampón et al. 2023). In addition, for a planet with a stronger gravitational potential, Φp, it is expected that its atmosphere (and the He(23S) concentration) is more compressed and hence HHe,0 should be smaller. It is then reasonable that in this optically thick limit we have EWthick ∝RpR⋆2FXuVΦp.$E{W_{{\rm{thick }}}} \propto {{{R_{\rm{p}}}} \over {R_ \star ^2}}{{{F_{{\rm{XuV}}}}} \over {{\Phi _{\rm{p}}}}}.$(B.5)

B.2 Optically thin

In this case the transmission over the interval Δν can be approximated by T(b)≃1−∫−TOATOAk(x)n(x)dx=1−km(b),${\cal T}(b) \simeq 1 - \int_{ - {\rm{TOA}}}^{{\rm{TOA}}} k (x)n(x){\rm{d}}x = 1 - km(b),$(B.6)

where m(b)=∫−TOATOAn(x)  dx$\[m(b)=\int_{-\text{TOA}}^{\text{TOA}}{n}(x)\,\,\text{d}x\]$ is the column density along the line of sight at impact parameter b (see Fig. B.1) and we have assumed that the absorption coefficient does not depend on x. Assuming spherical symmetry and changing the integration variable to r, the distance from the center of the planet, e.g., x=r2−b2$\[x=\sqrt{{{r}^{2}}-{{b}^{2}}}\]$ and dx=rr2−b2 dr$\[\text{d}x=\frac{r}{\sqrt{{{r}^{2}}-{{b}^{2}}}}~\text{d}r\]$, we obtain m(b)=2∫b∞n(r)rr2−b2 dr.$m(b) = 2\int_b^\infty {{{n(r)r} \over {\sqrt {{r^2} - {b^2}} }}} {\rm{d}}r.$(B.7)

To further evaluate m(b) and the EW let us make some assumptions on n(r). The He(23S) concentration can be well approximated by n(r)=n0(r0/r)p,$n(r) = {n_0}{\left( {{r_0}/r} \right)^p},$(B.8)

where the exponent p usually takes values between 2 and 5 and n0 is the He(23S) concentration at r0 (see, e.g., Fig. A.1(c) in Lampón et al. 2023). Note that the He(23S) peak concentration, n0, usually occurs very close to the lower boundary of the atmosphere; hence r0 ≃ RP. Then, we obtain m(b)≃2n0RPp∫b∞r1−pr2−b2 dr,$m(b) \simeq 2{n_0}R_P^p\int_b^\infty {{{{r^{1 - p}}} \over {\sqrt {{r^2} - {b^2}} }}} {\rm{d}}r,$(B.9)

and, by performing the integral, we obtain m(b)≃πn0RPpΓ((p−1)/2)Γ(p/2)b1−p,$m(b) \simeq \sqrt \pi {n_0}R_P^p{{\Gamma ((p - 1)/2)} \over {\Gamma (p/2)}}{b^{1 - p}},$(B.10)

valid for p > 1, which is amply met in our case.

thumbnail Fig. B.2

He I 10 830 triplet equivalent width, plotted against FXUV,He. 1σ error bands to the fit are displayed in light blue. Colors and symbols as in Fig. 4. Pearson’s coefficient is r = 0.579
thumbnail Fig. B.3

He I 10 830 triplet equivalent width, multiplied by the stellar area, plotted against FXUV,He. The color scheme indicates the stellar spectral types, with symbols as in Fig. 4. The fit gives r = 0.782.

Including this expression into Eq. B.6, and considering Eqs. B.1 and B.2, we obtain EW≃2πΓ((p−1)/2)Γ(p/2)k n0RPpR⋆2∫RPR⋆b2−p db.$EW \simeq 2\sqrt \pi {{\Gamma ((p - 1)/2)} \over {\Gamma (p/2)}}k\,{n_0}{{R_{\rm{P}}^p} \over {R_ \star ^2}}\int_{{R_P}}^{{R_ \star }} {{b^{2 - p}}} {\rm{d}}b.$(B.11)

Performing the integral in Eq. B.11 and considering that R∗ ≫ RP, we find that the integral is independent of RP for 1 < p < 3, it is proportional to ln(R*/RP) for p = 3, and is proportional to RP3−p$R_P^{3 - p}$ for p > 3. Hence, as the Γ functions are constants, EWthin ∝1R⋆2FXUVΦp×{ Rpp for 1<p<3,RP3ln(R*/RP) for p=3, and RP3 for p>3, $E{W_{{\rm{thin }}}} \propto {1 \over {R_ \star ^2}}{{{F_{{\rm{XUV}}}}} \over {{\Phi _{\rm{p}}}}} \times \left\{ {\matrix{ {R_p^p} \hfill & {{\rm{ for }}1 < p < 3,} \hfill \cr {R_P^3\ln \left( {{R_*}/{R_P}} \right)} \hfill & {{\rm{ for }}p = 3,{\rm{ and }}} \hfill \cr {R_P^3} \hfill & {{\rm{ for }}p > 3,} \hfill \cr } } \right.$(B.12)

where we also considered that n0 ∝ FXUV and the EW is, as in the case of the optically thick, proportional to 1/Φp. Then, for a given planet with an He(23 S) concentration n(r) profile with a slope p as in Eq. B.8, the EW in the optically thin limit would be proportional to Rpγ$R_p^\gamma $ with γ ranging from 1 to 3. For the optically thick limit we obtain a dependence directly proportional to Rp. Hence, overall, we expect a dependence of EW of the form of EW∝1R⋆2FXuVΦpRpγ,$EW \propto {1 \over {R_ \star ^2}}{{{F_{{\rm{XuV}}}}} \over {{\Phi _{\rm{p}}}}}R_{\rm{p}}^\gamma ,$(B.13)

with γ varying between 1 and 3 depending on the specific conditions of the planets.

thumbnail Fig. B.4

He I 10 830 triplet equivalent width, multiplied by the stellar area, plotted against FXUV,He multiplied by planet radius Rp , divided by the planet gravitational potential Φp (in Jovian units). Colors and symbols are similar to Fig. 4. The fit gives r = 0.891.
Table B.1

Fits using different exponents on planet radiia .

We probed the dependence on the stellar area in Fig. B.3, with a substantial improvement with respect to Fig. B.2. If we consider the relation between EW⋅R⋆2$EW \cdot R_ \star ^2$ and FXUV,He/Φp${F_{{\rm{XUV}},{\rm{He}}}}/{\Phi _{\rm{p}}}$ and FXUV,He/ΦΡ we get a Pearson’s correlation factor of r = 0.803. For the relation between EW⋅R⋆2$EW \cdot R_ \star ^2$ and FXUV,He⋅Rp2${F_{{\rm{XUV}},{\rm{He}}}} \cdot R_{\rm{p}}^2$ we get a correlation factor of r = 0.843, and for that against FXUV,He · Rp/Φp we reach r = 0.891 (Fig. B.4). Finally, a dependence on FXUV,He⋅Rp2/Φp${F_{{\rm{XUV}},{\rm{He}}}} \cdot R_{\rm{p}}^2/{\Phi _{\rm{p}}}$ results in a further improvement (Fig. 4, r = 0.898). Table B.1 shows the r and RMS of the fits with different exponents of Rp . If we use EW · R★ against FXUV,He⋅Rp2/Φp~ρp${F_{{\rm{XUV}},{\rm{He}}}} \cdot R_{\rm{p}}^2/{\Phi _{\rm{p}}}\~{\rho _p}$ as in Zhang et al. (2023a) assuming that RXUV =Rp , our data improve their log-log fit, with a correlation coefficient of r = 0.857, but it is still worse than the fit using EW⋅R⋆2$EW \cdot R_ \star ^2$.

Appendix C Main tables

Table C.1

X-rays observation log of stars with exoplanets.

Table C.2

UV observations of stars in the samplea.

Table C.3

X-ray (5–100 Å), EUVH (100–920 Å), and EUVHe (100–504 Å) luminosities of stars in the sample a.

Table C.4

He I 10 830 Å triplet equivalent width and XUV (5–504 Å) flux at planet distance.

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1

Lines at 10829.09, 10830.25, 10830.34 Å in the air, and 10832.06, 10833.22, 10833.31 Å in vacuum.

3

The XMM-Newton pointings were not always properly corrected for the proper motion of the star, resulting in small radial velocity shifts between different datasets.

4

Sensitivity ranges and resolution of the gratings: E140M 1144–1710 Å, λ/Δλ = 45 800; G140L 1150–1730 Å, λ/Δλ ~ 960–1440; G140M 1140–1740 Å, λ/Δλ ~ 11 400–17 400.

5

Sensitivity ranges and resolution in the gratings: G130M 900–1450Å, λ/Δλ ~ 12000–17 000; G160M 1360–1775Å, λ/Δλ ~ 13 000–20 000.

6

The fluxes of this multiplet, calculated with current version of ATOMDB, do not match those of the observed counterparts.

10

We are more confident on our calculation assuming a blackbody emission than on the X-ray flux upper limit provided in Table C.3. The XUVH flux in this star is more than four orders of magnitude higher than XUVHe flux if we assume a blackbody emission.

11

DUV21 DEM was based on a different dataset from ours.

All Tables

Table A.1

Comparison of modeled EUV broadband luminositiesa .

In the text
Table B.1

Fits using different exponents on planet radiia .

In the text
Table C.1

X-rays observation log of stars with exoplanets.

In the text
Table C.2

UV observations of stars in the samplea.

In the text
Table C.3

X-ray (5–100 Å), EUVH (100–920 Å), and EUVHe (100–504 Å) luminosities of stars in the sample a.

In the text
Table C.4

He I 10 830 Å triplet equivalent width and XUV (5–504 Å) flux at planet distance.

In the text

All Figures

thumbnail Fig. 1

Coronal models of Proxima Cen (left) and AU Mic (right), combining data from XMM-Newton, EUVE, HST/STIS, and FUSE. Upper panels: emission measure distributions (EMDs, thick line). The thin lines represent the contribution function for each ion (the emissivity function multiplied by the EMD at each point). The small numbers indicate the ionization stages of the species. Lower panels: observed-to-predicted line flux ratios for the ion stages in the upper panels. The dashed lines denote a factor of 2.
In the text
thumbnail Fig. 2

Same as in Fig. 1, but for AD Leo (GJ 388, left) and Lalande 21185 (right), combining data from Chandra, EUVE, and HST/STIS (AD Leo), and XMM-Newton and HST/STIS (Lalande 21185).
In the text
thumbnail Fig. 3

EUV vs X-ray luminosities in two different EUV ranges for the H (100–920 Å) and He ionization (100–504 Å). There are different scales for the two EUV luminosity ranges. Left: linear fit over EUV against X-ray luminosity. Right: quadratic fit over the luminosity ratios with the bolometric luminosity.
In the text
thumbnail Fig. 4

He I 10 830 triplet equivalent width, multiplied by the stellar area, plotted against FXUV,He, weighted by ϕp/Rp2${\phi _{\rm{p}}}/R_{\rm{p}}^2$, i.e., by the planet density. The 1σ error bands to the fit, calculated only with positive detections (filled symbols), are displayed in light blue. Different colors indicate the method used to calculate the XUV flux in the 5–504 Å range (see Sect. 4.4). Half-filled symbols are used for the equivalent width upper limits calculated by our team, while those calculated by other authors are shown in open symbols.
In the text
thumbnail Fig. 5

He I 10 830 triplet equivalent width, multiplied by the stellar area, plotted against planet density 1σ error bars are indicated. Same colors and symbols to Fig. 4 apply for an easier identification. Labels are included for some planets detected as upper limits (see Sect. 5.2).
In the text
thumbnail Fig. A.1

EMD calculated in our work, with shaded 1σ error bands, as compared with those of LOU17 and DUV21. Dashed lines indicate an uncertain EMD despite formal error bands. The results from our global fit to the X-ray spectra are indicated with error bars.
In the text
thumbnail Fig. A.2

EMDs calculated from the DEM published in LOU17 and DUV21, using our line fluxes measurements to test the quality of the fit. Symbols and lines as in Fig. 1. In the lower panels the axis range has been adapted to show all available line fluxes ratios. An offset of one order of magnitude is indicated with dotted lines.
In the text
thumbnail Fig. A.3

EUV vs. X-ray flux with our data and the fitby SF11. 1σ error bands to both fits, and their original datasets, are displayed in light gray and red respectively.
In the text
thumbnail Fig. A.4

EUV vs. X-ray surface flux with our data and some literature fits. 1σ error bands to our fit is displayed in light gray.
In the text
thumbnail Fig. A.5

X-ray vs. EUV (in the range 200–504 Å) luminosity with our data and the fits calculated by Poppenhaeger (2022). 1σ error bands to our fit are displayed in light gray.
In the text
thumbnail Fig. B.1

He(23S) column along the line of sight, x, at the impact parameter, b, and distance from the center of the planet, r.
In the text
thumbnail Fig. B.2

He I 10 830 triplet equivalent width, plotted against FXUV,He. 1σ error bands to the fit are displayed in light blue. Colors and symbols as in Fig. 4. Pearson’s coefficient is r = 0.579
In the text
thumbnail Fig. B.3

He I 10 830 triplet equivalent width, multiplied by the stellar area, plotted against FXUV,He. The color scheme indicates the stellar spectral types, with symbols as in Fig. 4. The fit gives r = 0.782.
In the text
thumbnail Fig. B.4

He I 10 830 triplet equivalent width, multiplied by the stellar area, plotted against FXUV,He multiplied by planet radius Rp , divided by the planet gravitational potential Φp (in Jovian units). Colors and symbols are similar to Fig. 4. The fit gives r = 0.891.
In the text

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