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Estimated energy balance in the jovian upper atmosphere during an auroral heating event
Icarus 181 (2006) 256–265 www.elsevier.com/locate/icarus
Estimated energy balance in the jovian upper atmosphere during an auroral heating event Henrik Melin a , Steve Miller a,∗ , Tom Stallard a , Chris Smith a , Denis Grodent b a Atmospheric Physics Laboratory, Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK b Laboratoire de Physique Atmosphérique et Planétaire, Institut d’Astrophysique et de Géophysique, Université de Liège,
Avenue de Cointe 5, B-4000 Liège, Belgium Received 13 June 2005; revised 28 October 2005 Available online 22 December 2005
Abstract We present an analysis of a series of observations of the auroral/polar regions of Jupiter, carried out between September 8 and 11, 1998, making use of the high-resolution spectrometer, CSHELL, on the NASA InfraRed Telescope Facility (IRTF), Mauna Kea, Hawaii; these observations spanned an “auroral heating event.” This analysis combines the measured line intensities and ion velocities with a one-dimensional model vertical profile of the jovian thermosphere/ionosphere. We compute the model line intensities both assuming local thermodynamic equilibrium (LTE) and, relaxing this condition (non-LTE), through detailed balance calculations, in order to compare with the observations. Taking the model parameters derived, we calculate the changes in heating rate required to account for the modelled temperature profiles that are consistent with the measured line intensities. We compute the electron precipitation rates required to give the modelled ion densities that are consistent with the measured line intensities, and derive the corresponding Pedersen conductivities. We compute the changes in heating due to Joule heating and ion drag derived from the measured ion velocities, and modelled conductivities, making use of ion-neutral coupling coefficients derived from a 3-D global circulation model. Finally, we compute the cooling due to the downward conduction of heat and the radiation-to-space from the H+ 3 molecular ion and hydrocarbons. Comparison of the various heating and cooling terms enables us to investigate the balance of energy inputs into the auroral/polar atmosphere. Increases in Joule heating and ion drag are sufficient to explain the observed heating of the atmosphere; increased particle precipitation makes only a minor heating contribution. But local cooling effects—predominantly radiation-to-space—are shown to be too inefficient to allow the atmosphere to relax back to pre-event thermal conditions. Thus we conclude that this event provides observational, i.e. empirical, evidence that heat must be transported away from the auroral/polar regions by thermally or mechanically driven winds. © 2005 Elsevier Inc. All rights reserved. Keywords: Aurorae; Ionospheres; Jupiter, atmosphere; Jupiter, infrared
1. Introduction For over three decades there has been considerable debate about the energy balance of the upper atmosphere of the giant planets: the basic problem is that observed exospheric temperatures at mid-to-low latitudes are far higher than can be produced by solar Extreme Ultraviolet (EUV) heating alone (Strobel and Smith, 1973; Yelle and Miller, 2004). The discovery of Jupiter’s aurorae (Broadfoot et al., 1979) focused attention on the high rates of particle precipitation required to produce these im* Corresponding author. Fax: +44 (0) 20 7679 9024.
E-mail address: [email protected] (S. Miller). 0019-1035/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2005.11.004
pressive displays (Waite et al., 1983). Plasma flows measured by Voyager (Evitiar and Barbosa, 1984) indicated that electric fields would be imposed on the jovian ionosphere, which could drive currents that would produce Joule heating. Waite et al. (1983) proposed that the heating of the auroral regions resulting from particle precipitation and Joule heating could drive meridional winds that would transport energy to lower latitudes. Sommeria et al. (1995) tried to account for high H Lyman-α UV emission at the equator (McGrath et al., 1989) by invoking energy-transporting winds flowing around Jupiter’s auroral oval, which could be deviated meridionally, although the high velocities their model required—∼20 km s−1 —seem unfeasibly large Yelle and Miller (2004). More recently, heating due to
Jovian upper atmosphere energy balance
breaking gravity waves has been proposed as a global source of energy to produce the high exospheric temperatures observed (Young et al., 1997). But there appears to be considerable controversy over whether gravity waves heat (Young et al., 2005), have little effect (Matcheva and Strobel, 1999) or even cool the upper atmosphere (Hickey et al., 2000). In considering the energy balance of the atmosphere, account also has to be taken of loss mechanisms. Energy can be lost in the upper atmosphere through downward conduction, transferring the energy to lower altitudes (e.g., Achilleos et al., 1998; Grodent et al., 2001; Bougher et al., 2005). Since the detection of infrared emission H+ 3 in the jovian auroral regions (Drossart et al., 1989) and from the body of the planet (Ballester et al., 1994) it has been clear that radiation to space by this ion—which we denote as E(H+ 3 )—is another important coolant above the jovian homopause (Miller et al., 1994, 1997; Lam et al., 1997; Waite et al., 1997). (NB the homopause— defined as the level above which convective mixing ceases to be important—is generally located around the 2 µbar pressure level on Jupiter.) Around and below the homopause, infrared colling by hydrocarbons is extremely important (Drossart et al., 1993). The measurement of H+ 3 ro-vibrational emission lines has proven extremely important in determining the temperature structure of the jovian upper atmosphere and the degree of ionisation there (Drossart et al., 1989; Lam et al., 1997; Miller et al., 1990, 1997, 2000; Oka and Geballe, 1990; Stallard et al., 2002). The extent to which H+ 3 vibrational levels can be considered to be in local thermal equilibrium (LTE) has been investigated by Miller et al. (1990), Kim et al. (1992), and Stallard et al. (2002). Miller et al. (1990) measured lines from both the first and second vibrationally excited states and concluded that the ratio of vibrational level populations was approximately thermal. But the modelling study of Kim et al. (1992) showed that even if this were the case, the high rate of radiative de-excitation of vibrationally excited levels meant that they were underpopulated compared with the ground state at altitudes above 650 km, the ionisation peak in their model. We have recently carried out a modelling study, which combines the vertical profiles produced by the one-dimensional, two-stream, model of Jupiter’s auroral/polar regions due to Grodent et al. (2001) with the detailed balance calculations of Oka and Epp (2004), to examine the effects on H+ 3 in conditions of non-LTE (Melin et al., 2005; hereafter Paper I). Paper I confirmed that the assumption that H+ 3 is in local thermodynamic equilibrium (LTE) is not valid in all parts of the upper atmosphere of Jupiter, by comparing the H+ 3 spectra in the K (Raynaud et al., 2004) and L (Stallard et al., 2001, 2002) windows with the modelled line intensities. It found that only the non-LTE model could produce consistent intensities for a given atmospheric temperature profile. This paper is based on the results of Paper I to examine an auroral heating event observed by Stallard et al. (2001, 2002) between the 8th and 11th of September 1998. That study made use of the facility high-resolution infrared echelle spectrometer, CSHELL, on NASA Infrared Telescope Facility, to measure ion velocities and H+ 3 temperatures and column densities across the
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auroral/polar region. During this event the line-of-sight velocity of the auroral electrojet doubled, from 0.5 to 1.0 km s−1 . At the same time, the H+ 3 temperature—derived assuming a thin shell source in LTE—rose from 940 to 1065 K and the + 16 column density of H+ 3 , N (H3 ), increased from 1.55 × 10 to 16 −2 1.80 × 10 m (Stallard et al., 2002; NB the column densities in that paper should be scaled up by (2π)1/2 ). The simultaneous increase of all the parameters they studied indicates that energy was being injected into the auroral region. We now combine the results of Paper I with density profiles from Grodent et al. (2001), to estimate the changes in heating/cooling that would have occurred to Jupiter’s upper atmosphere during the auroral event of September 8–11, 1998 (Stallard et al., 2001, 2002). We also make use of parameters derived from the Jovian Ionospheric Model (JIM: Achilleos et al., 1998). This paper aims to examine what the main energy sources are and where the energy is deposited. At present, there is no fully self-consistent model of the jovian upper atmosphere. JIM (Achilleos et al., 1998) is designed to simulate the dynamics, particle precipitation and time-dependent chemistry of the jovian system. It is not able to model changes in the atmospheric thermal profile of Jupiter, due to the changing energy balance, self-consistently, however, because its original thermal profile was input at the initiation of the model, rather than derived as a result of equilibration. NB in 1998, no one had an adequate inventory of the energy inputs into the jovian upper atmosphere, nor of the mechanisms for distributing energy, and insolation was known to produce exospheric temperatures much lower than those measured—see (Strobel and Smith, 1973) and (Yelle and Miller, 2004). So it was hardly surprising that this technique was necessary. As far as 1-D vertical models go, that of Grodent et al. (2001) is best fitted to the measured properties of the jovian upper atmospheres. But it cannot simulate energy inputs such as Joule heating and ion drag—which depend on essentially horizontal motions—in a totally self-consistent way. So an approach that involves a combination of the JIM and Grodent models can be insightful, making use of the best features of both. Later in this paper, we compare our semi-empirical results with those of the Jupiter Thermospheric Global Circulation Model (JTGCM) of Bougher et al. (2005), which makes direct use of the Grodent et al. (2001) model auroral atmosphere, and is more (but not fully) capable of self-consistent simulations. 2. Magnetosphere–ionosphere–thermosphere coupling in the jovian system The input of energy from Jupiter’s enormous magnetosphere into the planet’s upper atmosphere is absolutely critical to understanding the balance of energy. Hill (1979) proposed a mechanism by which the upper atmosphere of Jupiter is coupled, magnetically, with the equatorial plasma sheet in the magnetosphere, which results from the volcanic activity of the moon Io. The plasma sheet corotates with the magnetosphere close to the planet. But further away from the planet corotation breaks down, setting up a current system through the plasma sheet, which follows the magnetic field lines down onto the planet
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and closes in the ionosphere. This closure results from the imposition of an equatorward electric field, which we denote Eeqw in the frame of reference that corotates with Jupiter (the planetary reference frame, PRF). Charged particles—kiloelectron volt electrons—are accelerated from the plasma sheet onto the planet, ionising the upper atmosphere and producing bright auroral emission at wavelengths from the far ultraviolet to the infrared. This process produces far greater precipitation than is observed on Earth and results in a net heating rate in the upper atmosphere of around 1013 to 1014 W (Waite et al., 1983; Clarke et al., 1989). Eeqw drives an ionospheric Pedersen current equatorward to close the magnetosphere–ionosphere coupling current system. The lag in corotation of the plasma sheet gives rise to an ion wind in the (magnetically linked) ionosphere—the electrojet, as observed by Rego et al. (1999) and Stallard et al. (2001) and described theoretically by Cowley and Bunce (2001) and Hill (2001). In the PRF, the ion wind velocity is given by the Hall drift formula: vion = Eeqw × BJ /BJ2 ,
(1)
where BJ is the strength of the jovian magnetic field in the auroral regions; we assume BJ to be vertical. Eeqw is the equatorward electric field imposed on the ionosphere by the magnetosphere as a resulting from the corotation enforcement mechanism. The resulting ion winds are westwards in both hemispheres in the PRF. Westward flowing ions collide with the neutral thermosphere. Thus the magnetospheric energy is converted to heat via Joule heating and by ion drag (Miller et al., 2000, 2005; Vasyliunas and Song, 2005; Smith et al., 2005) through momentum transfer to the neutrals. Note that in the inertial— Sun–Jupiter—reference frame these winds are still eastwards, but sub-corotational, and represent an upper atmosphere lag to corotation. In what follows, however, we will use the PRF. This is because our study concerns the input of energy from the magnetosphere into the planet, rather than the driving of the magnetosphere by the transfer of rotational energy from the planet. 3. Scaling the Grodent et al. (2001) temperature profile The observed temperatures of Stallard et al. (2002) are derived from the ratio of intensities in the hotband R(3, 4+ ) and the fundamental Q(1, 0− ) H+ 3 lines, using the linelist calculated by Neale et al. (1996). We shall use this intensity ratio to parameterise the Grodent et al. (2001) temperature profile such that it can be described by a single number, which, in turn, can be related to the measured line ratio. We define a scaling factor, NG , so that the temperature, Ti , at each model level i becomes: Ti (NG ) = TiG − T0 × NG + T0 , (2) where TiG is the original temperature profile at level i and T0 is the temperature at, or just below, the homopause; Grodent et al. (2001) give T0 = 161 K. The jovian homopause temperature is thus kept constant regardless of NG . This is a reasonable assumption since it is known to be fairly constant over time (e.g., Hubbard et al., 1995; Seiff et al., 1997). The physical reason
Fig. 1. The temperature profile of Grodent et al. (2001) scaled by NG = 0.8, 0.9, 1.0, 1.1, and 1.2 as defined in Eq. (2).
for this was shown by Drossart et al. (1993), who demonstrated that T0 is controlled by radiation to space by hydrocarbons at, or just below, the homopause. Equation (2) represents a first-order, linear, approximation to model the response of the jovian thermosphere to varying energy inputs. Comparison of the cases of discrete and diffuse auroral precipitation modelled in Grodent et al. (2001) shows that this is a reasonable approach. More detailed modelling, which would require explicit and iterative recalculation of the Grodent et al. (2001) profiles, ion concentrations and the resulting H+ 3 line intensities for a range of particle precipitation fluxes and energies, and the simulation of Joule/ion-drag heating, is beyond the scope of this study. We shall return to this issue in the discussion and conclusions. The temperature profiles for different NG ’s are shown in Fig. 1. Using this scaling factor the intensity of R(3, 4+ ) and Q(1, 0− ) at a particular NG can be modelled through the Grodent et al. (2001) atmosphere, as explained in Paper I. The ratio of the integrated intensities of the two lines observed by Stallard et al. (2002) for a range of NG can be seen in Fig. 2. From Fig. 2 the line ratio can be related to the scaling factor, NG , which itself defines a temperature profile as per Eq. (2). The hotband/fundamental line ratio is 0.014 in the beginning of the auroral event, on September 8, and 0.022 in the end, on September 11 (Stallard et al., 2001). This gives NG = 0.85 at the beginning of the event and 1.02 at the end of the event for the LTE scenario. For the non-LTE scenario is NG = 0.97 and 1.17. The corresponding scaled temperature profiles are shown in Fig. 3. 4. Energy required to heat the auroral region The additional energy, Q, needed to heat the mixture of gas that makes up the thermosphere can be calculated using the following formula: Q = cp T ,
(3)
Jovian upper atmosphere energy balance
Fig. 2. Intensity ratio of the two lines observed by Stallard et al. (2002) as a function of the scaling factor, NG , for both LTE and non-LTE scenarios.
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Fig. 4. The difference between the start and end temperature profiles of the event.
In what follows we take the average increase in net heating rate to be given by [dQ/dt]ave = Q/t,
(4)
2.5 × 105
where t is s, calculated from the difference in median UT times between the observations on September 8 and 11, 1998. This gives a column-integrated change in the net heating rate of 65 mW m−2 for the LTE case and 73 mW m−2 for the non-LTE case. These net heating rates are not radically different. Paper I showed that the H+ 3 density was overestimated in Grodent et al. (2001) for both the LTE and non-LTE cases. But only in the case of the non-LTE profiles was it possible to account consistently for the relative intensities observed in the vibrationally excited levels. In what follows, therefore, we shall now only consider the non-LTE case. Fig. 3. Temperature profiles at the start and at the end of the event observed by Stallard et al. (2002) for both LTE and non-LTE. The profiles are derived from the observed line ratio and scaled as the Grodent et al. (2001) temperature profile. The arrow shows the direction of the event.
where cp is the total heat capacity (in J K−1 m−3 ) of the gas mixture and T is the increase in temperature. Note that Q is the local additional heat required, with units of J m−3 . Since the predominant species in the upper atmosphere are H, H2 , and He, only these species have been considered when calculating the heat capacity. The temperature increase during the event for each scenario can be seen in Fig. 4. From these, we can calculate how much heat is required to produce the temperature increase at each altitude, and as well as the total change in column heating. Note that this represents the net heating additional to that prevailing on September 8; for the purposes of this study, we initially assume that the jovian upper atmosphere was in steady state on September 8, prior to the auroral heating event. In Section 9, we present our calculations of the total heating and cooling rates, which show that this assumption is justified.
5. Derivation of electron precipitation rates and Pedersen conductivity In principle, it is possible to vary inputs of precipitating particles in the Grodent et al. (2001) model to produce different heating rates and ion densities. What we present here, however, is a less demanding technique of estimating precipitation rates from measured line intensities. Millward et al. (2002) modelled the response of auroral H+ 3 column density to different precipitation energies, using JIM (Achilleos et al., 1998). H+ 3 in the auroral regions is produced via the following reactions: H2 + e∗ / hν → H+ 2 + e[+e],
+ H 2 + H+ 2 → H3 + H.
(5)
For 10 keV electrons, Millward et al. (2002) found the empirical relationship log10 N H+ (6) 3 = 0.435 log10 Fe + 12.28, where Fe is the incident flux of auroral electrons in ergs s−1 cm−2 (mW m−2 ) and N is the column density of H+ 3 in cm−2 . Of note here is that the H+ 3 column density does not
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Fig. 5. Left panel: H+ 3 number density profile on September 8, at the start of the event. Right panel: Increase in H+ 3 number density profile between September 8 and September 11, at the end of the event. Both panels are for the non-LTE profiles.
increase linearly with electron flux, but more slowly. This is because the overall density is controlled chiefly by dissociative recombination with electrons: H3 + + e → H2 + H/H + H + H.
(7)
The rate at which this occurs clearly depends on the electron density, itself a measure of the level of ionisation of the atmosphere. Equation (6) can be written in the form: + log10 N H+ 3 − log10 N0 H3 = 0.435[log10 Fe − log10 F0 ],
(8)
where N0 (H+ 3 ) and F0 are the values in Grodent et al. (2001): 12 −2 F0 = 110 ergs s−1 cm−2 ; N0 (H+ 3 ) = 18 × 10 cm . Note that in Eq. (8), we take the same scaling of the log10 N (H+ 3 ) production rate irrespective of individual electron energy. For the non-LTE case, Paper I showed that the H+ 3 column density was overestimated by a factor of ∼3, depending upon the exact intensity of the lines being modelled. To account for this, we scale the local H+ 3 density in the Grodent profile by a factor, which is constant with respect to altitude, in order to produced the measured Q(1, 0− ) line intensity for September 8 and 11 for the non-LTE case. This factor is 36.4% for September 8 and 38.1% for September 11. This altitude independent scaling is consistent with the first-order, linear, approximation to scaling the temperature profile implied in Eq. (2). The scaled H+ 3 densities are shown in Fig. 5 as a function of altitude. These densities are required to calculate both the conductivity of the ionosphere and the energy input from precipitating electrons. The column densities resulting from the scaled profiles are 8.74 × 1016 m−2 for September 8 and 9.14 × 1016 m−2 for September 11. Using Eq. (8), the precipitation fluxes required to produce the observed line intensities are 10.8 mW m−2 on September 8 and 12.0 mW m−2 on September 11, which gives an increase in auroral precipitation of 1.2 mW m−2 . This is a small (∼10%) increase in the required precipitation, and leads to the conclusion that our analysis is
Fig. 6. As Fig. 5 for the Pedersen conductivity.
not overly sensitive to the exact value of the scaling in Eq. (8). Assuming a linear increase over the period from September 8 to 11, the average increase in heating from particle precipitation would be 0.6 mW m−2 . The Pedersen conductivity in the jovian atmosphere is almost entirely due to the positive ions. Then ΣP , is given by (Luhmann, 1995) 2 ΣP = N e2 νin mi νin (9) + Ωi2 , where νin is the collision frequency between the ion and the neutrals and Ωi is the gyrofrequency of the charged particle with number density N and mass mi . e is the elemental charge. In our case the relevant charged particle is H+ 3 . The relevant collision frequency is taken to be that of Geiss and Buergi (1986), which is used in JIM (Achilleos et al., 1998). Note that the gyrofrequency depends on the value of BJ , which we take as 10−3 T in the northern auroral region, consistent with the value used in JIM studies (see Millward et al., 2005). The resulting conductivity, as a function of altitude, can be seen in Fig. 6. The integrated conductivity is 0.44 mhos in the beginning of the event and 0.46 mhos at the end. 6. Joule heating and ion drag Smith et al. (2005) have shown that the total energy that the magnetosphere puts into the upper atmosphere resulting from the equatorward electric field, Eeqw is given by 2 2 ΣP + k(1 − k)Eeqw ΣP . HMag = (1 − k)2 Eeqw
(10)
The first term on the right-hand side represents Joule heating. The second term is the kinetic energy input due to ion drag, which must ultimately dissipate as heat. k is the ratio between the velocity of the westward neutral wind in the auroral oval and the corresponding ion wind, discussed by Cowley and Bunce (2001) and Millward et al. (2005): note that 0 < k < 1. Taking BJ = 10−3 T, and remembering that Eeqw = vion BJ , means that an observed value of vion = 1 km s−1 corresponds to Eeqw = 1 V m−1 and so on. As previously stated, the line-of-sight ion velocity in the auroral oval increases from 0.5 km s−1 at the beginning to
Jovian upper atmosphere energy balance
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Fig. 7. As Fig. 5 for Joule heating and ion drag.
1.0 km s−1 at the end of the event. The value of k is not known observationally. But JIM gives values of 0.5–0.7 at the ion peak (Millward et al., 2005), and we take the lower value of 0.5 in this calculation. (It follows from Eq. (10) that taking k = 0.5 results in the Joule heating and ion drag making equal contributions to the heating rate.) The observed line-of-sight (l.o.s.) velocities of 0.5 and 1.0 km s−1 would translate to Eeq = 0.5 and 1.0 V m−1 , respectively. We assume that the electric field is height-independent. With the increases in conductivity and ion velocity noted above, Eq. (10) can be used to calculate the increase in local heating rate. Using the l.o.s. velocities, the column integrated heating rate due to Joule heating and ion drag is 55 mW m−2 on September 8 and 229 mW m−1 on September 11, giving an increase of 174 mW m−2 . The l.o.s. velocities are minimum values for the true ion velocity, however. Depending on the geometry of the electrojet, the true ion velocity in the auroral electrojet may be as high as 0.75 km s−1 on September 8 and 1.5 km s−1 on September 11. Stallard et al. (2002) found that observations made on September 8 and 11 with a central meridian longitude λIII = 155◦ to 160◦ (jovian System III longitude) showed the electrojet most clearly. For these observations, the slit colatitude was ∼20◦ , and the angle of the electrojet to the XZ plane was between 2◦ and 7◦ . At the time, the sub-Earth latitude of Jupiter was +3◦ . For the northern hemisphere, the geometry resulting from these angles require the l.o.s velocities to be increased by 10%, to give 0.55 km s−1 on September 8 and 1.1 km s−1 on September 11. Using these velocities, heating rates due to Joule heating and ion drag for the two dates are shown in Fig. 7. The column integrated heating rates are 67 and 277 mW m−2 , respectively, giving an increase of 210 mW m−2 . Assuming that the heating rate increases linearly during the September 8 to 11 event, then the average increase in heating rate during the event is between 87 mW m−2 , based on the l.o.s. velocities, and 105 mW m−2 , after l.o.s. correction. In what follows we take the average increase in heating rate as 105 mW m−2 , and show that this is sufficient to produce the observed temperature increase.
Fig. 8. Heating and cooling due conduction on September 8 (full line) and September 11 (dashed line).
7. Downward heat conduction The downward conduction of heat is given by Hcond = λ dT /dz,
(11)
where dT /dz is the temperature gradient, where the thermal conductivity λ is given by λ = AT s mW m−2 (K/m)−1
(12)
with A = 2.5 and s = 0.75. From Fig. 3, for the non-LTE case we can see that the exospheric temperature is 1280 K at the start of our auroral event and 1500 K at the end. The homopause temperature remains constant at 161 K. The conducted heat flux as a function of altitude is shown in Fig. 8. To calculate the overall effect, we approximate Eq. (11): Hcond = λT /z,
(13)
where T and z refer to the difference between the exospheric and homopause temperatures and altitudes, respectively. Equation (12) is approximated by taking T as the mean temperature between the homopause and the exosphere. Hcond represents the rate at which heat (eventually) flows through the lower boundary of the atmospheric region under consideration to be lost to the lower atmosphere or to space. These approximations give λ = 0.35 and 0.39 mW m−2 (K/m)−1 at the start and end of the auroral event, respectively, while T /z is similarly 0.75 × 10−3 and 0.90 × 10−3 K/m. These figures give Hcond = 0.26 and 0.35 mW m−2 at the start and the end, respectively, which—in turn—give Hcond = 0.09 mW m−2 between the start and the end of the auroral event. If we assume that this change is linear with time during the event, the average value of Hcond = 0.045 mW m−2 . A somewhat larger value of Hcond = 0.06 mW m−2 is derived if one only considers the atmosphere at and below the peak in Joule/ion drag heating. Either way, these cooling rates are very small.
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Fig. 9. As Fig. 5 for radiation to space by H+ 3.
Fig. 10. As Fig. 5 for radiation to space by hydrocarbons.
8. Energy lost through infrared cooling
Table 1 Heating and cooling rates
Above the homopause, which occurs for Jupiter around the 2 µbar pressure level, infrared emission from the H+ 3 molecular ion is known to be the main coolant in the jovian upper atmosphere (Miller et al., 1994, 1997; Lam et al., 1997; Waite et al., 1997), other than downward conduction of heat to the homopause. A study by Rego et al. (2000) showed that energy inputs due to particle precipitation were approximately + balanced by H+ 3 emission to space, denoted as E(H3 ) (see Lam et al., 1997). Bougher et al. (2005) have termed this effect the H+ 3 thermostat. In considering the September 8–11, 1998, auroral event it is therefore important to take this effect into account. Since more than 90% of the H+ 3 emission in Jupiter’s upper atmosphere arises from the ν2 vibrational level (Miller et al., 1990; Grodent et al., 2001), we assume that the overall attenuation of E(H+ 3 ) due to non-LTE effects can be approximated, as a function of altitude, by the population of this level. The H+ 3 emission as a function of altitude is plotted in Fig. 9, allowing for the scaling of the H+ 3 density profile in the auroral model of Grodent et al. (2001). We calculate that the column-integrated −2 (2π sr)−1 on Sepvalues of E(H+ 3 ) are 5.1 and 10.0 mW m tember 8 and 11, respectively. This gives an overall change the energy lost through H+ 3 emission, between September 8 and 11, of 4.9 mW m−2 . If we assume the change to be linear during −2 the period, the average change in E(H+ 3 ) is 2.5 mW m , about four times the increase in particle precipitation, and 50 times the change in downward conduction. Below the homopause, Drossart et al. (1993) showed that infrared cooling to space by hydrocarbons plays a key role in controlling the thermal structure of Jupiter’s atmosphere. The most important hydrocarbons are methane and ethyne (Bougher et al., 2005; Grodent et al., 2001). We adopt the Drossart et al. (1993) formulation for this, using the vertical density profiles for CH4 and C2 H2 in the Grodent et al. (2001) model. The local cooling rates for these two gases combined are shown in Fig. 10 for September 8 and 11. We calculate that the columnintegrated values of the combined hydrocarbon cooling rate are 65.5 and 103.3 mW m−2 (2π sr)−1 on September 8 and 11, re-
Heating/cooling term Joule heating and ion drag Particle precipitation Downward conduction E(H+ 3 ) cooling Hydrocarbon cooling Net heating rate
September 8 67.0 mW m−2
10.8 mW m−2 (−)0.3 mW m−2 (−)5.1 mW m−2 (−)65.5 mW m−2 7.4 mW m−2
September 11 277.0 mW m−2 12.0 mW m−2 (−)0.4 mW m−2 (−)10.0 mW m−2 (−)103.3 mW m−2 175.3 mW m−2
spectively. (NB CH4 accounts for ∼80% of this.) This gives the change in the energy lost through hydrocarbon emission, between September 8 and 11, as 37.8 mW m−2 . Once more assuming the change to be linear during the period, the average change in hydrocarbon cooling is 18.9 mW m−2 , showing the importance of this effect for cooling the lower reaches of the upper atmosphere. 9. Discussion Table 1 summarises the heating and cooling rates that we have calculated. Our analysis of the heating and cooling terms of September 8 shows that we have rates of 67.0 mW m−2 due to Joule heating and ion drag, and 10.8 mW m−2 due to particle precipitation, making a total of 77.8 mW m−2 . This is balanced by downward convection at 0.3 mW m−2 , H+ 3 cooling at 5.1 mW m−2 and hydrocarbon cooling at 65.5 mW m−2 , making 70.4 mW m−2 . There is a net heating rate of just 7.4 mW m−2 , which indicates that the atmosphere is close to thermal balance. This might be expected, since the value of NG is 0.97, and the Grodent et al. (2001) profile was based on an equilibrated atmosphere. For September 11, we have rates of 277.0 mW m−2 due to Joule heating and ion drag, and 12.0 mW m−2 due to particle precipitation, making a total of 289.0 mW m−2 . Downward −2 and convection is 0.3 mW m−2 , H+ 3 cooling is 10.0 mW m −2 hydrocarbon cooling is 103.3 mW m , making 113.7 mW m−2 in total, and a net heating rate of 175.3 mW m−2 . This shows that even if the atmospheric heating and cooling rates were
Jovian upper atmosphere energy balance
Table 2 Average changes in heating and cooling rates Heating/cooling term
Amount (mW m−2 )
Required net increased heating rate (non-LTE case)
73
Average increase in Joule heating and ion drag Average increase in particle precipitation Average increase in downward conduction Average increase in E(H+ 3 ) cooling Average increase in hydrocarbon cooling
105 0.6 (−)0.04–0.06 (−)2.5 (−)18.9
Calculated net increased heating rate available
84.1
Fig. 11. Net average changes in energy inputs in the jovian atmosphere during the auroral heating event. This is compared with the vertical profile of the net energy required (solid line) to produce the modelled increase in temperature.
more or less balanced on September 8, considerable heating was occurring on September 11. The value of NG for September 11 is 1.17, indicating an atmosphere very much out of balance. Table 2 summarises the overall changes in heating/cooling rates derived from our analysis. The analysis of the auroral heating event observed by Stallard et al. (2001) gives us an insight to the energy balance in the jovian auroral/polar upper atmosphere. We require an average net increase in heating of 73 mW m−2 to account for the changes in temperature derived from the measured line intensities and the Grodent model, if we take the non-LTE case. The combined Joule and ion drag heating provides the atmosphere with by far the largest contribution to this energy. In turn, this energy is primarily created by the increase in the electric field imposed on the ionosphere by coupling to the middle magnetosphere, which is manifested by a doubling in the ion velocity in the auroral oval. The energy added by particle precipitation is smaller by ∼2 orders of magnitude. The main losses are through H+ 3 radiation, above the homopause, and hydrocarbons, below. Overall, energy is being input into the atmosphere at a rate of 84.1 mW m−2 , in fairly good agreement with the rate required (73 mW m−2 ). Fig. 11 compares the increased heating rate due to particle precipitation, Joule heating and ion drag, minus the increase in H+ 3 and hydrocarbon emission, with the required increase
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in heating rate, as a function of altitude. It is clear that not all of the energy is being deposited where it is required to heat the atmosphere. In fact, Joule heating and ion drag deposit energy about 150 km higher than where it is required. This altitude corresponds to the peak in the H+ 3 ion density, which— in turn—corresponds to the peak in the Pedersen conductivity. Heat is thus conducted downward, with part of the energy reradiated by hydrocarbons. Above ∼1000 km there appears to be a shortfall in the increase in heating rate required to produce the temperatures modelled from scaling the Grodent et al. (2001) profile. This shortfall may be made good by advection or by a slowing in the rate at which energy is conducted downwards. Our figures for column heating and cooling may be compared with those published by Bougher et al. (2005) for their Case 2 run (their Table 3). All the terms we calculate are comparable in magnitude to theirs, showing that the Bougher et al. (2005) Case 2 is fairly representative of actual jovian conditions. [NB there appear to be errors in the axis labelling of Figs. 11 and 13 of their paper, which make their results seem inconsistent with those of Grodent et al. (2001) and this paper.] Bougher et al. Case 2 run involved scaling down the inputs due to Joule heating, ion drag (which they include in Joule heating) and particle precipitation to avoid very large temperatures; without the scaling down, these reached 1950–2450 K in the auroral ovals at the H+ 3 concentration peak, much higher than any ever measured, and 2800–3100 K at the top of their model. Their preferred scaling factor was 30%. In their paper, Bougher et al. (2005) suggested that a convection electric field smaller than that deduced by Voyager should be used. But it may be that their use of the Grodent et al. (2001) H+ 3 concentrations, which are three times those compatible with the analysis in Paper I, are responsible for producing a higher value of ΣP . As can be seen from Eq. (10), this would naturally lead to the Joule heating and ion drag terms being too large, for a given electric field, and explain the need for scaling to produce a reasonable fit to observations. 10. Conclusions In following through this auroral event observed by Stallard et al. (2001, 2002) during September 8–11, 1998, we have been able to deduce a considerable amount about the energy balance in the auroral/polar regions. Particle precipitation clearly cannot account for the increased temperatures observed. Instead the heating required comes mainly from a doubling of the equatorward electric field imposed on the ionosphere by the magnetosphere, as implied by the ion velocities. This, in turn, results both in higher currents flowing through the upper atmosphere and in the transfer of additional energy from westwards Hall drifting ions to the neutrals, which eventually gets converted into heat. Since local cooling terms—downward conduction of heat and H+ 3 and hydrocarbon radiation-to-space—total about 20% of the increased heating terms, the atmosphere is heated considerably during the event. As previously discussed, ionospheric electric fields result from a lag to corotation in the equatorial plasma sheet
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(Hill, 1979). Our derived increases in Eeqw indicate an increased lag to corotation (Stallard et al., 2002). Cowley and Bunce (2001) and Southwood and Kivelson (2001) have both suggested that this may occur as a result of a falling off of the ram pressure on Jupiter’s magnetosphere due to a rarefaction in the solar wind, although jovian auroral emission is intrinsically variable. The increased temperature in the auroral/polar region observed by Stallard et al. (2002) has—at some point—to be counteracted by cooling, if the thermospheric temperature is not to rise inexorably, particularly given the large excess heating rate deduced for September 11. We have demonstrated that the main mechanism for such cooling is through H+ 3 and hydrocarbon emission, with a little due to downward conduction. These terms would take over if the conditions of Joule heating, ion drag and particle precipitation were suddenly to return to those of September 8, and the atmosphere would then cool again. But—at an average total cooling rate of 21.5 mW m−2 —even if the precipitation, Joule heating and ion drag rates returned instantaneously to those of September 8, it would take between 10 to 15 days to bring the temperature down again from that seen on September 11 to that seen on September 8. This time is comparable with expected solar wind cycles of ∼30 days, during which further heating events are likely. The only conclusion from the discussion of the heating/ cooling rates for the individual days and the change in rates is that the auroral/polar regions cannot be cooled by local mechanisms alone. Increased temperatures must therefore result in (increased) equatorward winds, which transport energy to lower latitudes, as suggested by Waite et al. (1983) over two decades ago. Our current study indicates that this wind-driven process may be particularly important when atmospheric conditions are changing. Recent modelling studies—either under conditions of high heating (Bougher et al., 2005) or changing conditions (Millward et al., 2005)—have shown that thermally driven winds are indeed produced. The offset between the magnetic and rotational poles on Jupiter implies that the ion winds flowing around the auroral oval have a meridional component at some longitudes, so driving hot neutrals equatorwards. Models (Bougher et al., 2005; Millward et al., 2005) show that at least part of the meridional wind system generated is due to the mechanical acceleration of neutrals by ion drag. Our observationally based study now provides an empirical measure of how much of the energy generated in the auroral/polar regions may be distributed equatorward, contributing to the high equatorial exospheric temperatures that are measured on Jupiter. Acknowledgments The UK Engineering and Physical Sciences Research Council are thanked for a studentship for H.M.; the Particle Physics and Astronomy Research Council are thanked for supporting the 1998 IRTF observations of Stallard et al. (2001, 2002). Miller and Stallard were visiting astronomers on the IRTF, which is operated on behalf of NASA by the Institute for As-
tronomy, University of Hawaii. D.G. is supported by the Belgian Fund for Scientific Research (FNRS). References Achilleos, N., Miller, S., Tennyson, J., Aylward, A.D., Mueller-Wodarg, I., Rees, D., 1998. JIM: A time-dependent, three-dimensional model of Jupiter’s thermosphere and ionosphere. J. Geophys. Res. 103, 20089– 20112. Ballester, G.E., Miller, S., Tennyson, J., Trafton, L.M., Geballe, T.R., 1994. Latitudinal temperature variations of jovian H+ 3 . Icarus 107, 189–194. Bougher, S.W., Waite Jr., J.H., Majeed, T., Gladstone, G.R., 2005. Jupiter Thermospheric General Circulation Model (JTGCM). 1. Global structure and dynamics driven by auroral and Joule heating. J. Geophys. Res. 110. 4008. Broadfoot, A.L., and 16 colleagues, 1979. Extreme ultraviolet observations from Voyager 1 encounter with Jupiter. Science 204, 8259. Clarke, J., Caldwell, J., Skinner, T., Yelle, R., 1989. The aurora and airglow of Jupiter. In: Belton, M.J.S., West, R.A., Rahe, J. (Eds.), Time Variable Phenomena in the Jovian System. NASA, Washington, pp. 211–220. Cowley, S.W.H., Bunce, E.J., 2001. Origin of the main auroral oval in Jupiter’s coupled magnetosphere–ionosphere system. Planet. Space Sci. 49, 1067– 1088. Drossart, P., and 11 colleagues, 1989. Detection of H+ 3 on Jupiter. Nature 340, 539–541. Drossart, P., Bézard, B., Atreya, S.K., Bishop, J., Waite Jr., J.H., Boice, D., 1993. Thermal profiles in the auroral regions of Jupiter. J. Geophys. Res. 98, 18803–18811. Evitiar, A., Barbosa, A.D., 1984. Jovian magnetospheric neutral wind and auroral precipitation. J. Geophys. Res. 89. 7393. Geiss, J., Buergi, A., 1986. Diffusion and thermal diffusion in partially ionized gases in the atmospheres of the sun and planets. Astron. Astrophys. 159, 1–15. Grodent, D., Waite Jr., J.H., Gerard, J.-C., 2001. A self-consistent model of the jovian auroral thermal structure. J. Geophys. Res. 106, 12933–12952. Hickey, M.P., Walterscheid, R.L., Schubert, G., 2000. Gravity wave heating and cooling in Jupiter’s thermosphere. Icarus 148, 266–281. Hill, T.W., 1979. Inertial limit on corotation. J. Geophys. Res. 84, 6554–6558. Hill, T.W., 2001. The jovian auroral oval. J. Geophys. Res. 106, 8101–8108. Hubbard, W.B., Haemmerle, V., Porco, C.C., Rieke, G.H., Rieke, M.J., 1995. The occultation of SAO 78505 by Jupiter. Icarus 113, 103–109. Kim, Y.H., Fox, J.L., Porter, H.S., 1992. Densities and vibrational distribution of H+ 3 in the jovian auroral atmosphere. J. Geophys. Res. 97, 6093–6101. Lam, H.A., Achilleos, N., Miller, S., Tennyson, J., Trafton, L.M., Geballe, T.R., Ballester, G.E., 1997. A baseline spectroscopic study of the infrared auroras of Jupiter. Icarus 127, 379–393. Luhmann, J.G., 1995. Ionospheres. In: Kivelson, M.G., Russell, C.T. (Eds.), Introduction to Space Physics. Cambridge Univ. Press, Cambridge, UK, pp. 183–202. McGrath, M.A., Feldman, P.D., Moos, H.W., Ballester, G.E., 1989. IUE observations of the jovian dayglow emission. Geophys. Res. Lett. 18, 583–586. Matcheva, K.I., Strobel, D.F., 1999. Heating of Jupiter’s thermosphere by dissipation of gravity waves due to molecular viscosity and heat conduction. Icarus 140, 328–340. Melin, H., Miller, S., Stallard, T., Grodent, D., 2005. Non-LTE effects on H+ 3 emission in the jovian upper atmosphere. Icarus 178, 97–103. + Miller, S., Joseph, R.D., Tennyson, J., 1990. Infrared emissions of H3 in the atmosphere of Jupiter in the 2.1 and 4.0 micron region. Astrophys. J. 360, L55–L58. Miller, S., Lam, H.A., Tennyson, J., 1994. What astronomy has learned from observations of H+ 3 . Can. J. Phys. 72, 760–771. Miller, S., Achilleos, N., Ballester, G.E., Lam, H., Tennyson, J., Geballe, T.R., Trafton, L.M., 1997. Mid-to-low latitude H+ 3 emission from Jupiter. Icarus 130, 57–67. Miller, S., and 10 colleagues, 2000. The role of H+ 3 in planetary atmospheres. Philos. Trans. R. Soc. 358, 2485–2502. Millward, G., Miller, S., Stallard, T., Aylward, A., Achilleos, N., 2002. On the dynamics of the jovian ionosphere and thermosphere. III. The modelling of auroral conductivity. Icarus 160, 95–107.
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Millward, G., Miller, S., Stallard, T., Aylward, A., Achilleos, N., 2005. On the dynamics of the jovian ionosphere and thermosphere. IV. Ion-neutral coupling. Icarus 173, 200–211. Neale, L., Miller, S., Tennyson, J., 1996. Spectroscopic properties of the H+ 3 molecule: A new calculated linelist. Astrophys. J. 464, 516–520. Oka, T., Geballe, T.R., 1990. Observations of the 4 micron fundamental band of H+ 3 in Jupiter. Astrophys. J. 351, L53–L56. Oka, T., Epp, E., 2004. Non-thermal rotational distribution of H+ 3 . Astrophys. J. 613, 349–354. Raynaud, E., Lellouch, E., Maillard, J.-P., Gladstone, G.R., Waite Jr., J.H., Bézard, B., Drossart, P., Fouchet, T., 2004. Spectro-imaging observations of Jupiter’s 2-µm auroral emission. I. H+ 3 distribution and temperature. Icarus 171, 133–152. Rego, D., Achilleos, N., Stallard, T., Miller, S., Prangé, R., Dougherty, M., Joseph, R.D., 1999. Supersonic winds in Jupiter’s aurorae. Nature 399, 121– 124. Rego, D., Miller, S., Achilleos, N., Prangé, R., Joseph, R.D., 2000. Latitudinal profiles of the jovian IR emissions of H+ 3 at 4 µm with the NASA Infrared Telescope Facility: Energy inputs and thermal balance. Icarus 147, 366– 385. Seiff, A., Kirk, D.B., Knight, T.C.D., Young, L.A., Milos, F.S., Venkatapathy, E., Mihalov, J.D., Blanchard, R.C., Young, R.E., Schubert, G., 1997. Thermal structure of Jupiter’s upper atmosphere derived from the Galileo probe. Science 276, 102–104. Smith, C.G.A., Miller, S., Aylward, A., 2005. Magnetospheric energy input into the upper atmospheres of giant planets. Ann. Geophys. 23, 1943–1947. Sommeria, J., ben Jaffel, L., Prangé, R., 1995. On the existence of supersonic jets in the upper atmosphere of Jupiter. Icarus 118, 2–24.
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Southwood, D.J., Kivelson, M.G., 2001. A new perspective on the influence of the solar wind on the jovian magnetosphere. J. Geophys. Res. 106, 6123– 6130. Stallard, T., Miller, S., Millward, G., Joseph, R.D., 2001. On the dynamics of the jovian ionosphere and thermosphere. I. The measurement of ion winds. Icarus 154, 475–491. Stallard, T., Miller, S., Millward, G., Joseph, R.D., 2002. On the dynamics of the jovian ionosphere and thermosphere. II. The measurement of H+ 3 vibrational temperature, column density and total emission. Icarus 156, 498–514. Strobel, D.F., Smith, G.R., 1973. On the temperature of the jovian thermosphere. J. Atmos. Sci. 30, 718–725. Vasyliunas, V.M., Song, P., 2005. Meaning of ionospheric Joule heating. J. Geophys. Res. 110, 2301–2308. Waite Jr., J.H., Cravens, T., Kozyra, J., Nagy, A.F., Atreya, S.K., 1983. Electron precipitation and related aeronomy of the jovian thermosphere and ionosphere. J. Geophys. Res. 88, 6143–6163. Waite Jr., J.H., Gladstone, G.R., Lewis, W.S., Drossart, P., Cravens, T.E., Maurellis, A.N., Mauk, B.H., Miller, S., 1997. Equatorial X-ray emissions: Implications for Jupiter’s high exospheric temperatures. Science 267, 104– 108. Yelle, R.V., Miller, S., 2004. Jupiter’s upper atmosphere. In: Bagenal, F., Dowling, T., McKinnon, W. (Eds.), Jupiter: The Planet, Satellites and Magnetosphere. Cambridge Univ. Press, Cambridge, UK, pp. 185–218. Young, L.A., Yelle, R.V., Young, R., Seiff, A., Kirk, D.B., 1997. Gravity waves in Jupiter’s thermosphere. Science 376, 108–111. Young, L.A., Yelle, R.V., Young, R., Seiff, A., Kirk, D.B., 2005. Gravity waves in Jupiter’s stratosphere, as measured by the Galileo ASI experiment. Icarus 173, 185–199.
Estimated energy balance in the jovian upper atmosphere during an auroral heating event Henrik Melin a , Steve Miller a,∗ , Tom Stallard a , Chris Smith a , Denis Grodent b a Atmospheric Physics Laboratory, Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK b Laboratoire de Physique Atmosphérique et Planétaire, Institut d’Astrophysique et de Géophysique, Université de Liège,
Avenue de Cointe 5, B-4000 Liège, Belgium Received 13 June 2005; revised 28 October 2005 Available online 22 December 2005
Abstract We present an analysis of a series of observations of the auroral/polar regions of Jupiter, carried out between September 8 and 11, 1998, making use of the high-resolution spectrometer, CSHELL, on the NASA InfraRed Telescope Facility (IRTF), Mauna Kea, Hawaii; these observations spanned an “auroral heating event.” This analysis combines the measured line intensities and ion velocities with a one-dimensional model vertical profile of the jovian thermosphere/ionosphere. We compute the model line intensities both assuming local thermodynamic equilibrium (LTE) and, relaxing this condition (non-LTE), through detailed balance calculations, in order to compare with the observations. Taking the model parameters derived, we calculate the changes in heating rate required to account for the modelled temperature profiles that are consistent with the measured line intensities. We compute the electron precipitation rates required to give the modelled ion densities that are consistent with the measured line intensities, and derive the corresponding Pedersen conductivities. We compute the changes in heating due to Joule heating and ion drag derived from the measured ion velocities, and modelled conductivities, making use of ion-neutral coupling coefficients derived from a 3-D global circulation model. Finally, we compute the cooling due to the downward conduction of heat and the radiation-to-space from the H+ 3 molecular ion and hydrocarbons. Comparison of the various heating and cooling terms enables us to investigate the balance of energy inputs into the auroral/polar atmosphere. Increases in Joule heating and ion drag are sufficient to explain the observed heating of the atmosphere; increased particle precipitation makes only a minor heating contribution. But local cooling effects—predominantly radiation-to-space—are shown to be too inefficient to allow the atmosphere to relax back to pre-event thermal conditions. Thus we conclude that this event provides observational, i.e. empirical, evidence that heat must be transported away from the auroral/polar regions by thermally or mechanically driven winds. © 2005 Elsevier Inc. All rights reserved. Keywords: Aurorae; Ionospheres; Jupiter, atmosphere; Jupiter, infrared
1. Introduction For over three decades there has been considerable debate about the energy balance of the upper atmosphere of the giant planets: the basic problem is that observed exospheric temperatures at mid-to-low latitudes are far higher than can be produced by solar Extreme Ultraviolet (EUV) heating alone (Strobel and Smith, 1973; Yelle and Miller, 2004). The discovery of Jupiter’s aurorae (Broadfoot et al., 1979) focused attention on the high rates of particle precipitation required to produce these im* Corresponding author. Fax: +44 (0) 20 7679 9024.
E-mail address: [email protected] (S. Miller). 0019-1035/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2005.11.004
pressive displays (Waite et al., 1983). Plasma flows measured by Voyager (Evitiar and Barbosa, 1984) indicated that electric fields would be imposed on the jovian ionosphere, which could drive currents that would produce Joule heating. Waite et al. (1983) proposed that the heating of the auroral regions resulting from particle precipitation and Joule heating could drive meridional winds that would transport energy to lower latitudes. Sommeria et al. (1995) tried to account for high H Lyman-α UV emission at the equator (McGrath et al., 1989) by invoking energy-transporting winds flowing around Jupiter’s auroral oval, which could be deviated meridionally, although the high velocities their model required—∼20 km s−1 —seem unfeasibly large Yelle and Miller (2004). More recently, heating due to
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breaking gravity waves has been proposed as a global source of energy to produce the high exospheric temperatures observed (Young et al., 1997). But there appears to be considerable controversy over whether gravity waves heat (Young et al., 2005), have little effect (Matcheva and Strobel, 1999) or even cool the upper atmosphere (Hickey et al., 2000). In considering the energy balance of the atmosphere, account also has to be taken of loss mechanisms. Energy can be lost in the upper atmosphere through downward conduction, transferring the energy to lower altitudes (e.g., Achilleos et al., 1998; Grodent et al., 2001; Bougher et al., 2005). Since the detection of infrared emission H+ 3 in the jovian auroral regions (Drossart et al., 1989) and from the body of the planet (Ballester et al., 1994) it has been clear that radiation to space by this ion—which we denote as E(H+ 3 )—is another important coolant above the jovian homopause (Miller et al., 1994, 1997; Lam et al., 1997; Waite et al., 1997). (NB the homopause— defined as the level above which convective mixing ceases to be important—is generally located around the 2 µbar pressure level on Jupiter.) Around and below the homopause, infrared colling by hydrocarbons is extremely important (Drossart et al., 1993). The measurement of H+ 3 ro-vibrational emission lines has proven extremely important in determining the temperature structure of the jovian upper atmosphere and the degree of ionisation there (Drossart et al., 1989; Lam et al., 1997; Miller et al., 1990, 1997, 2000; Oka and Geballe, 1990; Stallard et al., 2002). The extent to which H+ 3 vibrational levels can be considered to be in local thermal equilibrium (LTE) has been investigated by Miller et al. (1990), Kim et al. (1992), and Stallard et al. (2002). Miller et al. (1990) measured lines from both the first and second vibrationally excited states and concluded that the ratio of vibrational level populations was approximately thermal. But the modelling study of Kim et al. (1992) showed that even if this were the case, the high rate of radiative de-excitation of vibrationally excited levels meant that they were underpopulated compared with the ground state at altitudes above 650 km, the ionisation peak in their model. We have recently carried out a modelling study, which combines the vertical profiles produced by the one-dimensional, two-stream, model of Jupiter’s auroral/polar regions due to Grodent et al. (2001) with the detailed balance calculations of Oka and Epp (2004), to examine the effects on H+ 3 in conditions of non-LTE (Melin et al., 2005; hereafter Paper I). Paper I confirmed that the assumption that H+ 3 is in local thermodynamic equilibrium (LTE) is not valid in all parts of the upper atmosphere of Jupiter, by comparing the H+ 3 spectra in the K (Raynaud et al., 2004) and L (Stallard et al., 2001, 2002) windows with the modelled line intensities. It found that only the non-LTE model could produce consistent intensities for a given atmospheric temperature profile. This paper is based on the results of Paper I to examine an auroral heating event observed by Stallard et al. (2001, 2002) between the 8th and 11th of September 1998. That study made use of the facility high-resolution infrared echelle spectrometer, CSHELL, on NASA Infrared Telescope Facility, to measure ion velocities and H+ 3 temperatures and column densities across the
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auroral/polar region. During this event the line-of-sight velocity of the auroral electrojet doubled, from 0.5 to 1.0 km s−1 . At the same time, the H+ 3 temperature—derived assuming a thin shell source in LTE—rose from 940 to 1065 K and the + 16 column density of H+ 3 , N (H3 ), increased from 1.55 × 10 to 16 −2 1.80 × 10 m (Stallard et al., 2002; NB the column densities in that paper should be scaled up by (2π)1/2 ). The simultaneous increase of all the parameters they studied indicates that energy was being injected into the auroral region. We now combine the results of Paper I with density profiles from Grodent et al. (2001), to estimate the changes in heating/cooling that would have occurred to Jupiter’s upper atmosphere during the auroral event of September 8–11, 1998 (Stallard et al., 2001, 2002). We also make use of parameters derived from the Jovian Ionospheric Model (JIM: Achilleos et al., 1998). This paper aims to examine what the main energy sources are and where the energy is deposited. At present, there is no fully self-consistent model of the jovian upper atmosphere. JIM (Achilleos et al., 1998) is designed to simulate the dynamics, particle precipitation and time-dependent chemistry of the jovian system. It is not able to model changes in the atmospheric thermal profile of Jupiter, due to the changing energy balance, self-consistently, however, because its original thermal profile was input at the initiation of the model, rather than derived as a result of equilibration. NB in 1998, no one had an adequate inventory of the energy inputs into the jovian upper atmosphere, nor of the mechanisms for distributing energy, and insolation was known to produce exospheric temperatures much lower than those measured—see (Strobel and Smith, 1973) and (Yelle and Miller, 2004). So it was hardly surprising that this technique was necessary. As far as 1-D vertical models go, that of Grodent et al. (2001) is best fitted to the measured properties of the jovian upper atmospheres. But it cannot simulate energy inputs such as Joule heating and ion drag—which depend on essentially horizontal motions—in a totally self-consistent way. So an approach that involves a combination of the JIM and Grodent models can be insightful, making use of the best features of both. Later in this paper, we compare our semi-empirical results with those of the Jupiter Thermospheric Global Circulation Model (JTGCM) of Bougher et al. (2005), which makes direct use of the Grodent et al. (2001) model auroral atmosphere, and is more (but not fully) capable of self-consistent simulations. 2. Magnetosphere–ionosphere–thermosphere coupling in the jovian system The input of energy from Jupiter’s enormous magnetosphere into the planet’s upper atmosphere is absolutely critical to understanding the balance of energy. Hill (1979) proposed a mechanism by which the upper atmosphere of Jupiter is coupled, magnetically, with the equatorial plasma sheet in the magnetosphere, which results from the volcanic activity of the moon Io. The plasma sheet corotates with the magnetosphere close to the planet. But further away from the planet corotation breaks down, setting up a current system through the plasma sheet, which follows the magnetic field lines down onto the planet
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and closes in the ionosphere. This closure results from the imposition of an equatorward electric field, which we denote Eeqw in the frame of reference that corotates with Jupiter (the planetary reference frame, PRF). Charged particles—kiloelectron volt electrons—are accelerated from the plasma sheet onto the planet, ionising the upper atmosphere and producing bright auroral emission at wavelengths from the far ultraviolet to the infrared. This process produces far greater precipitation than is observed on Earth and results in a net heating rate in the upper atmosphere of around 1013 to 1014 W (Waite et al., 1983; Clarke et al., 1989). Eeqw drives an ionospheric Pedersen current equatorward to close the magnetosphere–ionosphere coupling current system. The lag in corotation of the plasma sheet gives rise to an ion wind in the (magnetically linked) ionosphere—the electrojet, as observed by Rego et al. (1999) and Stallard et al. (2001) and described theoretically by Cowley and Bunce (2001) and Hill (2001). In the PRF, the ion wind velocity is given by the Hall drift formula: vion = Eeqw × BJ /BJ2 ,
(1)
where BJ is the strength of the jovian magnetic field in the auroral regions; we assume BJ to be vertical. Eeqw is the equatorward electric field imposed on the ionosphere by the magnetosphere as a resulting from the corotation enforcement mechanism. The resulting ion winds are westwards in both hemispheres in the PRF. Westward flowing ions collide with the neutral thermosphere. Thus the magnetospheric energy is converted to heat via Joule heating and by ion drag (Miller et al., 2000, 2005; Vasyliunas and Song, 2005; Smith et al., 2005) through momentum transfer to the neutrals. Note that in the inertial— Sun–Jupiter—reference frame these winds are still eastwards, but sub-corotational, and represent an upper atmosphere lag to corotation. In what follows, however, we will use the PRF. This is because our study concerns the input of energy from the magnetosphere into the planet, rather than the driving of the magnetosphere by the transfer of rotational energy from the planet. 3. Scaling the Grodent et al. (2001) temperature profile The observed temperatures of Stallard et al. (2002) are derived from the ratio of intensities in the hotband R(3, 4+ ) and the fundamental Q(1, 0− ) H+ 3 lines, using the linelist calculated by Neale et al. (1996). We shall use this intensity ratio to parameterise the Grodent et al. (2001) temperature profile such that it can be described by a single number, which, in turn, can be related to the measured line ratio. We define a scaling factor, NG , so that the temperature, Ti , at each model level i becomes: Ti (NG ) = TiG − T0 × NG + T0 , (2) where TiG is the original temperature profile at level i and T0 is the temperature at, or just below, the homopause; Grodent et al. (2001) give T0 = 161 K. The jovian homopause temperature is thus kept constant regardless of NG . This is a reasonable assumption since it is known to be fairly constant over time (e.g., Hubbard et al., 1995; Seiff et al., 1997). The physical reason
Fig. 1. The temperature profile of Grodent et al. (2001) scaled by NG = 0.8, 0.9, 1.0, 1.1, and 1.2 as defined in Eq. (2).
for this was shown by Drossart et al. (1993), who demonstrated that T0 is controlled by radiation to space by hydrocarbons at, or just below, the homopause. Equation (2) represents a first-order, linear, approximation to model the response of the jovian thermosphere to varying energy inputs. Comparison of the cases of discrete and diffuse auroral precipitation modelled in Grodent et al. (2001) shows that this is a reasonable approach. More detailed modelling, which would require explicit and iterative recalculation of the Grodent et al. (2001) profiles, ion concentrations and the resulting H+ 3 line intensities for a range of particle precipitation fluxes and energies, and the simulation of Joule/ion-drag heating, is beyond the scope of this study. We shall return to this issue in the discussion and conclusions. The temperature profiles for different NG ’s are shown in Fig. 1. Using this scaling factor the intensity of R(3, 4+ ) and Q(1, 0− ) at a particular NG can be modelled through the Grodent et al. (2001) atmosphere, as explained in Paper I. The ratio of the integrated intensities of the two lines observed by Stallard et al. (2002) for a range of NG can be seen in Fig. 2. From Fig. 2 the line ratio can be related to the scaling factor, NG , which itself defines a temperature profile as per Eq. (2). The hotband/fundamental line ratio is 0.014 in the beginning of the auroral event, on September 8, and 0.022 in the end, on September 11 (Stallard et al., 2001). This gives NG = 0.85 at the beginning of the event and 1.02 at the end of the event for the LTE scenario. For the non-LTE scenario is NG = 0.97 and 1.17. The corresponding scaled temperature profiles are shown in Fig. 3. 4. Energy required to heat the auroral region The additional energy, Q, needed to heat the mixture of gas that makes up the thermosphere can be calculated using the following formula: Q = cp T ,
(3)
Jovian upper atmosphere energy balance
Fig. 2. Intensity ratio of the two lines observed by Stallard et al. (2002) as a function of the scaling factor, NG , for both LTE and non-LTE scenarios.
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Fig. 4. The difference between the start and end temperature profiles of the event.
In what follows we take the average increase in net heating rate to be given by [dQ/dt]ave = Q/t,
(4)
2.5 × 105
where t is s, calculated from the difference in median UT times between the observations on September 8 and 11, 1998. This gives a column-integrated change in the net heating rate of 65 mW m−2 for the LTE case and 73 mW m−2 for the non-LTE case. These net heating rates are not radically different. Paper I showed that the H+ 3 density was overestimated in Grodent et al. (2001) for both the LTE and non-LTE cases. But only in the case of the non-LTE profiles was it possible to account consistently for the relative intensities observed in the vibrationally excited levels. In what follows, therefore, we shall now only consider the non-LTE case. Fig. 3. Temperature profiles at the start and at the end of the event observed by Stallard et al. (2002) for both LTE and non-LTE. The profiles are derived from the observed line ratio and scaled as the Grodent et al. (2001) temperature profile. The arrow shows the direction of the event.
where cp is the total heat capacity (in J K−1 m−3 ) of the gas mixture and T is the increase in temperature. Note that Q is the local additional heat required, with units of J m−3 . Since the predominant species in the upper atmosphere are H, H2 , and He, only these species have been considered when calculating the heat capacity. The temperature increase during the event for each scenario can be seen in Fig. 4. From these, we can calculate how much heat is required to produce the temperature increase at each altitude, and as well as the total change in column heating. Note that this represents the net heating additional to that prevailing on September 8; for the purposes of this study, we initially assume that the jovian upper atmosphere was in steady state on September 8, prior to the auroral heating event. In Section 9, we present our calculations of the total heating and cooling rates, which show that this assumption is justified.
5. Derivation of electron precipitation rates and Pedersen conductivity In principle, it is possible to vary inputs of precipitating particles in the Grodent et al. (2001) model to produce different heating rates and ion densities. What we present here, however, is a less demanding technique of estimating precipitation rates from measured line intensities. Millward et al. (2002) modelled the response of auroral H+ 3 column density to different precipitation energies, using JIM (Achilleos et al., 1998). H+ 3 in the auroral regions is produced via the following reactions: H2 + e∗ / hν → H+ 2 + e[+e],
+ H 2 + H+ 2 → H3 + H.
(5)
For 10 keV electrons, Millward et al. (2002) found the empirical relationship log10 N H+ (6) 3 = 0.435 log10 Fe + 12.28, where Fe is the incident flux of auroral electrons in ergs s−1 cm−2 (mW m−2 ) and N is the column density of H+ 3 in cm−2 . Of note here is that the H+ 3 column density does not
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Fig. 5. Left panel: H+ 3 number density profile on September 8, at the start of the event. Right panel: Increase in H+ 3 number density profile between September 8 and September 11, at the end of the event. Both panels are for the non-LTE profiles.
increase linearly with electron flux, but more slowly. This is because the overall density is controlled chiefly by dissociative recombination with electrons: H3 + + e → H2 + H/H + H + H.
(7)
The rate at which this occurs clearly depends on the electron density, itself a measure of the level of ionisation of the atmosphere. Equation (6) can be written in the form: + log10 N H+ 3 − log10 N0 H3 = 0.435[log10 Fe − log10 F0 ],
(8)
where N0 (H+ 3 ) and F0 are the values in Grodent et al. (2001): 12 −2 F0 = 110 ergs s−1 cm−2 ; N0 (H+ 3 ) = 18 × 10 cm . Note that in Eq. (8), we take the same scaling of the log10 N (H+ 3 ) production rate irrespective of individual electron energy. For the non-LTE case, Paper I showed that the H+ 3 column density was overestimated by a factor of ∼3, depending upon the exact intensity of the lines being modelled. To account for this, we scale the local H+ 3 density in the Grodent profile by a factor, which is constant with respect to altitude, in order to produced the measured Q(1, 0− ) line intensity for September 8 and 11 for the non-LTE case. This factor is 36.4% for September 8 and 38.1% for September 11. This altitude independent scaling is consistent with the first-order, linear, approximation to scaling the temperature profile implied in Eq. (2). The scaled H+ 3 densities are shown in Fig. 5 as a function of altitude. These densities are required to calculate both the conductivity of the ionosphere and the energy input from precipitating electrons. The column densities resulting from the scaled profiles are 8.74 × 1016 m−2 for September 8 and 9.14 × 1016 m−2 for September 11. Using Eq. (8), the precipitation fluxes required to produce the observed line intensities are 10.8 mW m−2 on September 8 and 12.0 mW m−2 on September 11, which gives an increase in auroral precipitation of 1.2 mW m−2 . This is a small (∼10%) increase in the required precipitation, and leads to the conclusion that our analysis is
Fig. 6. As Fig. 5 for the Pedersen conductivity.
not overly sensitive to the exact value of the scaling in Eq. (8). Assuming a linear increase over the period from September 8 to 11, the average increase in heating from particle precipitation would be 0.6 mW m−2 . The Pedersen conductivity in the jovian atmosphere is almost entirely due to the positive ions. Then ΣP , is given by (Luhmann, 1995) 2 ΣP = N e2 νin mi νin (9) + Ωi2 , where νin is the collision frequency between the ion and the neutrals and Ωi is the gyrofrequency of the charged particle with number density N and mass mi . e is the elemental charge. In our case the relevant charged particle is H+ 3 . The relevant collision frequency is taken to be that of Geiss and Buergi (1986), which is used in JIM (Achilleos et al., 1998). Note that the gyrofrequency depends on the value of BJ , which we take as 10−3 T in the northern auroral region, consistent with the value used in JIM studies (see Millward et al., 2005). The resulting conductivity, as a function of altitude, can be seen in Fig. 6. The integrated conductivity is 0.44 mhos in the beginning of the event and 0.46 mhos at the end. 6. Joule heating and ion drag Smith et al. (2005) have shown that the total energy that the magnetosphere puts into the upper atmosphere resulting from the equatorward electric field, Eeqw is given by 2 2 ΣP + k(1 − k)Eeqw ΣP . HMag = (1 − k)2 Eeqw
(10)
The first term on the right-hand side represents Joule heating. The second term is the kinetic energy input due to ion drag, which must ultimately dissipate as heat. k is the ratio between the velocity of the westward neutral wind in the auroral oval and the corresponding ion wind, discussed by Cowley and Bunce (2001) and Millward et al. (2005): note that 0 < k < 1. Taking BJ = 10−3 T, and remembering that Eeqw = vion BJ , means that an observed value of vion = 1 km s−1 corresponds to Eeqw = 1 V m−1 and so on. As previously stated, the line-of-sight ion velocity in the auroral oval increases from 0.5 km s−1 at the beginning to
Jovian upper atmosphere energy balance
261
Fig. 7. As Fig. 5 for Joule heating and ion drag.
1.0 km s−1 at the end of the event. The value of k is not known observationally. But JIM gives values of 0.5–0.7 at the ion peak (Millward et al., 2005), and we take the lower value of 0.5 in this calculation. (It follows from Eq. (10) that taking k = 0.5 results in the Joule heating and ion drag making equal contributions to the heating rate.) The observed line-of-sight (l.o.s.) velocities of 0.5 and 1.0 km s−1 would translate to Eeq = 0.5 and 1.0 V m−1 , respectively. We assume that the electric field is height-independent. With the increases in conductivity and ion velocity noted above, Eq. (10) can be used to calculate the increase in local heating rate. Using the l.o.s. velocities, the column integrated heating rate due to Joule heating and ion drag is 55 mW m−2 on September 8 and 229 mW m−1 on September 11, giving an increase of 174 mW m−2 . The l.o.s. velocities are minimum values for the true ion velocity, however. Depending on the geometry of the electrojet, the true ion velocity in the auroral electrojet may be as high as 0.75 km s−1 on September 8 and 1.5 km s−1 on September 11. Stallard et al. (2002) found that observations made on September 8 and 11 with a central meridian longitude λIII = 155◦ to 160◦ (jovian System III longitude) showed the electrojet most clearly. For these observations, the slit colatitude was ∼20◦ , and the angle of the electrojet to the XZ plane was between 2◦ and 7◦ . At the time, the sub-Earth latitude of Jupiter was +3◦ . For the northern hemisphere, the geometry resulting from these angles require the l.o.s velocities to be increased by 10%, to give 0.55 km s−1 on September 8 and 1.1 km s−1 on September 11. Using these velocities, heating rates due to Joule heating and ion drag for the two dates are shown in Fig. 7. The column integrated heating rates are 67 and 277 mW m−2 , respectively, giving an increase of 210 mW m−2 . Assuming that the heating rate increases linearly during the September 8 to 11 event, then the average increase in heating rate during the event is between 87 mW m−2 , based on the l.o.s. velocities, and 105 mW m−2 , after l.o.s. correction. In what follows we take the average increase in heating rate as 105 mW m−2 , and show that this is sufficient to produce the observed temperature increase.
Fig. 8. Heating and cooling due conduction on September 8 (full line) and September 11 (dashed line).
7. Downward heat conduction The downward conduction of heat is given by Hcond = λ dT /dz,
(11)
where dT /dz is the temperature gradient, where the thermal conductivity λ is given by λ = AT s mW m−2 (K/m)−1
(12)
with A = 2.5 and s = 0.75. From Fig. 3, for the non-LTE case we can see that the exospheric temperature is 1280 K at the start of our auroral event and 1500 K at the end. The homopause temperature remains constant at 161 K. The conducted heat flux as a function of altitude is shown in Fig. 8. To calculate the overall effect, we approximate Eq. (11): Hcond = λT /z,
(13)
where T and z refer to the difference between the exospheric and homopause temperatures and altitudes, respectively. Equation (12) is approximated by taking T as the mean temperature between the homopause and the exosphere. Hcond represents the rate at which heat (eventually) flows through the lower boundary of the atmospheric region under consideration to be lost to the lower atmosphere or to space. These approximations give λ = 0.35 and 0.39 mW m−2 (K/m)−1 at the start and end of the auroral event, respectively, while T /z is similarly 0.75 × 10−3 and 0.90 × 10−3 K/m. These figures give Hcond = 0.26 and 0.35 mW m−2 at the start and the end, respectively, which—in turn—give Hcond = 0.09 mW m−2 between the start and the end of the auroral event. If we assume that this change is linear with time during the event, the average value of Hcond = 0.045 mW m−2 . A somewhat larger value of Hcond = 0.06 mW m−2 is derived if one only considers the atmosphere at and below the peak in Joule/ion drag heating. Either way, these cooling rates are very small.
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Fig. 9. As Fig. 5 for radiation to space by H+ 3.
Fig. 10. As Fig. 5 for radiation to space by hydrocarbons.
8. Energy lost through infrared cooling
Table 1 Heating and cooling rates
Above the homopause, which occurs for Jupiter around the 2 µbar pressure level, infrared emission from the H+ 3 molecular ion is known to be the main coolant in the jovian upper atmosphere (Miller et al., 1994, 1997; Lam et al., 1997; Waite et al., 1997), other than downward conduction of heat to the homopause. A study by Rego et al. (2000) showed that energy inputs due to particle precipitation were approximately + balanced by H+ 3 emission to space, denoted as E(H3 ) (see Lam et al., 1997). Bougher et al. (2005) have termed this effect the H+ 3 thermostat. In considering the September 8–11, 1998, auroral event it is therefore important to take this effect into account. Since more than 90% of the H+ 3 emission in Jupiter’s upper atmosphere arises from the ν2 vibrational level (Miller et al., 1990; Grodent et al., 2001), we assume that the overall attenuation of E(H+ 3 ) due to non-LTE effects can be approximated, as a function of altitude, by the population of this level. The H+ 3 emission as a function of altitude is plotted in Fig. 9, allowing for the scaling of the H+ 3 density profile in the auroral model of Grodent et al. (2001). We calculate that the column-integrated −2 (2π sr)−1 on Sepvalues of E(H+ 3 ) are 5.1 and 10.0 mW m tember 8 and 11, respectively. This gives an overall change the energy lost through H+ 3 emission, between September 8 and 11, of 4.9 mW m−2 . If we assume the change to be linear during −2 the period, the average change in E(H+ 3 ) is 2.5 mW m , about four times the increase in particle precipitation, and 50 times the change in downward conduction. Below the homopause, Drossart et al. (1993) showed that infrared cooling to space by hydrocarbons plays a key role in controlling the thermal structure of Jupiter’s atmosphere. The most important hydrocarbons are methane and ethyne (Bougher et al., 2005; Grodent et al., 2001). We adopt the Drossart et al. (1993) formulation for this, using the vertical density profiles for CH4 and C2 H2 in the Grodent et al. (2001) model. The local cooling rates for these two gases combined are shown in Fig. 10 for September 8 and 11. We calculate that the columnintegrated values of the combined hydrocarbon cooling rate are 65.5 and 103.3 mW m−2 (2π sr)−1 on September 8 and 11, re-
Heating/cooling term Joule heating and ion drag Particle precipitation Downward conduction E(H+ 3 ) cooling Hydrocarbon cooling Net heating rate
September 8 67.0 mW m−2
10.8 mW m−2 (−)0.3 mW m−2 (−)5.1 mW m−2 (−)65.5 mW m−2 7.4 mW m−2
September 11 277.0 mW m−2 12.0 mW m−2 (−)0.4 mW m−2 (−)10.0 mW m−2 (−)103.3 mW m−2 175.3 mW m−2
spectively. (NB CH4 accounts for ∼80% of this.) This gives the change in the energy lost through hydrocarbon emission, between September 8 and 11, as 37.8 mW m−2 . Once more assuming the change to be linear during the period, the average change in hydrocarbon cooling is 18.9 mW m−2 , showing the importance of this effect for cooling the lower reaches of the upper atmosphere. 9. Discussion Table 1 summarises the heating and cooling rates that we have calculated. Our analysis of the heating and cooling terms of September 8 shows that we have rates of 67.0 mW m−2 due to Joule heating and ion drag, and 10.8 mW m−2 due to particle precipitation, making a total of 77.8 mW m−2 . This is balanced by downward convection at 0.3 mW m−2 , H+ 3 cooling at 5.1 mW m−2 and hydrocarbon cooling at 65.5 mW m−2 , making 70.4 mW m−2 . There is a net heating rate of just 7.4 mW m−2 , which indicates that the atmosphere is close to thermal balance. This might be expected, since the value of NG is 0.97, and the Grodent et al. (2001) profile was based on an equilibrated atmosphere. For September 11, we have rates of 277.0 mW m−2 due to Joule heating and ion drag, and 12.0 mW m−2 due to particle precipitation, making a total of 289.0 mW m−2 . Downward −2 and convection is 0.3 mW m−2 , H+ 3 cooling is 10.0 mW m −2 hydrocarbon cooling is 103.3 mW m , making 113.7 mW m−2 in total, and a net heating rate of 175.3 mW m−2 . This shows that even if the atmospheric heating and cooling rates were
Jovian upper atmosphere energy balance
Table 2 Average changes in heating and cooling rates Heating/cooling term
Amount (mW m−2 )
Required net increased heating rate (non-LTE case)
73
Average increase in Joule heating and ion drag Average increase in particle precipitation Average increase in downward conduction Average increase in E(H+ 3 ) cooling Average increase in hydrocarbon cooling
105 0.6 (−)0.04–0.06 (−)2.5 (−)18.9
Calculated net increased heating rate available
84.1
Fig. 11. Net average changes in energy inputs in the jovian atmosphere during the auroral heating event. This is compared with the vertical profile of the net energy required (solid line) to produce the modelled increase in temperature.
more or less balanced on September 8, considerable heating was occurring on September 11. The value of NG for September 11 is 1.17, indicating an atmosphere very much out of balance. Table 2 summarises the overall changes in heating/cooling rates derived from our analysis. The analysis of the auroral heating event observed by Stallard et al. (2001) gives us an insight to the energy balance in the jovian auroral/polar upper atmosphere. We require an average net increase in heating of 73 mW m−2 to account for the changes in temperature derived from the measured line intensities and the Grodent model, if we take the non-LTE case. The combined Joule and ion drag heating provides the atmosphere with by far the largest contribution to this energy. In turn, this energy is primarily created by the increase in the electric field imposed on the ionosphere by coupling to the middle magnetosphere, which is manifested by a doubling in the ion velocity in the auroral oval. The energy added by particle precipitation is smaller by ∼2 orders of magnitude. The main losses are through H+ 3 radiation, above the homopause, and hydrocarbons, below. Overall, energy is being input into the atmosphere at a rate of 84.1 mW m−2 , in fairly good agreement with the rate required (73 mW m−2 ). Fig. 11 compares the increased heating rate due to particle precipitation, Joule heating and ion drag, minus the increase in H+ 3 and hydrocarbon emission, with the required increase
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in heating rate, as a function of altitude. It is clear that not all of the energy is being deposited where it is required to heat the atmosphere. In fact, Joule heating and ion drag deposit energy about 150 km higher than where it is required. This altitude corresponds to the peak in the H+ 3 ion density, which— in turn—corresponds to the peak in the Pedersen conductivity. Heat is thus conducted downward, with part of the energy reradiated by hydrocarbons. Above ∼1000 km there appears to be a shortfall in the increase in heating rate required to produce the temperatures modelled from scaling the Grodent et al. (2001) profile. This shortfall may be made good by advection or by a slowing in the rate at which energy is conducted downwards. Our figures for column heating and cooling may be compared with those published by Bougher et al. (2005) for their Case 2 run (their Table 3). All the terms we calculate are comparable in magnitude to theirs, showing that the Bougher et al. (2005) Case 2 is fairly representative of actual jovian conditions. [NB there appear to be errors in the axis labelling of Figs. 11 and 13 of their paper, which make their results seem inconsistent with those of Grodent et al. (2001) and this paper.] Bougher et al. Case 2 run involved scaling down the inputs due to Joule heating, ion drag (which they include in Joule heating) and particle precipitation to avoid very large temperatures; without the scaling down, these reached 1950–2450 K in the auroral ovals at the H+ 3 concentration peak, much higher than any ever measured, and 2800–3100 K at the top of their model. Their preferred scaling factor was 30%. In their paper, Bougher et al. (2005) suggested that a convection electric field smaller than that deduced by Voyager should be used. But it may be that their use of the Grodent et al. (2001) H+ 3 concentrations, which are three times those compatible with the analysis in Paper I, are responsible for producing a higher value of ΣP . As can be seen from Eq. (10), this would naturally lead to the Joule heating and ion drag terms being too large, for a given electric field, and explain the need for scaling to produce a reasonable fit to observations. 10. Conclusions In following through this auroral event observed by Stallard et al. (2001, 2002) during September 8–11, 1998, we have been able to deduce a considerable amount about the energy balance in the auroral/polar regions. Particle precipitation clearly cannot account for the increased temperatures observed. Instead the heating required comes mainly from a doubling of the equatorward electric field imposed on the ionosphere by the magnetosphere, as implied by the ion velocities. This, in turn, results both in higher currents flowing through the upper atmosphere and in the transfer of additional energy from westwards Hall drifting ions to the neutrals, which eventually gets converted into heat. Since local cooling terms—downward conduction of heat and H+ 3 and hydrocarbon radiation-to-space—total about 20% of the increased heating terms, the atmosphere is heated considerably during the event. As previously discussed, ionospheric electric fields result from a lag to corotation in the equatorial plasma sheet
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(Hill, 1979). Our derived increases in Eeqw indicate an increased lag to corotation (Stallard et al., 2002). Cowley and Bunce (2001) and Southwood and Kivelson (2001) have both suggested that this may occur as a result of a falling off of the ram pressure on Jupiter’s magnetosphere due to a rarefaction in the solar wind, although jovian auroral emission is intrinsically variable. The increased temperature in the auroral/polar region observed by Stallard et al. (2002) has—at some point—to be counteracted by cooling, if the thermospheric temperature is not to rise inexorably, particularly given the large excess heating rate deduced for September 11. We have demonstrated that the main mechanism for such cooling is through H+ 3 and hydrocarbon emission, with a little due to downward conduction. These terms would take over if the conditions of Joule heating, ion drag and particle precipitation were suddenly to return to those of September 8, and the atmosphere would then cool again. But—at an average total cooling rate of 21.5 mW m−2 —even if the precipitation, Joule heating and ion drag rates returned instantaneously to those of September 8, it would take between 10 to 15 days to bring the temperature down again from that seen on September 11 to that seen on September 8. This time is comparable with expected solar wind cycles of ∼30 days, during which further heating events are likely. The only conclusion from the discussion of the heating/ cooling rates for the individual days and the change in rates is that the auroral/polar regions cannot be cooled by local mechanisms alone. Increased temperatures must therefore result in (increased) equatorward winds, which transport energy to lower latitudes, as suggested by Waite et al. (1983) over two decades ago. Our current study indicates that this wind-driven process may be particularly important when atmospheric conditions are changing. Recent modelling studies—either under conditions of high heating (Bougher et al., 2005) or changing conditions (Millward et al., 2005)—have shown that thermally driven winds are indeed produced. The offset between the magnetic and rotational poles on Jupiter implies that the ion winds flowing around the auroral oval have a meridional component at some longitudes, so driving hot neutrals equatorwards. Models (Bougher et al., 2005; Millward et al., 2005) show that at least part of the meridional wind system generated is due to the mechanical acceleration of neutrals by ion drag. Our observationally based study now provides an empirical measure of how much of the energy generated in the auroral/polar regions may be distributed equatorward, contributing to the high equatorial exospheric temperatures that are measured on Jupiter. Acknowledgments The UK Engineering and Physical Sciences Research Council are thanked for a studentship for H.M.; the Particle Physics and Astronomy Research Council are thanked for supporting the 1998 IRTF observations of Stallard et al. (2001, 2002). Miller and Stallard were visiting astronomers on the IRTF, which is operated on behalf of NASA by the Institute for As-
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