Open Access
Issue
A&A
Volume 673, May 2023
Article Number A37
Number of page(s) 16
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/202245667
Published online 03 May 2023

© The Authors 2023

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

Seager & Sasselov (2000) and Oklopčić & Hirata (2018) showed that the metastable He I (23S) triplet at ≈10 830 Å in the near-infrared can probe exoplanetary upper atmospheres as an alternative to the ultraviolet (UV) band. Thus, the He I triplet can constrain atmospheric loss, which plays a pivotal role in the evolution of exoplanets and in shaping their observed mass–radius distribution (e.g. Lopez & Fortney 2013; Jin et al. 2014; Jin & Mordasini 2018; Owen & Wu 2017; Kubyshkina et al. 2018; Modirrousta-Galian et al. 2020).

The He I atoms lying in the upper atmosphere can be excited to the metastable state either through photoionisation, followed by recombination, or through collisional excitation from the ground state (Andretta & Jones 1997). The former mechanism requires that the He I atoms be irradiated by high-energy photons at wavelengths shorter than the He I ionisation energy (~504 Å or 24.6 eV), while the latter mechanism requires a high density of energetic electrons. Oklopčić & Hirata (2018) showed that in planetary atmospheres the photoionisation and recombination mechanism is significantly more efficient than the collisional excitation mechanism in producing metastable He I. Instead, depopulation of the metastable state occurs through ionisation, radiative emission, and electron collisions, where the latter two mechanisms bring a He I atom directly to the ground state or to the excited singlet state, which then decays to the ground state.

The relative efficiency of the mechanisms mentioned above, particularly those relying on photoionisation, strongly depend on the shape of the stellar spectral energy distribution (SED) irradiating a planet. Oklopčić (2019) showed that the most likely planets to show metastable He I absorption are those in a close orbit around an active star with low near-ultraviolet (NUV; <2600 Å) emission, that is, an active K-type star. This is because intense stellar X-ray and extreme ultraviolet (EUV; together XUV; <912 Å) emission enables ionisation of He I atoms from the ground state, which can then recombine into the metastable state, while low stellar NUV emission reduces the photoionisation of metastable He I atoms.

Primary transit observations designed to detect metastable Hel absorption have been carried out for about 30 planets, with a positive detection in approximately ten cases (e.g. Spake et al. 2018; Nortmann et al. 2018; Salz et al. 2018; Allart et al. 2018; Alonso-Floriano et al. 2019; Ninan et al. 2020). The observed systems span a wide range of stellar spectral types, from early A- to late M-type, and planetary properties, from small (presumably) rocky planets to gas giants. Some non-detections can therefore be explained by the fact that the star lacks the appropriate SED (e.g. KELT-9 having insufficient XUV flux and excessive NUV flux; Nortmann et al. 2018) and/or by the planet lacking a sufficient amount of He in its atmosphere (e.g. super-Earths such as Trappist-1b and 55Cnce; Krishnamurthy et al. 2021; Zhang et al. 2021). Furthermore, the observations so far have been obtained with different instruments and techniques, namely ground-based high-resolution spectroscopy, ground- or space-based low-resolution spectrophotometry, and ground-based narrow-band photometry.

However, there have also been unexpected non-detections with the most striking being that of WASP-80b, which is an inflated hot Jupiter orbiting a K-type star. Fossati et al. (2022) reported the results of three high-quality transit observations of WASP-80b collected with the GIANO-B high-resolution spectrograph (Oliva et al. 2006), obtaining an upper limit on the He I absorption of 0.7% (at the 2σ level). This non-detection was further confirmed by narrow-band photometry observations (Vissapragada et al. 2022).

Fossati et al. (2022) also presented the results of three-dimensional (3D) hydrodynamic simulations of the upper atmosphere of WASP-80b and of its interaction with the stellar wind. These authors concluded that stellar wind pressure is unlikely to cause the non-detection and suggested instead that the atmosphere may have a low helium abundance relative to hydrogen (He/H) of at least ten times less than solar. However, Vissapragada et al. (2022) suggested that confinement of the planetary atmosphere by a large-scale magnetic field might be responsible for the non-detection of metastable He I.

As mentioned above, one of the key elements controlling the population and depopulation of the metastable 23S level is the stellar SED and in particular the part of the XUV emission primarily responsible for He I photoionisation (i.e. 200–504 Å). This part of the stellar SED lies in the EUV band and is observationally poorly constrained (see e.g. France et al. 2019). Poppenhaeger (2022) derived scaling relations enabling one to infer the EUV emission in the 200–504 Å band on the basis of the stellar X-ray luminosity and [Fe/O] coronal abundance ratio, which could be measured from sufficiently high-quality X-ray spectra or inferred from stellar activity and age. Poppenhaeger (2022) concluded that for stars of similar X-ray luminosity, young and active stars with [Fe/O] < 1 tend to have lower EUV emission in the 200–504 Å band than old and inactive stars, which show [Fe/O] > 1.

In this work, we reanalyse the available X-ray spectra of WASP-80, as well as those of other planet hosts, using the resulting X-ray flux to infer the EUV flux by employing the scaling relations of Poppenhaeger (2022). We then use the obtained XUV flux as input to 3D hydrodynamic (HD) simulations to identify the possible origin of the non-detection of metastable He I absorption. To test the suggestion of Vissapragada et al. (2022), we also employ 3D magneto hydrodynamic (MHD) modelling to estimate the impact of a planetary magnetic field on metastable He I absorption. Finally, we place the results obtained for WASP-80b in the context of metastable He I observations carried out for other systems.

This paper is organised as follows. Section 2 presents the results of a reanalysis of the XMM-Newton X-ray spectra of WASP-80. In Sect. 3, we describe the employed modelling scheme, while Sect. 4 presents the results of the (M)HD simulations. Section 5 shows a comparison of the results obtained for WASP-80b with those of past detections and non-detections present in the literature. Finally, Sect. 6 gathers the conclusions.

thumbnail Fig. 1

Image of WASP-80 in the two XMM-Newton observations (pn detector). The circles show the regions where the spectra of the source and background were accumulated.

2 High-energy emission of WASP-80

WASP-80 has been observed twice with XMM-Newton1 for durations of 17 ks (obsid 0744940101, P.I. Salz) and 32 ks (obsid 0764100801, P.I. Wheatley). We retrieved the data from the XMM-Newton archive2 and reduced the constituent observation data files (ODFs) with the science analysis software (SAS) version 20.0 to obtain FITS tables of X-ray events calibrated in astrometry, arrival times, energies of events, and quality flags.

We selected the events in the 0.3–10 keV range, with PATTERN ≤12 and FLAG = 0 as prescribed by the SAS guide3. We checked the light curves of events at high energies (>10 keV) to find periods of high background count rate during the observations. Observation 0744940101 was deemed free of high background intervals, while observation 0764100801 was affected by highly variable background, mostly for the pn detector. We retained only 5.3 ks of the 32 ks of the pn exposure at the end of this screening.

To accumulate the spectra of WASP-80, we extracted the events related to the target in circular regions of radius 30″ centred on the centroid of the X-ray source corresponding to WASP-80. The events used for background subtraction were extracted from a nearby circular region of radius 35″ (Fig. 1). The spectra and the related response files were created with SAS. The spectra obtained for each observation from the MOS and pn detectors were combined to obtain a summed spectrum with higher count statistics. The response matrices and the background spectra were also combined together with the SAS task EPICSPECCOMBINE4. The resulting so-called EPIC spectra were then grouped to have a minimum of 30 counts per bin. Summing up all spectra from MOS and pn, the spectra from the first and second exposures had 272 and 370 counts, respectively.

We then used the XSPEC5 software version 12.11.b to model the two EPIC spectra of both observations and infer NH absorption (i.e. hydrogen column density of the interstellar medium), mean temperatures (T1, T2), emission measure, and flux (fX) in the 0.2–10.0 keV band. The model was composed of two absorbed (TBABS model) thermal components (APEC) summed together. Hydrogen absorption and metal abundances were kept fixed. The resulting best-fit parameters are listed in Table 1. The choice of this model was motivated by the fact that a simple one-temperature model with an absorbed APEC component gave ambiguous results. In fact, with this model, the EPIC spectra could be described either by a low gas absorption of about 5×1020 cm−2 and a mean temperature of around 0.7 keV or with a high gas absorption of around 1022 cm−2 and a cooler temperature of ≤0.1 keV. As described below, there are robust reasons to discard this second solution at high NH.

The distance to the star is of about 49.7 pc (Gaia Collaboration 2021) and at such a distance an interstellarmedium hydrogen column density of order 1022 cm−2 is highly unlikely. To infer a more reliable NH value, we estimated an E(B – V) value of 0.161 by combining the observed B – V colour of 1.501 mag and the estimated intrinsic colour (BV)0 = 1.34 mag expected for a main sequence star with an effective temperature Teff of 4100 K, such as WASP-806 (Pecaut & Mamajek 2013). We note that the (BV) value reported by Salz et al. (2015) appears to be too low for a star of spectral type K7 (i.e. Teff ~ 4100 K).

From E(BV) = 0.161, we inferred a value of AV ~ 0.5 mag (RV = 3.1) and thus NH ~ 1020 cm−2, which is of the same order as the value obtained from the best fit to the EPIC spectra (~5 × 1020 cm−2). Fixing the hydrogen interstellar absorption to 5×1020 cm−2, the best fit gives an unabsorbed flux of 1.7 × 10−14 erg s−1 cm−2 in the 0.2–10 keV band and an X-ray luminosity of ~ 5 × 1027 erg s−1.

This X-ray luminosity is comparable to those reported by Salz et al. (2015, ~7×1027 erg s−1), King et al. (2018, ~7×1027 erg s−1), and Fossati et al. (2022, ~5×1027 erg s−1). We also note that the values given by Salz et al. (2015) and King et al. (2018) were obtained whilst considering a larger and less precise distance to the star compared to that measured by Gaia, which was not available at the time. Instead, Fossati et al. (2022) rescaled the X-ray luminosity given by King et al. (2018), accounting for the updated stellar distance, but did not consider that a shorter distance also implies a smaller NH value.

We estimated the EUV emission of WASP-80 in the 200–504 Å wavelength range starting from the measured X-ray flux value and considering the scaling relations of Poppenhaeger (2022), which we recall account for the [Fe/O] abundance in the stellar corona (i.e. high or low relative to solar). The X-ray spectrum of WASP-80 does not allow the [Fe/O] coronal abundance to be measured reliably, and therefore we attempted to use the stellar age as a proxy. In particular, it is possible to assign a [Fe/O] > 1 coronal abundance to inactive stars older than 1 Gyr and with X-ray luminosity below 1028 erg s−1 and a [Fe/O] < 1 coronal abundance to younger stars. This choice is driven by the low first ionisation potential (FIP) effect observed in the Sun and in low-activity stars (Laming 2021), where low FIP elements (such as Fe) appear to be overabundant with respect to high-FIP elements. At the same time, an inverse FIP effect is observed in high-activity stars with underabundant Fe with respect to low-FIP elements. Following Poppenhaeger (2022), this has a strong impact on the presence and strength of emission lines in the EUV band, and therefore on the total EUV flux, such that at equal X-ray luminosity, young and active stars have a lower EUV emission in the 200–504 Å range than old and inactive stars.

We estimated the age of WASP-80 using the isochrone placement algorithm presented in Bonfanti et al. (2015, 2016). This routine interpolates the input parameters (in this case Teff, [Fe/H], and R) within pre-computed grids of PARSEC7 v1.2S (Marigo et al. 2017) isochrones and tracks to retrieve the best-fit age. For WASP-80, we obtained an age of , Gyr. Therefore, the stellar age is unconstrained, implying that it is not possible to clearly infer the coronal iron abundance, and thus the EUV emission. In the following, we consider that the star can have either a low or a high [Fe/O] coronal abundance, and therefore either a low or high EUV emission (221 and 1520 erg cm−2 s−1 at the planetary orbit in the 200–504 Å wavelength range), and investigate the consequence in terms of formation and possible detection of He I metastable absorption in the planetary atmosphere. However, we note that the measured log value of about −4.04 (Fossati et al. 2022) implies an age of Myr (Mamajek & Hillenbrand 2008), which would therefore suggest that the lower EUV emission value might be preferable.

Table 1

Best-fit parameters of the EPIC spectra of WASP-80

3 Modelling scheme

To simulate the upper atmosphere of WASP-80b and its interaction with the stellar wind, we employ the 3D (M)HD code described by Shaikhislamov et al. (2018), Khodachenko et al. (2021b). This code self-consistently simulates the expansion and escape of the planetary upper atmosphere – which is controlled by the stellar radiative heating and gravitational forces – and its interaction with the surrounding stellar wind, which is also simulated within the model. The extension enabling consideration of the planetary magnetic field strength is achieved by adding the magnetic field induction equation and the Ampere force in the momentum equations for the ionised species to the set of hydrodynamic equations. Below, we provide a brief description of the modelling scheme.

The 3D hydrodynamic multi-fluid numerical model is run in a spherical coordinate system for which the polar axis Z is taken perpendicular to the orbital plane. To present the results, we also use a Descart frame with the X-axis directed along the planet–star line. The simulation reference frame is attached to the planet. This geometry is well suited to simulating tidally locked planets with the stellar radiation impinging on the planet from just one direction, but we note that the code also enables the simulation of planets with arbitrary rotation. The code solves the continuity, momentum, and energy equations numerically for separate components, which can be written in the following form (Shaikhislamov et al. 2016): (1) (2)

and (3)

respectively. In the above equations, nj is the density of species j, t is time, Vj is the velocity of species j, mj is the mass of a particle of species j, Tj is the temperature of species j, ne is the electron density, Te is the electron temperature, U describes the gravitational interaction (see below), and WXUV,j is the heating term for the planetary atmosphere (see below). The terms NXUV,j, Nexh,j, , and are the photoionisation, charge-exchange, and collisional terms listed in Table 1 of Shaikhislamov et al. (2016).

The main processes responsible for the transformation between neutral and ionised particles are photoionisation, electron impact ionisation, and dielectronic recombination, which are included in the term NXUV,j in Eq. (1) and are applied to all species. Photoionisation also results in heating of the planetary gas through impacts with the produced photoelectrons. The corresponding heating term WXUV,j in Eq. (3) (see Shaikhislamov et al. 2014, 2016; Khodachenko et al. 2015) comprises terms derived by integrating the stellar XUV spectrum in the 10–912 Å wavelength range (e.g. Eq. (4) of Khodachenko et al. 2015 and Eq. (5) of Shaikhislamov et al. 2016). The model assumes that the energy released in the form of photoelectrons is rapidly and equally redistributed among all nearby particles with an efficiency of ηh = 0.5 ÷ 1. This is a commonly used assumption, which we adopted on the basis of qualitative analyses (Shaikhislamov et al. 2014). The heating term, which also includes energy loss due to excitation and ionisation of hydrogen atoms in a simplified form can be written as (4)

where ν is the frequency of the stellar irradiation, Eion is the ionisation energy, σXUV is the cross-section to the stellar XUV flux FXUV, E21 is the excitation energy, and σion and σ12 are the ionisation and excitation cross sections, respectively, averaged over a Maxwellian distribution of electrons.

The model further accounts for resonant charge-exchange collisions (Nexh); at low energies these have a cross-section of σexc = 6×10−15 cm−2, which is an order of magnitude larger than the elastic collision cross-section. Experimental data on the differential cross-sections can be found, for example, in Lindsay & Stebbings (2005). As planetary atoms and protons have different thermal-pressure profiles and protons are affected by electron pressure while atoms are not, when they pass close to each other, the charge-exchange between them leads to velocity (ν) and temperature (T) exchanges. We describe this process with the collision rate , where the upper index indicates the value being exchanged. For example, in the momentum equation for planetary protons, there is the term , where the interaction velocity depends in general on the thermal and relative velocities of the interacting fluids; in this specific case, protons and neutral atoms of the planetary wind. More accurate expressions for the chargeexchange terms present in the continuity, momentum, and energy equations – obtained by averaging the collision operator over the Maxwell distribution (e.g. Meier & Shumlak 2012) – differ from those used in our model by less than a factor of a few, which is negligible for the purposes of the simulations.

In the model, we considered the following cross-sections: σXUV = 6.3×10−18(λ/λthr)3 cm2 as the wavelength-dependent XUV ionisation cross-section; cm2 as the electron impact ionisation cross-section; σrec = 6.7×10−21T−3/2 cm2 as the cross-section for recombination with electrons; and cm2 and σ21 = 7×10−16T−1 cm2 as the hydrogen excitation and de-excitation cross-sections, respectively, where the temperature is scaled in units of the characteristic temperature of the model (i.e. T4 K), except in the exponents for the expressions of σion and σ12, where the temperature is given in erg.

For the typical parameters of planetary plasmaspheres, Coulomb collisions with protons effectively couple the ions of the minor species. For example, at T < 104 K and cm−3, the collisional equalisation time (Braginskii 1965) for temperature and momentum, that is, (5)

is about 2 s for protons and about 8 s for He. This is several orders of magnitude shorter than the typical gas-dynamic timescale of the problem treated here, which is of the order of 104 s.

The strong coupling of charged particles in the planetary wind on the considered typical spatial scale of the problem (i.e. about Rrmp; ~1010 cm) is further justified by the presence of a chaotic and sporadic magnetic field in the planetary wind, which affects the relative motion of the ions so that they become coupled through the Lorentz force and exchange their momentum on the timescale of the Larmor period. For the same reason, charged particles can be treated as strongly coupled in the hot and rarefied stellar wind as well, even in spite of the fact that Coulomb collisions are negligible there. Therefore, there is no need to calculate the dynamics of every charged component of the plasma fluid species, and we assume all of them to have the same temperature and velocity. Instead, the temperature and velocity are calculated for each neutral component individually by solving the corresponding energy and momentum equations. The neutral hydrogen atoms are also approximately coupled to the main flow by elastic collisions. With a typical cross-section of >10−16 cm2, the mean-free path at a density of 106 cm−3 is comparable to the planetary radius. Besides elastic collisions, charge exchange ensures more efficient coupling between hydrogen atoms and protons (Shaikhislamov et al. 2016; Khodachenko et al. 2017). Furthermore, the simulation is simplified by assuming that all charged particles have the same velocity, while each neutral fluid has its own particular velocity, including He I and He I (23s).

The model further accounts for molecular hydrogen and the corresponding ions (, ; see Khodachenko et al. 2015; Shaikhislamov et al. 2018), which allows more accurate treatment of the inner regions of the planetary thermosphere and cooling by the efficient infrared emitter . The model also enables the inclusion of minor species, which are described as separate fluids by the corresponding momentum and continuity equations. The population of different ionisation states for each element is calculated assuming the specific photoionisation (Verner & Ferland 1996) and recombination rates (Le Teuff et al. 2000; Nahar & Pradhan 1997). We note that we do not consider chemical reactions among the different minor species, while the list of modelled hydrogen reactions can be found in Khodachenko et al. (2015), and is comparable to that used in other aeronomy models (e.g. García Muñoz 2007; Koskinen et al. 2007).

To account for the geometry of the problem, we employ a gravitational potential that accounts for rotational effects of the form (6)

where the subscript s indicates the star.

The numerical scheme is explicit and uses an upwind donor cell method for flux calculations. To achieve second-order spatial accuracy for differentials, we consider two grids shifted by half a step along each dimension. One grid is reserved for densities, temperatures, and gravity potential, and the other for velocities. For second-order temporal accuracy at each time step, the code first calculates (n, T) values using the velocity field V and then recomputes V using the new (n, T) values. The numerical scheme fully conserves flux and total mass, and conserves the Bernoulli constant along the characteristics. For energy, a simple non-conservative equation is used. The energy conservation is checked by global integration and is used to evaluate the accuracy of the simulation. Usually, the energy is balanced within 25%. We do not use any particular method to capture the shock between planetary and stellar wind. For the problems under consideration, the accurate position of the shock and high front resolution are not crucial.

The spatial spherical grid uses uniform step for azimuth angle (in this particular study we employ 96 points along a circumference; i.e. Δϕ = 0.065). The radial grid is exponential with steps varying linearly with radius as Δr = Δrmin + (Δrmax − Δrmin)(rRp)/(RmaxRp), where r is the planetocentric radial distance. At the planetary surface Δr is as small as Rp/200. For Δrmax, we employ a value equal to Δϕ · Rmax. Therefore, in the shock region of about 20 Rp, the resolution is approximately equal to Rp. For the polar angle, the grid is quadratic, Θ = ΔΘmini + αi2, with the smallest step located at the equatorial plane. Usually, ΔΘ = Δϕ at the equator and ΔΘ = 2Δϕ along the polar axis. We note that the exponential radial spacing in the spherical coordinate system allows the same resolution to be maintained in all three dimensions, if the azimuthal and latitudinal steps are chosen so that Δϕ ≈ ΔΘ ≈ Δr/r. We verified the influence of spatial resolution by doubling the number of grid points for each dimension, obtaining comparable results.

Each simulation is started from an initial static atmosphere and proceeds in the case of WASP-80b for about 500 dimension-less times (corresponding to about 14 orbits) until the overall planetary mass-loss rate reaches 95% of its asymptotic level, which is judged to be sufficient to assume that the simulation has reached the steady state.

To compute the column densities along stellar rays, we use integration from the star to each cell in the planetary spherical frame, using the density values interpolated from nearby pixels along the path. The calculated column density is used to determine the attenuation of the stellar XUV flux in each spectral bin of 0.1 nm. To save numerical time, the radiation transfer is usually calculated each forth step of fluid dynamics and chemistry. We assume optically thin approximation for the photons generated by proton recombination to the ground state, and thus the total recombination coefficients are used.

The chemical reactions are calculated by direct conversion of the matrix dni = Rji(t, r)njni at each time step and at each pixel. This is not efficient numerically, but eliminates convergence problems due to the vastly different reaction rates Rji.

Because of the large scale of the considered system, the dynamics of the magnetic field is assumed to be dissipationless in most of the area surrounding the planet, which in the numerical model is achieved by taking a sufficiently high, though finite, electric conductivity corresponding to a magnetic Reynolds number of about 105. This value was found empirically to exceed the numerical diffusion in the magnetic field induction equation. The planetary magnetic dipole moment m is directed perpendicularly to the equatorial plane, which is considered to be coplanar to the ecliptic plane.

In the case of the MHD simulations, we calculate the magnetic field induction equation assuming that the divergence of the magnetic field is zero. At the inner boundary of the computation domain (i.e. at the optical radius of the planet r = Rp), we fix the flux of the magnetic field by fixing the radial component of the magnetic dipole field (i.e. Br = constant). Instead, the perturbations of the azimuthal (i.e. toroidal; Bf) and poloidal (B) components of the field obey an open boundary condition that is r(r · δB), where the symbol δ indicates the perturbation (Khodachenko et al. 2021b). The code has already been used to interpret the observations of metastable He I absorption for GJ3470 b (Shaikhislamov et al. 2021), WASP-107 b (Khodachenko et al. 2021a), and HD 189733 b (Rumenskikh et al. 2022), as well as for HD 209458 b in case it hosts a magnetic field (Khodachenko et al. 2021b).

4 Results

4.1 Non-magnetised planet

For all simulations, we considered the NUV and near-infrared stellar emission given by Fossati et al. (2022) and a planetary orbital separation of 0.0344 (Triaud et al. 2015). We ran simulations for a range of stellar EUV (i.e. 200–504 Å) and XUV (10–912 Å) emission flux values that encompass those derived in Sect. 2, as well as three He/H abundance values of 0.01, 0.03, and 0.1 (by number), where the latter is the solar He/H abundance ratio. At the lower atmospheric boundary, which we locate at a pressure of 0.05 bar, we considered a planetary atmospheric temperature of 1000 K. To model the stellar wind, we considered the same parameters taken by Fossati et al. (2022), namely a velocity of 200 km s−1, a temperature of 0.7 MK, and a density of 103 cm−3 at the position of the planet, corresponding to an integral stellar mass-loss rate of 1011 g s−1. The main difference with the work of Fossati et al. (2022) lies in the significantly smaller stellar XUV emission: these latter authors employed a stellar XUV emission at 1 AU of 7.5 erg cm−2 s−1, which is the largest value considered in this work. This is due to the fact that the scaling relations of Poppenhaeger (2022) lead to smaller EUV flux values compared to those of King et al. (2018), with these latter being used by Fossati et al. (2022). Given the measured X-ray luminosity, the stellar wind strength expected for WASP-80 is 2×1013 g s−1 (Vidotto 2021). Therefore, we performed two additional runs considering a He/H abundance ratio of 0.1, a stellar wind mass-loss rate of 2×1013 g s−1, and the two XUV flux values (221 and 1520 erg cm−2 s−1) computed from the scaling relations of Poppenhaeger (2022), either assuming a low or high [Fe/O] coronal abundance.

The detailed results of the hydrodynamic simulations, such as the density distribution and temperature profile, resemble those presented by Fossati et al. (2022). As an example, Fig. 2 shows the proton density distribution in the planetary orbital plane obtained from the run computed considering a He/H abundance ratio of 0.01 and an EUV stellar flux at 1 AU of 0.7 erg cm−2 s−1. The map shows the presence of two gas streams departing from the planet, one in front of the planet and the other behind it. The planetary material after initial spherical expansion is forced to move close to the planetary orbit due to momentum conservation. The stream ahead of the planet is composed of escaped gas that is under the influence of the stellar gravitational pull and stops as a result of the interaction with the stellar wind. The stream behind the planet, also composed of planetary escaped gas, is a typical characteristic of close-in giant planets with an escaping atmosphere (e.g. Bourrier et al. 2016; Esquivel et al. 2019; Shaikhislamov et al. 2018; McCann et al. 2019; Debrecht et al. 2020; Carolan et al. 2021; MacLeod & Oklopčić 2022). Figure 3 shows the absorption profiles obtained from time averaging (see Dos Santos et al. 2022) in the −0.1 to +0.1 planetary orbital phase range – the same range taken into account to extract the observed transmission spectrum from the data (see Fig. 1 of Fossati et al. 2022) – as an example, considering a He/H abundance ratio of 0.01. We note that averaging reduces the peak absorption by less than 5%. Interestingly, in the case of WASP-80b, we find that the cometary tail forming behind the planet does not produce significant metastable He I absorption, in contrast to what is found by MacLeod & Oklopčić (2022) for other systems.

Given the similarities of the detailed results with those of the simulations presented by Fossati et al. (2022), we focus here on the obtained planetary metastable He I absorption and mass-loss-rate values. All results derived from the HD simulations are summarised in Table 2 and displayed in Fig. 4. The full width at half maximum (FWHM) listed in Table 2 is a measure of the velocity of the He I metastable atoms along the line of sight, and is therefore directly linked to the structure and asymmetry of the absorbing atmosphere. This is key information that can be accurately extracted and compared with observations exclusively employing 3D simulations such as those adopted in this work.

We find that both metastable He I absorption and mass-loss rate increase roughly linearly with increasing high-energy stellar emission and the He I absorption is strongly dependent on the He/H abundance ratio. Furthermore, with increasing He/H abundance ratio, the mean molecular weight increases, which leads to a decrease in the pressure scale height, and therefore also in the atmospheric extension and consequently the mass-loss rate.

Considering stellar EUV emission at the planetary orbit of 1520 erg cm−2 s−1 (i.e. the higher of the two obtained from the scaling relations; see Sect. 2), we find that the non-detection of metastable He I absorption implies a He/H abundance ratio of smaller than ten times less than that of the Sun. Instead, with the lower EUV stellar emission value, which is favoured by the measured log value, we obtain that metastable He I absorption would have been undetectable for a solar He/H abundance ratio in combination with a stellar wind stronger than that expected on the basis of the measured X-ray luminosity, or for a slightly subsolar He/H abundance ratio, or for a combination of the two. For a solar He/H abundance ratio and the foreseen stellar-wind strength, the metastable He I detectability level of the observations corresponds to a stellar XUV flux value that is about 1.5 times lower than the smaller one obtained following the scaling relations of Poppenhaeger (2022). As expected, an increase in the stellar wind mass-loss rate leads to a decrease in the metastable He I absorption signal (Vidotto & Cleary 2020; Fossati et al. 2022), however it does not appear to be enough to explain the non-detection without the need for a subsolar He/H abundance ratio or a stellar wind stronger than that foreseen on the basis of the measured X-ray luminosity, or both.

thumbnail Fig. 2

Proton-density distribution in the orbital plane of the whole simulated domain for the run computed considering a He/H abundance ratio of 0.01 and an EUV stellar flux at 1 AU of 0.7 erg cm−2 s−1. The planet is at the centre of coordinate (0,0) and moves counter-clockwise relative the star, which is located at (76,0). Proton fluid streamlines originating from the planet (black) and from the star (grey) are shown. The axes are scaled in planetary radii.

thumbnail Fig. 3

He I (23S) triplet absorption profiles obtained considering a He/H abundance ratio of 0.01 and different values of the stellar XUV flux in comparison with the observations (black asterisks). The XUV flux values at 1 AU in erg cm−2 s−1 and the corresponding line colours are given in the legend. The absorption profiles are the result of time averaging from −0.1 to +0.1 in planetary orbital phase. The zero Doppler-shifted velocity on the x axis corresponds to a wavelength of 10 830.25 Å. The horizontal dashed line marks the 2σ upper limit derived from the observations (Fossati et al. 2022). The horizontal dotted line at 1.00 is for reference.

Table 2

Input parameters and results of the hydrodynamic simulations.

4.2 Magnetised planet

To test the suggestion of Vissapragada et al. (2022), we further modelled the WASP-80 system considering a magnetised planet with a field strength of up to 1 G (i.e. comparable to that of Jupiter). To properly study the impact of a planetary magnetic field on the absorption of metastable He I, we employed a stellar SED with an XUV emission strong enough to ensure the production of enough metastable He I to lead to significant absorption. Therefore, for the MHD simulations, we considered the stellar SED used by Fossati et al. (2022), namely an XUV and EUV flux equal to the strongest one considered for the HD simulations. To isolate the effect of the planetary magnetic field, we take a sufficiently low He/H abundance ratio that it does not influence the formation of the planetary wind and its interaction with the stellar wind yet provides sufficient metastable He I absorption, namely 0.01. Finally, we employed a stellar wind with a mass-loss rate of 1011 g s−1.

We ran simulations for a planet with a very low magnetic field of 0.01 G, which leads to results equivalent to those of a non-magnetised planet, and two cases with a relatively strong magnetic field of 0.5 and 1.0 G. For the strongest planetary magnetic field, we also simulated the case of a moderately strong stellar wind, that is 20 times higher density, in which the magnetised planet generates a typical magnetosphere. The main input parameters and resulting planetary mass-loss rate and metastable He I absorption are summarised in Table 3.

Figures 5 and 6 show the electric currents generated by a magnetised planet. As obtained from previous 2D and 3D simulations (Khodachenko et al. 2015, 2021b), as well as earlier semi-analytical considerations (Khodachenko et al. 2012), the outflowing planetary wind gas stretches and opens the magnetic dipolar field lines, forming an equatorial current layer, that is the so-called magnetodisk.

The magnetodisk is thin and surrounds the planet in the equatorial plane, but not uniformly, because of the planetary flow clockwise rotation due to the Coriolis force. Also, there is a cavity close to the planet, the so-called dead zone, where planetary material is stagnant. The generated magnetospheric system of currents is characterised by a region around the planet dominated by the dipolar magnetic field, a current sheet at the front of the magnetosphere (i.e. the magnetopause), a current sheet at high latitudes, and a current sheet forming a tail behind the planet. The strong stellar wind generates a clear bow shock around the planet, which appears to have a structure similar to that of the magnetised Solar System planets (Fig. 6).

Figure 7 shows the proton density distribution obtained from the model run N3 (see Table 3). A comparison between Figs. 2 and 7 indicates that a strong planetary magnetic field truncates the tail behind the planet, which is predicted to be a prominent feature for non-magnetised planets (MacLeod & Oklopčić 2022). This suggests that the presence of a cometary tail could indicate the absence of a strong planetary magnetic field. The field also shortens the gas stream lying ahead of the planet, bending it further towards the star.

The profiles shown in Fig. 8 provide further details of the structure of the planetary outflow. In the case of the weaker planetary magnetic field (model run N1), the expanding planetary atmosphere is stopped relatively far from the planet, with the acceleration being driven by absorption of the stellar XUV emission and subsequent atmospheric heating. In this case, the atmosphere becomes supersonic at a distance of about 4.5 planetary radii. For a planetary magnetic field strength of 0.5 G (model run N2), the planetary flow is strongly decelerated by the force of the magnetic tension (except at the region with open field lines; see Khodachenko et al. 2015, 2021b, for more details) and the velocity is lower by a factor of two at distances shorter than five planetary radii compared to the case of a weakly magnetised planet. In the case of the strongest planetary magnetic field and stellar wind (model run N4), there is the formation of a magnetopause and bow shock. The position of the magnetopause, analytically computed as (7)

is close to the one obtained by the simulation (about 5.5 Rp). Within the magnetopause, the planetary wind velocity is about an order of magnitude lower than that obtained for the case of the weakly magnetised planet. Indeed, the magnetic pressure prevails over the thermal pressure up to 3 Rp, instead becoming comparable close to the magnetopause.

Figure 9 shows the synthetic metastable He I absorption profiles in comparison to the observations of Fossati et al. (2022). Despite the fact that the planetary magnetic field has significantly modified the structure of the upper atmosphere, the He I absorption decreases by less than a factor of two compared to the almost non-magnetised case. However, with a stronger stellar wind, the absorption increases, reaching almost the same level as that obtained for the almost non-magnetised planet. This occurs because the magnetosphere compresses with the stronger stellar wind, increasing the overall density of the absorbing material around the planet.

These results indicate that a planetary magnetic field is unlikely to be the source of the non-detection of metastable He I absorption in the atmosphere of WASP-80b. This is primarily because most of the absorption (i.e. the peak absorption) takes place close to the planet for which the influence of the magnetic field is not particularly strong, while the differences in the absorption maps shown in Fig. 10 affect mostly the line wings, which form farther away from the planet and therefore depend on the planetary magnetic field strength.

In regards to the polar regions, the simulations indicate that the planetary magnetic field reduces the outflow velocity, resulting in a decreased density over the poles (see Trammell et al. 2014; Khodachenko et al. 2015; Carolan et al. 2021, for a detailed discussion on the effect of a planetary magnetic field on the outflow velocity at the polar regions). However, because of the lower velocity, the planetary outflowing gas is more strongly photoionised, resulting in larger electron densities, which lead to a larger population of metastable He I atoms produced through recombination of Hell. Furthermore, by reducing the outflow velocity, the planetary magnetic field reduces the width of the absorption of the He I (23S) feature from about 19 km s−1 at Bp = 0.01 G to about 12 km s−1 at Bp = 1.0 G. Indeed, Fig. 8 shows that close to the planet the outflow velocity decreases with increasing magnetic field, but the outflow velocity is generally low and therefore the reduction in the velocity does not significantly impact the absorption strength. Finally, Fig. 9 shows that with increasing planetary magnetic field from 0.5 to 1.0 G, the population of high-velocity (i.e. from about −30 to −10 km s−1) metastable He I atoms decreases significantly, in agreement with the previous analysis.

Table 3

MHD simulation scenarios with corresponding key modelling parameters and resulting metastable He I absorption values.

thumbnail Fig. 4

Summary of the results of the hydrodynamic simulations. Top: peak absorption of the He I (23S) triplet resulting from the HD simulations as a function of the stellar EUV emission at the planetary orbital separation, assuming He/H abundance ratios of 0.01 (black asterisks), 0.03 (red rhombs), and 0.1 (blue triangles) and a stellar wind mass-loss rate of 1011 g s−1. The blue squares are for a He/H abundance ratio of 0.1 and a stronger stellar wind of 2×1013 g s−1. The horizontal dashed line marks the 2σ upper limit derived from the observations. The vertical dotted lines correspond to the low and high values of the EUV flux obtained following the reanalysis of the X-ray data and the scaling relations of Poppenhaeger (2022). Bottom: Same as the top panel, but for the planetary mass-loss rate.

thumbnail Fig. 5

Distribution of the electric currents obtained from the MHD simulations. Distribution of the azimuthal component of the electric currents (Jϕ) in the orbital (top) and meridional (bottom) planes in the case of the weak stellar wind and a planetary magnetic field strength of 0.5 G (i.e. model N2 in Table 3). The axes are in planetary radii. The magnetic field lines are shown in black. For presentation purposes, the plots show just one-eighth of the whole simulation domain. The star is located to the right at X = 76. The current in normalised units can be converted to physical units, statampere cm−3, by multiplying the values in the colour bar by 0.35.

thumbnail Fig. 6

Same as the bottom panel of Fig. 5, but for a planetary magnetic field strength of 1.0 G and the strong stellar wind (i.e. model N4 in Table 3). The star is located to the right at X = 76.

thumbnail Fig. 7

Proton density distribution in the orbital plane of the whole simulated domain for the run computed considering the weak stellar wind and a planetary magnetic field of 1 G (i.e. model N3 in Table 3). The planet is at the centre of coordinate (0,0) and moves counter-clockwise relative the star, which is located at (76,0). Proton fluid streamlines originating from the planet (black) and from the star (grey) are shown. The axes are scaled in planetary radii.

thumbnail Fig. 8

Profiles of the main physical quantities along the star-planet connecting line. Top: Proton bulk (solid line) and thermal (dotted line) velocity in the X direction along the star–planet connecting line. The black and red lines are for the runs computed considering a planetary magnetic field of 0.01 and 0.5 G, respectively (runs N1 and N2). The dark green lines are for the run computed considering the strongest planetary magnetic field and stellar wind (run N4). The bright green dash-dotted line shows the Alfvén velocity in the X direction for the case of the strongest planetary magnetic field and stellar wind (run N4). Bottom: Electron (solid line) and He I (23S) density (dotted line) profiles in the X direction. As in the top panel, the black and red lines are for the runs computed considering a planetary magnetic field of 0.01 and 0.5 G, respectively (runs N1 and N2), while the dark green lines are for the run computed considering the strongest planetary magnetic field and stellar wind (run N4).

thumbnail Fig. 9

He I (23S) triplet absorption profiles obtained considering different values of the planetary magnetic field at a fixed He/H abundance ratio of 0.01 in comparison with the observations (black asterisks). The blue, red, and green lines are for a stellar XUV flux at 1 AU of 7.5 erg cm−2 s−1 and a planet with a magnetic field strength of 0.01, 0.5, and 1.0 G, respectively (i.e. model runs N1, N2, N3). The grey line is for a planet with a magnetic field of 1.0 G and a strong stellar wind (i.e. model run N4). The absorption profiles are the result of time averaging from −0.1 to +0.1 in planetary orbital phase. The zero Doppler-shifted velocity on the x axis corresponds to a wavelength of 10 830.25 Å. The horizontal dashed line marks the 2σ upper limit derived from the observations (Fossati et al. 2022). The horizontal dotted line at 1.00 is for reference.

5 Discussion

We place our results in the context of observations published for other systems. We collected the physical properties of the systems for which either measurements or non-detections of metastable He I absorption have been published (Table A.1). For consistency, we reanalysed archival X-ray data for some of the systems and applied the scaling relations of Poppenhaeger (2022) to all of them.

5.1 High-energy emission

We gathered the system parameters from the literature, giving priority to more recent and/or homogeneous sources. For the systems considered by Poppenhaeger (2022, KELT-9, HD 209458, WASP-127, HD 97658, HD 189733, HAT-P-11, WASP-69, WASP-107, GJ9827, GJ3470, GJ436, GJ1214), we took the X-ray luminosity reported by these authors, while for the other systems we derived the X-ray luminosity from archival observations (Table B.1). To this end, we searched for X-ray observations in the XMM-Newton and Chandra archives. All necessary data, except for WASP-52, were found in pointed XMM-Newton observations or in the slew survey. WASP-52 was observed with Chandra for about 10 ks. For the targets in pointed and publicly available XMM-Newton observations (WASP-80, 55Cnc, HAT-P-32, and Trappist-1), we reduced the datasets with SAS version 20.0, extracted the spectra, and performed the best-fit analysis using XSPEC version 12.11.

Details about the X-ray data of WASP-80 are given in Sect. 2. In general, we used a combination of 1 or 2 APEC thermal models absorbed by a global equivalent H column (TBABS model), where the free parameters were the temperature (kBT), the normalisation of each component, the NH equivalent column gas absorption, and the global abundances (Z/Z). However, we kept NH and Z/Z fixed for WASP-80; our motivation to do this is outlined in Sect. 2. For Trappist-1, observed in six different XMM-Newton visits, we extracted the pn and MOS spectra separately, combining them with SAS to obtain an average spectrum with the highest count statistics to then perform a simultaneous fit. For WASP-52, we accumulated the count rate in a region 5″ wide and used PIMMS8 to estimate its flux using a single APEC model with kBT = 0.1 keV and solar abundance. For the undetected stars in XMM-Newton, we computed the flux starting from the pn count rate in the 0.2–12 keV band, using an optically thin thermal APEC model at 0.1 keV with solar abundances and NH = 1020 cm−2 to estimate the unabsorbed flux in the 0.2–10 keV band. For V 1298 Tau, we adopted the results of Maggio et al. (2022), who employed the same data-analysis technique as we used for the other stars.

As for WASP-80, we estimated the stellar EUV emission in the 200–504 Å wavelength range starting from the X-ray measurements and considering the scaling relations of Poppenhaeger (2022). The [Fe/O] abundance of the stellar corona was measured from the available X-ray spectra for just a few stars in our sample. For the systems in common, we took the [Fe/O] abundance value given by Poppenhaeger (2022), while for the other systems we estimated the [Fe/O] abundance based on the activity and age of the host stars (Table C.1). For each star in the sample, we estimated the age using the isochrone placement algorithm briefly described in Sect. 2 (Bonfanti et al. 2015, 2016).

We derived the isochronal age for each star in the sample, except for Trappist-1 and GJ1214, which are extremely low-mass stars. For stars of this type, the stellar parameters are almost constant over time. For example, PARSEC models predict maximum Teff variations of ~0.2% on a timescale comparable to the age of the Universe. Therefore, it is not possible to infer the age from evolutionary models; however, other indicators may help distinguish between young and old stars.

Filippazzo et al. (2015) studied a sample of ultra-cool dwarfs, also containing Trappist-1. These authors evaluated the ages according to youth indicators, such as the membership to nearby young moving groups (see e.g. Gagné et al. 2015) or the β–γ gravity suffix that can be inferred from spectra (Kirkpatrick 2005; Cruz et al. 2009). In the case of Trappist-1, no clear youth signatures were detected, yielding a lower age limit of 0.5 Gyr. For GJ1214, Berta et al. (2011) did not detect any kind of activity-induced chromospheric emission in either Hα or the Na I D lines. These authors estimated the stellar rotation period, finding it to be a multiple of 53 days, which suggests a low magnetic activity. By applying the relation from West et al. (2008) between magnetic activity and kinematic age, Berta et al. (2011) inferred an age of greater than 3 Gyr and confirmed this by computing the stellar motion in the (U, V, W) velocity space finding (−47, −4, −40) km s−1, which is consistent with membership to the Galactic old disk.

thumbnail Fig. 10

Distribution of the absorption of the metastable He I line at ≈10 830 Å across the stellar disk integrated in the ±5 km s−1 range as seen by an Earth-based observer at mid-transit resulting from the N1 (top), N2 (middle), and N4 (bottom) simulations.

5.2 Comparison with WASP-80b

Figure 11 shows the size of the measured He I absorption signal or upper limit (δRp), normalised to the atmospheric scale height (Heq), as a function of incident stellar EUV flux in the 200–504 Å wavelength range (Poppenhaeger 2022). For each system, we estimated Heq using the data listed in Table A.1 and following Fossati et al. (2022, see their Sect. 5). The upper limits on the He I absorption values are at the 90% confidence level. In Fig. 11, we divided the sample taking into account the (possible) presence of an extended hydrogen-dominated atmosphere and considering the observational technique (high- vs. low-resolution). The majority of the observations reported in the literature were collected employing ground-based high-resolution spectroscopy, except for a handful of systems that were observed using either space-based low-resolution spectroscopy or ground-based narrow-band photometry (Kreidberg & Oklopčić 2018; Vissapragada et al. 2022). Also, about 70% of the observations targeted gas giants, while the remaining observations targeted planets that probably do not host an extended hydrogen-dominated atmosphere and that for simplicity we defined ‘rocky’ in Fig. 11.

As first suggested by Nortmann et al. (2018), the systems presenting metastable He I absorption and a measured X-ray luminosity (HD 209458, HD 189733, WASP-107, WASP-69, GJ3470, HAT-P-11, HAT-P-32, WASP-52, TOI560, TOI1430, TOI1683; labelled as number 2, 3, 4, 5, 8, 11, 22, 23, 29, 30, and 31, respectively) show a positive trend between the amplitude of the absorption signal and the stellar high-energy flux impinging on the planet (see also Poppenhaeger 2022). This trend shows some scatter, particularly due to WASP-69 b (labelled 5), HAT-P-11 b (labelled 11), WASP-52 b (labelled 23), TOI560 b (labelled 29), TOI1430 b (labelled 30), and TOI1683 b (labelled 31), which have a He I absorption that is rather different from that expected following the trend drawn by the other planets. Interestingly, TOI560 b, TOI1430 b, TOI1683 b, and TOI2076 b (the latter does not have an X-ray detection), which show a strong He I absorption signal, are significantly less massive and smaller than the other planets in the sample, and yet likely host a primary hydrogen-dominated atmosphere. This might suggest that for sub-Neptunes the trend between metastable He I absorption and stellar high-energy emission could be different from that drawn by Neptune-and Jupiter-mass planets, or that sub-Neptunes possess a high He/H abundance ratio.

In agreement with the results of the HD simulations, in case where WASP-80 has a high [Fe/O] coronal abundance ratio (labelled 1b in Fig. 11), the non-detection of He I is in contrast to the trend outlined by HD 209458, HD 189733, WASP-107, GJ3470, and HAT-P-32, particularly considering that the planet is a close-in gas giant and that the host star is supposed to be of a favourable spectral type for the production of metastable He I in the planetary atmosphere (Oklopčić 2019). Instead, in case where WASP-80 has a low [Fe/O] coronal abundance ratio (labelled 1a in Fig. 11), the He I non-detection appears to be in line with the trend drawn by the other planets.

6 Conclusions

We reanalysed archival XMM-Newton observations of the planet-hosting star WASP-80. We then used the stellar X-ray luminosity obtained from the data as input to the scaling relations of Poppenhaeger (2022) to estimate the EUV flux in the 200–504 Å, which controls He I metastable production, and therefore absorption, in the planetary atmosphere. However, the quality of the X-ray spectrum and the large uncertainty on the stellar age prevented us from constraining the [Fe/O] coronal abundance, which led us to consider two different EUV flux values resulting from the scaling relations; we find the lower one to be favoured by the measured log value.

In light of the XUV flux values obtained for WASP-80, we ran both HD and MHD simulations of the planetary upper atmosphere and of its interaction with the stellar wind to test the impact on the He I metastable absorption signal of the XUV stellar emission, of the He/H abundance ratio in the planetary atmosphere, and of the possible presence of a planetary magnetic field. For a stellar wind about ten times weaker than solar, that is about 100 times weaker than that expected on the basis of the measured X-ray luminosity, the HD simulations revealed that He I metastable absorption should have been detectable for a He/H abundance ratio of larger than about ten times less than solar, independently of the considered X-ray-to-EUV scaling relation. For a solar He/H abundance ratio and the lower of the two EUV flux values derived for WASP-80 – which is favoured by the measured log value –, the He I non-detection can be explained by a stellar wind stronger than that expected on the basis of the measured X-ray luminosity. For the higher of the two EUV flux values derived for WASP-80, reproducing the He I non-detection implies He/H abundance ratios smaller than ten times less than solar. The MHD simulations indicate that the inclusion of a planetary magnetic field of stronger than 0.5 G decreases the metastable He I absorption feature by about a factor of two, but this decrease can be compensated by a stronger stellar wind. In summary, for a low stellar [Fe/O] coronal abundance ratio (i.e. low XUV flux) and a solar He/H abundance ratio in the planetary atmosphere, the non-detection of metastable He I absorption could be explained by the presence of a strong stellar wind. Otherwise, the non-detection would imply a subsolar He/H abundance ratio.

The case of WASP-80b demonstrates that the presence of an active host star, even if of favourable spectral type (i.e. K-type), cannot be used as a reliable characteristic for predicting the possible detectability of He I in the atmosphere of a close-in giant planet. Actually, a high stellar X-ray emission might imply an insufficient EUV emission to produce a detectable He I feature. As a matter of fact, the large uncertainties of scaling relations involving the inference of EUV stellar fluxes from observables (X-ray, far-ultraviolet, near-ulraviolet, optical; e.g. Linsky et al. 2013; Sreejith et al. 2020) suggest that the EUV emission of WASP-80 might simply be insufficient to produce a detectable He I absorption signal, removing the need to invoke a subsolar He/H abundance ratio in the planetary atmosphere, an especially strong stellar wind, or the presence of a planetary magnetic field, or a combination of the above. The example of the WASP-80 system demonstrates the importance and urgency of bringing forward theoretical and observational studies designed to constrain the high-energy emission of late-type stars. In particular, direct observations of the EUV spectral range, such as those proposed by the ESCAPE mission concept (France et al. 2019), would be invaluable to better understand the impact of stellar radiation on the structure and evolution of planetary atmospheres.

thumbnail Fig. 11

Size of the measured He I absorption signal normalised to the atmospheric scale height computed considering the planetary parameters listed in Table A.1 and a mean molecular weight of a pure hydrogen atmosphere, as a function of the incident stellar EUV flux (in logarithmic scale) in the 200–504 Å wavelength range. Arrows indicate upper limits. The numbers close to each point are the labels listed in the first column of Table A.1. Gas giants are marked by filled circles, while rocky planets are marked by empty squares (we apply the term ‘rocky’ to planets that presumably do not host an extensive primary hydrogen-dominated atmosphere). Black and red symbols indicate planets for which the search for metastable He I absorption has been conducted employing high- and low-resolution techniques, respectively (low-resolution techniques comprise both low-resolution spectroscopy, R < 10 000, and narrow-band photometry). The dashed horizontal line connects the two possible locations of WASP-80b, which differ solely on the assumption of a high or low [Fe/O] coronal abundance. V 1298 Tau d (#35) is not shown, because the estimated He I absorption signal lies significantly out of scale compared to the rest of the sample and has an uncertainty of larger than 100% (see Table A.1).

Acknowledgements

Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. This research has made use of data obtained from the Chandra Data Archive and the Chandra Source Catalog, and software provided by the Chandra X-ray Center (CXC) in the application packages CIAO and Sherpa. I.F.S. and M.S.R. acknowledge the support of Ministry of Science and Higher Education of the RF, grant 075-15-2020-780. G.G. acknowledges financial contributions from PRIN INAF 2019, and from the agreement ASI-INAF number 2018-16-HH.0 (THE StellaR PAth project). I.F.S. and M.S.R. acknowledge funding from ILP research project 121033100062-5 and RNF project 21-72-00129.

Appendix A Properties of the considered systems with He I absorption measurements and non-detections

Table A.1

Properties of the systems for which either measurements or non-detections of the He I metastable triplet have been published.

Appendix B X-ray luminosity from XMM-Newton and Chandra observations

Table B.1

Log of the X-ray observations of the sample analysed in this work.

Appendix C Properties of the host stars

Table C.1

Stellar ages derived in this work and used to infer the stellar coronal iron abundance.

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7

PAdova and T Rieste Stellar Evolutionary Code: http://stev.oapd.inaf.it/cgi-bin/cmd

All Tables

Table 1

Best-fit parameters of the EPIC spectra of WASP-80

Table 2

Input parameters and results of the hydrodynamic simulations.

Table 3

MHD simulation scenarios with corresponding key modelling parameters and resulting metastable He I absorption values.

Table A.1

Properties of the systems for which either measurements or non-detections of the He I metastable triplet have been published.

Table B.1

Log of the X-ray observations of the sample analysed in this work.

Table C.1

Stellar ages derived in this work and used to infer the stellar coronal iron abundance.

All Figures

thumbnail Fig. 1

Image of WASP-80 in the two XMM-Newton observations (pn detector). The circles show the regions where the spectra of the source and background were accumulated.

In the text
thumbnail Fig. 2

Proton-density distribution in the orbital plane of the whole simulated domain for the run computed considering a He/H abundance ratio of 0.01 and an EUV stellar flux at 1 AU of 0.7 erg cm−2 s−1. The planet is at the centre of coordinate (0,0) and moves counter-clockwise relative the star, which is located at (76,0). Proton fluid streamlines originating from the planet (black) and from the star (grey) are shown. The axes are scaled in planetary radii.

In the text
thumbnail Fig. 3

He I (23S) triplet absorption profiles obtained considering a He/H abundance ratio of 0.01 and different values of the stellar XUV flux in comparison with the observations (black asterisks). The XUV flux values at 1 AU in erg cm−2 s−1 and the corresponding line colours are given in the legend. The absorption profiles are the result of time averaging from −0.1 to +0.1 in planetary orbital phase. The zero Doppler-shifted velocity on the x axis corresponds to a wavelength of 10 830.25 Å. The horizontal dashed line marks the 2σ upper limit derived from the observations (Fossati et al. 2022). The horizontal dotted line at 1.00 is for reference.

In the text
thumbnail Fig. 4

Summary of the results of the hydrodynamic simulations. Top: peak absorption of the He I (23S) triplet resulting from the HD simulations as a function of the stellar EUV emission at the planetary orbital separation, assuming He/H abundance ratios of 0.01 (black asterisks), 0.03 (red rhombs), and 0.1 (blue triangles) and a stellar wind mass-loss rate of 1011 g s−1. The blue squares are for a He/H abundance ratio of 0.1 and a stronger stellar wind of 2×1013 g s−1. The horizontal dashed line marks the 2σ upper limit derived from the observations. The vertical dotted lines correspond to the low and high values of the EUV flux obtained following the reanalysis of the X-ray data and the scaling relations of Poppenhaeger (2022). Bottom: Same as the top panel, but for the planetary mass-loss rate.

In the text
thumbnail Fig. 5

Distribution of the electric currents obtained from the MHD simulations. Distribution of the azimuthal component of the electric currents (Jϕ) in the orbital (top) and meridional (bottom) planes in the case of the weak stellar wind and a planetary magnetic field strength of 0.5 G (i.e. model N2 in Table 3). The axes are in planetary radii. The magnetic field lines are shown in black. For presentation purposes, the plots show just one-eighth of the whole simulation domain. The star is located to the right at X = 76. The current in normalised units can be converted to physical units, statampere cm−3, by multiplying the values in the colour bar by 0.35.

In the text
thumbnail Fig. 6

Same as the bottom panel of Fig. 5, but for a planetary magnetic field strength of 1.0 G and the strong stellar wind (i.e. model N4 in Table 3). The star is located to the right at X = 76.

In the text
thumbnail Fig. 7

Proton density distribution in the orbital plane of the whole simulated domain for the run computed considering the weak stellar wind and a planetary magnetic field of 1 G (i.e. model N3 in Table 3). The planet is at the centre of coordinate (0,0) and moves counter-clockwise relative the star, which is located at (76,0). Proton fluid streamlines originating from the planet (black) and from the star (grey) are shown. The axes are scaled in planetary radii.

In the text
thumbnail Fig. 8

Profiles of the main physical quantities along the star-planet connecting line. Top: Proton bulk (solid line) and thermal (dotted line) velocity in the X direction along the star–planet connecting line. The black and red lines are for the runs computed considering a planetary magnetic field of 0.01 and 0.5 G, respectively (runs N1 and N2). The dark green lines are for the run computed considering the strongest planetary magnetic field and stellar wind (run N4). The bright green dash-dotted line shows the Alfvén velocity in the X direction for the case of the strongest planetary magnetic field and stellar wind (run N4). Bottom: Electron (solid line) and He I (23S) density (dotted line) profiles in the X direction. As in the top panel, the black and red lines are for the runs computed considering a planetary magnetic field of 0.01 and 0.5 G, respectively (runs N1 and N2), while the dark green lines are for the run computed considering the strongest planetary magnetic field and stellar wind (run N4).

In the text
thumbnail Fig. 9

He I (23S) triplet absorption profiles obtained considering different values of the planetary magnetic field at a fixed He/H abundance ratio of 0.01 in comparison with the observations (black asterisks). The blue, red, and green lines are for a stellar XUV flux at 1 AU of 7.5 erg cm−2 s−1 and a planet with a magnetic field strength of 0.01, 0.5, and 1.0 G, respectively (i.e. model runs N1, N2, N3). The grey line is for a planet with a magnetic field of 1.0 G and a strong stellar wind (i.e. model run N4). The absorption profiles are the result of time averaging from −0.1 to +0.1 in planetary orbital phase. The zero Doppler-shifted velocity on the x axis corresponds to a wavelength of 10 830.25 Å. The horizontal dashed line marks the 2σ upper limit derived from the observations (Fossati et al. 2022). The horizontal dotted line at 1.00 is for reference.

In the text
thumbnail Fig. 10

Distribution of the absorption of the metastable He I line at ≈10 830 Å across the stellar disk integrated in the ±5 km s−1 range as seen by an Earth-based observer at mid-transit resulting from the N1 (top), N2 (middle), and N4 (bottom) simulations.

In the text
thumbnail Fig. 11

Size of the measured He I absorption signal normalised to the atmospheric scale height computed considering the planetary parameters listed in Table A.1 and a mean molecular weight of a pure hydrogen atmosphere, as a function of the incident stellar EUV flux (in logarithmic scale) in the 200–504 Å wavelength range. Arrows indicate upper limits. The numbers close to each point are the labels listed in the first column of Table A.1. Gas giants are marked by filled circles, while rocky planets are marked by empty squares (we apply the term ‘rocky’ to planets that presumably do not host an extensive primary hydrogen-dominated atmosphere). Black and red symbols indicate planets for which the search for metastable He I absorption has been conducted employing high- and low-resolution techniques, respectively (low-resolution techniques comprise both low-resolution spectroscopy, R < 10 000, and narrow-band photometry). The dashed horizontal line connects the two possible locations of WASP-80b, which differ solely on the assumption of a high or low [Fe/O] coronal abundance. V 1298 Tau d (#35) is not shown, because the estimated He I absorption signal lies significantly out of scale compared to the rest of the sample and has an uncertainty of larger than 100% (see Table A.1).

In the text

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