Toroidal Atmospheres around Extrasolar Planets

In addition to their usual spherical atmospheres, giant planets have highly extended, often toroidal atmospheres that are the gaseous envelopes of material orbiting the planet as rings or satellites. At Jupiter and Saturn, these atmospheres are produced by the ejection of atoms and molecules from their moons and rings by outgassing, volcanism, sputtering, and meteoroid bombardment. Such atmospheres are also likely to be present on giant extrasolar planets.

The sodium cloud at Jupiter, associated with its moon Io, was the first observation of such an extended atmosphere (Brown & Chaffee 1974). Because of its considerable tidal stressing, Io is volcanically active (e.g., Bagenal et al. 2004), producing an atmosphere that is stripped at a rate of about 10⁶ g s⁻¹ by the plasma trapped in Jupiter's magnetosphere (Thomas et al. 2004), a process often called atmospheric sputtering (Johnson 1990, 1994). The ejected neutrals are eventually ionized, adding to the trapped plasma in a self‐limiting feedback process (Johnson & McGrath 1993; McGrath et al. 2004). The neutral cloud and its ionized component are confined to a region around Io's orbit but have a radial scale comparable to the size of Jupiter (Fig. 1 a). Observations using the Hubble Space Telescope have shown that Saturn has a similar extended, roughly toroidal atmosphere composed primarily of water products (Shemansky et al. 1992; Jurac et al. 2002). In this case it is the gaseous envelope of a disk of icy debris (Fig. 1 b) apparently produced by venting from the icy moon Enceladus (Waite et al. 2006; Tokar et al. 2006). This atmosphere is also sustained by sputtering of the ice grains in Saturn's tenuous E ring (Jurac et al. 2002) and has an extended component formed by charge exchange (Johnson et al. 2005, 2006a). Saturn's main rings also have a toroidal atmosphere of molecular oxygen produced by the decomposition of ice by the solar UV (Johnson et al. 2006b). Associated with these extended neutral atmospheres are magnetically confined plasmas that are representative of the source material (Fig. 1 c).

The toroidal atmospheres observed around Jupiter and Saturn are expected to be present in other planetary systems and to be ubiquitous as the gaseous envelopes of satellites and grains in the early epochs of planet formation. These extended atmospheres should be more readily detected than the moons or rings of a giant extrasolar planet. Such a detection would therefore provide a means for determining the presence and the composition of satellites or rings orbiting an extrasolar planet. The possibility of detecting gas from a star‐grazing comet orbiting an extrasolar body has been considered but not yet observed (Mendelowitz et al. 2004). However, sodium (Charbonneau et al. 2002), hydrogen, oxygen, and carbon (Vidal‐Madjar et al. 2004) have been seen in absorption in the atmosphere of the Jupiter‐sized extrasolar planet HD 209458b.

In this paper we first review the properties of the toroidal atmospheres of Jupiter and Saturn and use the observations of the atmosphere of HD 209458b as a measure of the amount of absorbing material that can be detected in a transit. We then examine under what circumstances giant toroidal atmospheres produced by orbiting moons or ring particles might be observed around an extrasolar planet.

Jupiter's closest moon Io has lost most of its early volatile inventory, but it has a thin, volcanically produced atmosphere composed primarily of SO₂, with other trace gases (e.g., McGrath et al. 2004). The atmosphere is stripped by interaction with ions trapped in Jupiter's magnetosphere, producing an extended toroidal atmosphere of neutral atoms and ions. Due to its strong resonance fluorescence in the visible, sodium was the first species detected in this extended atmosphere (Brown & Chaffee 1974). The cloud of escaping sodium shown in Figure 1 a co‐orbits with Io and is now nearly continuously imaged from Earth. Using the stripping rate of sodium, ∼3 × 10²⁶ atoms s⁻¹, and the average electron‐impact lifetime, ∼2 hr, this Jupiter‐sized cloud contains ∼2 × 10³⁰ Na i atoms (e.g., Thomas et al. 2004). The sodium that is ionized in this cloud is confined by the local magnetic fields and contributes to the ambient plasma. It is eventually lost, primarily by charge exchange, producing energetic neutrals that form a giant sodium nebula with a radial extent of ∼500 Jupiter radii (R_J) containing ∼10³² Na i atoms (Mendillo et al. 1990).

The total rate of stripping from Io's atmosphere is more than 100 times that for sodium. The principal species ejected are sulfur and oxygen, which have longer lifetimes than sodium. This material also orbits Jupiter, forming a giant torus of neutrals with a density and spatial distribution determined primarily by electron‐impact ionization. The neutral sulfur and oxygen tori so formed have cross‐sectional areas that are comparable to Jupiter's and contain ∼3 × 10³² S i atoms and ≳1 × 10³³ O i atoms (Smyth & Marconi 2003). Because Io is embedded deeply in Jupiter's magnetic field, the ionized plasma formed from the orbiting neutrals is also confined, leading to peak ion densities ≳2000 cm⁻³ (e.g., Thomas et al. 2004). This toroidal plasma has been imaged in emission in lines of S ii, S iii, and O ii. The spatial distribution of the S ii λ6731 emission is shown in Figure 1 c. Since the plasma lifetimes are much longer than the neutral lifetimes, the plasma torus has a significantly larger total content than the neutral torus, ≳3 × 10³⁴ ions, with an average column density of ∼2 × 10¹⁴ cm⁻² and a cross‐sectional area comparable to Jupiter's. The torus of ejected material from the surface of Jupiter's moon Europa has a comparable content of water products from Europa's icy surface (Burger & Johnson 2004; Hansen et al. 2005).

The more distant giant planet Saturn has a small icy moon, Enceladus, that is ejecting ice grains (Spahn et al. 2006) and gas, primarily H₂O, with trace carbon and nitrogen species (Waite et al. 2006). The orbiting grains make up Saturn's tenuous E ring, which extends from ∼3 to 8 Saturn radii (R_S; Showalter et al. 1991). The gas ejected from Enceladus and the sputtering of the E‐ring grains create a large toroidal atmosphere of H₂O (Johnson et al. 2006a; Jurac et al. 2002) and its products, initially detected by the Hubble Space Telescope (Fig. 1 b; Shemansky et al. 1992; Jurac et al. 2002). This atmosphere also has a toroidal ionized plasma composed principally of H₃O⁺, H₂O⁺, OH⁺, O⁺, and H⁺ (Young et al. 2005). However, unlike the Io torus, the average neutral density is larger than the ion density. The neutral toroidal cloud contains ∼10³⁵ OH molecules and comparable amounts of H₂O, O, and H, with an average line‐of‐sight column density of ∼10¹⁵ cm⁻² over a region of ∼1 R_S (see Fig. 1 b). Saturn's giant moon Titan also produces a toroidal cloud (Smith et al. 2004) of nitrogen, methane, and hydrogen. Because it resides in Saturn's outer magnetosphere, the atmospheric stripping rate is low (Johnson 2004; Michael et al. 2005) and the ions that are formed are rapidly lost down the magnetotail. Therefore, due to its location in the magnetosphere, Titan's toroidal cloud is not nearly as robust as the water‐product torus in the inner magnetosphere. Although the atmospheres described above were detected in emission, we consider the likelihood of seeing such features in absorption associated with a giant planet transiting the disk of its parent star. However, we first consider the observations of the HD 209458b transit as an example of the size of the absorbing column of gas that can be detected at present.

Sodium has been observed at the extrasolar planet HD 209458b in absorption when the planet crosses the disk of its parent star (Charbonneau et al. 2002). This sodium is likely to be a component of the planet's gravitationally bound atmosphere (e.g., Charbonneau et al. 2002, 2006) or its escaping atmosphere (Vidal‐Madjar et al. 2004). The sodium absorption feature that is detected corresponds to a small change in intensity (ΔI/I = 0.0232%) at the λλ5890, 5896 doublet (Charbonneau et al. 2002), and we use this to estimate the minimum number of sodium atoms in a cloud that are needed to produce an absorption feature at this level, realizing that new detection techniques will soon be available (e.g., Arribas et al. 2006). Ignoring the effects of the background stellar spectrum, the absorption signal can be expressed as ΔI/I∼W_λ/Δλ, where W_λ is the equivalent width and Δλ is the observing width, ∼12 Å. In the optically thin, linear absorption regime, the equivalent width is given by the expression W_λ = 8.9 × 10^-5N_aveλ²f_ikÅ, where N_ave is the average column density of the absorbing species and f_ik is the oscillator strength: 0.641 and 0.320 for the 5890 and 5895 Å lines, respectively (Sansonetti & Martin 2005). The minimum average column density, N_ave, associated with this feature is therefore ∼1.2 × 10¹⁰ cm⁻² spread over the area of the stellar disk (∼2 × 10²² cm²). If the sodium is a component of the planet's atmosphere, then the absorbing area is very small, so that the actual column density is large and the line is heavily saturated. If, however, the sodium were in an extended cloud of a radius of one or a few planet radii, the actual attenuating column density would be ∼10¹¹–10¹² cm⁻². The total minimum number of sodium atoms in the linear regime is ∼2 × 10³². However, sodium is a trace gas, and there are much larger amounts of more abundant species.

Vidal‐Madjar et al. (2004) observed H i, O i, and C ii at HD 209458b by detecting a reduction in the parent star's emission features in the UV during transit. They find that their results can be understood if the absorbing material has a velocity dispersion that is comparable to or greater than the widths of the stellar lines (∼15 and 25 km s⁻¹ for O i and C ii, respectively) and conclude that the absorbing species are components of an escaping atmosphere. For the observations of O i λ1302, Vidal‐Madjar et al. show that the collisionally excited λ1304 and λ1306 lines also contribute to the absorption. For simplicity, we assume that the lines contribute equally to the absorption and that the band depth of ∼0.13 applies to each one. A rough lower limit on the column of absorbing material can be placed by writing the average absorption cross section as σ ≈ af_ik/Δν, with a ≈ 0.027 cm² s⁻¹. Using 15 km s⁻¹ for the stellar line widths, Δν = 1.1 × 10¹¹ s⁻¹ and f_ik ≈ 0.05 (Sansonetti & Martin 2005), so that σ ≈ 1.2 × 10^-14 cm². The number of absorbing atoms in each sublevel is then ∼0.13A_*/σ, where A_* is the area of the stellar disk, which gives ∼2.3 × 10³⁵ O i atoms. If they have a radial distribution of a few planet radii, the corresponding O i column density is ∼10¹⁴ cm⁻². In a low‐density extended atmosphere, the sublevels above the ground state will not be excited, so the single line values are appropriate. Similarly, for the observations of C ii λ1335, the excited λ1336 line also contributes. Treating this in the same way, with a band depth of ∼0.075 and f_ik ≈ 0.12 (Sansonetti & Martin 2005), implies σ ≈ 2 × 10^-14 cm² and a total content of ∼8 × 10³⁴ C ii ions, which gives a similar column density.

We expect that extended atmospheres like those observed around Jupiter and Saturn are present around gas giants in other planetary systems and are likely to be ubiquitous as the gaseous envelopes of satellites and grains in the early epochs of planet formation. The toroidal gas clouds around Jupiter and Saturn are seen in emission, excited by resonance fluorescence or electron impact. Because of the extremely low density, the atoms and ions are typically in the ground state. In an extrasolar planetary system, these extended atmospheres could give rise to absorption spectra when the planet transits the disk of the star.

In order to assess the feasibility of observing the extended atmospheres of exoplanets, we compare the content of these atmospheres in Jupiter and Saturn with the minimum content needed to account for the absorption features measured for HD 209458b as it transits its parent star. The minimum number of Na i atoms that contribute to the absorption feature detected at HD 209458b, ∼2 × 10³², is approximately 2 orders of magnitude larger than that in the sodium cloud immediately surrounding Io. It is, however, fortuitously close to the number of Na i atoms in the very extended Jovian sodium nebula. Similarly, the minimum amount of O i at HD 209458b, ∼2 × 10³⁵ atoms, is about 2 orders of magnitude larger than the O i content in Io's torus, but it is comparable to the amount of oxygen‐containing species in Saturn's more substantial neutral torus. In addition, the minimum amount of ionized carbon seen at HD 209458b, ∼8 × 10³⁴ C ii ions, is comparable to the sulfur and oxygen ion content in the Io plasma torus. Therefore, detection of sulfur ions at this level during a planet transit could be evidence for the presence of an Io‐like moon.

Thus, the ion or neutral content of a toroidal atmosphere produced by a satellite or ring about a transiting extrasolar planet could be sufficient to give a detectable absorption feature. The steady state densities formed in the vicinity of a transiting giant planet are dependent on a number of different factors, and we consider below whether there are situations in which toroidal atmospheres like those around Jupiter or Saturn might be seen around a giant planet transiting its parent star.

4.1. Orbit Size and Stability

4.2. Structure of a Toroidal Atmosphere

The total content, morphology, and kinematics all affect the absorption characteristics of an extended atmosphere. These depend on several parameters, including the source rate (S) and lifetime (τ) of the species of interest, as well as the ejection velocity (v_e) and the orbital velocity of the source (v_o). The total number of atoms or molecules in a neutral cloud depends on the product Sτ. Atoms and molecules ejected from an orbiting moon in a region where τ is much shorter than the orbital period, τ₀, will form a neutral cloud with a morphology resembling the sodium cloud at Io shown in Figure 1 a. The mean radial extent of the cloud is given by R_c∼v_eτ, so that the cloud has a cross section of A_c∼πR²_c, and the average column density is N∼S/πv²_eτ. A cloud with a toroidal morphology is formed if the atoms and molecules are ejected from a continuous ring of material or if they are ejected from an orbiting moon but with lifetimes τ≫τ_o. A toroidal atmosphere of ionized gas can be formed from the ions produced by either short‐lived or long‐lived neutrals that are picked up and distributed azimuthally by the rotating magnetic field, which is the case for the S ii torus shown in Figure 1 c.

In order to illustrate the characteristics of a neutral torus, we show in Figure 2 the line‐of‐sight column densities calculated using a Monte Carlo model (see, e.g., Jurac et al. 2002; Johnson et al. 2006a) for an outgassing moon orbiting a planet with the mass of Saturn. The orbit radius R_ps = 3.9R_S, the orbital velocity v_o = 12.6 km s⁻¹, the ejection velocity v_e = 2 km s⁻¹, and the product Sτ = 10³⁵ atoms. These quantities correspond to the orbital parameters of the moon Enceladus and the content of its neutral toroidal atmosphere, but a higher ejection speed (Johnson et al. 2006a). The column densities in Figure 2 are obtained by viewing the torus edge‐on. This is approximately the alignment expected in a transit, because the planet's rotational axis is typically aligned with its orbital axis, and most known satellites and all rings orbit near their planets' equatorial planes. Small tilts in the orbital plane will reduce the line‐of‐sight column density somewhat. The neutrals in this torus have an average speed that is roughly equal to the orbital speed, which for Enceladus is ∼13 km s⁻¹. The plasma formed from ionized neutrals would corotate with the planet, which corresponds at the orbital radius of Enceladus to a speed of ∼40 km s⁻¹. These speeds would result in line widths that are comparable to the stellar line widths discussed in § 3 for the HD 209458b observations. If the absorption lines could be observed at high spectral resolution, the change in line profile at the beginning and end of the transit would be a valuable diagnostic.

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The neutral content of the extended atmosphere is given by the quantity Sτ, as noted above, but the vertical and radial extents of the torus depend on the ratio of the mean ejection speed, v_e, and the orbital speed, v_o. When v_e/v_o is small, which is the case for the model in Figure 2 and for the features in Figures 1 a–1 c, centrifugal confinement dominates. That is, in a collisionless torus, the vertical and radial extents of the cloud are determined by the distribution in the eccentricities and inclinations of the orbiting neutrals. For small v_e/v_o, the maximum excursion above or below the orbital plane is approximately equal to the vertical component of v_e divided by the angular velocity of the source, v_o/R_ps, where R_ps is the distance from the planet to the ring or satellite source. Using isotropic emission from the source, the average vertical distribution about the orbital plane is roughly H∼R_psv_e/v_o. Similarly, the radial extent along the orbit plane is ∼4H (e.g., Johnson 1990; Johnson et al. 2006a). Observing a torus with an average circumference of 2πR_ps seen edge‐on, the extent along the line of sight through the source region is ∼4(R_psH)^1/2. Therefore, an average column density N∼Sτ/[2πR²_ps(v_e/v_o)^3/2] can be observed over an area A∼4H² = 4R²_ps(v_e/v_o)² centered on the source. Using the parameters of the model given above, this expression gives a column density of ∼10¹⁴ cm⁻², roughly consistent with the simulation shown in Figure 2. For this toroidal atmosphere, the average column density and area over which the gas is distributed are comparable to those for the atmosphere detected at HD 209458b.

In the simulation shown in Figure 2, the initial molecular motion is controlled by the mean ejection speed v_e. However, if the neutrals are long‐lived, they can be heated by interaction with the co‐orbiting plasma, which expands the cloud, as is the case for the OH torus shown in Figure 1 b (Johnson et al. 2006a). We also note that v_o varies as R^-1/2_ps, so that toroidal neutral clouds formed at smaller orbital radii give higher line‐of‐sight column densities, and hence deeper absorption features.

4.3. Scaling to Smaller Orbits

The giant planets Jupiter and Saturn have large emission features associated with ejecta from satellites and ring particles. These ejecta can form clouds of neutrals and ions that have cross sections that are comparable to or much larger than the planet, as seen in Figure 1. We point out that such features in our solar system have sizes and contents that are comparable to the escaping atmosphere already observed in absorption when HD 209458b transits its parent star. Therefore, we suggest that although it is difficult to observe a moon or ring on an extrasolar planet (Sartoretti & Schneider 1999; Brown et al. 2001; Arnold & Schneider 2004), one might be more likely to observe the torus of gas escaping from a satellite or a ring of debris when a giant planet makes a transit across the disk of its star.

Since the probability of observing a transiting planet increases with decreasing distance from the parent star, detection of giant planets with small orbital radii is favored. Such planets very likely had toroidal atmospheres from orbiting debris or satellite venting early in their history. For instance, the large Jovian satellites, which have been fully stripped of their primordial atmospheres (e.g., Johnson 2004), likely had robust atmospheres at earlier epochs. However, for a planet with a small orbital radius, such as HD 209458b, maintaining satellites in stable orbits is problematic (Barnes & O'Brien 2002).

For stars with giant planets that have larger orbital radii, an observable toroidal atmosphere formed from refractory materials could be present, as is the case at Jupiter. In addition, a planet orbiting a much cooler star at a relatively small radius could maintain a toroidal atmosphere formed from icy bodies like that seen at Saturn. Detecting such features on an extrasolar planet would be important. It would indicate the presence of satellites or rings, and possibly the presence of a magnetic field.