Lyα Absorption at Transits of HD 209458b: A Comparative Study of Various Mechanisms Under Different Conditions

To shed more light on the nature of the observed Lyα absorption during transits of HD 209458b and to quantify the major mechanisms responsible for the production of fast hydrogen atoms (the so-called energetic neutral atoms, ENAs) around the planet, 2D hydrodynamic multifluid modeling of the expanding planetary upper atmosphere, which is driven by stellar XUV, and its interaction with the stellar wind has been performed. The model self-consistently describes the escaping planetary wind, taking into account the generation of ENAs due to particle acceleration by the radiation pressure and by the charge exchange between the stellar wind protons and planetary atoms. The calculations in a wide range of stellar wind parameters and XUV flux values showed that under typical Sun-like star conditions, the amount of generated ENAs is too small, and the observed absorption at the level of 6%–8% can be attributed only to the non-resonant natural line broadening. For lower XUV fluxes, e.g., during the activity minima, the number of planetary atoms that survive photoionization and give rise to ENAs increases, resulting in up to 10%–15% absorption at the blue wing of the Lyα line, caused by resonant thermal line broadening. A similar asymmetric absorption can be seen under the conditions realized during coronal mass ejections, when sufficiently high stellar wind pressure confines the escaping planetary material within a kind of bowshock around the planet. It was found that the radiation pressure in all considered cases has a negligible contribution to the production of ENAs and the corresponding absorption.


Introduction
The study of planets beyond the solar system, or exoplanets, is one of the fastest growing and intriguing fields in space science. After just 20 years, more than 3500 exoplanets, including about 600 multiple systems, have been discovered (e.g., NASA exoplanet archive:https://exoplanetarchive. ipac.caltech.edu/). Among those, more than 2700 are transiting exoplanets, which admit spectral probing. A large number of Jupiter-type giant exoplanets and an even larger number of less-massive planets are found to orbit at extremely close distances0.05 au (e.g., http://exoplanets.org/). Lammer et al. (2003) were the first to show that a hydrogen-rich atmosphere of such planets will be heated to several thousand Kelvin and dynamically expand. Vidal-Madjar et al. (2003) observed the transiting exoplanet HD 209458b with the HST/STIS instrument and discovered a 15% intensity drop in the high-velocity blue part of the stellar Lyα line, which can be explained only by the presence of energetic neutral atoms (ENAs) of planetary origin moving away from the star with velocities of up to 150 km s −1 . Further reanalysis of the data gave slightly smaller and more symmetric absorption profiles at the level of (6-9)% (Ben-Jaffel 2007; Ehrenreich et al. 2008;Vidal-Madjar et al. 2008;Ben-Jaffel & Sona Hosseini 2010). The absorption in Lyα was also observed in the hot Jupiter  (Ehrenreich et al. 2012). The measurements at the transit of warm Neptune GJ 436b  revealed 50%, mostly blueshifted, absorption, well beyond the measurement uncertainty. Altogether, these observations indicate the existence of an essentially dynamic and expanding hot hydrogen envelope around the close-orbit exoplanets, driven by the complex processes of stellar planetary interaction and radiative energy deposition. The presence of an outflowing exosphere is also qualitatively supported by the observation of heavier element lines, such as carbon, oxygen, and silicon at HD 209458b Linsky et al. 2010), which show absorption beyond the Roche lobe at velocities of up to 50 km s −1 in the blue and red wings of the corresponding lines (Ben-Jaffel & Sona Hosseini 2010), as well as by measurements of Si III absorption during a transit of HD 189733b ) and of Mg IIsignatures in WASP-12 b (Fossati et al. 2010), which were found as significant near-UV absorption.
Soon after the discovery of the first hot Jupiters, 1D gasdynamic models were developed to describe their exospheres (Yelle 2004;Tian et al. 2005;García Muñoz 2007;Penz et al. 2008;Murray-Clay et al. 2009;Koskinen et al. 2010;Guo 2011;Trammell et al. 2011;Shaikhislamov et al. 2014). It was found that due to extreme heating by the ionizing XUV stellar radiation, close-orbit planets should indeed possess atmospheric material (partially ionized gas) outflow in the form of a supersonic planetary wind (hereafter PW), which overcomes the planet's gravity and expands beyond the Roche lobe. The calculated exosphere temperature of ∼10 4 K, outflow velocity of ∼10 km s −1 , and mass loss in the range of ∼10 9 -10 11 g s −1 qualitatively agree with transit spectral observations. The major factors and processes influencing the formation of a PW, such as the spectra of ionizing stellar XUV radiation and the particulars of its absorption, gravitational/ tidal effects, hydrogen plasma and photochemistry, effects of heavier species in atmospheric composition, and processes of infrared and ultraviolet cooling, have been analyzed in these works.
With the detection of absorption by HD 209458b in the highvelocity wings of stellar Lyα, it has been proposed that ENAs are produced by the acceleration of hydrogen atoms by the radiation pressure of Lyα in the thermosphere of a planet that has expanded beyond the Roche lobe (Vidal-Madjar et al. 2003;Lecavelier des Etangs et al. 2004, 2008. It appears that the radiation pressure acting on a hydrogen atom is several times higher than the stellar gravity. Thus, it is able to accelerate the atom significantly during the time span of its ionization. At the same time, as demonstrated by Erkaev et al. (2005), Khodachenko et al. (2007aKhodachenko et al. ( , 2007b, and Lammer et al. (2009), the hot exosphere of exoplanets should experience the nonthermal escape of particles. As proposed by Holmström et al. (2008) and Ekenbäck et al. (2010), the escaping planetary atoms are ionized in the flow of stellar wind (hereafter SW) protons via charge-exchange reaction. This mechanism produces fast hydrogen atoms (i.e., ENAs), which are necessary to explain the asymmetric absorption in the blue spectral wing of Lyα not by the acceleration of particles, but due to the presence of fast and hot protons in the SW. Nowadays, to simulate such an ENA generation process, kinetic models of test particles that take into account both the effects of radiation pressure and charge exchange are widely applied. This approach has been realized, in particular, for the interpretation of transit depletion in Lyα for HD 209458b (Kislyakova et al. 2014), HD 189733b , and GJ 436b . However, a significant limitation of such a modeling consists in the launching of planetary particles into the SW from a semi-empirically predefined boundary of the planetary exosphere, without taking into account the realities of PW formation, structure, and plasma flow (i.e., PW and SW) interaction.
In the meantime, the concept of HD/MHD modeling of the escaping PW and its interaction with the SW was being developed. Murray-Clay et al. (2009) estimated that for HD 209458b, the typical SW ram pressure, based on the solar wind parameters, equals the PW thermal and ram pressures at a distance of about 4-5 planetary radii, R p , which is close to the point where the PW flow becomes a supersonic one. This conclusion was later confirmed in our simulations (Shaikhislamov et al. 2014;Khodachenko et al. 2015), which provided the location of the pressure balance point beyond the Roche lobe at the distance of ∼5 R p . Despite the obvious necessity of properly merging the above-mentioned HD/MHD and kinetic test-particle models in order to build a complete and consistent view of PW initiation, propulsion, and consequent interaction with the SW, such attempts still remain quite rare and of limited use. Several reasons for these include a complication of the modeling approach, which requires switching from 1D to at least 2D geometry, a separate description of the interacting and essentially different plasma components (i.e., PW and SW partially ionized plasmas), and an appropriate accounting and combination of the large-scale processes of plasma-flow interaction and micro-processes of PW initiation and propulsion at atmospheric scale heights. There are a number of works where some of the abovementioned complexities have been addressed by adapting various astrophysical codes. In particular, a shock wave at the PW and SW collision region was modeled in Stone & Proga (2009). Later on, a 3D picture of planetary material, overflowing the Roche lobe and falling onto the star in irregular clumps, was simulated in Bisikalo et al. (2013) for very close exoplanets like WASP-12 b. In the course of the parametric study of different SW conditions performed by Matsakos et al. (2015), it was shown that if the SW stops the planetary material flow inside the Roche lobe, then a material flow structure with a comet-like trailing tail is formed. In the opposite case, an escaping PW stream is formed at the day-and nightsides, with the dayside stream accretion on the star accompanied by the fast loss of its rotational momentum due to interaction with the SW. Tremblin & Chiang (2013) proposed, for the first time, that the formation of an ENA cloud around a hydrogen-rich exoplanet can be considered within the framework of HD description by modeling four interconnected fluids: (1) planetary hydrogen atoms, (2) protons of planetary origin, (3) stellar protons, and (4) ENAs. However, in this work, as well as in Christie et al. (2016), besides the numerous empirical simplifications, such an approach was not fully realized because the motions of planetary hydrogen atoms and proton fluids were not distinguished from one another. This led to erroneous conclusions, with the result that charge exchange and the production of ENAs were possible only in a thin boundary layer of turbulent mixing. In recent years, some of the previously used 1D fluid models have been upgraded to 3D ones, which still retained ungrounded simplifications of the physics of the PW formation (for example, Tripathi et al. 2015).
In our previous paper, Shaikhislamov et al. (2016), we performed a 2D four-fluid simulation of the PW-SW interaction for an unmagnetized analogue of the tidally locked exoplanet HD 209458b. Because of the completely selfconsistent approach developed in Shaikhislamov et al. (2014) and Khodachenko et al. (2015), which does not rely on any quasi-empirical simplifying assumptions while employing an independent description of planetary hydrogen atoms and protons interacting with stellar protons and ENAs, we were able to combine the microphysics of PW generation with its large-scale expansion and interaction with SW. This enabled us to make (on the basis of the obtained results) several important conclusions. First, depending on natural (about an order of magnitude) variations in the dynamic pressure of the solar-type SW, the PW of HD 209458b can exist in two essentially different regimes of its outflow (Shaikhislamov et al. 2016): (1) the "blown by the wind"regime, wherein sufficiently strong SW confines the escaping PW at the dayside and channels it away from the star into the tail, forming a kind of an elongated planetary plasmasphere, and (2) the "captured by the star"regime, wherein the tidal force exceeds the action of the SW ram pressure, and a stream-type structure of the escaping PW is formed along the planet-star line (tailwards and toward the star). The planetary material flow is sufficiently dense to remain strongly collisional even rather far from the planet (several tens of R p ). In both regimes, a thin boundary, or a kind of ionopause, between the PW and SW plasmas is formed, at which the corresponding PW and SW plasma pressures are balanced. However, while the planetary protons are fully stopped, or redirected, at the ionopause, atoms can penetrate through it into the SW, where they undergo charge-exchange reaction and generate ENAs. In the case of the "captured by the star"regime, the extended boundary between the quasi-parallel PW stream and the SW flow is distorted by a kind of interchange instability, which generates a turbulent vortex layer. It appears that more ENAs are generated under the conditions of the "blown by the wind"regime of PW-SW interaction, because in this case a shocked region is formed beyond the ionopause (Shaikhislamov et al. 2016). However, we found that for the parameters used in this model, such as the solar-type XUV flux of 4.466 erg cm −2 s −1 at 1 au and the typical-for-the-Sun density, velocity, and temperature of the SW resulting in a pressure of about 5 × 10 −6 μbar, the number of ENAs obtained in simulations of HD 209458b appears an order of magnitude smaller than needed to influence the transit observations in the Lyα line.
In the present paper, we analyze in detail the absorption of the Lyα line in the dynamical environment of the interacting PW and SW around HD 209458b with the purpose of understanding what information can be derived from the planet's transit measurements in EUV. In particular, we look for conditions where the absorption is more or less symmetric over the blue and red wings of the Lyα line caused by the nonresonant natural line broadening within the dense exosphere of the planet inside the Roche lobe, as well as for conditions where the absorption is asymmetric and caused by the resonant, or thermal line, broadening produced by the ENAs, increasing the depth of the transit in the blueshifted wing. To make our model relevant to the case under study, first of all, we included in it the Lyα radiation pressure as one of the factors influencing the generation and distribution of ENAs. Then, we varied parameters of the model such as the stellar XUV flux and SW ram pressure (controlled by the SW density and velocity) by more than an order of magnitude. It was found that under the conditions explored and the Lyα flux based on actual measurements, the radiation pressure cannot be a dominating factor in explaining the observations. At the PW densities predicted by the simulations, its influence on the formation of the ENA cloud around HD 209458b is small in comparison with the charge exchange. We support these conclusions with physical explanations and quantitative estimations. This paper is organized in the following way. In Section 2, we describe the model used for the simulation of the PW-SW interaction, paying attention to the basic processes, equations, and important details regarding the formation of the Lyα absorption line. In Section 3, the results of the numerical simulations of the HD 209458b case under different XUV and SW conditions, and the related peculiarities of the Lyα absorption line expected during the planet transits, are presented. In particular, Sections 3.1 and 3.2 are dedicated to the study of the role of resonant thermal and non-resonant natural line broadening absorption, the contribution of ENAs, and the influence of XUV flux on the whole Lyα absorption profile. A comparative study of radiation pressure and charge exchange, as the two major mechanisms for the production of ENAs in the vicinity of the planet, is presented in Section 3.3, whereas the Lyα absorption features expected in the case of the "blown by the wind" regime of the PW-SW interaction are investigated in Section 3.4. Section 4 is dedicated to the discussion of the obtained results and conclusions.

Model
Our model has been described in previous works by Shaikhislamov et al. (2016) and Khodachenko et al. (2015), where the details regarding the physical processes, equations, hydrogen photochemistry, problem geometry, numerical code implementation, boundary conditions, and imposed approximations as well as their justification, are provided. In that respect, here we just address (and repeat) the most essential points. To simulate the interaction of the PW and SW, we apply a multifluid model that includes, as separate fluids, the hydrogen and helium components of planetary origin As an initial state, the neutral atmosphere in barometric equilibrium with the base temperature of 1000 K is taken, which consists of molecular hydrogen and helium at a ratio of x x 1 5 He H2 = . The radiative energy deposition is calculated by the spectral integration of the XUV flux, for which we use the solar proxy spectrum in the range 10-912 Å, compiled by Tobiska (1993), and binned by 1 Å. The total integrated XUV flux at 1 au for this spectrum is F XUV = 4.466 erg s −1 cm −2 . To investigate the effect of varying XUV flux on the absorption at the highvelocity blue wing of the stellar Lyα line during the HD 209458b transit, the proportionally reduced/increased values of the basic solar proxy flux were used. As reference parameters of a typical SW at 0.047 au, we use the simulated data from Johnstone et al. (2015) and consider the slow and fast SW with the following ranges of density n sw = (0.46 -2.5)× 10 4 cm −3 , velocity V sw = (230 -500) km s −1 , and temperature T sw = (1.2-2.9)×10 6 K, which correspond to the total SW pressure range of p 5 10 1.3 10 bar . To employ our 2D axially symmetric hydrodynamic (HD) numerical model with the symmetry axis taken along the planet-star line and with the center of reference attached to the center of the planet (Khodachenko et al. 2015;Shaikhislamov et al. 2016), we disregard the Coriolis force and ignore the transverse component of the SW velocity, ∼140 km s −1 for HD 209458b, which is related to the orbital motion of the planet around the star. As shown in Shaikhislamov et al. (2016), the last assumption is still possible for the considered planet in both cases of fast and slow SW velocities. As the characteristic values of the numerical problem, we use the planet radius R p , a temperature of 10 4 K, and a corresponding thermal velocity of ions V 9.07 o = km s −1 . The interpenetration of counterstreaming plasma flows of PW and SW is restricted by gyro-rotation in the background magnetic field. The frozen-in magnetic fields, either laminar or chaotic, are always present in both stellar and planetary plasmas. Compared to the characteristic scale of the considered system, ∼R p (>10 10 cm), even for a very weak magnetic field of 1 nT, the proton gyroradius is at least 10 times smaller than the characteristic scale. Thus, under the natural conditions of colliding PW and SW of HD 209458b, the interpenetration of planetary and stellar protons should be microscopically small. Because of this, the interaction between the planetary and stellar protons was described in Shaikhislamov et al. (2016) by effective collisions with a very small mean free path (about a particle gyroradius). Such a strong coupling means that proton fluids of planetary and stellar origin have the same velocity and temperature whenever they mix. In view of this, in the present paper we simplify the model by using a physically equivalent single proton fluid, which is subject to two different boundary conditions, one at the planet's surface (zero density and velocity) and the other at the outer boundary (SW parameters).
An important modification of the model consists in the inclusion of the radiation pressure by Lyα photons. The reconstructed data of the Lyα line profile based on actual measurements for HD 209458 can be found in either Wood et al. (2005) or in . In our simulations, we use its simplified analytical version, in which it has a constant value of F 8 10 Ly , 3 = a l · erg cm −2 s −1 Å −1 in the range of Doppler-shifted velocities ±45 km s −1 , and drops outside this range linearly to zero at the velocities ±140 km s −1 . This flux (with a total value of ≈13 erg cm 2 s −1 at 1 au) is absorbed with the integrated cross-section of σ Lyα, λ = d 5.5 10 abs 15 , which is about 3.5 times larger than the stellar gravity pull and consistent with the value calculated, e.g., in .
The spectral absorption of Lyα photons is described by assuming the so-called Voigt convolution of a Lorentz line shape with a natural width and Gaussian distribution profile, which depends on the temperature T, velocity along the line of sight V z , and hydrogen atom density n H : is the Voigt profile, which takes into account the convolution of two broadening mechanisms, one of which alone would produce a Gaussian profile (as a result of Doppler broadening) and the other would produce a Instead of wavelength, the absorption is expressed in terms of Doppler-shifted velocity in the reference frame of the star. The averaging in Equation (1) covers the stellar disk of radius R St . The mean fluid values of n H , T, and V z are calculated using the numerical model. For the length L, we take an empirical value of L=10 R p . This length is limited by the spiraling of the planetary material stream due to Coriolis force (clockwise in the planet-based reference frame), which is not included in our model. In other words, L corresponds approximately to the size of our modeling box, where the spiraling might still be ignored. It can also be considered as the width of the PW streams, which appear to be roughly ∼10 R p . The assumed size of the ignored spiraling is also consistent with the large-scale 3D simulations by Kislyakova et al. (2014) and .
At temperatures above 2 K, which is a definitely satisfied condition in our case, the Voigt profile integral can be fitted (with accuracy better than 1%) by an analytical expression (Tasitsiomi 2006): ) Therefore, the corresponding absorption cross-section can be approximated as follows: The applied analytical fit explicitly shows that there are two different kinds of Lyα absorption, which are caused by essentially different populations of particles. First is the resonant, or thermal line, broadening absorption related to resonant atoms matching the Doppler-shifted velocity of the line profile, which, at the typical temperature of order 10 4 K, has a significant cross-section of the order of 10 −13 cm 2 (the first term in Equation (2) for the absorption cross-section). Second is the non-resonant natural line broadening absorption related to the far wings of the Lorentz line profile with a much smaller cross-section, which, at a velocity of 100 km s −1 , is of the order of 10 −19 cm 2 (the second term in Equation (2)). Note that the same formula, albeit differently normalized and without the correcting factor q(x 2 ), is widely used in the literature. In our simulations, we apply the entirety of Equation (2) to calculate the Lyα line absorption in order to account for the self-shielding of radiation pressure.

PW-SW Interaction Under Typical Conditions of HD 209458b,and the Related Lyα Absorption Features
The modeled structure of the escaping PW of HD 209458b interacting with the SW flow is shown in the color plots of Figure 1. The total integrated XUV flux F XUV in this simulation run was taken to be 4.466 erg cm −2 s −1 at 1 au, while the SW parameters were n 4600 cm . These values are typical for the so-called slow wind of a solar-type star. As has been shown in our previous paper, Shaikhislamov et al. (2016), the "captured by the star"regime of the PW-SW interaction is realized for such parameters, when, besides a tailward planetary material outflow, the partially ionized plasma stream pulled by the stellar gravity is formed on the dayside of the planet. This dayside stream is surrounded by the counterstreaming SW plasma, and the whole planetary plasmasphere is separated from the SW by a thin ionopause layer, where sporadic interchange instabilities develop. Although the expansion of the PW protons across the stream is stopped by the thermal pressure of the SW protons, the planetary atoms penetrate the ionopause and are injected into the SW where they are accelerated by the pressure gradient and radiation pressure while undergoing the charge exchange. These processes result in the generation of ENAs. The ENAs are mostly produced in the vicinity of the ionopause where the density of atoms is largest. Both ENAs and planetary atoms expand farther across the stream and are gradually swept away from the star. As can be seen in the streamline plots in Figure 1, only a small portion of the total amount of escaped planetary atoms passes sufficiently close to the ionopause to be able to penetrate into the SW (mainly due to the boundary instabilities and pressure gradient).
The absorption profile of the Lyα line revealed in this simulation is given in Figure 2. In particular, the absorption is rather significant at low Doppler-shifted velocities, i.e., within the range of ±50 km s −1 . However, this range of velocities cannot be probed with the existing observations, due to the geocoronal contamination and interstellar extinction of the line. At the same time, one can see that at blue-and redshifted velocities beyond±100 km s −1 , the absorption reaches values of about 6%, which are in the range of those actually detected. An important insight into the nature of the absorption line profile can be derived from the analysis of the different kinds of Lyα absorption related to the different contributions of different particle populations in the modeled system. In Figure 2, the calculated absorption due to resonant atoms (the . Here, and further on in similar plots, the white circle indicates the planet, the plotted values are in log scale, the streamlines of the corresponding components are shown in black, the values outside the indicated variation ranges of the plotted parameters are colored in either red if smaller than minimum, or blue, if higher than maximum.  Figure 1 (slow SW;"captured by the star"regime of interaction). A decomposition of the total absorption into the resonant thermal (black dotted) and non-resonant natural line broadening (black dashed) parts is shown. Another decomposition represents the contributions to the absorption of ENAs (gray dotted) and planetary atomic hydrogen Ha (gray solid). resonant thermal line broadening part) is shown separately. By subtracting it from the total absorption, the non-resonant natural line broadening part can be found in the first approximation. It is also shown in Figure 2. In a similar way, a decomposition to distinguish between the contributions of ENAs and planetary atoms is performed. Note that the absorption by the planet disk, equal to 0.0156%, is not included in either the resonant or ENA parts. One can see in Figure 2 that the strong absorption within the±50 km s −1 interval of velocities is produced by the resonant planetary atoms in the PW streams moving in direction toward and outward the star (along the observation line). According to the simulation, at distances of ∼10 R p from the planet, the escaping PW streams are accelerated up to velocities of about 50 km s −1 (for details, see also Shaikhislamov et al. 2016), resulting in resonant thermal line broadening. At larger Doppler-shifted velocities, the absorption by planetary atoms due to nonresonant natural line broadening becomes dominant. It has been found that this absorption is produced by an extended, but still sufficiently dense, planetary exosphere with n 10 cm H 7 3 > at relatively close distances from the planet within the Roche lobe. For example, 90% of it comes from the region approximately bounded by a cylinder with r R 2.5 p = , elongated along the planet-star line over Due to the relatively low bulk velocity of material in this region, the absorption due to non-resonant natural line broadening is symmetric and gives practically the same contribution at both the red and blue wings of the Lyα line.
This conclusion is in full agreement with the analysis by Ben-Jaffel (2007, 2008, who found that the absorption measured during the transits of HD 209458b is about the same in the blue and red parts of the Lyα line. It is also in agreement with its physical interpretation given in Ben-Jaffel (2007, 2008, as well as in Koskinen et al. (2010) In our simulation, after averaging over the same line intervals as reported in Ben-Jaffel (2007), we obtain a slightly lower transit depth value of 6%. In our simulation, the transit depth calculated at the same line intervals as those used in Ben-Jaffel (2007) for the medium-resolution mode gives 6.6% and 6.3% at F XUV = 4 erg s −1 cm −2 and F XUV = 8 erg s −1 cm −2 , respectively. The absorption over the whole line (excluding the core V 64 km s 42 km s 1 1 -< < --) gives about the same values, i.e., (6.1-6.3)%.
An interesting feature is that the absorption due to nonresonant natural line broadening does not depend on XUV intensity and the total mass loss in a wide range of values from M 4 10 g s --. This is because the temperature of the escaping material in close vicinity of the planet changes with XUV rather weakly, while the flow velocity, which defines the mass loss, builds up at several planetary radii. Thus, the densest exosphere at distances below (1-2)R p around the planet, which contributes the Lyα nonresonant natural line broadening absorption, remains mostly in barometric equilibrium and is not affected by the PW outflow at higher altitudes. However, we found that the hydrogen chemistry somewhat affects the transit depth caused by the non-resonant natural line broadening absorption. For example, taking a purely atomic hydrogen atmosphere (instead of a molecular one) decreases absorption by about 0.5%. This is because of dissociation, which makes the atomic hydrogen more abundant in the molecular atmosphere up to the H 2 /H dissociation front, which in our simulations is located at about 0.3 μbar.

On the Lyα Resonant Thermal Line Broadening Absorption Controlled by Stellar XUV
Regarding the resonant thermal line broadening absorption of Lyα, one can see in Figure 2 that at high velocities, i.e., for V 60 km s 1 > -

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, it is an order of magnitude lower than the non-resonant natural line broadening absorption. Therefore, as has been found in our previous paper, Shaikhislamov et al. (2016), and confirmed in the present work, for typical Sun-like star XUV flux and SW conditions at the distance of D=0.047 au, the amount of ENAs generated due to charge exchange and radiation pressure is too small to produce any detectable asymmetry between the red and blue wings of the absorption line during the transits of HD 209458b. To explain such a small population of ENAs, the following important physics points were emphasized in Shaikhislamov et al. (2016).
First, the escaping PW, either as a supersonic stream or an expanding cloud surrounding the planet, is strongly collisional due to proton-atom resonant charge exchange. Although theplanetary and stellar proton flows colliding with each other form a thin contact ionopause, where their respective pressures balance each other, the planetary atoms on their way toward the region filled with SW plasma have to drag through the volume occupied by planetary protons. Since the mean free path of momentum exchange in this case appears to be significantly smaller than the typical size of the plasmosphere, the relative atom-proton velocity is proportionally reduced in comparison with that of the thermal motion. In particular, assuming an approximate pressure-friction force balance, This ratio is determined mostly by the ionization of atoms due to the stellar XUV and to a lesser degree by recombination. In the first approximation, the number of atoms can be supposed to be decreasing exponentially with time, as they stream away from the planet, and the typical ionization time is proportional to the total XUV flux. For the typical XUV flux estimated for a Sun-like star at the orbital distance of HD 209458b, this indeed results in the small amount of planetary hydrogen atoms reaching the SW region. It may be, however, expected that the decrease of XUV intensity would result in the rapid increase of the number of atoms that survive the exposure to the ionizing radiation before they penetrate into the SW. The decrease of XUV flux also results in the total decrease of the temperature of the escaping PW and, consequently, in a faster recombination, again increasing the ratio n n H H+ . We note that the above-mentioned circumstances are also important for the acceleration of hydrogen atoms by radiation pressure and have to be properly taken into account. In particular, the PW flow is sufficiently dense to be shielded from Lyα photons, and the momentum received by the atoms is additionally reduced because it is shared with the much more numerous protons (Shaikhislamov et al. 2016). As is empirically known for the Sun, its XUV flux is highly variable in time. Even the annually averaged value changes by about three times between the solar minimum and maximum phases. Therefore, the possibility of similar variations of the XUV flux on a Sun-like star such as HD 209458 should be taken into consideration. In order to check whether reducing the XUV flux might increase the absorption at the high-velocity blue wing of the stellar Lyα line during the transit of HD 209458b, we performed a set of dedicated simulations. Figure 3 shows the transit profiles of the total Lyα absorption (left panel) and its resonant thermal line broadening part (right panel) for different values of XUV flux, decreasing twofold from 16 to 1 erg cm −2 s −1 . According to the simulation results, the amount of ENAs steeply increases with the decrease of XUV flux, and one can see in Figure 3 that indeed, the Lyα absorption in the blueshifted velocity wing reaches the level of ∼15% at the XUV flux value of 1 erg cm −2 s −1 . At the same time, the absorption in the red wing at velocities above 60 km s −1 , which is produced by non-resonant natural line broadening, remains practically independent of the XUV flux. It is worth mentioning that at XUV fluxes of 4 erg cm −2 s −1 and higher, the absorption profile is very much symmetric, while at lower fluxes, a strong asymmetry of the absorption line develops with a significantly increased absorption in blue wing.
To illustrate in detail the influence of XUV on the generation of ENAs, we show in Figure 4 the profiles across the PW stream of the hydrogen atom to proton density ratio n n H H+ and the transverse atom-proton relative flux n V H H,H D + (see Equation (3)) at a distance of Z=5 R p upstream from the planet for different values of XUV flux. These plots demonstrate that the ratio n n H H+ and hydrogen atom flux injected into the SW area vary roughly in inverse proportion to the XUV intensity. Figure 4 also shows that there is a region adjacent to the planetary stream boundary where atoms have a distinct radial velocity relative to protons, which varies from V 10 3 õ for the XUV4 case up to V 10 2 õ for the XUV1 case. The PW stream width predictably contracts from about 5 R p to about 3 R p for the XUV4 and XUV1 cases, respectively, because it is controlled by the thermal pressure, which depends on the XUV heating. Figure 5 shows density plots similar to the ones in Figure 1, but calculated for the XUV flux of 1 erg cm −2 s −1 . Qualitatively, these plots are very much the same and show that the ENAs are produced close to the PW stream boundary, penetrated by just a small number of atoms. The only difference between Figures 1 and 5 consists in the particular amount of generated ENAs, which could be seen in the figures' color-coding bars.

The ENA Production Mechanisms: Radiation Pressure Versus Charge Exchange
In this section, we compare the efficiency of two possible mechanisms for the production of ENAs in the close vicinity of a hot Jupiter. One of these mechanisms is related to the acceleration of neutral hydrogen atoms by the radiation pressure force f F c rad Ly , Ly , Vidal-Madjar et al. 2003;Lecavelier des Etangs et al. 2004, 2008, and the other is due to the charge-exchange reaction between the planetary atmospheric neutrals and fast protons of the SW (Holmström et al. 2008;Ekenbäck et al. 2010;Kislyakova et al. 2014). To quantify (distinguish) the effect of the radiation pressure, we performed the simulations with the radiation pressure switched on and off in the presence and absence of a typical slow SW, taking the XUV flux at the lowest considered level of  Figures 1 and 5, with the typical dayside and nightside PW streams but having a larger width (7-9)R p , which in the absence of SW is controlled by the competing processes of lateral thermal expansion and tidal acceleration. Such a structure of the tidally locked hot Jupiter's PW without taking SW into account was obtained first in Khodachenko et al. (2015). Both day-and nightside PW streams have sharp boundaries. However, some of the hydrogen atoms passing close to these boundaries, where the density is rarefied, are decoupled from protons and accelerated by the radiation pressure away from the star. The increase of their velocity is shown in Figure 6(B). One can see that on the path of 20 R p , the radiation pressure accelerates the hydrogen atoms up to velocities of more than 100 km s −1 , which is required to interpret the spectral transit features of HD 209458b, supposing them to be caused by the Lyα resonant thermal line broadening absorption in the planetary ENA corona. However, the acceleration of atoms by the radiation pressure takes place only outside the relatively dense planetary stream, while inside the stream it is negligible, partially due to the self-shielding of Lyα photons and mostly due to the sharing of propulsion momentum received by atoms with more protons.
The resulting Lyα absorption lines for the considered cases, i.e., with and without SW, as well as with the radiation pressure switched on and off, are presented in Figure 7. The effect of the radiation pressure is clearly visible in the blue wing at the expected range of velocities up to 150 km s −1 in both cases, with and without SW. However, its total value is quite small, and for the higher realistic XUV fluxes, F XUV = 1-8 erg cm −2 s −1 at 1 au, it is negligible.
The smallness of the radiation pressure effect is additionally demonstrated in the same figure by (showing) the calculation (results) performed under the typical slow SW conditions with and without accounting for the radiation pressure. One can see that the difference between these cases does not exceed 1% and is within the natural time variability of the absorption caused by the local density and velocity fluctuations due to the instabilities developing at the contact boundary between the PW and SW. Therefore, the comparison of the ENA generation mechanisms reveals that under the considered parameters of the hot Jupiter HD 209458b, the production of ENAs due to the acceleration of atoms by the Lyα radiation pressure appears insignificant. The ENAs in the considered case (if they are created) are mainly produced by the charge-exchange reaction between the planetary atoms and SW protons. Thus, the observed absorption features during the planet transits are caused by non-resonant natural line broadening.
In spite of the fact that the radiation pressure is in principle able to accelerate the escaping planetary hydrogen atoms up to velocities typical for the observed transit spectral features (see Figure 6(B)), our hydrodynamic model shows that under the conditions of HD 209458b, the amount of such accelerated particles is not sufficient to produce measurable effects in the Lyα absorption line at velocities of the order of −100 km s −1 . According to the simulations, only a small number of atoms can reach the rarefied region where they may be efficiently accelerated by the radiation pressure. Even when assuming that due to the more complex 3D structure of the PW streams the Lyα radiation can penetrate into their denser layers, as argued in Shaikhislamov et al. (2016), its acceleration effectiveness will be drastically reduced by the coupling between hydrogen atoms and protons via resonant charge exchange. It can be estimated analytically that under the typical conditions expected at HD 209458b, the effect of acceleration by the radiation pressure force f F c rad Ly , Ly , s = a l a l · is much weaker in the production of ENAs compared to charge exchange. The latter can be represented as the acceleration of an atom to the velocity of a stellar proton V SW with a rate equal to the charge-exchange reaction rate n V exch SW SW exch s G = , which can be attributed to an effective volume force f exch . The ratio of the radiation pressure and the effective chargeexchange forces then looks as follows:

·
. So, finally we obtain f f 0.15 rad exch~. Therefore, even in spite of the fact that the stellar radiation force for HD 209458 is several times larger than its gravity, it is nevertheless significantly smaller than the effective "acceleration" of atoms due to SW. These analytical estimates are in full agreement with the results of our simulations.

Lyα Absorption in the "Blown by the Wind" Regime of the PW-SW Interaction
It has been shown in Shaikhislamov et al. (2016) that at the "blown by the wind" regime of PW-SW interaction, when the SW is strong enough to overcome the stellar gravitation acting on the escaping planetary material and to confine it within a kind of a paraboloid-shaped region bounded by an ionopause, more ENAs are generated. This is because the SW forms a bowshock, and planetary atoms can directly penetrate it through the ionopause. It has been found that for HD 209458b, such a regime is realized for relatively strong SW, with a pressure about 25 times larger than that of the typical slow SW considered above in this paper. Figure 8 shows the results of the calculation with the following parameters: XUV flux at 1 au F XUV = 4 erg s −1 cm −2 , n 2.5 10 cm ). One can see from the n H+ plot that the substellar position of the ionopause is at ∼3 R p . This is below the first Lagrange point R R 4.1 L1 p » . The PW flow is fully redirected toward the tail. The stellar protons form a bowshock and a shocked region, penetrated by planetary atoms. Differently from the "captured by the star" regime, in this case a significant amount of atoms, expanding from the dayside of the planet, reach the SW region. The ENAs are formed in a relatively thin layer near the ionopause, where the product of the SW protons and planetary atom densities has its maximum value. Practically all of the ENAs are confined within the shocked region, i.e., between the ionopause and the bowshock. Figure 9 shows the Lyα absorption profiles and their decompositions (done similarly to Figure 2) for two sets of conditions. The first one (Figure 9(A)) is identical to that used in the simulations presented in Figure 8, whereas the second is characterized by twice higher XUV flux and SW density. The results show a distinct asymmetry of the absorption line in the case shown in Figure 9(A), similar to the above considered cases of low XUV fluxes (seen in Figure 3). However, in the "blown by the wind" regime, a significant part of the absorption at the high-velocity blue wing is produced by the relatively fast atoms in the transition layer of the ionopause. At the ionopause, the proton velocity and temperature rapidly change from the relatively low values of the expanding PW to the high values in the shocked SW. In such a transition layer, the proton density is sufficiently high for strong coupling with atoms, resulting in their efficient pick-up due to momentum exchange (Shaikhislamov et al. 2016).
This scenario has been tested with the simulations under the same conditions as in Figure 8, but with the terms responsible for the production of ENAs due to charge exchange and the radiation pressure switched off. At higher XUV flux (Figure 9 (B)), the role of ENAs, produced by charge exchange, becomes totally negligible, and the asymmetry producing the additional absorption at the blue wing is related to the pick-up of atoms in the transition layer of the ionopause.
It has been also confirmed with dedicated simulation runs that the contribution of the radiation pressure to the production of ENAs is small under the considered system parameters expected for HD 209458b and that it increases the Lyα absorption by less than just 1%.

Discussion and Conclusions
In the present paper, we simulated the Lyα absorption line at Doppler-shifted velocities of the order of 100 km s −1 for the transits of HD 209458b using for the first time the selfconsistent 2D hydrodynamic model of the expanding PW, which interacts with the plasma flow of SW in the vicinity of the planet. The model enables the detailed quantitative description of the structure of the ENA envelope around the planet, formed due to charge exchange between the planetary hydrogen and stellar protons, as well as by the acceleration of atoms by the radiation pressure. It was demonstrated that the most crucial factor affecting the ENA environment of the planet is the XUV flux. At the same time, it was shown that for typical XUV fluxes expected at HD 209458 during a moderate or high level of activity, e.g., 4-16 erg cm -2 s -1 at 1 au, and for moderate SW, the corresponding Lyα absorption appears to be symmetric, resulting in the transit depth at the level of (6-6.3)%. This is equally produced in the Lyα blue and red wings by the non-resonant natural line broadening absorption, which occurs in the warm expanding upper atmosphere of HD 209458b deep inside the Roche lobe. Through this, the contribution of ENAs to the absorption process under the considered conditions remains negligible. This result is in full agreement with the conclusions made by Ben-Jaffel (2007, 2008 and Koskinen et al. (2010), who used the 1D models of the expanding exosphere of HD 209458b. The novel feature found in the present work consists of the fact that the intensity of the PW and the integral mass loss cannot be inferred from this kind of absorption. With a series of dedicated modeling runs, the Lyα non-resonant natural line broadening absorption has been shown to be insensitive to the level of XUV flux and the intensity of SW in a wide range of values, which, at the  . Profile of the Lyα absorption line for the slow SW is shown in the cases with radiation pressure (gray solid) and without it (black solid). For comparison, the case with no SW but with radiation pressure (dotted) is shown (same conditions as in Figure 6). XUV flux for all cases is 1 erg cm −2 s −1 at 1 au. An error bar shows the range of variations of absorption caused by the local density and velocity fluctuations. same time, define the planetary upper atmosphere escape and the related mass loss to a significant degree.
Under the typical conditions expected on HD 209458b, the Lyα resonant, or thermal line, broadening absorption related to the fast hydrogen atoms (ENAs), either accelerated by radiation pressure or produced during charge exchange with the SW protons, is small. However, under certain (somewhat unusual, but nevertheless possible) parameters of the SW and stellar radiation, the ENA population increases. This finally results in the increase of the thermal line broadening absorption. In particular, it was found that at XUV fluxes at 1 au below 2 erg cm −2 s −1 , the increase in the amount of ENAs results in a perceptible increase of absorption at the blue wing of the Lyα line. Under the typical SW parameters, the Lyα profile becomes distinctly asymmetric, with the absorption level in the blue wing increased by several percent. The main reason for this is that at lower XUV fluxes, the planetary hydrogen atoms survive for a longer time before being photoionized. This increases the amount of atoms that reach the boundary of the PW-SW interaction region and penetrate into the SW where they undergo the charge-exchange reaction and form ENAs.
A detailed analysis shows that in the relatively rarefied exosphere, which is optically thin to XUV photons, about 95% of ionization happens due to the VUV photons in the 500-912 Å range. The ionization by EUV and X-ray photons takes place in a dense optically thick upper atmosphere where VUV photons do not penetrate. In the spectra used for our modeling, the energy contained in the 500-912 Å range constitutes 22% of the total energy in the entire considered range of 20-912 Å. Thus, the total XUV flux at 1 au of 2 erg cm −2 s −1 , considered in the model, includes 0.44 erg cm −2 s −1 of its VUV part. Although no measurements in VUV can be made in other stars, the Sun may be considered as a kind of proxy in that respect. The data regarding the solar spectral luminosity (e.g., Tobiska 1993;Ribas et al. 2005;Linsky et al. 2013) and the related coronal modeling reveal, in particular, that the VUV flux between solar maximum and minimum varies by about 2 times (for EUV it can be up to 3 times). At the same time, during the activity minimum, a kind of minimal flux is achieved, the level of which is not related to any magnetic activity and is determined only by the basic stellar parameters, such as age, mass, and temperature (i.e., the stellar type). The solar irradiance at 1 au, measured during the last activity minimum in 2008, was about 1.9 erg cm −2 s −1 and 0.46 erg cm −2 s −1 in the ranges 100-912 Å and 500-912 Å, respectively (see the data analysis by Linsky et al. 2013). Close values have also been measured at 1 au in the solar minimum of 1974, e.g., 2.1 erg cm −2 s −1 and 0.42 erg cm −2 s −1 in the ranges 100-912 Å and 500-912 Å, respectively (Heroux & Hinteregger 1978). These values are close to those, where the effect of ENAs becomes noticeable in our model. The star HD 209458 is rather similar to the Sun, so the use of solar values as a kind of reference seems reasonable. However, because of the slightly larger size and total luminosity of HD 209458 compared to the Sun, some particular values might be up to 30%-50% higher. Reconstructing the ionizing flux (i.e., <912 Å) of HD 209458, based on the near-UV measurements with the HST COS instrument and X-ray measurements on XMM-Newton using the Differential Emission Measure coronal models, gave the values at 1 au of 6.4 erg cm −2 s −1 (Louden et al. 2017) and 2 erg cm −2 s −1 (Sanz-Forcada et al. 2011). Such a difference in the estimations of the ionizing flux comes from the uncertainty in the X-ray measurements. At the same time, it could be concluded that the possibility of the XUV radiation flux of HD 209458 at 1 au being at the level of 2 erg cm −2 s −1 or even lower cannot be excluded. It should also be noted that so far, no direct or indirect data on the VUV for the stars are available, whereas for the Sun, the measurements remain rather fragmented and does not cover many solar cycles. Nevertheless, a bit higher flux in the range (4-8) erg cm −2 s −1 at 1 au seems to be more realistic. Altogether, the above arguments might support the idea of a possibly lower level of ionizing radiation flux on HD 209458, which provides the conditions under which a relatively large number of upper atmospheric hydrogen atoms in HD 209458b reaches the ionopause boundary and penetrates into the SW region, where it produces via charge exchange a sufficient amount of ENAs capable of resulting in the measured Lyα absorption profiles during the planetary transits.
There is another aspect that concerns the atomic hydrogen content in the expanding upper atmosphere of a hot Jupiter. As has been pointed out in our previous paper (Shaikhislamov et al. 2016), the comparison of different models dedicated to the study of PW generation reveals the significant diversity in the predicted estimates of the radius of half-ionization (the distance from the planet where n n H H = + ) for HD 209458b. It varies from 1.6 R p in Murray-Clay et al. (2009) up to 3.1 R p in Koskinen et al. (2013) and to 4 R p in García Muñoz (2007). This difference comes from either the specific stellar XUV spectrum used in the models or the boundary conditions, as well as the different atmospheric compositions and different involved photochemistries. In our present calculations, the halfionization radius measured in the substellar direction varies from 2.5 R p to 4.2 R p for the XUV flux changing from 4 erg cm −2 s −1 to 1 erg cm −2 s −1 , respectively. The first value is significantly less, whereas the second one is practically equal to the value obtained in García Muñoz (2007) under a much higher XUV flux of 6.4 erg cm −2 s −1 .
The difference in the atomic hydrogen content results in different values for the Lyα non-resonant natural line broadening absorption, e.g., 6.3% in our simulations, 6.6% in Koskinen et al. (2010), and 8% calculated by Ben-Jaffel (2008) based on the model by García Muñoz (2007). At the same time, all of these results do not differ by more than an error and variability margins. Although the value of 8% is closest to the absorption measured in high-resolution observations (Ben-Jaffel 2007), it is not consistent with the presence of even a moderate SW. Otherwise, as can be judged from our modeling, the expected large content of planetary hydrogen atoms should produce enough ENAs via charge exchange, which will be visible as a strong absorption in the blue wing. Such contradictions and discrepancies leave room for improving the models of the hot Jupiters' upper thermospheres and exospheres on the one hand, and show the necessity for further spectral measurements of the planetary transits on the other hand.
Besides the low XUV flux, we found other conditions where the observed additional absorption at the blue wing of Lyα can take place. These are realized in the case of a strong SW typical for a strong solar CME. In this case, as was also predicted in our previous paper (Shaikhislamov et al. 2016), the "blown by the wind"regime of the PW-SW interaction is realized, when the SW stops the escaping planetary material from sweeping it toward the tail, and more ENAs are produced, as compared to the case of the "captured by the star"regime, when the material outflowing from the dayside of the planet flies in the direction of the star. To exceed the tidal pull in the case of HD 209458b, the SW ram pressure has to be an order of magnitude higher than its typical value in the quiet solar wind. In particular, for SW pressures above 10 bar 4 m at an orbital distance of 0.047 au, under the "blown by the wind" regime of the PW-SW interaction, the amount of atoms penetrating through the ionopause into the shocked region, formed around the planetary obstacle by the SW and filled by its fast and hot protons, greatly increases. This results in more effective production of ENAs, the amount of which becomes large enough to explain the observations even at XUV fluxes at 1 au higher than 4 erg cm −2 s −1 . Note that the ENAs are formed in this case not only via charge exchange between the planetary hydrogen atoms and protons, but also via momentum exchange and direct pick-up of atoms by protons in the boundary layer.
In all of the explored possible conditions expected at HD 209458b, also including the case with no SW, we found that the contribution of the radiation pressure (as an ENA accelerating factor) to the formation of the Lyα absorption line does not exceed the value of 0.01, and in most cases is even less than that. At the current level of sensitivity and reproducibility of the measurements, it cannot be distinguished relative to the symmetric non-resonant natural line broadening absorption at a level beyond 6%. Moreover, analytical estimations, supported by simulations, show that for the typical Sun-like SW, the action of the SW total pressure and charge exchange produce a significantly stronger effect than the Lyα radiation pressure. This study was performed under the assumption of a non-or weakly magnetized planet with a small intrinsic planetary magnetic dipole moment, which, according to the planetary dynamo scaling laws, is a reasonable approximation in the case of HD 09458b (Grießmeier et al. 2004(Grießmeier et al. , 2005Khodachenko et al. 2012). It should be noted, however, that for a magnetized analogue of HD 209458b (Trammell et al. 2014;Khodachenko et al. 2015), the planetary magnetic field influences the character of material escape and results in the appearance of a dead zone, where the plasma is stagnant, and a wind zone of the outflowing plasma. According to Khodachenko et al. (2015), a relatively strong planetary magnetic field, >0.3 G, at the equator causes a sufficiently large dead zone size, which reduces the overall material escaping from the planet. This in turn should affect the interaction of the escaping PW with the SW and the production of ENAs. In view of the strong coupling between the protons and neutrals in the PW, in the case of a large dead zone, fewer planetary atoms will be able to reach and penetrate the stellar wind, and therefore fewer ENAs will be finally produced.
Although the present study does not give an essentially new interpretation of the spectral observations of the HD 209458b transit, the analysis of various mechanisms of Lyα absorption is revealing and can be useful for other systems, as well as for the diagnostics of the dynamical plasma environments in the vicinity of the planet and its mass loss. Among other exoplanets in that respect, the most promising seems to be the warm Neptune GJ 436b. Its small size relative to the stellar disk makes the non-resonant natural line broadening absorption insignificant, while the low XUV flux and extended exosphere, weakly bounded by the planet's gravity, provide favorable conditions for the generation of ENAs by charge exchange.