Royal Society Publishing

Graphic: the driver of giant planet atmospheres

Steve Miller, Tom Stallard, Chris Smith, George Millward, Henrik Melin, Makenzie Lystrup, Alan Aylward

Abstract

We present a review of recent developments in the use of Embedded Image molecular ion as a probe of physics and chemistry of the upper atmospheres of giant planets. This ion is shown to be a good tracer of energy inputs into Jupiter (J), Saturn (S) and Uranus (U). It also acts as a ‘thermostat’, offsetting increases in the energy inputs owing to particle precipitation via cooling to space (J and U). Computer models have established that Embedded Image is also the main contributor to ionospheric conductivity. The coupling of electric and magnetic fields in the auroral polar regions leads to ion winds, which, in turn, drive neutral circulation systems (J and S). These latter two effects, dependent on Embedded Image, also result in very large heating terms, approximately 5×1012 W for Saturn and greater than 1014 W for Jupiter, planet-wide; these terms compare with approximately 2.5×1011 W of solar extreme UV absorbed at Saturn and 1012 W at Jupiter. Thus, Embedded Image is shown to play a major role in explaining why the temperatures of the giant planets are much greater (by hundreds of kelvin) at the top of the atmosphere than solar inputs alone can account for.

1. Introduction

Upper atmospheres are the subject of study as an important transition region between the planets themselves and the interplanetary space that surrounds them. This interplanetary space is permeated by stellar radiation and winds generated by the star (or stars) around which the planets orbit; stellar winds are ionized plasma—mainly protons and electrons—which may contain magnetic fields imposed by the star(s) that generated them. Thus, the upper atmosphere of a planet is sensitive to radiation and particle inputs from its central star(s); it acts as an indicator of what has been called the ‘space weather’ in its neighbourhood. In the case of unmagnetized planets, such as Venus and Mars in our Solar System, the interaction with the stellar wind is direct. But in the case of magnetized planets, such as Earth and all of the Solar System's giant planets, this interaction is mediated by the magnetosphere, the region of space that is controlled by the planetary magnetic field.

The upper atmosphere is usually defined as the atmospheric region that exists above the homopause—a boundary above which various gases are no longer convectively mixed, but settle out diffusively under the force of gravity according to their atomic or molecular weights. Each component gas then follows a height-dependent composition gradient, given byEmbedded Image(1.1)with Na0 the number density at the homopause, while the characteristic scale height of component a is given byEmbedded Image(1.2)with T the temperature of the atmosphere, ma the atomic/molecular weight and g the gravitational acceleration of the planet. Typically, the upper atmosphere consists of 10−6 or less by mass of the planet's atmosphere; in the Solar System's giant planets, the homopause occurs at pressures of 10−6–10−7 bar (1–0.1 μbar), with number densities of approximately 1019 m−3 or less. Nonetheless, it is an active region of considerable interest in its own right. Most of this region is composed of neutral gases, and it is termed the thermosphere, which has the further significance that it is a region of the atmosphere where the temperature increases steadily with height until a (often very large) constant exospheric temperature is reached, which will be described in detail later. Since the neutral gases are affected by ionizing stellar radiation and particle impacts from the stellar wind, there is also an ionized component to the upper atmosphere, the ionosphere. In the Solar System, the ionosphere and thermosphere are more or less coincident in the cases of giant planets. Thus, an important area of study is the coupling between magnetospheres, ionospheres and thermospheres, and the roles of solar radiation and the solar wind.

This article concentrates on the role played by the simple molecular ion Embedded Image in the upper atmospheres of the giant planets, particularly Jupiter, where it was first detected in 1988 (Drossart et al. 1989), and Saturn and Uranus, where the ion was detected in 1992 (Geballe et al. 1993; Trafton et al. 1993). Since then, Embedded Image has been shown to play an extremely significant role in the atmospheres of these planets, and planetary scientists have used the infrared emissions of this ion—particularly the fundamental ν2 and overtone 2ν2 bands—to carry out imaging and spectroscopic studies in physics and chemistry of giant planet atmospheres. (Embedded Image emission has still not been detected from Neptune.) This article reviews the role of Embedded Image as an indicator of energy inputs, as a ‘thermostat’ (with potential significance to the evolution of extrasolar planets), as a major contributor to the conductivity of ionosphere and as a driver of planetary winds, paying particular attention to developments since the Royal Society last addressed these issues (see Miller et al. 2000). The consequences of the last two effects—conductivity and winds—for heating giant planets are also discussed.

2. Embedded Image as an indicator of energy inputs

The atmospheres of the giant planets in the Solar System (and, by analogy, elsewhere) consist mainly of hydrogen gas (approx. 90%), in atomic and molecular form, and helium (approx. 10%), with minor components such as methane, ethyne (acetylene), ethane, ammonia, water and phosphorus- and sulphur-bearing species. Since the impact of Comet Shoemaker-Levy 9 (SL9) in July 1994, Jupiter also has a global presence of HCN (Griffith et al. 2004). Equations (1.1) and (1.2) show that concentrations of all but the lightest species should fall off rapidly with altitude above the homopause. Thus, the upper atmospheres of giant planets consist almost entirely of H, H2 and He, except very close to the homopause itself. Photoionization of these gases by extreme ultraviolet (EUV) radiation produces the ions H+, Embedded Image and He+ (see Atreya 1986, for a complete review); as H2 is the dominant neutral gas at all but the highest altitudes, the production of Embedded Image initially dominates, with H+ and minor amounts of He+, which we shall not consider further. Embedded Image is then produced by two further (rapid) reactions,Embedded Image(2.1)

Embedded Image(2.2a)

Embedded Image(2.2b)

The first of these (equation (2.1)) is the protonation of molecular hydrogen, which is virtually instantaneous in the conditions that prevail in giant planet atmospheres, and the second (equation (2.2a)) involves a charge exchange reaction in which the difference in ionization potential between H (13.6 eV) and H2 (14.2 eV) is made up of four or more quanta of vibrational energy in the reacting hydrogen molecule. The major destruction mechanisms of Embedded Image are owing to proton exchange and dissociative recombination (DR) with the electrons produced during ionization,Embedded Image(2.3)where X is most likely to be CH4 or C2H2 andEmbedded Image(2.4)

Reaction (2.3) is clearly significant only near the homopause and gives rise to a web of chemical reactions that produce longer chain hydrocarbons (see Strobel (2005) for a review, and Moses & Baas (2000) and Moses et al. (2000) for a detailed chemical scheme for Saturn). DR is a rapid reaction, with a rate constant of kDR∼5×10−14×[300/T]0.5 (see Strobel 2005) m3 5−1. Therefore, Embedded Image is destroyed much more readily than H+, and this significantly affects the balance between the dayside and nightside composition of the ionosphere.

Since the concentration of Embedded Image must be dependent on the strength of the incident EUV radiation, one might expect it to peak at the planet's sub-solar latitude around local noon, when the Sun is directly overhead; radiation-produced Embedded Image should be least at the poles (depending on the season). Such behaviour has been observed, on an average, for the planet Uranus, for which there is a clear planet-wide glow owing to this ion (figure 1). Planet-wide Embedded Image emission has been observed from Jupiter (Lam et al. 1997; Miller et al. 1997) and (perhaps) from Saturn (Stallard et al. 1999). But the overall emission morphology of these planets is not at all as might be produced by EUV ionization alone. Instead, the Embedded Image emission of these two planets is strongly concentrated around the poles (figures 2 and 3), where high-energy particles—mainly electrons with energies from a few to a few hundred kiloelectron volts (keV)—are accelerated out of the magnetosphere along the magnetic field lines into the upper atmosphere. These electrons produce ionization directly and by the secondary electrons produced by the following reaction:Embedded Image(2.5)

Figure 1

Four infrared images of Uranus, taken at 3.42 μm (a wavelength sensitive to Embedded Image) on the NASA IRTF. The IAU longitudes of each are given. On an average, the emission is maximized at the centre of the planetary disk.

Figure 2

North–south intensity profile of the 3.953 μm ν2 Q(1,0) line of Embedded Image on Saturn (Stallard et al. 1999). The intensity is measured along the local noon meridian.

Figure 3

Infrared image of Jupiter taken at 3.42 μm showing the footprints of magnetic field lines in the VIP4 model (courtesy J. E. P. Connerney, T. Satoh). Note that the main auroral oval is clearly visible together (especially in the southern hemisphere) with the Io footprint at lower latitudes.

The ions, including Embedded Image, produced by particle impact are termed auroral ions, and the regions in which they are produced are termed auroral/polar regions.

The considerations outlined above show that Embedded Image is an excellent indicator of energy inputs into the upper atmosphere for two reasons—first, it is produced rapidly by energetic ionizing processes and, second, because the reactions involved in its destruction are themselves highly exothermic, they lead to further heating of the atmosphere. (Note that this process is part of the pathway by which solar EUV/particle precipitation is ‘degraded’ to heat the atmosphere.) Before going further, it should be noted that there have been many comparisons between Embedded Image and EUV auroral emission from Jupiter in particular, since this latter emission is also produced by particle precipitation. However, two important distinctions must be made. First, EUV emission is a prompt emission, via a ‘pump-and-dump’ mechanism, whereas Embedded Image emission is (more or less) thermalized; second, EUV emission occurs from lower in the atmosphere—at or below the homopause—than Embedded Image emission, and is thus sensitive to higher energy, more deeply penetrating particles.

For Jupiter, Connerney and co-workers (Connerney et al. 1993, 1998; see Connerney & Satoh (2000), for a complete review) have carried out a series of brilliant studies that make use of auroral Embedded Image emission on Jupiter to map the planet's magnetic field. This has resulted in an accurate model of the field, the VIP4 model, which takes into account not only the highly offset and tilted nature of the magnetic dipole, but also the influence of higher order multipolar terms (Connerney et al. 1998). In particular, this group has exploited their early detection (Connerney et al. 1993) of the magnetic footprint of the innermost Galilean moon, Io, to pin down the exact location of the field line that cuts through the equatorial plane at 5.9 Jovian radii (RJ; 1RJ =71 420 km), and hence constrain other field parameters to high accuracy (figure 3).

These workers have also shown that there is an influence owing to the strength of the solar wind on the auroral brightness of Jupiter (Baron et al. 1996), although it may be more indirect than they initially supposed (Southwood & Kivelson 2001). More recently, solar wind conditions have been shown to be important for the both the brightness and morphology of Saturn's Embedded Image auroral emission (Stallard et al. 2004, 2005), following the discovery that the solar wind controls the planet's EUV auroral emission (Clarke et al. 2005; Crary et al. 2005). The influence of the Solar Cycle (rather than solar wind) has been demonstrated for the planet Uranus (Trafton et al. 1999). But it is still unclear to what extent the emission from Uranus is owing to auroral ionization rather than that caused by solar EUV. Another continuing puzzle is the mid-to-low latitude Embedded Image emission observed from Jupiter (Miller et al. 1997); Rego et al. (2000) demonstrated that this could not be solely owing to solar EUV ionization, and that equatorward diffusion of Embedded Image ions from the auroral/polar regions was too slow to account for the intensities observed at latitudes as low as 25°. Abel & Thorne (2003) demonstrated that the emission pattern observed was consistent with the ion being produced in situ by particle precipitation from the radiation belts—a solution proposed by Waite et al. (1997)—but they doubted that the quantities of particles available were sufficient to produce the Embedded Image emission intensities.

3. The ‘Embedded Image thermostat’

Both solar EUV radiation and particle precipitation can heat a planetary atmosphere. If it is to stay in thermal balance, there must be cooling mechanisms. Conduction to lower altitudes is clearly possible in the thermosphere, since the temperature increases monotonically with altitude until reaching the exospheric constant value. However, this is a rather inefficient process (see Yelle & Miller 2004; Melin et al. 2006). Radiation to space is another possibility. Since the neutral thermosphere is mainly molecular and atomic hydrogen, these species should be looked on as potential coolants via radiation. Atomic hydrogen could cool via its electronic transitions, as could He. But the upper emitting levels require high temperatures for them to be populated significantly. On the other hand, molecular hydrogen has vibrational levels, which can be populated at temperatures found in planetary atmospheres. Indeed, some emission lines of H2 are observed, particularly in the spectral region of the fundamental vibration, around 2 μm (Trafton et al. 1989). (The strongest of these is the S(1) line at 2.112 μm.) However, H2 emission is fairly weak, since this homonuclear diatomic molecule does not have an allowed dipole IR spectrum, and only the much weaker quadrupole emission lines are allowed, with typical values of the Einstein Aif coefficient of approximately 10−7 s−1.

In some regions of the infrared spectrum, particularly between 3 and 4 μm (the L and L′ windows), the emission of the giant planets is dominated by lines of Embedded Image (figure 4). This is an important region, because the upper atmosphere temperatures of Jupiter and Uranus have been shown to lie between 900–1100 K and 550–750 K, respectively. Using the Wien displacement lawEmbedded Image(3.1)with C a constant, one finds that for T=1000 K, λmax (the wavelength at which the maximum emission is produced for a blackbody)=3 μm, while it is 4 μm for T=750 K. Thus, the (dipole allowed) fundamental ν2 band emission region of Embedded Image, for which Aif values are typically 10–100 s−1, is precisely what is required for it to act as an efficient coolant for Jupiter and Uranus. (We shall return to Saturn later.)

Figure 4

Spectrum of Jupiter in the 3.85–4.05 μm spectral window, taken on UKIRT with the facility spectrometer, CGS4, with λλ∼2000.

Within a few years of the discovery of Embedded Image in the auroral/polar regions of Jupiter, it was realized that this ion was emitting considerable amounts of radiation (Miller et al. 1994). Lam et al. (1997) used various emission lines observed at moderate (λλ∼1000–2000) spectral resolution to determine Embedded Image temperatures and column densities across the whole of Jupiter. They had found that individual spectra could be fitted with a wide range of T, N(Embedded Image) pairs of values, but a parameter they defined as the total Embedded Image emission—E(Embedded Image)—turned out to be stable within ±10% for each pair of values. E(Embedded Image) was determined by summing all the individual emission lines for a single molecule for a given value of T, assuming local thermodynamic equilibrium (LTE), and multiplying it by the N(Embedded Image) value corresponding to the fitted value of T. For Jupiter, values of E(Embedded Image) were of the order of approximately 0.1 mW m−2 (2πsr)−1 at the equator, rising to one to tens of mW m−2 (2πsr)−1 in the auroral polar regions. Two points were immediately apparent: first, E(Embedded Image) at the equator was two to three times greater than the solar EUV absorbed locally by the thermosphere and second, the amount radiated by the auroral/polar regions was comparable to the energy input to the atmosphere by particle precipitation (see Rego et al. 2000). Using a self-consistent one-dimensional model of Jupiter's upper atmosphere (Grodent et al. 2001), Melin et al. (2006) have demonstrated that emission by Embedded Image more than compensates for increased particle precipitation in their analysis of a Jovian auroral heating even observed in 1998 (Stallard et al. 2001, 2002).

This ability of Embedded Image emission to cool the upper atmosphere of Jupiter and—to a certain extent—of Uranus (Trafton et al. 1999) has led to the effect being termed the ‘Embedded Image thermostat’. It might also have been important for Saturn, had the original Embedded Image temperature determination of approximately 600 K turned out to be correct (Miller et al. 2000). However, this turned out to have been erroneously derived, and Melin et al. (in press) have now demonstrated that the temperature is in the range of 380–425 K. At this temperature, Embedded Image is not an efficient coolant, and it may only re-radiate a small proportion of the energy input in the auroral/polar regions by particle precipitation (Melin et al. in press).

Of further interest is the possibility of Embedded Image cooling and stabilizing the upper atmospheres of extrasolar planets that have been found orbiting close to their central stars. Early work had suggested that so-called ‘super-Jupiters’, orbiting at fractions of an astronomical unit (AU; 1 AU=150 million kilometres), would evaporate on relatively short time-scales as a result of Jeans escape (Lammer et al. 2003). So, could Embedded Image have a role to play? Put simply, the argument is that the increase in stellar radiation at relatively small orbital distances would result in considerable heating of the upper atmosphere. But in atmospheres that were predominantly H2, increased radiation would also produce more Embedded Image that would cool the atmosphere by radiation to space. Yelle (2004) showed that Jeans escape would occur, but on time-scales that were long compared with the age of the Solar System even at orbital distances as small as 0.1 AU. More recently, Smith has used a completely coupled, three-dimensional model of Jupiter's upper atmosphere to demonstrate that the Embedded Image plays an important cooling and stabilizing role at orbital distances of approximately 0.4 AU or greater, although its cooling effect is less pronounced at smaller distances owing to the photodissociation of H2, which leads to lower Embedded Image production rates and column densities (Smith 2006).

4. Embedded Image as a source of conductivity

Traditional studies of planetary magnetospheres have considered the ionosphere as a conducting layer through which charge flows to close magnetospheric current systems. In the auroral regions of Jupiter, for example, field-aligned currents flow to and from the ionosphere to regions in the magnetosphere, where large electric fields are generated as a result of shear in the magnetospheric plasma, to close the current system and equator-ward current (driven by an equator-ward electric field) flows in the ionosphere. In this process, the relevant conductivities are given by (Luhmann 1995)Embedded Image(4.1a)Embedded Image(4.1b)where σP and σH are the Pedersen and Hall conductivity, respectively, Ni is the number of ions of mass mi, νin is the ion–neutral collision frequency and Ωi is the ion gyrofrequency. Note that all these parameters are altitude-dependent: for a given flux, Ni depends on the energy of the precipitating particles and the atmospheric density and composition; νin depends on the atmospheric density and composition; Ωi depends on the value of the magnetic field, B (weakly dependent on h). The Pedersen conductivity is the conductivity parallel to the electric field and is generally larger by about an order of magnitude; the Hall conductivity is perpendicular to the electric field. The conductivity clearly depends on the number of ions produced. It is useful to define the height-integrated conductivity byEmbedded Image(4.2)where the integral is over the altitudes spanned by the ionosphere. Studies using the Jovian Ionospheric Model (JIM) of Achilleos et al. (1998) have shown that the altitude at which ionization of the atmosphere is maximized depends critically on the energy of the precipitating particles (keV electrons). Millward et al. (2002) showed that for JIM, 60 keV electrons—electrons of energies considered likely to be responsible for auroral ionization in the Jovian system—penetrated to altitudes, where the production of Embedded Image was most efficacious (figure 5), such that the value of N(Embedded Image) was several times greater than N(H+). This altitude also corresponded to the one at which νin and Ωi were such that the Pedersen conductivity was maximized. Thus, for Jupiter's auroral/polar regions, Embedded Image was responsible for producing approximately 90% of the value of both ΣP and ΣH. The consequences of this will be discussed shortly.

Figure 5

Plot of (a) ion and electron column densities and (b) height-integrated Pedersen and Hall conductivities versus electron energy, for a constant flux of 6.25×1016 electrons m−2 s−1, produced by JIM (Millward et al. 2002). (Note that for 10 keV electrons, this flux corresponds to a power input of 10 mW m−2.)

For reasonable particle precipitation fluxes, JIM generates values of ΣP between 1 and 10 mho (reciprocal ohms) in the auroral ionosphere. Although a comparable three-dimensional model has not been developed either for Saturn or Uranus, similar values for the Pedersen conductivity are probably expected in both the Saturnian (Cowley et al. 2004) and Uranian ionospheres, at least where there is particle precipitation.

5. Embedded Image as a driver of planetary winds

In the past 5 years, there has been considerable progress in understanding the mechanisms that produce aurorae in both Jupiter (e.g. Cowley & Bunce 2001; Hill 2001; Southwood & Kivelson 2001) and Saturn (e.g. Cowley et al. 2004). The Earth's aurorae are produced as a result of the plasma shears caused by the interaction of the solar wind and the terrestrial magnetosphere, and occur (more or less) along the footprints of magnetic flux tubes that mark the boundary between open and closed field lines. The terrestrial aurorae are said to be under solar wind control, and there is a cycle, known as the Dungey cycle (Dungey 1961) during which flux tubes are dragged from local noon to midnight across the Earth's polar cap by the (magnetic field embedded in the) solar wind, and return back to the dayside (to local dawn and dusk). This Dungey cycle takes about 3 h, about 1/8 of a terrestrial rotation. All the giant planets rotate faster than the Earth and are much larger; their magnetospheres are also much larger. Therefore, one might expect that the Dungey cycle for these planets is appreciable for these planets, i.e. for Saturn, the cycle takes around 70 h (Cowley et al. 2004) compared with the rotation period of 10 h and 46 min. This might be expected to have an impact on magnetospheric plasma flows and the consequent auroral processes. There are other differences with the Earth.

For Jupiter, in particular, the differences are striking. While most of the plasma in the Earth's magnetosphere is derived from the solar wind, the Jovian system is continually filled with plasma from the volcanic activity of Io, at a rate of approximately 1 ton s−1. This plasma is then swept into corotation with the planet by Jupiter's rotating magnetic field and centrifugal forces cause it to diffuse outwards, forming a vast equatorial plasma sheet. Angular momentum is supplied to the plasma sheet by drawing on Jupiter's vast reserve of rotational energy; collisions between neutrals and ions in the upper atmosphere provide a force on the flux tubes that pass through the plasma sheet, forcing them (and the sheet itself) into corotation. (A similar process occurs at Saturn, but to a lesser extent with ionized material from the rings taking the place of Io's volcanoes.) At a certain distance—approximately 20RJ—from the centre of the planet, this mechanism breaks down, and the plasma sheet lags behind complete corotation (Hill 1979). At this point, enormous electric fields (megavolt) are generated that drive the aurora-producing field-aligned current system described earlier (Cowley & Bunce 2001; Hill 2001).

Looking at the planetary reference frame, the imposition of an equator-ward electric field, which may be several volts/metre in strength, has two main effects: first, a current flows, as previously described; second, in the high-latitude auroral regions, the magnetic field is (nearly) perpendicular to the surface of the planet, and thus to the electric field. This produces a Hall ion drift, perpendicular to both the electric and magnetic fields, with a velocity given byEmbedded Image(5.1)

In the auroral regions, the Jovian magnetic field is about 10−3 T. Equation (5.1) shows that an electric field of 1 V m−1 will produce an ion wind of 1 km s−1, westward, anti-rotational, in the planetary reference frame in both hemispheres. Looking at another way, the ions are fixed (to a greater or lesser degree) to flux tubes that are lagging behind corotation, and their angular velocity is thus less than that of the planet itself. The ion winds were detected on Jupiter in 1996 (Rego et al. 1999) and have been studied since by Stallard et al. (2001, 2002). The ion winds have similarly been detected on Saturn; Stallard et al. (2004) found that ions in the entire auroral/polar cap region lagged to corotation such that they had only approximately 1/3 of the angular velocity of the planet, an effect that was consistent with a model proposed by Cowley et al. (2004).

In the same way as neutrals accelerate the ions fixed at the foot of flux tubes passing through magnetospheric plasma to bring it into (partial, at least) corotation with the planet, ions lagging to corotation in the ionosphere retard the neutral atmosphere. Thus, the ion winds also generate neutral wind systems, with consequences for the overall circulation system of the upper atmosphere. In their study of the Jovian magnetosphere–ionosphere–thermosphere coupling, Cowley & Bunce (2001) defined a height-independent parameter, K, such thatEmbedded Image(5.2)so that K is a measure of the relative velocity of the neutral wind to the ion wind, measured in the planetary reference frame. A study using JIM (Achilleos et al. 1998) found that K reached values between 0.4 and 0.7 at the peak of the Embedded Image ion concentration for fields of approximately 3 V m−1 (Millward et al. 2005). This indicates that Embedded Image ions, drifting at 1 km s−1 or more, generate neutral winds of several hundred metres per second or more.

6. The heating of giant planet atmospheres

One of the outstanding problems of the giant planets is to explain why they are so hot. Since the early 1970s, it has been known that solar inputs are not sufficient to explain the exospheric temperature measured on Jupiter (Strobel & Smith 1973); Yelle & Miller (2004) have recently compared measured exospheric temperatures with those calculated from the absorption of solar EUV and found that all the giant planets are hundreds of degrees hotter than expected. Two decades ago, Waite et al. (1983) proposed that energy generated in the Jovian auroral regions might be transferred to lower latitudes via meridional winds, helping to heat the upper atmosphere.

One source of heating in the auroral regions is particle precipitation, although as we have seen above this tends to be balanced by Embedded Image cooling to space, at least for Jupiter and (probably) Uranus. However, there are two other sources of heating associated with the ionosphere that are of great interest—Joule heating and the friction owing to ion drag. In general terms, the former is given simply by the product of the electric field and the current flowing through the ionosphere. However, care needs to be taken to ensure that the field is defined in the correct frame of reference, which is the frame of reference fixed in the neutral atmosphere that coexists with the ionosphere through which the current is flowing. As we have already pointed out, that part of the neutral atmosphere lags behind corotation with the planet, owing to collisions with the Hall drifting ions. If we define Eeq in the frame of reference that corotates with the planet, thenEmbedded Image(6.1)where we have substituted (1−K)EeqΣP for the Pedersen current, iP.

We have previously pointed out that there is considerable energy stored in the neutral winds driven by Hall drifts, which might be transformed into heating as a result of friction between neutrals corotating with the planet and those that are lagging owing to ion–neutral collisions (Miller et al. 2000, 2005). Smith et al. (2005a) have recently shown that heating owing to ion drag is given byEmbedded Image(6.2)and the total heating given byEmbedded Image(6.3)

For K∼0.5, Eeq∼1 V m−1 and ΣP∼1 mho, equation (6.3) gives Htot∼500 mW m−2. It is interesting to compare the planet-wide heating owing to Joule heating and ion drag with solar EUV inputs. For Jupiter, insolation provides approximately 1012 W (1 terawatt, TW) to the whole planet's upper atmosphere energy balance; for Saturn, insolation provides about 25% of this amount. For Jupiter, Joule heating and ion drag integrated over the auroral region produce greater than 100 TW, two orders of magnitude more than insolation, and for Saturn, the figure is approximately 5 TW, about 20 times the solar EUV absorbed.

However, high upper atmosphere temperatures are found not only in the auroral/polar regions, but planet-wide (Lam et al. 1997; Miller et al. 1997). If energy generated at high latitudes is the answer to the high temperatures found at low latitudes, then the issue is to distribute it planet-wide, as Waite et al. (1983) proposed. Sommeria et al. (1995) showed that for Jupiter, high-velocity winds at high latitudes could be deflected equatorward and carry energy to low latitudes. But the velocities required by their model, greater than 20 km s−1, seem unfeasibly large (Yelle & Miller 2004). Global circulation models of Jupiter show that energy can be distributed equatorward by thermal-driven circulation (Bougher et al. 2005) or by waves (Millward et al. 2005). Smith et al. (2005b) have also demonstrated that energy inputs of approximately 5 TW in Saturn's auroral/polar regions can generate the required (approx. 400 K) exospheric temperature measured around the equator.

7. Conclusions

Fifteen years ago, Embedded Image was just a curiosity as far as planets were concerned; its detection in the Jovian aurora remained just a detection. But this fundamental and ubiquitous molecular ion is now proving to be much more than just a chemical oddball, an ephemeral member of a web of cosmic chemistry. For Jupiter (J), Saturn (S) and Uranus (U), it is now proven to play a significant role in at least three of the four areas discussed: as a tracer of energy inputs (J, S and U); as a coolant/thermostat (J and U); as a source of conductivity (J, S and U); and as a driver of winds (J and S). Embedded Image may hold the key to the stability of the atmospheres of giant extrasolar planets; it may even prove to be a probe of their physical and chemical conditions.

Discussion

J. Glosik (Department of Electronic and Vacuum Physics, Charles University, Prague, Czech Repulic). Why is it that ionospheric conductivity is (mainly) proportional to the Embedded Image number density rather than the electron number density?

S. Miller. Clearly, the total conductivity, Σ, will be given by the sum of the conductivity due to both the positive ions and the electrons. (Note that the ionosphere is electrically neutral, so that the densities of positive ions and electrons are equal.)Embedded Image

The key factor in determining which plays a more important role is the relative mobility of (positive) ions versus electrons. It is well known thatEmbedded Imagewhere νan is the ion/electron–neutral collision frequency and Ωa is the ion/electron gyrofrequency. This latter quantity is given by eB/ma, where B is the magnetic field of the planet and ma is the mass of the ion or the electron. It is easy to see that this quantity is approximately 5500 times larger for electrons than for Embedded Image ions. For the conditions prevailing in giant planet ionospheres/thermospheres, νin and Ωi are of the same order of magnitude. But the effect of the relatively much larger value of Ωe compared to Ωi means that Σe is much smaller than Σi. So the ions provide virtually all the conductivity.

Another way of looking at this is that in the absence of the neutral thermosphere, ions and electrons would simply gyrate around the planet's magnetic field lines; they would be ‘tied’ to the magnetic field and immobilized in this way. What makes them mobile and gives rise to conductivity is the rate at which they are knocked off their field lines by collisions with neutral atoms and molecules. The similar magnitudes of νin and Ωi mean that ions suffer many more collisions than electrons per gyration, and are thus much freer to be knocked off their fieldline; ions are consequently more mobile and conducting than electrons, for which νen is much smaller than Ωe.

D. C. Schram (Technische Universiteit Eindhoven, The Netherlands). Is there any evidence of significant rotation/vibration excitation of H2? If so, does this not help to produce H ions?

S. Miller. In the thermosphere of giant planets, number densities of H2 are approximately 1020–1016 m−3 (going down with altitude) in the regions where conductivity due to Embedded Image is important. This is well above the critical density of approximately 1012 m−3 at which H2 can be considered to be in LTE. So the population of both vibrationally excited and rotationally excited states will be given by a Boltzmann distribution at the relevant altitude-dependent temperature—900–1200 K for Jupiter, 400 K for Saturn and 600–800 K for Uranus (increasing with altitude). Emission from vibrationally excited H2 lines (which are produced by quadrupole, rather than dipole, moments) is observed both for Jupiter and Uranus, but not yet for Saturn. Clearly, therefore, there are populations in the rovibrationally excited states of H2 in these atmospheres.

As to whether this leads to any significant production of H ions, none of the one-dimensional or three-dimensional models of the giant planet upper atmospheres predict any significant density of this species. They all produce ionospheres dominated by positive ions (mainly H+ and Embedded Image) produced by photoionization and electron impact ionization (in the auroral/polar regions). Harris et al. (2004) have recently modelled the effect of H3/Embedded Image as an electron donor system in low metallicity stars, in which the electrons are attached to H to form H in large amounts. But this occurs at temperatures and densities much higher than those prevailing in giant planet upper atmospheres.

M. Galand (Department of Physics, Imperial College of Science, Technology and Medicine, London, UK). Having discussed Embedded Image emission at Jupiter, Saturn and Uranus, what is your prediction for Neptune?

S. Miller. Our group and others have looked for Embedded Image emission from Neptune for several hours at a time on several occasions, using spectrometers with a range of resolving powers of λλ from a 1000 to 40 000 and more, without any indication that this emission is detectable. Individual Embedded Image emission lines for Jupiter have intensities typically of a few times 10−15 W m−2. It takes only a minute to detect such lines with signal to noise (S/N) ratios of 10–100, depending on the resolving power and the conditions prevailing on the planet at the time. For Uranus and Saturn, the line intensity is weaker by approximately 100, but these are clearly detectable with exposures of approximately 1 h. The fact that several hours of observations of Neptune have produced nothing means Neptune cannot have individual line intensities much more than 10−18 W m−2.

Why this should be so is another matter. Saturn's lines are weaker than Jupiter's, because the temperature of the emitting gas layer is only approximately 400 K, compared with the Jovian thermosphere/ionosphere temperature of 900–1200 K. Uranus is hotter than Saturn, but seems to have lower Embedded Image column densities, and its emission is relatively uniform planet-wide, with auroral enhancements of approximately 20%, compared with Jupiter and Saturn where particle precipitation in the auroral/polar regions increases emissions by an order of magnitude or more. That indicates that Uranus' emission has a major UV-photoionization component. It may be that the lower solar UV radiation levels at Neptune mean that it does not have the same level of planet-wide emission that occurs on Uranus, and that it does not have the auroral enhancements of Jupiter and Saturn.

Acknowledgments

This work was supported by grants from the UK Particle Physics and Astronomy Research Council (PPARC), and studentships from PPARC and the Engineering and Physical Sciences Research Council. Computer modelling was carried out on the Sun Sunfire computers run by the Miracle Computing Consortium, which is part of the UCL HiPerSPACE centre. Observations were made using the United Kingdom Infrared Telescope (UKIRT) and the NASA Infrared Telescope Facility (IRTF), which is operated on behalf of NASA by the Institute for Astronomy, University of Hawaii. Larry Trafton and Tom Geballe are thanked for their contribution to the observations discussed here and their continuing scientific support.

Footnotes

  • One contribution of 26 to a Discussion Meeting Issue ‘Physics, chemistry and astronomy of H3+’.

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