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date: 21 October 2019

# Exoplanets: Atmospheres of Hot Jupiters

## Summary and Keywords

The history of exoplanetary atmospheres studies is strongly based on the observations and investigations of the gaseous envelopes of hot Jupiters—exoplanet gas giants that have masses comparable to the mass of Jupiter and orbital semi-major axes shorter than 0.1 AU. The first exoplanet around a solar-type star was a hot Jupiter discovered in 1995. Researchers found an object that had completely atypical parameters compared to planets known in the solar system. According to their estimates, the object might have a mass about a half of the Jovian mass and a very short orbital period (four days), which means that it has an orbit roughly corresponding to the orbit of Mercury. Later, many similar objects were discovered near different stars, and they acquired a common name—hot Jupiters. It is still unclear what the mechanism is for their origin, because generally accepted theories of planetary evolution predict the formation of giant planets only at large orbital distances, where they can accrete enough matter before the protoplanetary disc disappears. If this is true, before arriving at such low orbits, hot Jupiters might have a long migration path, caused by interactions with other massive planets and/or with the gaseous disc. In favor of this model is the discovery of many hot Jupiters in elliptical and highly inclined orbits, but on the other hand several observed hot Jupiters have circular orbits with low inclination. An alternative hypothesis is that the cores of future hot Jupiters are super-Earths that may later intercept matter from the protoplanetary disk falling on the star.

The scientific interest in hot Jupiters has two aspects. The first is the peculiarity of these objects: they have no analogues in the solar system. The second is that, until recently, only for hot Jupiters was it possible to obtain observational characteristics of their atmospheres. Many of the known hot Jupiters are eclipsing their host stars, so, from their light curve and spectral data obtained during an eclipse, it became possible to obtain information about their shape and their atmospheric composition.

Thus it is possible to conclude that hot Jupiters are a common type of exoplanet, having no analogues in the solar system. Many aspects of their evolution and internal structure remain unclear. Being very close to their host stars, hot Jupiters must interact with the stellar wind and stellar magnetic field, as well as with stellar flares and coronal mass ejections, allowing researchers to gather information about them. According to UV observations, at least a fraction of hot Jupiters have extended gaseous envelopes, extending far beyond of their upper atmospheres. The envelopes are observable with current astronomical instruments, so it is possible to develop their astrophysical models. The history of hot Jupiter atmosphere studies during the past 20 years and the current status of modern theories describing the extended envelopes of hot Jupiters are excellent examples of the progress in understanding planetary atmospheres formation and evolution both in the solar system and in the extrasolar planetary systems.

# Hot Jupiter Atmospheres

## Aeronomical Models

Among solar system planets, the gas giants—Jupiter and Saturn—are closest to hot Jupiters in their parameters. This allows us to use models developed for them as the basis for models of hot Jupiter atmospheres. One of the first one-dimensional aeronomical models was presented by Yelle in 2004 (Yelle, 2004). The temperature of a planetary atmosphere (not only of hot Jupiters) is ruled by energy flows. For hot Jupiters, the energy flow from the host star might dominate among other processes, and Yelle predicted that the temperature of hot Jupiter thermospheres could reach 10000 K, due to heating by extreme ultraviolet (EUV) radiation from the star. Because of such high temperatures, the outer parts of the atmosphere will escape rapidly, taking out excessive heat, so the upper thermosphere is cooled primarily by adiabatic expansion. The mechanism for lower thermosphere cooling is different—it must be cooled primarily by radiative emissions from H+3 ions, created by photoionization of H2 and subsequent ion chemistry. Composition of the atmosphere is governed by the equilibrium between several photochemical processes, such as the thermal decomposition of H2 near the base of the thermosphere. The balance between photoionization, advection, and H+ recombination determines the composition of the upper thermosphere. The main conclusion, which follows from the Yelle model, is that the energy-limited atmospheric escape rate is approximately proportional to the stellar EUV flux. Although escape rates are large, the atmospheres are stable over time scales of billions of years.

Another aeronomical model was developed by García Muñoz in 2007 (Garcia Munoz, 2007). This work was inspired by the detections of hydrogen, carbon, and oxygen atoms obscuring about one-tenth of the disk of the host star of the hot Jupiter HD 209458b. The author showed that for this planet EUV stellar irradiation might lead to the massive escape of its atmosphere, shortening the lifetime of the planet to a few gigayears. The model used was complicated enough; it took into account processes such as a mass-consistent treatment of molecular and ambipolar diffusion suitable for multitemperature, multicomponent gases.

The theoretically estimated high escape rate for HD 209458b’s atmosphere was a problem, because it strictly constrained the lifetime of the planet. An attempt to explain the stability of an observed hot Jupiter was performed by Murray-Clay, Chiang, and Murray (2009) by developing a more complicated model for the HD 209458b atmosphere. The model included realistic heating and cooling, ionization balance, tidal gravity, and pressure confinement by the host star wind. They showed that atmospheric mass loss looks like hydrodynamic (Parker) wind on the planet’s dayside only during lulls in the stellar wind. But when dayside winds are suppressed by stellar wind dynamic pressure, nightside winds might appear, picking up the mass loss rate if there is sufficient horizontal transport of heat. The model shows that a hot Jupiter might lose about 0.06% of its mass during its host star’s pre-main-sequence phase and about 0.6% of its mass during the star’s main-sequence lifetime.

Koskinen, Harris, Yelle, and Lavvas (2013) and Koskinen, Yelle, Lavvas, and Lewis (2010) published the first hydrodynamic escape model for the upper atmosphere of HD209458b. The proposed model includes all of the detected species in order to explain their presence at high altitudes and to further constrain the temperature and velocity profiles. The model used better estimates of photoelectron heating efficiencies than previous ones and included the photochemistry of heavy atoms and ions in addition to hydrogen and helium. The composition at the lower boundary of the escape model is constrained by a full photochemical model of the lower atmosphere. Using this model, the authors obtained temperature and velocity profiles and found that the outflow speed and temperature gradients depend strongly on the assumed heating efficiencies. The model predicted an upper limit of 8000 K for the mean temperature below 3 planetary radii, with a typical value of 7000 K based on the average solar soft X-rays and extreme UltraViolet (XUV) flux at the orbit of HD209458b.

The temperature of the upper atmosphere is a very important parameter, because a linear increase of the temperature leads to exponential growth of the mass loss rate. The model proposed by Shaikhislamov et al. (2014) gives the temperatures of hot Jupiter atmospheres as high as 9000 to 10,000 K. The model is self-consistent and shows that taking into account reabsorption and transfer of Lyman-α‎ (Ly-α‎) photons in the thermosphere of a typical hot Jupiter can increase its temperature by about 1500 K. The extension of the model to the 2D case (Shaikhislamov et al., 2016) includes stellar-planetary tidal interactions and a realistic sun-like spectrum of XUV radiation from the host star. This allows the authors to simulate in detail the hydrodynamic interaction between the planetary atoms, protons, and the stellar wind, as well as the production of energetic neutral atoms around the planet due to charge-exchange between planetary atoms and stellar protons. The flow structures revealed are important for the interpretation of Ly-α‎ absorption features in exoplanetary transit spectra and characterization of the plasma environments.

The photolysis of a hydrogen-rich atmosphere of a close-in exoplanet by the EUV radiation of the parent star leads to the formation of suprathermal particles (i.e., particles with an excess of kinetic energy). Using the model proposed in Ionov, Shematovich, and Pavlyuchenkov (2017), the authors showed that these particles with excess kinetic energies are an important source of thermal energy in the upper atmosphere of the hydrogen-rich exoplanets. For the atmosphere of HD209458b this model predicts that photoelectrons are an important cooling factor for the upper atmosphere of hot Jupiter, and their correct consideration can decrease the temperature by about 3000 K. Such cooling leads to great decrease of predicted mass loss rate, by up to five times for HD209458b, compared with other models.

## Physics of the Hot Atmosphere

As we can see from the previous paragraph, it is not easy to model a hot Jupiter atmosphere. To obtain the most important atmospheric parameters, like temperature, we have to take into account many nontrivial processes—suprathermal particles, radiation pressure, magnetic fields, atmospheric circulation, tidal forces, and so on. Next we take a deeper look at these processes.

### Suprathermal Particles

It is common to study gas dynamics assuming local thermodynamic equilibrium. If the considered volume is small enough, collisions between gas particles rapidly redistribute their kinetic energy according to the well-known Maxwell function. But chemical or photochemical reactions can produce high-energy particles, populating a high-energy tail of the distribution. For example, a photon can be absorbed by atom of hydrogen, producing a proton and a photoelectron. The law of energy conservation demands that the full energy of the produced particles (p + e) must be equal to the entire energy of the hydrogen atom and photon. If the photon belongs to the ultraviolet (UV) or EUV part of spectrum, the excess of its energy is enough to speed up the resulting particles significantly, producing a suprathermal fraction of the distribution function. The electron has about 1000 times less mass then the proton, so it gains a much higher velocity than the proton in this process. Not only hydrogen atoms can participate in these photoionization processes. He, H2, and other atoms and molecules can be also photoionized, producing suprathermal particles.

Another way to make suprathermal particles is via recombination processes in highly magnetized plasma. Charged particles (electrons and ions) composed of plasma rotate around magnetic field lines with so-called Larmor frequencies, which can be very high. While the particle can have a large linear velocity at each moment of time, its average motion is slow, as it moves along the small circular orbit. The only way for a charged particle to leave a magnetic field is to lose its charge via recombination or charge exchange. If an electron neutralizes an ion in a highly magnetized plasma, the resulting particle will still have high linear velocity, which is much higher than the mean thermal velocity of plasma particles. As aeronomic models have shown, suprathermal particles are an important component of the heating mechanisms acting in hot Jupiter atmospheres (Shematovich, Bisikalo, & Ionov, 2015).

Radiative pressure is not as important for planetary atmospheres in the solar system, but it can play a notable role for hot Jupiters, which are located in close-in orbits near their host stars. Almost all known hot Jupiters to date are orbiting around main sequence (solar type) stars with temperatures varying from ~3500 to ~7500 K. Stars of that type irradiate most of their energy in the continuum part of the spectrum. But spectral lines may contribute more in radiative pressure, because they are produced mainly by hydrogen and helium (i.e., the main constituents of hot Jupiter atmospheres). Estimates show (Cherenkov, Bisikalo, & Kosovichev, 2018) that hydrogen Ly-α‎ line gives the main contribution to radiation pressure in hot Jupiter envelopes. Other emission lines, free-bound absorption, free-free absorption, electron absorption, and absorption by negative ions of hydrogen (H) are negligible for the typical hot Jupiter range of parameters.

### Magnetic Fields

There is a common opinion expressed that hot Jupiters cannot have considerable magnetic fields. According to estimates given, for example, in Showman and Guillot (2002), strong tidal forces from the host star will synchronize the rotation of a typical hot Jupiter within several millions of years, so magnetic dynamo effects must be weak in such planets. The magnetic dipole moment, produced by slow synchronous rotation of a hot Jupiter, can be estimated as about 0.1 to 0.2 of the Jovian magnetic moment (Griebmeier et al., 2004; Kislyakova, Holmstrom, Lammer, Odert, & Khodachenko, 2014; Sanchez-Lavega, 2004). This is not enough to form a magnetosphere—the zone where magnetic pressure overcomes the dynamic pressure of stellar wind.

There have been several attempts to measure magnetic field strength on hot Jupiters. One of the first attempts was performed by Farwell, Lazio, Desch, Bastian, and Zarka (2004) using the Very Large Array radio telescope. They tried to detect the radio emission produced by hypothetical auroras on hot Jupiters HD 114762, 70 Vir, and τ‎ Boo. Unfortunately, no significant emission was detected on the predicted frequencies. Later, similar attempts were performed by other researchers but also without success. There is a current suggestion that the absence of the aurora is not an indicator of a weak magnetic field. Weber et al. (2017) have shown that cyclotron maser instability, the process responsible for the generation of radio waves by magnetized planets in the solar system, most likely will not operate on hot Jupiters. Another method of magnetic field measurement was used by Kislyakova et al. (2014). They performed transit observations of HD 209458b in the stellar Lyα‎ line to detect the size of its planetary magnetosphere. From a comparison with model results they showed that the magnetic moment of the planet cannot exceed 0.1 of the Jovian one.

Thus although hot Jupiters might have weak magnetic fields, magnetohydrodynamic effects can still play an important role in their extended envelopes. As the simplest criteria, we can use the comparison of magnetic pressure with gas pressure and the dynamic pressure of the stellar wind. Gas and dynamic pressure are proportional to gas density, while magnetic pressure is proportional to the square of magnetic induction. The magnetic induction of a dipole decreases proportionally to the third power of the distance, so magnetically driven regions must not be too far from the planet. Also, gaseous flows can deform the magnetic force lines, transporting planetary magnetic fields to larger distances, where magnetically driven regions also can be formed. The most favorable area for magnetic field domination is a weak gaseous tail behind the planet, shielded from the stellar wind by a planetary bow shock.

### Atmospheric Circulation

While the hot Jupiter itself is tidally locked, it must have a strong atmospheric circulation because of large temperature differences between the night and day sides of the planet. Komacek and Showman (2016) presented a three-dimensional model of such circulation. An analytic theory predicts that the longitudinal propagation of waves mediates dayside to nightside temperature differences in hot Jupiter atmospheres, analogous to the wave adjustment mechanism that regulates the thermal structure in Earth’s tropics. These waves can be damped in hot Jupiter atmospheres by either radiative cooling or potential frictional drag. This frictional drag would likely be caused by Lorentz forces in a partially ionized atmosphere threaded by a background magnetic field and would increase in strength with increasing temperature. Additionally, the amplitude of radiative heating and cooling increases with increasing temperature, and hence both radiative heating/cooling and frictional drag damp waves more efficiently with increasing equilibrium temperature. As also shown by Komacek and Showman, radiative heating and cooling play the largest role in controlling dayside–nightside temperature differences.

### Tidal Forces

Being so close to the host star, hot Jupiters must be a subject of strong tidal interactions. The sum of gravity forces and centrifugal force, appearing due to the orbital motion of the planet, can be presented as a gradient of Roche potential (see later discussion for details). Planetary atmospheres cannot be stable outside of specific drop-shaped Roche lobes, and all known planetary radii are found to be placed inside them. But the atmospheres have no clear borders, and the rarefied outer parts of a planetary atmosphere extend far beyond the observed photometric radius. The outer border of an atmosphere is usually called an exobase. The exobase radius is a distance where the scale height of the atmosphere (the distance where density falls to 1/e ~2.718 times its reference value) becomes equal to the mean free path of gas particles. The physical meaning of this boundary is based on the fact that, above this radius, the atmosphere can be considered as a collisionless one. If the exobase lies outside of the Roche lobe, the planet starts to lose its atmosphere with rather a high rate. There are two specific points where the gas can leave the planet by expending less energy—Lagrangian points L1 and L2. The L1 point lies between the planet and star centers; the star’s gravity assists the matter at this point, making the escape easier. The L2 point also lies on the star–planet line but on the opposite side with respect to L1. At this point, the centrifugal force is assisting the matter escape. The Roche lobe size is proportional to the orbital radius and the mass of the planet, so massive close-in planets have relatively small Roche lobes.

Because they have small Roche lobes, hot Jupiters are subject to strong tidal interactions. The first result of this interaction is tidal synchronization, leading to equalization of the planetary rotational period to the orbital one. The second important feature of this interaction is the possible outflows from hot Jupiter atmospheres, which result in the formation of their extended envelopes.

# Hot Jupiter Envelopes

Due to the proximity to the host star and the relatively large masses of hot Jupiters, in many cases we can consider the star–planet system in the same way as a binary star. Binary stars (or binaries) are very common objects. According to different estimates, more than half of the stars in our galaxy are members of binary or multiple systems. Some of the binaries are close enough to interact via mass transfer, releasing a lot of energy in accretion processes. Interacting binary stars have attracted the attention of researchers for many years, and now we have many theoretical models describing mass transfer in these objects. Some of these models can be adapted to star–planet systems containing hot Jupiters. In this section we describe the major physical processes determining the properties of the gaseous envelopes of hot Jupiters.

## The Roche Potential

A system consisting of a star and a hot Jupiter may be regarded as a close binary system with an extremely low mass ratio. Let us consider the force field in a binary system composed of a star and a hot Jupiter with masses M* and Mpl, respectively. It is reasonable to assume that orbits of the components are circular and their proper rotations are synchronized with the orbital motion so angular velocity Ω‎* = Ω‎pl = Ω‎ = 2π‎/Porb, where Porb is the orbital period. In addition, we consider the Roche approximation, in which the internal density of both the components sharply grows toward the center. This allows one to assume the star and planet as point masses and therefore to describe their gravitational potentials in the framework of classical Newtonian mechanics.

We further introduce a Cartesian coordinate system (x, y, z), rotating counter-clockwise along with the binary system and with the origin in the center of the star. The x-axis is directed along the line, connecting the centers of the components, the z-axis is perpendicular to the orbital plane and parallel to Ω‎, while the y-axis completes the right-handed coordinate system.

In the considered case of point masses, a potential Φ‎, describing the force field in the system, is known as the Roche potential. Since the components move in accordance with Kepler’s third law,

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where G is the gravitational constant, A is the orbital separation, and the center of mass of the system is located at a radius

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one can write the potential up to a constant as

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The Roche potential equation consists of three easy-to-understand terms. The first two terms are potentials from the star and planet masses, respectively. The third term corresponds to centrifugal force, appearing due to the system rotation. The gradient of the Roche potential represents the force acting on a material point in the system. Also in the non-inertial rotating coordinate frame the Coriolis force might appear, but this force, except for some specific cases, cannot be represented in potential form.

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Figure 1. Isosurfaces of Roche potential. Five libration (Lagrangian) points L1–L5 are show by red dots.

Figure 1 shows a 3D representation of some Roche equipotential surfaces. For clarity we have used the mass ratio Mpl/M* = 0.5, which is very high for a real hot Jupiter system, but the main features of the potential will present with small mass ratios too. As we can see from the figure, the Roche potential has five specific points, also called Lagrangian or libration points, where the gradient of the Roche potential is equal to zero, which means that all three forces (gravity forces and the centrifugal one) are compensating each other, allowing matter to flow through these points freely. All five Lagrangian points are located in the equatorial plane; three of them (L1, L2, and L3) lie on the x-axis and are the inflection points of Φ‎, while the L4 and L5 points are the maxima of Φ‎.

The equipotential, containing the inner Lagrangian point L1, encloses two contiguous volumes, known as critical surfaces or Roche lobes. The term “Roche lobe” is of particular importance in astronomy: for an object (star or planet’s atmosphere) whose boundary surface is inside the Roche lobe, one finds a stationary configuration where the gradient of the Roche potential is balanced by the gradient of gas pressure. Once the boundary of a component has reached the critical surface, because of the pressure gradient, mass outflow occurs at the inner Lagrangian point, where the total force is equal to zero.

General consideration of the mass loss rate assumes that the atmosphere is not completely bound to the planet by the planetary gravitational field; light atoms, such as hydrogen and helium, with sufficiently large velocities, can escape from the upper atmosphere into interplanetary space. This process is commonly called Jeans escape and depends on the temperature of the ambient atmospheric gas at an exobase altitude where the atmospheric gas is virtually collisionless (Chamberlain & Hunten, 1990). This is generally correct for all planets of the solar system but should be corrected for hot Jupiters.

The estimates show (Bisikalo, Kaygorodov, & Arakcheev, 2015) that more than 30% of known hot Jupiters have their exobases above the mean Roche lobe radius, which means a rather high mass loss rate through Lagrangian points L1 and L2. It is important to know that the mass outflow in this case is a self-accelerated process, because decreasing the planet mass leads to reducing of the Roche lobe and finally to higher outflow. It is hard to determine the real time scale of the mass loss processes, but it seems that, without any additional stabilization effects, most observed hot Jupiters must have very short lifetimes compared with the ages of their host stars. So the fact that we observe many Roche lobe overfilling hot Jupiters is in strong contrast with the estimates of mass loss rates via the Roche lobe boundary. This result raises an important question: Why are the hot Jupiters stable?

## Interaction with Stellar Wind

The stellar wind consists mostly of protons (nuclei of hydrogen), ions of He, and electrons. The mechanisms of stellar wind acceleration are not clear yet, but spacecraft observations give us an estimation of solar wind velocity, density, and temperature profiles. There is almost no information about stellar winds from hot Jupiter host stars, but almost all of them are solar-type stars, and we can assume that their winds are also like the solar one. Assuming that the typical hot Jupiter orbits are below the sonic point, the radial velocity of the stellar wind is subsonic for them. But orbital motions of hot Jupiters are high enough (a lower orbit means faster orbital motion) to make incoming stellar wind flow supersonic for them. The Mach numbers for those flows are not high; typically they are between 1.5 and 2. But that is enough to form a shock wave before the planet—a bow shock—followed by a contact discontinuity, a boundary between the gas of the stellar wind and the gas of the planet’s atmosphere. Behind the planet, there is a region of reduced pressure, called a rarefaction wave. The structure of the forming flow pattern is schematically shown in Figure 2, where one can see the location and shape of the shock wave (solid line), the contact discontinuity (bold line around the planet), stream lines, and velocity vectors of the wind before and after passing the shock front. The shape and position of the contact discontinuity, which is a border between the stellar wind and the hot Jupiter’s atmosphere, can be calculated as a surface, where the ram pressure of the stellar wind is equal to the gas pressure of the atmosphere. The head-on collision point (HCP) is located at the shortest distance between the planet center and the contact discontinuity. Therefore, it is possible to easily calculate the conditions under which the HCP is located inside of the planetary Roche lobe and stellar wind, locking the atmosphere and preventing outflow. In Figure 3 the results of 3D modeling of a closed atmosphere are presented. Here one can see the formation of a symmetrical bow shock that is almost spherical near the HCP and tends to the Mach cone far from this point. The contact discontinuity, enclosing the planet’s atmosphere, is totally within the Roche lobe of the planet. As a whole, the planet’s atmosphere differs very little from a sphere. The mass loss rate from the atmosphere Mdot in this model is less than ~109 g/sec.

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Figure 2. The shock wave and wind flow lines around a gaseous planet.

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Figure 3a. Hot Jupiter with closed envelope (3D gasdynamic modeling was made using a model [Bisikalo, Kaigorodov, Ionov, & Shematovich, 2013]).

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Figure 3b. Hot Jupiter with closed envelope (3D gasdynamic modeling was made using a model [Bisikalo, Kaigorodov, Ionov, & Shematovich, 2013]).

But what if the HCP is very close to the Roche lobe boundary? This case is shown in Figure 4. The shape of the atmosphere in this model is significantly nonspherical. In this case the HCP is shifted farther away from the planet in comparison to Figure 3, but it is still located within the Roche lobe of the planet. In Figure 4 one can clearly see two ledges, directed toward the L1 and L2 points, which results in important modifications to the shapes of the shock wave and contact discontinuity. In addition, the trail behind the planet (a region edged by the bow shock) is much broader than in Model 1. It is interesting to note that in this case we see no outflow toward the star from L1 while we obtain a weak outflow through the L2 point. The total mass loss rate from the atmosphere in this model is Mdot ~1.2 × 109 g/sec.

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Figure 4a. Hot Jupiter with near-to-closed envelope (3D gasdynamic modeling was made using a model (Bisikalo et al., 2013]).

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Figure 4b. Hot Jupiter with near-to-closed envelope (3D gasdynamic modeling was made using a model (Bisikalo et al., 2013]).

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Figure 5a. Hot Jupiter with quasi-closed envelope (3D gasdynamic modeling was made using a model [Bisikalo et al., 2013]).

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Figure 5b. Hot Jupiter with quasi-closed envelope (3D gasdynamic modeling was made using a model [Bisikalo et al., 2013]).

Adjusting the atmosphere parameters to shift the HCP outside of the Roche lobe gives us a new and interesting solution, shown in Figure 5. In this case, atmospheric pressure is enough to start outflows from the vicinities of the L1 and L2 points, but the dynamic pressure of the stellar wind can stop the most intensive outflow from L1 at rather large distances from the planet. Figure 6 illustrates the idea of this mechanism. On the figure the ballistic trajectory of the outflow from the L1 point is shown by a thick grey line. Arrows, crossing the line, depict the direction of stellar wind relative to the stream. As can be seen, there is a specific point that exists where the stellar wind is strictly antiparallel to the stream velocity. If the ram pressure at this point is larger than the ram pressure of the stream, the stream propagation will be stopped. In this case, a circulating extended envelope appears. Envelopes of that type are called quasi-closed. The mass loss rate in this case is not so different from the case of completely closed envelopes, for the presented parameters Mdot ~3 × 109 g/sec.

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Figure 6. Schematic representation of stream stopping mechanism.

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Figure 7a. Hot Jupiter with open envelope (3D gasdynamic modeling was made using a model [Bisikalo et al., 2013]).

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Figure 7b. Hot Jupiter with open envelope (3D gasdynamic modeling was made using a model [Bisikalo et al., 2013]).

If the ram pressure of the stellar wind cannot stop the stream from L1, an open envelope will be formed; this case is presented in Figure 7. On this figure the stream from the L1 point does not stop and keeps moving toward the star; the figure shows the moment when the stream just approaches the computational domain boundary. It is possible that, by analogy with close binary stars, in such systems accretion disks or tori of dense material may form. In the solution for this model a large mass loss rate of Mdot ≈ 3 × 1010 g/sec was obtained.

## Observational Manifestation of the Extended Envelopes

The presence of asymmetrical extended envelopes is supported by observations of hot Jupiters with the Hubble Space Telescope (HST). For example, observations of WASP-12b (Fossati et al., 2010; Haswell et al., 2012) indicate an earlier onset for the transit in the UV, which occurs at phase φ‎ ≅ 0.92, compared to the onset of the optical eclipse, which begins at phase φ‎ ≅ 0.94 (the orbital phase of the planet φ‎ is measured from the position of the main minimum). The phase angles are counted from the moment of main eclipse (φ‎ = 0) when the planet is in the middle of the star disk and varies from 0 to 1 covering a full revolution of the planet. The early eclipse starting at this phase means that absorbing matter exists around the planet up to several planetary radii.

Observations of WASP-12b carried out in 2013 (Nichols et al., 2015) indicated an even more complex character for the behavior of the planet’s atmosphere. These data, obtained with the HST Cosmic Origins Spectrograph, do not show an early UV eclipse at a phase near φ‎ ≅ 0.92. At the same time, beginning with phase φ‎ ≅ 0.83 (which actually corresponds to the beginning of the observations), appreciable time-variable absorption was detected in the near-UV (which was stronger than the optical absorption). Appreciable UV absorption of the stellar radiation beginning from phase φ‎ ≅ 0.83 was also noted in Haswell et al. (2012). Unfortunately, the behavior of the light curve at early phases is not known, since the beginning of the observations was also at φ‎ ≅ 0.83 in both studies (Haswell et al., 2012; Nichols et al., 2015). No additional UV absorption was observed at the time of the egress from the eclipse (at phases φ‎ ≅ 1.05).

The maximum size of a quasi-closed, stationary envelope is determined as the distance to the point where it is still possible to stop the flow from L1 with the dynamical pressure of the stellar-wind gas; otherwise, the envelope becomes open. The position of this point is determined only by the wind velocity profile, and varying the parameters of the stream and wind can attain equality of the dynamical pressures. This point can exist for any radial velocity of the stellar wind; it is close to L1 when the radial velocity of the wind is high and moves away from L1 when the wind velocity decreases. The maximum distance to which it can move is reached for zero wind speed.

According to simple ballistic estimates (Bisikalo, Kaigorodov, & Konstantinova, 2015), the size of a stationary, quasi-closed envelope associated with the exoplanet WASP-12b must be ≅ 0.17 in phase units. The presence of a bow shock around this envelope would give rise to excess absorption in the near-UV, starting from phase ≅ 0.78. In order for the eclipse to begin at phase φ‎ ≅ 0.83, the size of the bulge in the vicinity of L1 should be Δφ‎ = 0.95 − 0.83 ≅ 0.12, or 21 planetary radii. This size is in good agreement with estimates obtained under the assumption that the parameters of the stellar wind are close to the solar ones. A comparison of the theoretical envelope size with observational values suggests that the available observations can be described using a model with a quasi-closed envelope. Variations in the size of the envelope at different phases can be explained as resulting from variations in the parameters of the stellar wind. Unfortunately, the beginning of both sets of available observations also corresponds to phase φ‎ ≅ 0.83 (Haswell et al., 2012; Nichols et al., 2015). This hinders firm conclusions about the type of atmosphere possessed by WASP-12b. If the additional absorption actually begins at earlier phases, the size of the envelope may exceed the maximum size of a stationary, quasi-closed envelope, necessitating the use of a model with an open envelope when interpreting the observations.

## Influence of Stellar Activity on Extended Envelopes

Most of the host stars of hot Jupiters belong to the main sequence, like our sun. This fact allows us to expect sun-like stellar activity from them. The sun shows different types of activity, but the most energetic of them are stellar flares and coronal mass ejections (CMEs). A stellar flare is a rapid increase of star brightness, often accompanied by a CME. A CME is a major perturbation of the stellar wind due to large ejections of matter from the corona. In the case of the sun, CMEs are characterized by a mass of plasma ejected into the interplanetary medium of approximately 1015 g, an average total energy of about 1031 erg, and ejection velocities that vary from about 20 to 3000 km s−1, with averages of the order of 500 km s−1 (Vourlidas et al., 2010; Webb & Howard, 2012). For the sun, the frequency of CMEs is rather high, ranging from about 0.5 per day during solar minimum to up to about 4 per day during solar maximum. Although we do not have reliable statistics of CMEs as a function of stellar age, it is plausible to believe that CME events are much more frequent for young stars.

Extended envelopes are very weak structures, supported mostly by the equilibrium between the dynamic pressures of the stellar wind and gas stream from the inner Lagrangian point L1. The dynamic pressure is proportional to density, multiplied by the square of the velocity, which allows the rarefied, but high-speed, stellar wind to balance dense, but relatively low-speed, matter of the stream. Any fluctuations of densities or, especially, velocities of the flows affects the equilibrium and can destabilize the envelope. A typical CME has three phases—shock passage, early CMEs, and late CMEs. The fast phase is a shock wave, preceding the supersonic ejected matter. This phase is the shortest one; its duration must be about half an hour on a typical hot Jupiter orbit. Stellar wind parameters jump drastically in this phase: up to 10 times for density, up to 5 times for temperature, and up to 30 times for velocity. On the next phase (early CME), the density and temperature fall to the normal levels (or even below the normal ones) and velocity slightly decreases. On the third phase (later CME), stellar wind density rises again (to about five times the normal level), while wind velocity still slowly decreases.

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Figure 8. Hot Jupiter with quasi-closed envelope passing through coronal mass ejection (3D gasdynamic modeling was made using a model [Bisikalo et al., 2013]).

During CME shock passage, the dynamic pressure of the stellar wind is high enough to completely blow the extended envelope off (see Fig. 8) and block the outflow. The next phases also block atmosphere outflow and prevent envelope formation up to the end of the CME passage. The computations of Cherenkov, Bisikalo, Fossati, and Mostl (2017) show that additional mass loss due to periodic destruction of the extended envelope by CME passages is of the same order of magnitude as the mass lost by the planet under the effect of the high-energy stellar flux, and it is plausible that this similarity can be extended across the time spent by the star on the main sequence.

## Extended Envelopes and Planetary Magnetic Fields

No significant evidence of hot Jupiter magnetic fields has been detected yet. Also, theoretical models predict very weak magnetic fields due to their slow rotations. But extended envelopes are very rarefied and even a small magnetic pressure may affect them. The magnetic pressure is proportional to the square of the magnetic induction B and (for dipole magnetic fields) falls proportionally to the sixth degree of distance from the planet. This means that magnetic effects may be important only in the very close vicinity of the hot Jupiter. But the origins of the extended envelopes (Lagrangian points L1 and L2) may be inside of the magnetically driven region.

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Figure 9. Magnetic field lines of hot Jupiter with quasi-closed envelope (3D gasdynamic modeling was made using a model [Bisikalo et al., 2013]).

Numerical models show that even a weak magnetic field can significantly affect a hot Jupiter’s atmospheric outflow. For example, a magnetic moment of about 0.1 of the Jovian one for a hot Jupiter with the parameters of WASP-12b can significantly reduce its mass loss rate (by ∼70%; Arakcheev, Zhilkin, Kaigorodov, Bisikalo, & Kosovichev, 2017). This reduction of the mass-loss rate due to the influence of the magnetic field makes it possible for exoplanets to form closed and/or quasi-closed envelopes in the presence of more strongly overflowing Roche lobes than is possible without a magnetic field. Also, it is interesting to see how the magnetic field affects the dynamics of the flow in the envelope. The outflowing matter drags magnetic field lines outside of the planet, forming very long magnetic loops (see Fig. 9) so we can see not only matter outflow but also a “magnetic field outflow.” This causes a number of interesting features, including line magnetic field concentrations near the outflow tip and periodic pulsations of the flow due to magnetic braking (Bisikalo, Arakcheev, & Kaigorodov, 2017).

# Conclusion

We have presented a short review of modern (to the date of this article) theoretical models describing hot Jupiter atmospheres and their extended envelopes. The review does not pretend to be comprehensive, because the problem is very broad and still under extensive research by many scientific groups. The main goal of the article was to outline the most important physical processes and present the most advanced models of hot Jupiter atmospheres and envelopes. We have focused on the theoretical side of the problem to give the reader a picture of the complicated nature of these objects, hidden under limited astronomical data.

There are several upcoming observational missions, which will be focused, at least partially, on exoplanets. One of the Early Release Science Programs of the planned 6.5 m James Webb Space Telescope (JWST) is dedicated to exoplanetary observations. The infrared camera of JWST will allow observation of the transits of hot Jupiters and other planets with high signal to noise ratio. The planned World Space Observatory–Ultraviolet mission—the orbital UV telescope—will allow us to observe the extended envelopes of hot exoplanets, giving much more detailed information about their flow structure with the quality of the HST. Also, some smaller orbital missions are planned: the CHEOPS (CHaracterising ExOPlanet Satellite) mission is dedicated to searching for exoplanetary transits, while the PLATO (PLAnetary Transits and Oscillations of stars) and TESS (Transiting Exoplanet Survey Satellite) missions are set to search for new transiting exoplanets and others. Also, ground-based telescopes will contribute to this activity, especially the planned European Extremely Large Telescope, which will have a huge 39.3 m mirror.

Upcoming observational ground-based and space missions are promising much new information about exoplanets of different types. It is expected that a significant amount of new data will be obtained for hot Jupiters. The new data will require more advanced models to interpret it, so we are expecting the discovery of new physical processes taking place in planetary atmospheres, refining the parameters of exoplanets itself, their atmospheres, stellar winds, and the interplanetary medium around distant stars. We hope that the new data will shed light not only on the enigma of hot Jupiter evolution but on the evolution of planetary systems in general, allowing us to estimate the number of potentially habitable worlds in the galaxy.

In conclusion, we should admit that our understanding of hot Jupiter atmospheres and their extended envelopes is far from complete. We know some properties of hot Jupiters, their extended envelopes, and host stars from observations that allow us to estimate many more parameters using theoretical models. Of course, the models of atmospheres and envelopes are limited by the modern level of physics itself and, especially, by our knowledge about processes that we cannot reproduce in Earth-based laboratories. By observing hot Jupiters, developing more complicated models, and conducting their comparison with observational data we can push forward the physics itself and, maybe, discover something useful for down-to-Earth applications.

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