biomarkers unadjusted for the established biomarkers

Our Method Standard EM $\bm{\hat{\beta}}$ $\widehat{\mathrm{SE}}$ 2.5% 97.5%
$p-$value $\bm{\hat{\beta}}$ $\widehat{\mathrm{SE}}$ 2.5% 97.5% $p-$value
log(Urine albumin) 0.56 0.06 0.44 0.68 $<0.01$ 2.54 0.08 2.38 2.69 $<0.01$
Urine creatinine -11.98 1.33 -14.79 -9.30 $<0.01$ -11.88 1.33 -14.69 -9.29
$<0.01$ log(HS_CRP) 0.02 0.04 -0.04 0.11 0.54 -0.02 0.06 -0.12 0.10 0.76
log(BNP) 0.45 0.04 0.38 0.54 $<0.01$ 0.49 0.06 0.38 0.61 $<0.01$ CXCL12 266.41
27.17 212.50 318.62 $<0.01$ 265.34 27.12 210.83 316.36 $<0.01$ Scaled FETUIN_A
-0.69 0.51 -1.75 0.26 0.17 -0.72 0.51 -1.77 0.23 0.16 Fractalkine 0.16 0.01
0.14 0.18 $<0.01$ 0.22 0.02 0.19 0.26 $<0.01$ MPO 43.04 16.99 11.20 78.69 0.01
43.07 16.95 11.28 78.69 0.01 log(NGAL) 0.30 0.06 0.14 0.38 $<0.01$ 0.83 0.06
0.73 0.95 $<0.01$ Fibrinogen 0.29 0.04 0.23 0.39 $<0.01$ 0.76 0.05 0.65 0.88
$<0.01$ Troponini 0.01 2e-3 3e-3 0.01 $<0.01$ 8e-3 3e-3 2e-3 0.01 $<0.01$
log(Urine calcium) -0.41 0.03 -0.47 -0.36 $<0.01$ -0.58 0.045 -0.67 -0.48
$<0.01$ Urine sodium -7.51 1.33 -9.82 -4.82 $<0.01$ -7.49 1.32 -9.78 -4.79
$<0.01$ Urine potassium -3.40 0.50 -4.40 -2.44 $<0.01$ -3.33 0.4 -4.32 -2.37
$<0.01$ Urine phosphate -4.33 0.74 -5.77 -2.81 $<0.01$ -4.34 0.73 -5.79 -2.87
$<0.01$ TNTHS 20.22 1.64 17.19 23.58 $<0.01$ 20.12 1.63 17.12 23.48 $<0.01$
log(Aldosterone) 0.08 0.02 0.04 0.13 $<0.01$ 0.14 0.03 0.08 0.21 $<0.01$
C-peptide 0.37 0.06 0.24 0.49 $<0.01$ 0.64 0.10 0.45 0.84 $<0.01$ Insulin 1.31
1.05 -0.74 3.37 0.21 1.27 1.05 -0.79 3.34 0.23 TOTAL PTH 54.48 4.68 46.19
64.22 $<0.01$ 54.42 4.69 46.11 64.22 $<0.01$ $\mathrm{CO}_{2}$ -0.99 0.19
-1.17 -0.80 $<0.01$ -1.41 0.15 -1.69 -1.11 $<0.01$ log(24-hour urine protein)
0.44 0.04 0.36 0.53 $<0.01$ 2.06 0.06 1.94 2.19 $<0.01$ EGFR -13.07 0.47
-13.98 -12.13 $<0.01$ -12.95 0.47 -13.88 -12.00 $<0.01$

Figure 8: Histograms of the MSEs of the EM envelope estimator, the complete
case (CC) envelope estimator, the full data envelope estimator, the standard
EM estimator, the standard complete case (CC) estimator and the full data MLE
when $\bm{\Omega}_{0}=10\mathbf{I}_{q}$.

(a) EM envelope

(b) CC Envelope

(c) Full data envelope

(d) Standard EM

(e) Standard CC

(f) Full data MLE

## References

  * Anderson et al. (2015) Anderson, A., Yang, W., Townsend, R., Pan, Q., Chertow, G., Kusek, J., Charleston, J., He, J., Kallem, R., Lash, J., et al. (2015).  Time-updated systolic blood pressure and the progression of chronic kidney disease: a cohort study.  Annals of Internal Medicine, 162:258–265.
  * Bansal et al. (2013) Bansal, N., Keane, M., Delafontaine, P., Dries, D., Foster, E., Gadegbeku, C., Go, A., Hamm, L., Kusek, J., Ojo, A., et al. (2013).  A longitudinal study of left ventricular function and structure from CKD to ESRD: the CRIC study.  Clinical Journal of the American Society of Nephrology, 8:355–362.
  * Breiman and Friedman (1997) Breiman, L. and Friedman, J. H. (1997).  Predicting multivariate responses in multiple linear regression.  Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59:3–54.
  * Budoff et al. (2011) Budoff, M., Rader, D., Reilly, M., Mohler, E., Lash, J., Yang, W., Rosen, L., Glenn, M., Teal, V., and Feldman, H. (2011).  Relationship of estimated GFR and coronary artery calcification in the CRIC (Chronic Renal Insufficiency Cohort) study.  American Journal of Kidney Diseases, 58:519–526.
  * Capuano et al. (2003) Capuano, V., Bambacaro, A., D’Arminio, T., Vecchio, G., and Cappuccio, L. (2003).  Correlation between body mass index and others risk factors for cardiovascular disease in women compared with men.  Monaldi Archives for Chest Disease, 60:295–300.
  * Chen et al. (2008) Chen, Q., Ibrahim, J. G., Chen, M.-H., and Senchaudhuri, P. (2008).  Theory and inference for regression models with missing responses and covariates.  Journal of multivariate analysis, 99:1302–1331.
  * Cook (2018) Cook, R. D. (2018).  Principal Components, Sufficient Dimension Reduction, and Envelopes.  Annual Review of Statistics and Its Application, 5:533–559.
  * Cook et al. (2016) Cook, R. D., Forzani, L., and Su, Z. (2016).  A note on fast envelope estimation.  Journal of Multivariate Analysis, 150:42–54.
  * Cook et al. (2015) Cook, R. D., Forzani, L., and Zhang, X. (2015).  Envelopes and reduced-rank regression.  Biometrika, 102:439–456.
  * Cook et al. (2013) Cook, R. D., Helland, I., and Su, Z. (2013).  Envelopes and partial least squares regression.  Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75:851–877.
  * Cook et al. (2010) Cook, R. D., Li, B., and Chiaromonte, F. (2010).  Envelope models for parsimonious and efficient multivariate linear regression.  Statistica Sinica, 20:927–960.
  * Cook and Su (2013) Cook, R. D. and Su, Z. (2013).  Scaled envelopes: scale-invariant and efficient estimation in multivariate linear regression.  Biometrika, 100:939–954.
  * Cook and Zhang (2015a) Cook, R. D. and Zhang, X. (2015a).  Foundations for envelope models and methods.  Journal of the American Statistical Association, 110:599–611.
  * Cook and Zhang (2015b) Cook, R. D. and Zhang, X. (2015b).  Simultaneous envelopes for multivariate linear regression.  Technometrics, 57:11–25.
  * Cook and Zhang (2016) Cook, R. D. and Zhang, X. (2016).  Algorithms for envelope estimation.  Journal of Computational and Graphical Statistics, 25:284–300.
  * Cook and Zhang (2018) Cook, R. D. and Zhang, X. (2018).  Fast envelope algorithms.  Statistica Sinica, 28:1179–1197.
  * Dong and Li (2010) Dong, Y. and Li, B. (2010).  Dimension reduction for non-elliptically distributed predictors: second-order methods.  Biometrika, 97:279–294.
  * Eck and Cook (2017) Eck, D. J. and Cook, R. D. (2017).  Weighted envelope estimation to handle variability in model selection.  Biometrika, 104:743–749.
  * Feldman et al. (2003) Feldman, H., Appel, L., Chertow, G., Cifelli, D., Cizman, B., Daugirdas, J., Fink, J., Franklin-Becker, E., Go, A., Hamm, L., et al. (2003).  The chronic renal insufficiency cohort (CRIC) study: design and methods.  Journal of the American Society of Nephrology, 14:S148–S153.
  * Ferguson et al. (2013) Ferguson, J., Matthews, G., Townsend, R., Raj, D., Kanetsky, P., Budoff, M., Fischer, M., Rosas, S., Kanthety, R., Rahman, M., et al. (2013).  Candidate gene association study of coronary artery calcification in chronic kidney disease: findings from the CRIC study (Chronic Renal Insufficiency Cohort).  Journal of the American College of Cardiology, 62:789–798.
  * Foster et al. (2015) Foster, M. C., Coresh, J., Bonventre, J. V., Sabbisetti, V. S., Waikar, S. S., Mifflin, T. E., Nelson, R. G., Grams, M., Feldman, H. I., Vasan, R. S., et al. (2015).  Urinary biomarkers and risk of esrd in the atherosclerosis risk in communities study.  Clinical Journal of the American Society of Nephrology, 10:1956–1963.
  * He et al. (2012) He, J., Reilly, M., Yang, W., Chen, J., Go, A., Lash, J., Rahman, M., DeFilippi, C., Gadegbeku, C., Kanthety, R., et al. (2012).  Risk factors for coronary artery calcium among patients with chronic kidney disease (from the Chronic Renal Insufficiency Cohort study).  American Journal of Cardiology, 110:1735–1741.
  * Henderson and Searle (1979) Henderson, H. V. and Searle, S. (1979).  Vec and vech operators for matrices, with some uses in jacobians and multivariate statistics.  Canadian Journal of Statistics, 7:65–81.
  * Hotelling (1936) Hotelling, H. (1936).  Relations between two sets of variates.  Biometrika, 28:321–377.
  * Hristache and Patilea (2017) Hristache, M. and Patilea, V. (2017).  Conditional moment models with data missing at random.  Biometrika, 104:735–742.
  * Ibrahim et al. (2008) Ibrahim, J. G., Zhu, H., and Tang, N. (2008).  Model selection criteria for missing-data problems using the em algorithm.  Journal of the American Statistical Association, 103:1648–1658.
  * Inker et al. (2017) Inker, L. A., Coresh, J., Sang, Y., Hsu, C.-y., Foster, M. C., Eckfeldt, J. H., Karger, A. B., Nelson, R. G., Liu, X., Sarnak, M., et al. (2017).  Filtration markers as predictors of ESRD and mortality: individual participant data meta-analysis.  Clinical Journal of the American Society of Nephrology, 12:69–78.
  * Jia et al. (2010) Jia, J., Benjamini, Y., Lim, C., Raskutti, G., and Yu, B. (2010).  Envelope models for parsimonious and efficient multivariate linear regression comment.
  * Li and Wang (2007) Li, B. and Wang, S. (2007).  On directional regression for dimension reduction.  Journal of the American Statistical Association, 102:997–1008.
  * Li and Zhang (2017) Li, L. and Zhang, X. (2017).  Parsimonious tensor response regression.  Journal of the American Statistical Association, 112:1131–1146.
  * Little (1992) Little, R. J. (1992).  Regression with missing x’s: a review.  Journal of the American Statistical Association, 87:1227–1237.
  * Little and Rubin (2014) Little, R. J. and Rubin, D. B. (2014).  Statistical Analysis with Missing Data, volume 333.  John Wiley & Sons.
  * Louis (1982) Louis, T. A. (1982).  Finding the observed information matrix when using the em algorithm.  Journal of the Royal Statistical Society. Series B (Methodological), 44:226–233.
  * Madjid and Fatemi (2013) Madjid, M. and Fatemi, O. (2013).  Components of the complete blood count as risk predictors for coronary heart disease: in-depth review and update.  Texas Heart Institute Journal, 40:17–29.
  * Meng and Rubin (1991) Meng, X.-L. and Rubin, D. B. (1991).  Using em to obtain asymptotic variance-covariance matrices: The sem algorithm.  Journal of the American Statistical Association, 86:899–909.
  * Park et al. (2017) Park, M., Hsu, C.-Y., Go, A. S., Feldman, H. I., Xie, D., Zhang, X., Mifflin, T., Waikar, S. S., Sabbisetti, V. S., Bonventre, J. V., et al. (2017).  Urine kidney injury biomarkers and risks of cardiovascular disease events and all-cause death: The CRIC study.  Clinical Journal of the American Society of Nephrology, 12:761–771.
  * Robins and Rotnitzky (1995) Robins, J. and Rotnitzky, A. (1995).  Semiparametric efficiency in multivariate regression models with missing data.  Journal of the American Statistical Association, 90:122–129.
  * Robins et al. (1994) Robins, J. M., Rotnitzky, A., and Zhao, L. P. (1994).  Estimation of regression coefficients when some regressors are not always observed.  Journal of the American statistical Association, 89:846–866.
  * Shao (2003) Shao, J. (2003).  Mathematical Statistics.  Springer Science & Business Media.
  * Shapiro (1986) Shapiro, A. (1986).  Asymptotic theory of overparameterized structural models.  Journal of the American Statistical Association, 81:142–149.
  * Shi et al. (2020) Shi, Y., Ma, L., and Liu, L. (2020).  Mixed effects envelope models.  Stat.
  * Su and Cook (2012) Su, Z. and Cook, R. D. (2012).  Inner envelopes: efficient estimation in multivariate linear regression.  Biometrika, 99:687–702.
  * Su et al. (2016) Su, Z., Zhu, G., Chen, X., and Yang, Y. (2016).  Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression.  Biometrika, 103:579–593.
  * Sun et al. (2018) Sun, B., Liu, L., Miao, W.and Wirth, K., Robins, J., and Tchetgen Tchetgen, E. (2018).  Semiparametric estimation with data missing not at random using an instrumental variable.  Statistica Sinica, 28:1965–1983.
  * Sun and Liu (2018) Sun, Z. and Liu, L. (2018+).  Semiparametric inference with missing not at random confounders.  Statistica Sinica, in press.
  * Wang et al. (2020) Wang, J., Chen, H., and Liu, L. (2020).  Semiparametric envelope-based partial least square.  in preparation.
  * Wu (1983) Wu, C. J. (1983).  On the convergence properties of the em algorithm.  The Annals of statistics, 11:95–103.
  * Ye and Weiss (2003) Ye, Z. and Weiss, R. E. (2003).  Using the bootstrap to select one of a new class of dimension reduction methods.  Journal of the American Statistical Association, 98:968–979.
  * Yin et al. (2008) Yin, X., Li, B., and Cook, R. D. (2008).  Successive direction extraction for estimating the central subspace in a multiple-index regression.  Journal of Multivariate Analysis, 99(8):1733–1757.
  * Zhu and Zeng (2006) Zhu, Y. and Zeng, P. (2006).  Fourier methods for estimating the central subspace and the central mean subspace in regression.  Journal of the American Statistical Association, 101(476):1638–1651.


# Helium absorption in exoplanet atmospheres is connected to stellar coronal
abundances

K. Poppenhaeger1,2
1Leibniz Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, 14482
Potsdam, Germany
2Universität Potsdam, Institut für Physik und Astronomie, Karl-Liebknecht-
Straße 24/25, 14476 Potsdam, Germany E-mail<EMAIL_ADDRESS>
(Accepted 2022 February 17. Received 2022 February 17; in original form 2021
September 14)

###### Abstract

Transit observations in the helium triplet around 10830 Angstrom are a
successful tool to study exoplanetary atmospheres and their mass loss. Forming
those lines requires ionisation and recombination of helium in the
exoplanetary atmosphere. This ionisation is caused by stellar photons at
extreme ultra-violet (EUV) wavelengths; however, no currently active
telescopes can observe this part of the stellar spectrum. The relevant part of
the stellar EUV spectrum consists of individual emission lines, many of them
being formed by iron at coronal temperatures. The stellar iron abundance in
the corona is often observed to be depleted for high-activity low-mass stars
due to the first ionisation potential (FIP) effect. I show that stars with
high versus low coronal iron abundances follow different scaling laws that tie
together their X-ray emission and the narrow-band EUV flux that causes helium
ionisation. I also show that the stellar iron to oxygen abundance ratio in the
corona can be measured reasonably well from X-ray CCD spectra, yielding
similar results to high-resolution X-ray observations. Taking coronal iron
abundance into account, the currently observed large scatter in the
relationship of EUV irradiation with exoplanetary helium transit depths can be
reduced, improving the target selection criteria for exoplanet transmission
spectroscopy. In particular, previously puzzling non-detections of helium for
Neptunic exoplanets are now in line with expectations from the revised scaling
laws.

###### keywords:

stars: abundances – stars: coronae – planets and satellites: atmospheres –
stars: late-type – ultraviolet: stars – X-rays: stars

††pubyear: 2022††pagerange: Helium absorption in exoplanet atmospheres is
connected to stellar coronal abundances –7

##  1 Introduction

Atmospheres of exoplanets can be detected and characterised in a variety of
ways. While there are some possibilities to observe atmospheric features of
non-transiting planets (e.g. Snellen et al. 2014; Birkby et al. 2017), the
overwhelming majority of exoplanets whose atmospheres have been observed
successfully are exoplanets in transiting orbits around their host stars (e.g.
Charbonneau et al. 2002; Tinetti et al. 2007; Bean et al. 2010; Kreidberg et
al. 2014; Keles et al. 2020). Of particular interest is the fact that some
exoplanets appear to have evaporating atmospheres, which can produce gaseous
tails streaming behind the planet (Kulow et al., 2014; Ehrenreich et al.,
2015; Nortmann et al., 2018), or in some cases may even produce bow shocks in
front of the planet on its orbit (Llama et al., 2011; Cauley et al., 2015).

One method of observing such extended and escaping atmospheres is through
transmission spectroscopy, often by targeting spectral lines of volatile
atomic species such as hydrogen and helium. Typical targets are exoplanets
with a thick gaseous envelope, such as hot Jupiters and Neptunes. Observations
of the hydrogen Ly-$\alpha$ line in the ultraviolet have led to detections of
escaping atmospheres for a handful of exoplanets (Vidal-Madjar et al., 2003;
Lecavelier Des Etangs et al., 2010; Kulow et al., 2014; Ehrenreich et al.,
2015; Bourrier et al., 2018). However, such detections are complicated by the
fact that hydrogen in present in the universe all along the line of sight of
such observations. Specifically, the stellar Ly-$\alpha$ photons undergo
absorption by the extended planetary atmosphere, followed by absorption by the
interstellar medium in the line of sight between the exoplanet and the
observer. Finally, the geocorona contributes to the observed Ly-$\alpha$ line
with an emission component, so that the resulting observed line profile needs
to be analysed with great care in order to isolate the exoplanetary
atmospheric effect (Vidal-Madjar et al., 2003).

Oklopčić & Hirata (2018) presented calculations showing that the metastable
lines of helium in the infrared at 10830 Å should produce strong observable
signatures of exoplanetary absorption during transits, which was already
proposed by Seager & Sasselov (2000). In contrast to the hydrogen Ly-$\alpha$
line, this line of helium is not vulnerable to absorption by the interstellar
medium, because the lower level of the line transition is not the ground
state, but a metastable level reached after ionisation and recombination. The
helium in the interstellar medium is typically not present in this state and
therefore does not absorb at 10830 Å. Subsequently, several detections of
exoplanetary atmospheric absorption in the HeI10830 line have been made in the
past two years (see for example Mansfield et al. 2018; Nortmann et al. 2018;
Allart et al. 2019; Alonso-Floriano et al. 2019; Guilluy et al. 2020; Paragas
et al. 2021).

How helium atoms reach the lower state of the metastable HeI10830 transition
is a matter of detailed research in the solar and stellar community (see
Linsky (2017) for a review). The Sun displays some contrast in the He10830
line across the solar disk, with active regions being darker in HeI10830 than
the quiescent solar atmosphere. Understanding the profiles of the solar helium
lines, both the resonance lines in the UV and the metastable lines in the
near-infrared, is non-trivial. Early models of the solar transition region
struggled to produce the required ionisation fraction to match observed line
profiles and needed to impose ad hoc constraints on local temperatures
(Jordan, 1975; Vernazza et al., 1981). It turned out that ambipolar diffusion
– where ions diffuse into the cooler, less ionised regions and atoms diffuse
into the hotter, more ionised regions of the transition region – as well as
backwarming from the corona play an important role in the ionisation and
excitation balances of the transition region (Fontenla et al., 1990, 1993).

Andretta & Jones (1997) argued that in the solar case the metastable state of
helium can be reached with two main pathways, one being via photoionisation
plus recombination of helium, the other being collisional excitation from the
ground state. While the radiative transition from the metastable state to the
ground state is slow, electron collisions can still depopulate the metastable
state by transferring the atom either directly to the ground state or
alternatively to the excited singlet state, which easily decays to the ground
state as well. The photoionisation and recombination pathway requires photons
with energies typically found in the stellar corona, and lines that are formed
via this pathway display spatial features on the Sun that are co-located with
coronal features. Collisional excitation requires a high enough density of
electrons with sufficient energy, and lines formed via this pathway tend to
display features co-located with solar chromospheric structures. For the Sun,
features visible in the HeI10830 line are observed in spatial agreement with
both chromospheric and coronal structures (Dupree et al., 1996; Libbrecht et
al., 2019), indicating that both pathways take place.

For stellar samples Sanz-Forcada & Dupree (2008) argued that photoionisation-
recombination is the dominant process for giant stars, while main-sequence
cool stars with their dense chromospheres can populate the metastable level
through a mix of both pathways. However, there is observational evidence that
stars with a higher activity level also display deeper HeI10830 lines,
indicating that the formation of metastable helium in stellar atmospheres is
still dominated by the photoionization-recombination pathway, where stellar
EUV photons ionize the helium first. This was concluded from observations that
show that the helium triplet absorption is well correlated with stellar high-
energy emission for F, G and K stars (Zarro & Zirin, 1986). Recent studies of
M dwarfs and their HeI10830 triplet demonstrate that the HeI10830 lines become
deeper during flares of the stars, further strengthening the assumption that
an EUV-driven photoionization plus recombination is a dominant pathway of the
formation of this line in stars.

In contrast, the atmospheres of exoplanets display very different temperatures
and densities. Oklopčić & Hirata (2018) calculates that collisional excitation
is expected at a much lower rate than the EUV-driven photoionisation and
recombination in a planetary atmosphere. Oklopčić (2019) states that stars
with higher magnetic activity, i.e. higher X-ray and UV (together, XUV)
emission levels, should produce more helium in the relevant metastable state
in an exoplanetary atmosphere. This trend was observationally confirmed for a
small sample of exoplanets by Nortmann et al. (2018), who found larger
effective exoplanet radii at the HeI10830 wavelength compared to the broadband
optical ones with higher XUV irradiation of those exoplanets. Later works,
such as Kasper et al. (2020), reported the same trend for larger samples of
exoplanets.

The stellar spectrum has a strong effect on the formation of the exoplanetary
HeI10830 absorption line. The photoionisation threshold for helium in the
ground state of the exoplanetary atmosphere is at 504 Å (Fig. 1, top panel).
The photoionisation cross section of photons with shorter wavelengths
decreases by a factor of about 20 for wavelengths of about 200 Å and below
(Yan et al., 1998). The photoionisation of exoplanetary helium by stellar
photons therefore happens practically entirely in the extreme-ultraviolet
(EUV) regime between 504 and 200 Å. While scaling relations between the X-ray
and broad-band EUV output of stars have been investigated (Sanz-Forcada et
al., 2011; King & Wheatley, 2021), the narrow EUV wavelength range relevant
for HeI10830 absorption has not been studied for its relation to X-ray
luminosity yet. The observed correlation of HeI10830 absorption with X-ray
irradiation is expected because EUV and X-ray emission are driven by the same
phenomenon in cool stars, namely magnetic activity. The stellar X-ray photons
themselves, however, do not contribute directly to the production of
exoplanetary helium in the correct state for HeI10830 absorption. Since there
are currently no astrophysical observatories operating in the wavelength
regime between 200 and 504 Å, investigating scaling relationships between
stellar soft X-rays and the relevant narrow-band EUV range is therefore
important.

In this work I aim to characterize the relationship between helium ionisation
in exoplanetary atmospheres caused by the narrow-band EUV emission of stars –
as a precursor step to the recombination process which yields helium in the
ground state of the HeI10830 line – , and the stellar X-ray emission. Present-
day X-ray observatories observe sources routinely at energies of 0.2 keV and
above, corresponding to wavelengths of about 60 Å and below. The spectra of
cool stars in the EUV and X-rays are predominantly line emission spectra from
bound-bound transitions, and I will show that many of those lines originate
from the same coronal plasma. Particularly, emission lines of iron will be
shown to play an important role. The production rate of metastable helium in
exoplanetary atmospheres can be linked not only the to ionising EUV
irradiation, but also to the more easily measurable soft X-ray irradiation,
and specifically the temperature and iron abundance of the coronal plasma.

A secondary goal of this work is to explore the potential of medium-resolution
CCD spectra in X-rays to determine relative iron abundances in coronal
plasmas. Traditionally, high-resolution X-ray spectra are used to fit
abundances of a large number of elements. However, a few elements that produce
several strong lines in soft X-rays, such as iron, oxygen, and neon, can have
measurable effects also in lower resolution spectra. This can open up a range
of only moderately X-ray bright stars to coronal abundance determinations
which would be hard to obtain otherwise.

I describe the used observations and the respective data analysis procedures
in sections 2, the results are given in section 3, and a discussion in the
context of exoplanetary atmosphere studies is given in section 4.

Figure 1: Top panel: the relative photoionisation cross section of helium in
its ground state. Middle panel: EUVE spectrum of $\epsilon$ Eri, with the
helium line at 304 Å and several strong iron lines being visible. Bottom
panel: EUVE spectrum of AU Mic, where the iron lines are much weaker in
comparison to the HeII lines. The wavelengths of the typically strongest
emission lines as given in Table 1 are marked by vertical dotted lines.

##  2 Observations and Data Analysis

I chose to analyse a sample of stars from the Extreme Ultra-Violet Explorer
(EUVE) stellar atlas (Craig et al., 1997), specifically the main-sequence
stars from spectral type A to M, plus the only pre-main sequence cool star
contained in that atlas, AB Dor. The sample is listed in Table 3. I analysed
their EUV emission as well as their X-ray emission.

The EUVE stellar atlas contains several stars that are close binaries, such as
AB Dor and BF Lyn. Those binary stars are neither spatially resolved in their
EUVE observations nor in the analysed X-ray observations. Therefore I did not
attempt to distribute the observed emission at EUV and X-ray wavelengths
between their stellar components, but used the emission from the binary system
as a whole in the following analysis.

###  2.1 Extreme ultraviolet data

The Extreme Ultra-Violet Explorer (EUVE) was a space telescope operated by
NASA from 1992 to 2001 (Bowyer & Malina, 1991). It remains the most up-to-date
high-resolution spectrometer in the extreme-UV. EUVE carried three slitless
imaging spectrometers, covering overlapping spectral regions. Specifically,
the short-wavelength (SW) spectrometer covered a range of 90–170 Å, and the
medium (MW) and long (LW) spectrometers covered the 140–380 Å and 280–760 Å
range, respectively. The spectral resolution was ca. 0.5 Å, 1 Å, and 2 Å for
the SW, MW, and LW spectrometers, respectively. To remove spectral signatures
of the Earth’s airglow and geocoronal lines, EUVE used filters for all three
spectrometers and wire-grid collimators for the MW and SL spectrometers.

The archival EUVE spectra of the stellar atlas stars are available in their
reduced form via the Mikulski Archive for Space Telescopes
(MAST)***https://archive.stsci.edu/prepds/atlaseuve/datalist.html. These
spectra are co-added for targets where several observations were conducted.
The archive provides spectra in units of photons cm-2 s-1 Å-1, in a single
file each for each of the three arms of the spectrometer, and already
corrected with respect to the effective area of EUVE. The relevant wavelength
region between 200 and 504 Å is covered by the MW and LW spectrometer arms.
Since the noise level in each arms increases close to the ends of the covered
wavelength range, I chose to stitch together the MW and LW data at a
wavelength of 330 Å, meaning that data points with shorter wavelengths come
from the MW arm and data points with longer wavelength come form the LW arm.
For plotting purposes only, the MW data points were binned by a factor of two
to have the same bin size along the x-axis in the plots.

Two examples of the spectra in the 200–500 Å region are shown in Fig. 1,
middle and lower panel. The spectrum of the high-activity M dwarf binary EQ
Peg is dominated by the helium emission lines at 256 and 304 Å, while the
spectrum of the moderately active K dwarf $\epsilon$ Eri also shows other
emission lines, mainly stemming from iron. It needs to be pointed out that the
helium ionisation cross section, which is displayed in the top panel of the
same figure, also determines how much of the intrinsic stellar spectrum gets
absorbed by the interstellar medium (ISM) on its way to the observer.
Therefore, stellar emission lines closer to the helium ionisation edge will
already be strongly suppressed in the observed spectra. I discuss the
uncertainties this introduces into the analysis in section 3.4.

The used spectral atlas data sets are already cleaned from high-background
time stretches (Craig et al., 1997). One potential concern is the HeII line at
304 Å, which is contained in the spectral range we are interested in. This
line can contain contamination from Earth’s geocorona, which to a certain
extent should already be limited by the exclusion of high background times in
the reduced spectra. To check that geocoronal emission is not a dominant
effect in the spectra, I plotted photon line fluxes versus stellar distance,
for the HeII line as well as for the summed-up fluxes of other EUV emission
lines that do not have a potential geocoronal contamination (see Table 1). If
geocoronal emission were a dominant contribution, we would expect the HeII
line flux not to follow the same trend as the other line fluxes with distance,
especially at larger distances where the intrinsic stellar line flux would be
expected to be weaker compared to a hypothetical contamination. However, Fig.
2 (top panel) clearly shows that the HeII line follows the same trend as the
other lines, indicating that geocoronal contamination of the line is not a
dominant factor in the used spectra. As an additional test I calculated the
line ratio of the He304 line versus the Fe284 line, as shown in the middle and
bottom panels of Fig. 2. If geocoronal flux in the He304 were a dominant
contribution in the observed spectra, we would expect to see an increase of
this ratio with stellar distance, because the geocoronal He304 emission would
not be affected by the distance to the target. Likewise, we would expect to
see a decrease of this ratio with increasing Fe284 flux, because the nearer
and therefore brighter stars would experience a smaller relative contamination
by geocoronal He304 emission. However, none of those trends are evident in
Fig. 2, and I conclude that geocoronal contamination is not a strong factor in
the spectra analysed here.

###  2.2 X-ray data

The X-ray observations analysed here were collected with the XMM-Newton space
telescope (Jansen et al., 2001), with details being given in the following
section. XMM-Newton carries three types of instruments onboard: a set of three
X-ray CCD cameras (Turner et al., 2001; Strüder et al., 2001), collectively
called EPIC, which provide X-ray images, light curves, and low-resolution
spectra; two Reflection Grating Spectrometers (RGS, Den Herder et al. 2001),
which provide high-resolution X-ray spectra of individual sources; and an
Optical Monitor (Mason et al., 2001) that can provide images, light curves, or
low-resolution spectra in a range of optical and near-ultraviolet bands. This
work focuses on the EPIC data of the sample stars.

####  2.2.1 X-ray observations

X-ray emission from stellar coronae can be studied in intricate detail with
high-resolution ($R\approx 1000$) X-ray observations, for example with XMM-
Newton’s RGS and Chandra’s (Weisskopf et al., 2000) Low- and High-Energy
Transmission Grating (LETG and HETG, see Brinkman et al. 2000 and Canizares et
al. 2005) instruments. However, such high-resolution observations are limited
to the very brightest stellar X-ray sources due to the low throughput of those
spectrographs. This can be an issue for future observations of exoplanet host
stars, because many of those stars of interest are either too far away or too
inactive to make the collection of high-resolution X-ray spectra feasible.
Additionally, only stars positioned at the aimpoint of any given X-ray
observation with XMM-Newton or Chandra can be used to collect high-resolution
spectra with the grating spectrographs. If a star of interest has been in the
field of view of an observation, but not at the aimpoint of the telescope, by
default only CCD spectra of the star will be available.

I therefore perform an analysis of CCD spectra of the sample stars. CCD
spectra provide lower spectral resolution (FWHM ca. 70 eV, i.e. $R\approx$
30), but provide high S/N spectra of stars with lower X-ray flux. The majority
of the sample stars themselves are X-ray bright enough to have decently
exposed RGS or LETG/HETG spectra. Many of those high-resolution spectra have
been analysed for coronal abundances in the literature, with Wood et al.
(2018) presenting a recent compilation. The results derived here from CCD
spectra can therefore be compared to the ones derived from high-resolution
spectra; I will show in section 3.2.2 that the iron abundance results agree
well with each other, and X-ray CCD spectroscopy can be a useful tool to
determine relative coronal abundances of some key elements.

Most of the sample stars were observed with XMM-Newton, with the exception of
BF Lyn and GJ 644. All stars observed with XMM-Newton yielded a strong
detection. This is unsurprising, because the sample for the EUVE stellar atlas
was based on known magnetically active stars. As such, they tend to be X-ray
bright and are easily detected even in moderately short XMM-Newton exposures.

For the two stars that were not observed with XMM-Newton, namely GJ 644 and BF
Lyn, there are archival observations with Chandra ACIS-S and ROSAT,
respectively. However, it turned out that the CCD spectra extracted from those
observations were not of sufficient quality to allow a detailed fit with
varying coronal abundances. In the case of GJ 644, this was mainly due to the
Chandra observation suffering from severe pile-up, and for BF Lyn the ROSAT
spectrum contained only a few hundred counts and the energy resolution of
ROSAT is low with $\sim 0.5$ keV (FWHM). Since the coronal abundances are a
key point of this investigation, I excluded those two stars from the further
analysis.

If a source was observed with several X-ray telescopes, preference was given
to XMM-Newton data due to its large effective area. Many sources were observed
several times. The light curves of the stars, which are automatically provided
by the XMM-Newton data archive, were used for a visual check whether any large
flares were occurring during a given observation. This is not unusual for
stars of a high activity level. However, it is rather unlikely that a large
flare occurred during the short EUVE observations as well, therefore I
selected a single X-ray observation per star that did not contain any
extremely large flares. If several observations without large flares were
available, I chose the one with the longest non-flaring exposure time. In the
rare case that only one observation was available and the observation
contained a large flare, the flare was excluded from the subsequent data
analysis. The selected observations are specified in Table 2.

####  2.2.2 X-ray data analysis

Figure 2: Top: EUV line fluxes in the HeII304 line and other EUV lines listed in Table 1 versus stellar distance. If geocoronal contamination were a dominant effect in the observed HeII304 lines, the trend of HeII304 with distance would differ strongly from the trend seen for the other line fluxes, which is not the case. Middle: The line ratio of HeII304 to the nearby FeXV284 line as a function of distance. Bottom: The same line ratio as a function of the FeXV284 line flux. If the HeII304 line was mainly geocoronal, we should see an increase of the line ratio with distance as geocoronal emission does not get suppressed by stellar distance, and a decrease with increasing FeXV284 flux. However, this is not the case, demonstrating that the HeII304 emission in the sample is primarily stellar. Table 1: Strong stellar emission lines between 200 and 504 Å. Spectral line | Wavelength | Peak formation
---|---|---
|  | temperature
| (Å) | (MK)
FeXIII | 202.04 | 1.6
FeXIII | 204.95 | 1.6
FeXIV | 211.32 | 2.0
HeII | 256.32 | 0.1
FeXIV | 274.20 | 2.0
FeXV | 284.16 | 2.0
HeII | 303.79 | 0.08
FeXVI | 335.41 | 2.5
FeXVI | 360.76 | 2.5
MgIX | 368.06 | 1.0
NeVII | 465.22 | 0.5
SiXII | 499.41 | 2.0

The XMM-Newton data was reduced following the standard procedures in the XMM-
Newton user handbook. I used the official XMM-SAS software version 18.0.0.

To extract the spectra, I defined circular source regions, typically of 20′′
size, centered on the target and larger background regions free of obvious
sources. In cases where the target was very X-ray bright, I checked the photon
event pattern distributions to test for pile-up (i.e. more than one photons
hitting a pixel within the readout time, leading to them being registered as a
single photon with higher energy), using the XMM-SAS task epatplot. If pile-up
was present, I used an annulus source region instead of a circular one, so
that the center of the point spread function (PSF) was excluded from the
analysis and any pile-up related distortion in the extracted spectra was
avoided.

Source and background spectra were extracted from the PN detector if it was
run in imaging mode, or from one of the lower signal-to-noise MOS detectors in
case PN was run in a mode that did not yield imaging spectra. In the two cases
where only Chandra or ROSAT data were available, the procedure was analogous,
but using the Chandra CIAO software version 4.11 and the general-purpose
Xselect software for ROSAT instead.

The spectra were fitted using Xspec version 12.10. I used a coronal plasma
model, specifically several apec model components, to fit the stellar spectra.
Absorption by the interstellar medium could be neglected because all sources
are located within 30 pc of the Sun. In order to be able to compare the plasma
contributions at different temperatures across different sources, I defined a
6-temperature model grid with fixed temperatures of 1, 2, 4, 8, 16 and 32 MK.
I left the emission measure as a free parameter to fit, as well as the
abundances of the most prominent elements in X-ray spectra of moderately
active stars, namely oxygen, neon, and iron. The other abundances were fixed
at solar values (Grevesse & Sauval, 1998).

The spectral fits directly yield a fitted flux value; I chose an energy range
of 0.2-5 keV for the flux determination, as this contains the vast majority of
the stellar X-ray flux even for stars with a high activity level. The flux was
then converted into X-ray luminosity using Gaia DR2 distances of the stars
where available, using the geometric distances of Bailer-Jones et al. (2018).
If the stars did not have parallaxes in Gaia DR2, for example because they are
too bright, I used distances from Hipparcos (Perryman et al., 1997); this was
the case for Altair, Procyon, $\alpha$ Cen, and GJ 644. AT Mic is a binary
star whose two components are resolved by Gaia, but not by EUVE or XMM-Newton,
and I used the average distance to the two stars in the calculations.

Figure 3: The coronal emission measure distribution of the sample stars is
shown over six temperature bins (1, 2, 4, 8, 16, and 32 MK). Left: The
relative emission measure of each star is shown (i.e. normalised by the
largest EM component per star). The EM distributions are colour-coded by the
X-ray luminosity of each star. The shift of the peak in the emission measure
distribution to higher temperatures with increasing X-ray luminosity is
visible. Right: The absolute emission measure of each star is shown. The
increase in total emission measure with increasing coronal temperature is
visible.

##  3 Results

###  3.1 EUV iron emission lines are coronal lines

I selected stellar spectral lines in the wavelength range of 200 to 505 Å that
were detected in the highest signal-to-noise spectra of the EUVE stellar atlas
(Craig et al., 1997). I then queried the ATOMDB database (Smith et al., 2001)
for strong stellar emission lines with emissivity above $10^{-16}$ to update
the wavelengths for those lines with more precise values. The resulting
spectral lines, as well as their peak formation temperature from ATOMDB, are
listed in Table 1. The strongest emission line is the resonant HeI line at
303.79 Å, which is formed at temperatures around 80000 K, i.e. temperatures
typical for the stellar transition region. The other strong lines in the
relevant wavelength region are formed at significantly higher temperatures;
most of them have their peak formation temperature around 2 MK.

The only part of the stellar atmosphere where temperatures above a million K
are found is in the stellar corona. Many of these EUV lines are therefore
genuine coronal emission lines. This is relevant because these EUV lines
provide a direct link to the coronal emission at X-ray wavelengths, which is
easily observable with current X-ray telescopes.

I calculated the stellar EUV fluxes by summing up the counts within 2 Å of
each of the lines listed in Table 1. This way, noise from wavelength regions
devoid of strong lines was avoided in the flux determination. The resulting
EUV fluxes are listed in Table 3.

It is important to point out here that the EUV emission lines that are located
close to the helium ionization threshold, i.e. Mg368, Ne465 and Si499, are
subject to strong absorption by the interstellar medium. The observed EUVE
spectra are therefore different from the spectra seen by an exoplanet orbiting
the star; for the exoplanet, the irradiation in those lines will be much
stronger than what we see in the absorbed spectra. I perform an estimate of
the influence of those lines in section 3.4.

###  3.2 X-ray spectral results

The coronal iron line emission in the EUV is controlled by two factors: the
available emission measure in the correct temperature range for the formation
of those lines, and the coronal iron abundance. Both parameters are available
from the spectral X-ray fits; the individual fitting results are listed in
Table 4.

####  3.2.1 Emission measure distributions

The emission measure (EM) distributions fitted from the X-ray spectra of the
sample stars are shown in Fig. 3. In the left panel, the relative EM
distributions are displayed, normalised by the largest EM component of each
star. As is typically seen for stellar coronae, the peak of the relative EM
distribution moves to higher temperatures as the magnetic activity level and
the X-ray luminosity increases (see for example Johnstone & Güdel (2015) and
references therein).

This might give rise to the expectation that there is a "sweet spot" in
coronal temperature, namely when the peak of the EM distributions is near 2
MK, where a maximum of EUV iron lines is produced. However, when looking at
the absolute EMs, as shown in the right panel of Fig. 3, it becomes clear that
the absolute emission measure at 2 MK actually rises with increasing X-ray
luminosity, even if higher-temperature components become stronger in relation
to it for a given star.

####  3.2.2 Coronal abundances

Figure 4: FIP abundance bias, measured from high-resolution X-ray spectra
(Wood et al., 2018), versus the iron to oxygen abundance ratio measured from
low-resolution X-ray spectra in this work. A positive FIP bias is defined by a
low Fe/O ratio, a negative FIP bias conversely means a high Fe/O ratio. Both
measures agree in their determination of the abundance ratio, showing that
low-resolution data can be used for a division of stars into low versus high
relative iron abundances in stellar coronae.

The other quantity that influences EUV iron line emission is the coronal
abundance of iron. Abundances of various elements in stellar coronae have been
observed to display distinct patterns that relate to the first ionisation
potential (FIP) of those elements (Drake et al., 1997; Laming & Drake, 1999;
Güdel et al., 2001). Iron is one of the prominent elements with a low FIP. For
stars with low to moderate activity, the observed coronal abundance of low-FIP
elements (relative to solar photospheric abundances) is enhanced. In contrast,
for stars with high magnetic activity and/or late spectral type this pattern
is reversed, and an inverse FIP (iFIP) effect is observed where the elements
with a high FIP such as oxygen and neon are more abundant in the corona while
iron is depleted (Wood & Linsky, 2010; Liefke et al., 2008; Wood et al.,
2018). The reasons for the occurrence of this effect are thought to be rooted
in the Alfvén wave heating of the corona and the related ponderomotive force,
although the detailed physical processes are not fully understood yet (Laming,
2004, 2021).

The CCD spectra analysed here have a relatively low spectral resolution.
However, this is offset by the large number of photons in each spectrum which
provides a high enough S/N to detect significantly non-solar ratios of iron to
oxygen. To confirm that the identification of iron to oxygen ratios from CCD
spectra is reliable using only high S/N CCD spectra, I compared my results to
the "FIP bias" measurements by Wood et al. (2018), who compiled coronal
abundance measurements for stars from high-resolution X-ray observations. They
define the FIP bias as the logarithmic ratio of several high-FIP elements
(like oxygen) to several low-FIP elements (like iron). The overlap of their
sample and this work consists of 12 stars, and the low-resolution O/Fe ratios
derived in this work are in good agreement with the high-resolution FIP bias,
as shown in Fig. 4.

The observed iron to oxygen abundance ratio in the analysed stellar sample is
shown against the mean coronal temperature in Fig. 5. The previously noted
trend Liefke et al. (2008); Wood et al. (2018) of stars with higher activity
level (and therefore higher coronal temperature) having a lower relative iron
abundance is visible here is well.

Figure 5: Measured coronal iron to oxygen abundance ratios for the sample
stars shown against mean coronal temperature.

###  3.3 EUV spectra in comparison to coronal temperatures and abundances

Since the coronal emission measure around 2 MK increases with X-ray luminosity
and mean coronal temperature, and the iron abundance decreases, the iron line
emission in the EUV should be influenced by both effects. Indeed, the ratio of
the EUV iron line from Table 1 to the HeII304 line shows a peak over the mean
coronal temperature, see Fig. 6.

This can be explained by two contributing factors: On the one hand, as the
stellar activity level and the average coronal temperature increases, the
filling factor of active regions on the stellar surface goes up. Therefore,
even while the peak of the emission measure distribution moves to higher
temperatures, the total amount of emission measure available at 2–3 MK still
increases. On the other hand, at high activity levels and coronal temperatures
typically seen in M dwarfs, the inverse FIP effect comes into play, where the
abundance of iron and other low-FIP elements in the stellar corona decreases
compared to stars of lower activity and higher mass (Wood et al., 2018). The
decrease in abundance directly reduces the flux in the EUV iron lines. Note
that the resulting peak in EUV iron line emission does not coincide with the
peak formation temperature of those lines, which is around 2 MK, but is
instead closer to 5-6 MK.

Figure 6: Photon flux ratio of the coronal EUV lines versus the HeII304 line,
as a function of mean coronal temperature. The coronal iron abundance,
relative to solar photospheric values, is shown by the colourbar. The
decreasing iron abundance for highly active stars reduces the flux in the
coronal EUV lines, many of which are iron lines.

###  3.4 The influence of ISM absorption on the observed spectra

Neutral helium in the ISM is subject to the same ionisation process by the EUV
lines bluewards of 504 Å as the exoplanetary atmosphere. Therefore, stellar
emission lines close to the blue side of the ionization edge will undergo
significant absorption by the ISM before they reach our telescopes. The solar
EUV spectrum, which we can observe without strong absorption, shows some
moderately strong EUV emission lines in that wavelength range, namely NeVII465
and SiXII499 (see for example Del Zanna & Mason (2018); Linsky (2014)). In the
solar spectrum the SiXII499 line is of roughly comparable strength to the
stronger iron lines in the vicinity of HeII304, and NeVII465 line is inbetween
the iron lines and the HeII304 line in intensity (Del Zanna & Mason, 2018).

For the observed EUVE spectra of the stars discussed here, the NeVII465 and
SiXII499 lines are practically fully absorbed by the ISM. As a rough estimate
of the influence of those lines on the exoplanetary helium ionisation, I
assume that the relative lines strengths are similar to the Sun. Specifically,
I assume that the unabsorbed SiXII499 line is as strong as the Fexv284 line
for a given star, and the NeVII465 is as strong as the Heii304 line. Indiviual
abundances may vary, but since neon is a high-FIP element like helium and
silicon is a low-FIP element like iron, the relative line strength should be
more or less preserved. Since the ISM absorption is significantly weaker for
the observed EUV lines between 200 and 360 Å, I do not introduce any
correction for those line strengths. Taking all of this into account, the
estimate for the unabsorbed total EUV flux of a star between 200 and 504 Å is
about 1.5 times the observed absorbed flux, with a spread out to factors of
1.25 and 1.75 for individual stars in my sample.

Now, the actual ionisation in the exoplanetary atmosphere depends on the
ionisation cross-section at the wavelength of a given stellar emission line,
which is displayed in the top panel of Fig. 1. One can immediately see that
the ionisation cross-sections of the SiXII499 and NeVII465 lines are about
four and three times as large, respectively, as for the lines near 300 Å.
Therefore, they will have a relatively strong effect on the total helium
ionisation in the exoplanetary atmosphere. However, since these two lines have
opposite behaviours under the coronal FIP abundance effect as explained above,
it turns out that the total estimated ionizing flux after including those two
lines does not depend crucially on coronal abundance patterns. Rather, in
comparison to only the observed (absorbed) line fluxes, the total ionizing
flux is roughly a factor of three higher, but the slope of the relationship to
the X-ray fluxes, which is discussed in the following section, is largely
unaffected.

One caveat is that if the line fluxes of SiXII499 and NeVII465 are very
different from the solar case, then different ratios of the narrow-band EUV
fluxes observed at Earth and seen by the planet may occur. In cases where a
higher-precision estimate of the helium ionisation of a planet is desired, a
detailed differential emission measure analysis of the star may be in order,
so that the SiXII499 and NeVII465 fluxes can be reconstructed from information
gathered from other spectral lines in high-resolution X-ray observations, for
example.

###  3.5 The relation of X-ray and narrow-band EUV fluxes

To estimate the production of metastable helium in exoplanet atmospheres, we
are interested in the stellar narrow-band EUV flux bluewards of the helium
ionisation threshold at 504 Å. While the narrow-band EUV spectrum seen by the
exoplanet differs slightly from what is observed by EUVE, as detailed in the
previous section, I restrict myself to only the observed and therefore ISM-
absorbed EUV fluxes in the following analysis, since a correction for those
effects only amounts to multiplication with a constant small factor.

The relevant narrow-band EUV flux can be estimated from the observed stellar
X-ray properties, either for the whole sample or for the two sub-samples split
according to their coronal iron abundances. The resulting relationships can
then be applied to stars where no EUV spectra are available.

For the full sample, the relationship between the stellar narrow-band EUV
luminosities in the 200–504 Å wavelength range and the stellar X-ray
luminosity in the 0.2-5 keV energy range is shown in Fig. 7, left panel. The
EUV and X-ray luminosities are well correlated, as expected. I fitted the
relationship between $\log L_{\mathrm{X}}$ (0.2-5 keV) and $\log
L_{\mathrm{200-504\mbox{\footnotesize{\AA}}}}$ with a straight line, using the
Markov Chain Monte Carlo functionality of the python package emcee (Foreman-
Mackey et al., 2013).

For this whole sample, the relationship between the narrow-band EUV luminosity
between 200 and 504 Å and X-ray luminosity is given by

$\log L_{\mathrm{200-504\mbox{\footnotesize{\AA}}}}=(0.47\pm
0.09)\times\log\frac{L_{\mathrm{X}}}{10^{29}}+28.03\pm 0.08,$ (1)

which is shown together with the data in Fig. 7.

As expected from the previous considerations in section 3.3, there is some
visible stratification in the data set with regard to coronal iron abundance.
Specifically, stars with a high iron to oxygen abundance in their corona tend
to have a higher narrow-band EUV luminosity than the stars with low coronal
[Fe/O] abundance.

When splitting the sample into low-iron ([Fe/O]$<1$) and high-iron
([Fe/O]$\geq 1$) stellar coronae, two relationships with different slopes can
be found:

$\log L_{\mathrm{low\,Fe,\,200-504\mbox{\footnotesize{\AA}}}}=(0.72\pm
0.08)\times\log\frac{L_{\mathrm{X}}}{10^{29}}+27.84\pm 0.07$ (2)

and

$\begin{split}\log
L_{\mathrm{high\,Fe,\,200-504\mbox{\footnotesize{\AA}}}}=(0.36\pm
0.12)\times\log\frac{L_{\mathrm{X}}}{10^{29}}+28.19\pm 0.12\\\
\mathrm{(valid~{}for~{}T_{\mathrm{cor}}\gtrsim 2~{}MK}).\end{split}$ (3)

However, it needs to be pointed out that the relationship for the ”high Fe”
sample can only be expected to be valid for stars with (a) a high coronal iron
abundance and (b) a high enough coronal temperature to form the EUV iron lines
in the first place (see Fig. 6 and section 3.3). For coronae with very low
temperatures, even though the iron abundance may be high, the iron lines in
the EUV will not be formed because the required ionisation state for those
iron lines will not be reached in the first place. Therefore, stars with very
low coronal temperature will effective behave like stars in the ”low Fe”
sample with respect to their narrowband EUV emission.

Fig. 7, right panel, shows the relationship of the high and low iron samples.
The expected drop of ”high Fe” stars to the ”low Fe” track is qualitatively
depicted by the dashed arrow.

The two samples display different slopes and would nominally intersect around
an X-ray luminosity of $\sim 10^{30}$ erg/s. However, the sample of stars with
high coronal iron abundance does not include any extremely high activity
stars. This is not entirely surprising: the ”high Fe” sample contains stars of
earlier spectral type, with $\epsilon$ Eri having the latest spectral type of
K2V. The ”low Fe” sample consists mainly of M dwarfs, which remain on a high
activity level much longer than more massive stars (see for example Wright et
al. 2011). Coronal iron abundances are known to decrease with stellar mass,
being typically lowest in M dwarfs (Wood et al., 2018).

###  3.6 The physical meaning of non-unity slopes in the luminosity relations

The luminosity relations derived above have slopes shallower than unity. At
first glance, this is surprising: on a log-log plot, two quantities need to
have different dimensionalities of growth to display a non-unity slope. If
both luminosities, the 0.2-5 keV X-ray one and the EUV 200-504 Å one, both
come from the stellar corona, it is not immediately obvious how one could get
such different growth rates of the two luminosities. However, the key point
here is the narrow temperature range over which the 200-504 Å emission is
formed versus the quite broad temperature range that contributes to the X-ray
emission.

Coronal plasma at a temperature of 2 MK is at the peak formation temperature
of the 200-504 Å iron lines, and it also forms the very soft X-ray emission
towards the low-energy end of the 0.2-5 keV X-ray emission. If we go to stars
with higher X-ray luminosities, we see from Fig. 3 (right panel) that the 2 MK
emission measure increases slightly; if this were the only effect, we should
see a slope of unity in the $\log L_{\mathrm{200-504\textup{\AA}}}$ vs. $\log
L_{\mathrm{X}}$ relation. However, we also see from Fig. 3 that the emission
measure at higher temperatures increases much more dramatically. This hotter
plasma will not produce a significant increase in iron line emission in the
200-504 Å EUV range, but it will easily produce additional X-ray emission,
since many lines with peak formation temperatures of 3-10 MK exist in the
X-ray range, mainly bluewards of 0.5 keV. Therefore, the X-ray emission will
grow much more strongly than the narrow-band EUV emission for more active
stars, giving rise to a flatter-than-unity slope of the $\log
L_{\mathrm{200-504\textup{\AA}}}$ vs. $\log L_{\mathrm{X}}$ relation.

This also explains why the slope is flatter for the high-Fe sample than for
the low-Fe one: a large fraction of the lines around 1 keV that are formed at
3-10 MK are iron lines themselves. Stars with a low coronal iron abundance
will therefore display less of the aforementioned behavior, i.e. they will not
be able to create as much excess X-ray emission relative to a given growing
narrow-band EUV emission, leading to a slope closer to unity.

Figure 7: Stellar emission in the narrow-band EUV range (200-504 Å) versus the
stellar X-ray luminosity (0.2-5 keV) for the sample stars. The full sample and
the resulting fit is shown in the left panel, while the sample split by
coronal iron abundance and fitting two separate relationships is shown in the
right panel (see text for details).

##  4 Discussion

###  4.1 Helium transit depths of exoplanet atmospheres in the context of
their host stars’ coronae

Figure 8: Excess helium height of exoplanets, measured in atmospheric scale
heights, as a function of exoplanet irradiation. Left panel: Fluxes on the
horizontal axis are estimated broadband XUV (5-504 Å) fluxes from the
literature. Right panel: Fluxes on the horizontal axis are estimated narrow-
band EUV fluxes, assuming weak or strong iron line contributions based on
stellar coronal properties.

The results presented here show that the helium ionisation in exoplanetary
atmospheres – a precursor to producing atoms in the ground state of the
HeI10830 transition – depends on the EUV irradiation of those atmospheres in a
narrow wavelength region influenced by coronal iron lines. In the existing
literature observed transit depths of exoplanets in the HeI10830 line are
shown in relation to their broad-band XUV irradiation. Nortmann et al. (2018)
first showed that planets with strong XUV irradiation tend to display larger
excess absorption in the helium triplet, which was extended by measurements
performed for additional exoplanets (see for example Alonso-Floriano et al.
2019; Kasper et al. 2020). In those works, the XUV flux between 5 and 504 Å
was used, i.e. bluewards of the helium photoionisation edge, by applying a
modified version of the scaling relationship by Sanz-Forcada et al. (2011), or
by estimating the XUV flux between 5 and 504 Å from hydrogen Ly-$\alpha$
fluxes.

I show a compilation of the published helium absorption heights in the
exoplanet atmosphere versus their broadband XUV irradiation bluewards of 504 Å
in Fig. 8. As can be seen, the relationship contains significant scatter.
Especially the upper limits on helium absorption for exoplanets GJ 1214 b and
GJ 9827 b fall far below the trend line established by the other exoplanets
(Kasper et al., 2020).

However, it is the narrow-band EUV emission that actually drives the helium
ionisation, instead of the broadband XUV emission. I estimate the narrow-band
EUV irradiation of the exoplanet atmospheres from equations (2) and (3), using
available information on the stellar coronae to infer whether a given stars
falls into the ”high Fe” or ”low Fe” sample. I collected the stellar X-ray
luminosities from published works, typically from Foster et al. (2021) or
works on the individual host stars. In the case of GJ 9827, whose X-ray flux
was not found in published works, I used the latest data from the XMM-Newton
DR10 catalog †††http://xcatdb.unistra.fr/4xmmdr10/index.html with a matching
radius of 10′′ around the nominal position of the star. The XMM-Newton catalog
fluxes assume an underlying power law spectrum, which is not correct for
stellar coronae; I therefore use a correction factor of
$F_{\mathrm{X,\,coronal}}=0.87F_{\mathrm{X,\,powerlaw}}$ as derived by Foster
et al. (2021) to convert the DR10 catalog fluxes into coronal X-ray fluxes.

Very few of the host stars of those exoplanets have X-ray spectra of
sufficient quality to determine their coronal iron abundance; only HD 189733
has been directly studied for coronal abundances so far (Pillitteri et al.,
2014). I therefore rely on the results of Wood et al. (2018) to assign low
coronal iron abundance to all host stars with spectral types M0 or later.
Additionally, some other stars can be expected to follow the ”low Fe”
relationship as well due to very low coronal temperatures: KELT-9 is an A0V
star, and if it possesses a corona at all, it can be expected to be of very
low temperature around 1 MK in analogy to the corona of $\beta$ Pictoris
(Günther et al., 2012); HD 209458 has been measured to have a low-temperature
corona (Czesla et al., 2017) of about 1 MK; and WASP-127 has been modelled to
be very old with 11 Gyr (Lam et al., 2017), making it reasonable to assume its
coronal temperature is of the order of 1 MK as well. All other remaining stars
were assigned to the ”high Fe” group. The expected narrow-band EUV fluxes of
the host stars were then calculated accordingly.

The resulting relationship between helium absorption heights and the narrow-
band EUV irradiation is displayed in Fig. 8, and the numerical values are
listed in Table 2. The table gives the stellar spectral type, the planetary
semi-major axis $a_{\mathrm{sem}}$, the published helium absorption heights in
units atmospheric scale heights alongside the published broadband irradiation
of the planets in the broadband XUV ($F_{\mathrm{XUV,\,pl}}$); the stellar
narrow-band EUV luminosity ($\log L_{\mathrm{EUV}}$) and the planetary
irradiation in the same band ($F_{\mathrm{EUV,\,pl}}$) are derived from the
stellar X-ray luminosity according to the two relationships given in equations
2 and 3. The previously rather strong outlier positions of GJ 9827 d and GJ
1214 b are ameliorated. Also the position of HD 189733 b, which experiences a
strong broadband XUV irradiation while having only a moderately deep helium
transit, is now more in line with the other exoplanets due to the measured low
coronal iron abundance of its host star.

###  4.2 The nondetections of helium in sub-Neptunic exoplanet atmospheres

A number of small exoplanets were investigated for helium absorption in their
atmospheres, but even though they are subject to moderate estimated broad-band
XUV irradiation from their low-mass host stars, only upper limits could be
placed. This has led to questions whether Neptunic and sub-Neptunic exoplanets
may have different upper atmosphere layers than Hot Jupiters, where helium
absorption has been more readily observed at apparently similar XUV
irradiation levels. Examples for this are the planets GJ 1214b and GJ 9827d,
and a less stringent upper limit was placed on HD 97658b (Kasper et al.,
2020). Also recently investigated were the planets $b$, $e$ and $f$ around
Trappist-1 (Krishnamurthy et al., 2021); however, there the nondetection was
less surprising since the host stars is a very old and inactive M dwarf,
leading to low present-day XUV irradiation levels of the planets in the first
place (Wheatley et al., 2017).

Using the EUV-X-ray relationships derived in section 3.5, it turns out that
the sub-Neptunes GJ 1214b and GJ 9827d experience significantly lower levels
of narrow-band EUV irradiation than the stellar $L_{X}$ would imply when
ignoring the coronal iron lines. When one takes into account that the host
stars can be expected to have only weak iron line emission (one due to its low
coronal temperatue, the other due to expected low coronal iron abundance since
the host star is an M dwarf), the nondetections are actually in line with the
ionizing narrow-band EUV irradtion, see Fig. 8, right panel. This indicates
that those planets do not necessarily have small or helium-poor gaseous
envelopes, but rather that their M dwarf host stars do not have enough coronal
iron emission to excite the planetary helium into the observable metastable
state.

Future observations of exoplanet host stars with decently exposed X-ray CCD
spectra can be used to directly measure the relative iron abundance in the
stellar coronae and constrain the expected helium absorption signal of their
exoplanets further.

Table 2: Irradiation fluxes in the XUV and the EUV band of exoplanets with measured HeI10830 transit depths (see text for details). Name | stellar | $a_{\mathrm{sem}}$ | $\Delta_{\mathrm{depth}}$ | $F_{\mathrm{XUV,\,pl}}$ | $\log L_{\mathrm{X}}$ | coronal iron? | $\log L_{\mathrm{EUV}}$ | $F_{\mathrm{EUV,\,pl}}$ |  References $\Delta_{\mathrm{depth}}$
---|---|---|---|---|---|---|---|---|---
| spec. type | [AU] |  [$H_{\mathrm{scale}}$] |  [ erg s-1 cm-2] |  [ erg s-1] |  |  [ erg s-1] |  [ erg s-1 cm-2] |  and $F_{\mathrm{XUV,\,pl}}$, $\log L_{\mathrm{X}}$
KELT-9 b | A0V | 0.035 | <41.0 | <0.12 | <27.0 | low; cool/no corona | <26.4 | <0.07 | AF19, estimate
|  |  |  |  |  |  |  |  | based on spec. type
HD 209458 b | F9V | 0.047 | 49.0 | 1.0 | 26.92 | low; cool corona | 26.35 | 0.04 | AF19, Cz17
WASP-127 b | G5V | 0.052 | <18.77 | <0.024 | <27.0 | low; cool corona | <26.4 | <0.03 | dS20, estimate based
|  |  |  |  |  |  |  |  | on old stellar age
HD 97658 b | K1V | 0.08 | <84.0 | 1.11 | 27.21 | high | 27.55 | 0.2 | Ka20, Ki19
HD 189733 b | K2V | 0.031 | 78.0 | 15.0 | 28.3 | low; fitted abund. | 27.34 | 0.8 | AF19, Po13
HAT-P-11 b | K4V | 0.053 | 105.0 | 2.1 | 27.47 | high | 27.64 | 0.56 | AF19, Fo21
WASP-69 b | K5V | 0.045 | 86.0 | 4.2 | 28.11 | high | 27.87 | 1.29 | AF19, Fo21
WASP-107 b | K6V | 0.055 | 88.0 | 1.8 | 27.61 | high | 27.69 | 0.58 | AF19, Fo21
GJ 9827 d | K6V | 0.019 | <26.0 | 2.45 | 26.81 | low; cool corona | 26.27 | 0.19 | Ka20, this work
GJ 3470 b | M2V | 0.036 | 77.0 | 1.44 | 27.42 | low; M dwarf | 26.71 | 0.14 | Pa20, Fo21
GJ 436 b | M3V | 0.029 | <38.0 | 0.15 | 26.04 | low; M dwarf | 25.71 | 0.02 | AF19, Fo21
GJ 1214 b | M4.5V | 0.014 | <12.0 | 0.64 | 25.87 | low; M dwarf | 25.59 | 0.07 | Ka20, La14
AF19: Alonso-Floriano et al. (2019), Cz17: Czesla et al. (2017), dS20: Dos
Santos et al. (2020), Ka20: Kasper et al. (2020),
Ki19: King et al. (2019), Po13: Poppenhaeger et al. (2013), Fo21: Foster et
al. (2021), Pa20: Palle et al. (2020), La14: Lalitha et al. (2014)

###  4.3 A special role for K dwarfs as exoplanet hosts

Four out of six K dwarf host stars in the sample of exoplanets with observed
HeI10830 transits listed in Table 2 can be expected to have strong coronal
iron emission. However, for the M dwarfs the coronal iron abundances are low
even over larger samples (Wood et al., 2018). The G and F dwarfs tend to have
low X-ray luminosities and low coronal temperatures due to their faster spin-
down timescales and rapidly declining magnetic activity (Wright et al., 2011);
therefore, unless a given host star happens to be young, their coronae are
likely too cool to produce much of the relevant iron line emission. In terms
of sample statistics, it is therefore more likely to find K dwarf hosts with
moderately high activity as well as high coronal iron abundances than G, F or
M dwarfs with strong iron emission.

K dwarfs were also identified by Oklopčić (2019) as a sweet spot for helium
transit observability, however their argument was based on expected helium
ionisation versus depopulation of the excited level of the HeI10830
transitions through longer-wavelength UV photons. The broad spectral shapes of
G, K and M dwarf stars imply that especially M dwarfs should give rise to
frequent depopulation processes. Combined with the low coronal iron emission
for M dwarfs, this emphasises the important role of K dwarf hosts for future
detections of HeI10830 in exoplanet atmospheres.

##  5 Conclusions

Exoplanet transit measurements in the metastable line triplet of helium at
10830 Å have proven to be a valuable source of insight into extended exoplanet
atmospheres. However, the observability of atmospheres in this line depends on
the presence of exoplanetary helium in the correct state, which is typically
achieved through photoionization and recombination of helium. The relevant
ionization of exoplanetary helium is caused by a narrow part of the stellar
emission line spectrum in the EUV that depends sensitively on the iron
abundance and the temperature of the stellar corona. I have shown that the
relevant exoplanet irradiation in this band can be estimated from broadband
soft X-ray observations, which are readily available with current space
observatories. Together with information the coronal iron abundance a more
accurate estimate of the narrow-band EUV flux can be performed, which can
guide future transit observations of exoplanet atmospheres in the HeI10839
triplet with respect to the expected absorption signal.

## Acknowledgements

I thank the reviewer, Jeff Linsky, for his illuminating comments.

This work is based on data obtained with XMM-Newton, an ESA science mission
with instruments and contributions directly funded by ESA Member States and
NASA; data obtained with EUVE, a NASA mission; data obtained from the Chandra
Data Archive; and data obtained from the ROSAT Data Archive of the Max-Planck-
Institut für extraterrestrische Physik (MPE) at Garching, Germany. I
acknowledge support from the German _Leibniz-Gemeinschaft_ under project
number P67/2018.

## Data availability

The data in this article are available from the XMM-Newton Science Archive
(https://www.cosmos.esa.int/web/xmm-newton/xsa) with the observation IDs as
given in Table 3, and as High Level Science Products from the MAST archive
(https://archive.stsci.edu/prepds/atlaseuve/). The data products generated
from the raw data are available upon request from the author.

## References

  * Allart et al. (2019) Allart R., et al., 2019, A&A, 623, A58
  * Alonso-Floriano et al. (2019) Alonso-Floriano F. J., et al., 2019, A&A, 629, A110
  * Andretta & Jones (1997) Andretta V., Jones H. P., 1997, ApJ, 489, 375
  * Bailer-Jones et al. (2018) Bailer-Jones C. A. L., Rybizki J., Fouesneau M., Mantelet G., Andrae R., 2018, AJ, 156, 58
  * Bean et al. (2010) Bean J. L., Miller-Ricci Kempton E., Homeier D., 2010, Nature, 468, 669
  * Birkby et al. (2017) Birkby J. L., de Kok R. J., Brogi M., Schwarz H., Snellen I. A. G., 2017, AJ, 153, 138
  * Bourrier et al. (2018) Bourrier V., et al., 2018, A&A, 620, A147
  * Bowyer & Malina (1991) Bowyer S., Malina R. F., 1991, in Malina R. F., Bowyer S., eds, Extreme Ultraviolet Astronomy. p. 397
  * Brinkman et al. (2000) Brinkman B. C., et al., 2000, in Truemper J. E., Aschenbach B., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 4012, X-Ray Optics, Instruments, and Missions III. pp 81–90, doi:10.1117/12.391599
  * Canizares et al. (2005) Canizares C. R., et al., 2005, PASP, 117, 1144
  * Cauley et al. (2015) Cauley P. W., Redfield S., Jensen A. G., Barman T., Endl M., Cochran W. D., 2015, ApJ, 810, 13
  * Charbonneau et al. (2002) Charbonneau D., Brown T. M., Noyes R. W., Gilliland R. L., 2002, ApJ, 568, 377
  * Craig et al. (1997) Craig N., et al., 1997, ApJS, 113, 131
  * Czesla et al. (2017) Czesla S., Salz M., Schneider P. C., Mittag M., Schmitt J. H. M. M., 2017, A&A, 607, A101
  * Del Zanna & Mason (2018) Del Zanna G., Mason H. E., 2018, Living Reviews in Solar Physics, 15, 5
  * Den Herder et al. (2001) Den Herder J. W., et al., 2001, A&A, 365, L7
  * Dos Santos et al. (2020) Dos Santos L. A., et al., 2020, A&A, 640, A29
  * Drake et al. (1997) Drake J. J., Laming J. M., Widing K. G., 1997, ApJ, 478, 403
  * Dupree et al. (1996) Dupree A. K., Penn M. J., Jones H. P., 1996, ApJ, 467, L121
  * Ehrenreich et al. (2015) Ehrenreich D., et al., 2015, Nature, 522, 459
  * Fontenla et al. (1990) Fontenla J. M., Avrett E. H., Loeser R., 1990, ApJ, 355, 700
  * Fontenla et al. (1993) Fontenla J. M., Avrett E. H., Loeser R., 1993, ApJ, 406, 319
  * Foreman-Mackey et al. (2013) Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, PASP, 125, 306
  * Foster et al. (2021) Foster G., Poppenhaeger K., Ilic N., Schwope A., 2021, arXiv e-prints, p. arXiv:2106.14550
  * Grevesse & Sauval (1998) Grevesse N., Sauval A. J., 1998, Space Science Reviews, 85, 161
  * Güdel et al. (2001) Güdel M., et al., 2001, A&A, 365, L336
  * Guilluy et al. (2020) Guilluy G., et al., 2020, A&A, 639, A49
  * Günther et al. (2012) Günther H. M., Wolk S. J., Drake J. J., Lisse C. M., Robrade J., Schmitt J. H. M. M., 2012, ApJ, 750, 78
  * Jansen et al. (2001) Jansen F., et al., 2001, A&A, 365, L1
  * Johnstone & Güdel (2015) Johnstone C. P., Güdel M., 2015, A&A, 578, A129
  * Jordan (1975) Jordan C., 1975, MNRAS, 170, 429
  * Kasper et al. (2020) Kasper D., Bean J. L., Oklopčić A., Malsky I., Kempton E. M. R., Désert J.-M., Rogers L. A., Mansfield M., 2020, AJ, 160, 258
  * Keles et al. (2020) Keles E., et al., 2020, MNRAS, 498, 1023
  * King & Wheatley (2021) King G. W., Wheatley P. J., 2021, MNRAS, 501, L28
  * King et al. (2019) King G. W., Wheatley P. J., Bourrier V., Ehrenreich D., 2019, MNRAS, 484, L49
  * Kreidberg et al. (2014) Kreidberg L., et al., 2014, Nature, 505, 69
  * Krishnamurthy et al. (2021) Krishnamurthy V., et al., 2021, AJ, 162, 82
  * Kulow et al. (2014) Kulow J. R., France K., Linsky J., Loyd R. O. P., 2014, ApJ, 786, 132
  * Lalitha et al. (2014) Lalitha S., Poppenhaeger K., Singh K. P., Czesla S., Schmitt J. H. M. M., 2014, ApJ, 790, L11
  * Lam et al. (2017) Lam K. W. F., et al., 2017, A&A, 599, A3
  * Laming (2004) Laming J. M., 2004, ApJ, 614, 1063
  * Laming (2021) Laming J. M., 2021, ApJ, 909, 17
  * Laming & Drake (1999) Laming J. M., Drake J. J., 1999, ApJ, 516, 324
  * Lecavelier Des Etangs et al. (2010) Lecavelier Des Etangs A., et al., 2010, A&A, 514, A72
  * Libbrecht et al. (2019) Libbrecht T., de la Cruz Rodríguez J., Danilovic S., Leenaarts J., Pazira H., 2019, A&A, 621, A35
  * Liefke et al. (2008) Liefke C., Ness J. U., Schmitt J. H. M. M., Maggio A., 2008, A&A, 491, 859
  * Linsky (2014) Linsky J., 2014, Challenges, 5, 351
  * Linsky (2017) Linsky J. L., 2017, ARA&A, 55, 159
  * Llama et al. (2011) Llama J., Wood K., Jardine M., Vidotto A. A., Helling C., Fossati L., Haswell C. A., 2011, MNRAS, 416, L41
  * Mansfield et al. (2018) Mansfield M., et al., 2018, ApJ, 868, L34
  * Mason et al. (2001) Mason K. O., et al., 2001, A&A, 365, L36
  * Nortmann et al. (2018) Nortmann L., et al., 2018, Science, 362, 1388
  * Oklopčić (2019) Oklopčić A., 2019, ApJ, 881, 133
  * Oklopčić & Hirata (2018) Oklopčić A., Hirata C. M., 2018, ApJ, 855, L11
  * Palle et al. (2020) Palle E., et al., 2020, A&A, 638, A61
  * Paragas et al. (2021) Paragas K., et al., 2021, ApJ, 909, L10
  * Perryman et al. (1997) Perryman M. A. C., et al., 1997, A&A, 500, 501
  * Pillitteri et al. (2014) Pillitteri I., Wolk S. J., Lopez-Santiago J., Guenther H. M., Sciortino S., Cohen O., Kashyap V., Drake J. J., 2014, ApJ, 785, 145+
  * Poppenhaeger et al. (2013) Poppenhaeger K., Schmitt J. H. M. M., Wolk S. J., 2013, ApJ, 773, 62
  * Sanz-Forcada & Dupree (2008) Sanz-Forcada J., Dupree A. K., 2008, A&A, 488, 715
  * Sanz-Forcada et al. (2011) Sanz-Forcada J., Micela G., Ribas I., Pollock A. M. T., Eiroa C., Velasco A., Solano E., García-Álvarez D., 2011, A&A, 532, A6+
  * Seager & Sasselov (2000) Seager S., Sasselov D. D., 2000, ApJ, 537, 916
  * Smith et al. (2001) Smith R. K., Brickhouse N. S., Liedahl D. A., Raymond J. C., 2001, ApJ, 556, L91
  * Snellen et al. (2014) Snellen I. A. G., Brandl B. R., de Kok R. J., Brogi M., Birkby J., Schwarz H., 2014, Nature, 509, 63
  * Strüder et al. (2001) Strüder L., et al., 2001, A&A, 365, L18
  * Tinetti et al. (2007) Tinetti G., et al., 2007, Nature, 448, 169
  * Turner et al. (2001) Turner M. J. L., et al., 2001, A&A, 365, L27
  * Vernazza et al. (1981) Vernazza J. E., Avrett E. H., Loeser R., 1981, ApJS, 45, 635
  * Vidal-Madjar et al. (2003) Vidal-Madjar A., Lecavelier des Etangs A., Désert J., Ballester G. E., Ferlet R., Hébrard G., Mayor M., 2003, Nature, 422, 143
  * Weisskopf et al. (2000) Weisskopf M. C., Tananbaum H. D., Van Speybroeck L. P., O’Dell S. L., 2000, in J. E. Trümper & B. Aschenbach ed., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 4012, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series. pp 2–16 (arXiv:astro-ph/0004127)
  * Wheatley et al. (2017) Wheatley P. J., Louden T., Bourrier V., Ehrenreich D., Gillon M., 2017, MNRAS, 465, L74
  * Wood & Linsky (2010) Wood B. E., Linsky J. L., 2010, ApJ, 717, 1279
  * Wood et al. (2018) Wood B. E., Laming J. M., Warren H. P., Poppenhaeger K., 2018, ApJ, 862, 66
  * Wright et al. (2011) Wright N. J., Drake J. J., Mamajek E. E., Henry G. W., 2011, ApJ, 743, 48
  * Yan et al. (1998) Yan M., Sadeghpour H. R., Dalgarno A., 1998, ApJ, 496, 1044
  * Zarro & Zirin (1986) Zarro D. M., Zirin H., 1986, ApJ, 304, 365

##  6 Additional figures

Fig. 9 shows the EUVE spectra of the sample stars.

Figure 9: EUVE spectra of the sample stars in the 200-504 Å wavelength range.
The light blue lines show the unbinned spectra, the black lines show the
spectra smoothed by a Savitzky-Golay filter with a window length of 5, and the
vertical dotted lines show the wavelengths of the strong stellar emission
lines from Table 1.

##  7 Source tables

Information on the properties of the sample stars and their narrow-band EUVE
luminosity is given in Table 3 and their X-ray spectral properties are given
in Table 4.

Table 3: Properties of the observed stars. Distances are from Bailer-Jones et al. (2018) by default, and from Hipparcos when marked with (H).  Name | Other name | Spectral type | Distance (pc) | Observation ID | Detector used for | X-ray | $L_{\mathrm{200-504}\mbox{\tiny{\AA}}}$
---|---|---|---|---|---|---|---
|  |  |  |  | X-ray spectra | pile-up? | ( erg s-1)
Altair | HD 187642 | A7 V | 5.13 (H) | XMM 0502360101 | PN thick | no | $3.3\times 10^{27}$
Procyon | HD 61421 | F5 IV-V | 3.51 (H) | XMM 0123940101 | PN thick | no | $1.2\times 10^{28}$
$\chi$ Ori | HD 39587 | G0 V | 8.84 | XMM 0111500101 | MOS2 thick | no | $2.5\times 10^{28}$
$\alpha$ Cen AB | HD 128620 | G2 V | 1.35 (H) | XMM 0045340901 | PN thick | no | $4.2\times 10^{27}$
$\kappa$ Cet | HD 20630 | G5 V | 9.14 | XMM 0111410101 | MOS1 thick | no | $1.0\times 10^{28}$
$\xi$ Boo | HD 131156 | G8 V | 6.73 | XMM 0056030101 | MOS2 medium | no | $1.7\times 10^{28}$
LQ Hya | HD 82558 | K0V | 18.28 | XMM 0148880101 | PN medium | no | $1.6\times 10^{28}$
GJ 702AB | HD 165341 | K0V | 5.08 | XMM 0044741301 | PN thick | no | $7.0\times 10^{27}$
VW Cep | HD 197433 | K0V | 26.60 | XMM 0100650301 | PN thick | no | $5.1\times 10^{28}$
AB Dor | HD 36705 | K1 IIIp | 15.30 | XMM 0412580801 | PN thick | yes | $2.4\times 10^{28}$
GJ 117 | HD 17925 | K2V | 10.355 | XMM 0203060501 | PN thick | no | $9.5\times 10^{27}$
$\epsilon$ Eri | GJ 144 | K2V | 3.203 | XMM 0820070201 | PN thick | no | $5.4\times 10^{27}$
FK Aqr | GJ 867AB | M0 Vpe | 8.897 | XMM 0151450101 | PN medium | yes | $1.4\times 10^{28}$
YY Gem | GJ 278C | M1 Ve | 15.09 | XMM 0112880801 | PN thick | yes | $2.9\times 10^{28}$
AU Mic | GJ 803 | M2 Ve | 9.722 | XMM 0111420101 | PN medium | yes | $1.5\times 10^{28}$
AT Mic AB | GJ 799AB | M4 Ve | 9.85 | XMM 0111510101 | PN medium | yes | $1.2\times 10^{28}$
EQ Peg | GJ 896AB | M4 V | 6.260 | XMM 0112880301 | PN thick | yes | $9.1\times 10^{27}$
YZ CMi | GJ 285 | M4.5 Ve | 5.986 | XMM 0111460101 | PN medium | no | $3.1\times 10^{27}$
AD Leo | GJ 338 | M4.5 Ve | 4.965 | XMM 0111440101 | PN medium | yes | $2.4\times 10^{27}$
EV Lac | GJ 873 | M4.5 Ve | 5.049 | XMM 0111450101 | PN medium | yes | $3.2\times 10^{27}$
Prox Cen | GJ 551 | M5 Ve | 1.301 | XMM 0551120201 | PN medium | no | $1.5\times 10^{26}$
Table 4: Fitted X-ray spectral parameters Name |  EM${}_{\mathrm{1\,MK}}$‡‡‡Emission measures are given here as the Xspec "norm" parameter of the fitted "apec" model. They can be transformed to physical quantities in units of cm-3 by multiplying them with $4\pi d^{2}\times 10^{14}$, with $d$ being the distance to the star in cm. |  EM${}_{\mathrm{2\,MK}}$ |  EM${}_{\mathrm{4\,MK}}$ |  EM${}_{\mathrm{8\,MK}}$ |  EM${}_{\mathrm{16\,MK}}$ |  EM${}_{\mathrm{32\,MK}}$ |  T${}_{\mathrm{cor,\,mean}}$ |  [Fe/H]cor |  [O/H]cor |  [Ne/H]cor | $F_{\mathrm{X,\,0.2-5\,keV}}$ | $L_{\mathrm{X,\,0.2-5\,keV}}$
---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  |  (106 K) |  |  |  |  (10-12 erg s-1 cm-2) |  (1026 erg s-1)
Altair | – |  2.6$\pm$0.1 |  0.4$\pm$0.1 | – | – | – | 2.3 |  1.4$\pm$0.25 |  0.6$\pm$0.03 |  1.0$\pm$0.13 | 0.6 | 1.2
Procyon | – |  37.2$\pm$0.3 | – |  0.2$\pm$0.1 | – | – | 2.1 |  1.8$\pm$0.09 |  0.4$\pm$0.01 |  0.5$\pm$0.04 | 6.6 | 14.2
$\chi$ Ori | – |  2.5$\pm$1.0 |  31.7$\pm$1.6 |  16.1$\pm$0.8 |  1.0$\pm$0.7 |  1.0$\pm$0.5 | 6.0 |  0.9$\pm$0.03 |  0.4$\pm$0.03 |  0.5$\pm$0.05 | 9.6 | 20.8
$\alpha$ Cen | – |  56.4$\pm$1.5 |  12.9$\pm$2.0 |  2.8$\pm$0.5 | – | – | 2.6 |  1.4$\pm$0.13 |  0.4$\pm$0.02 |  0.6$\pm$0.10 | 13.1 | 28.5
$\kappa$ Cet | – |  3.0$\pm$0.9 |  20.8$\pm$1.5 |  11.6$\pm$0.8 |  1.7$\pm$0.4 | – | 5.7 |  1.1$\pm$0.05 |  0.6$\pm$0.04 |  1.4$\pm$0.08 | 8.6 | 18.6
$\xi$ Boo | – |  14.7$\pm$0.7 |  39.2$\pm$1.3 |  28.5$\pm$0.9 |  7.7$\pm$0.8 |  0.9$\pm$0.5 | 6.3 |  0.7$\pm$0.02 |  0.5$\pm$0.01 |  1.3$\pm$0.03 | 17.1 | 37.1
LQ Hya | – |  7.6$\pm$0.4 |  40.1$\pm$1.1 |  28.9$\pm$1.0 |  12.2$\pm$1.0 |  14.4$\pm$0.7 | 10.5 |  0.3$\pm$0.01 |  0.6$\pm$0.01 |  1.7$\pm$0.03 | 16.1 | 35.0
GJ 702 | – |  10.8$\pm$0.9 |  15.3$\pm$1.7 |  9.1$\pm$1.1 |  0.7$\pm$0.6 | – | 4.7 |  0.7$\pm$0.05 |  0.5$\pm$0.03 |  1.0$\pm$0.09 | 6.5 | 14.1
VW Cep | – |  1.4$\pm$0.7 |  13.3$\pm$1.8 |  21.8$\pm$1.7 | – |  5.8$\pm$0.9 | 10.0 |  0.4$\pm$0.02 |  0.8$\pm$0.06 |  2.0$\pm$0.12 | 7.5 | 16.2
AB Dor | – |  15.2$\pm$3.9 |  103.3$\pm$8.8 |  71.2$\pm$7.1 |  164.7$\pm$4.0 | – | 10.5 |  0.4$\pm$0.02 |  0.6$\pm$0.03 |  1.4$\pm$0.06 | 53.3 | 115.8
GJ 117 | – |  4.1$\pm$0.4 |  20.6$\pm$0.8 |  9.5$\pm$0.5 | – |  1.2$\pm$0.3 | 5.9 |  0.7$\pm$0.02 |  0.7$\pm$0.02 |  1.3$\pm$0.04 | 6.7 | 14.6
$\epsilon$ Eri | – |  23.0$\pm$1.1 |  61.7$\pm$2.2 |  24.6$\pm$1.3 | – |  1.0$\pm$0.6 | 4.8 |  0.7$\pm$0.02 |  0.6$\pm$0.02 |  1.2$\pm$0.03 | 20.9 | 45.3
FK Aqr |  3.8$\pm$0.4 |  15.7$\pm$0.5 |  46.6$\pm$1.2 |  21.7$\pm$1.1 |  16.6$\pm$0.8 | – | 6.4 |  0.4$\pm$0.01 |  0.7$\pm$0.01 |  1.5$\pm$0.03 | 17.2 | 37.4
YY Gem | – |  8.1$\pm$1.5 |  40.3$\pm$2.5 |  17.7$\pm$2.0 |  15.9$\pm$1.9 |  17.2$\pm$1.3 | 11.4 |  0.4$\pm$0.02 |  0.7$\pm$0.04 |  1.8$\pm$0.07 | 16.1 | 35.0
AU Mic | – |  14.0$\pm$1.3 |  64.4$\pm$2.0 |  26.8$\pm$1.6 |  32.0$\pm$0.9 | – | 7.5 |  0.4$\pm$0.01 |  0.7$\pm$0.02 |  1.6$\pm$0.03 | 22.1 | 48.0
AT Mic | – |  10.7$\pm$1.2 |  61.6$\pm$2.5 |  19.5$\pm$2.1 |  46.6$\pm$1.2 | – | 8.6 |  0.3$\pm$0.01 |  0.7$\pm$0.02 |  1.4$\pm$0.03 | 21.0 | 45.6
EQ Peg | – |  16.5$\pm$1.2 |  29.1$\pm$2.7 |  28.4$\pm$2.3 |  17.1$\pm$1.2 | – | 7.3 |  0.5$\pm$0.02 |  0.8$\pm$0.04 |  1.6$\pm$0.07 | 16.4 | 35.6
YZ CMi | – |  9.9$\pm$0.8 |  20.9$\pm$1.0 |  11.5$\pm$0.9 |  5.3$\pm$0.7 |  3.0$\pm$0.4 | 7.5 |  0.5$\pm$0.02 |  0.8$\pm$0.03 |  1.4$\pm$0.05 | 8.7 | 18.8
AD Leo | – |  16.5$\pm$1.2 |  43.5$\pm$1.6 |  25.2$\pm$1.5 |  9.9$\pm$1.4 |  5.7$\pm$0.9 | 7.6 |  0.4$\pm$0.01 |  0.7$\pm$0.02 |  1.7$\pm$0.04 | 17.1 | 37.1
EV Lac | – |  14.9$\pm$1.3 |  41.4$\pm$1.8 |  25.9$\pm$1.5 |  19.1$\pm$0.8 | – | 7.1 |  0.4$\pm$0.01 |  0.7$\pm$0.02 |  1.3$\pm$0.04 | 16.6 | 36.2
Prox Cen | – |  6.1$\pm$0.2 |  9.1$\pm$0.5 |  5.0$\pm$0.4 |  0.8$\pm$0.4 | – | 5.0 |  0.4$\pm$0.02 |  0.7$\pm$0.02 |  1.2$\pm$0.05 | 3.5 | 7.7