On the Dynamics of the Jovian Ionosphere and Thermosphere

On the Dynamics of the Jovian Ionosphere and Thermosphere

Icarus 160, 95–107 (2002) doi:10.1006/icar.2002.6951 On the Dynamics of the Jovian Ionosphere and Thermosphere III. The Modelling of Auroral Conducti...

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Icarus 160, 95–107 (2002) doi:10.1006/icar.2002.6951

On the Dynamics of the Jovian Ionosphere and Thermosphere III. The Modelling of Auroral Conductivity George Millward, Steve Miller,1 Tom Stallard, and Alan D. Aylward Department of Physics and Astronomy, University College London, Gower Street, London WC1 6BT, United Kingdom E-mail: [email protected]

and Nicholas Achilleos Space and Atmospheric Physics Group, Imperial College, London SW7 2AZ, United Kingdom Received October 31, 2001; revised June 10, 2002

derstanding how events in the magnetosphere produce atmospheric variability that can be detected by monitoring changes in auroral activity—at least, in theory. In two previous papers, we have analysed the results of infrared spectroscopic observations of the jovian auroral/polar regions to produce information about the ion winds (Stallard et al. 2001a—henceforth Paper I) and to investigate temperature variations and thermal balance (Stallard et al. 2001b—henceforth Paper II). For the sake of brevity, readers are referred to these papers for a fuller discussion of the main issues. This contribution concentrates on atmospheric modelling, rather than observations. One of the key parameters controlling the coupling between the jovian upper atmosphere and magnetosphere is the degree of ionospheric electrical conductivity. In the auroral region, for instance, the underlying theory due to Hill (1979) has a system of currents, which close through the ionosphere, responsible for transferring angular momentum from the planet to the equatorial plasmasheet. This plasmasheet, populated with plasma that derives mainly from Io’s volcanic activity, extends for up to 70 jovian radii (1 RJ = 71,492 km) from the centre of Jupiter and co-rotates for about a third of this distance. As Hill’s 1979 theory is developed by himself (2001) and Cowley and Bunce (2001), the breakdown in plasmasheet co-rotation is directly responsible for generating (jovian magnetic-) field-aligned currents, which in turn result in the precipitation of high-energy particles into the atmosphere. It is these particles that are responsible for producing much of the ionisation in the auroral region, resulting in a highly conducting ionosphere. One of the reasons for renewed interest in Hill’s theory is that there has been a buildup in supporting evidence over the past decade. The Ulysses spacecraft detected signatures of the required field-aligned currents when it passed over the jovian poles in February 1992 (Dougherty et al. 1993). Rego and co-workers

Recent work has been concerned with calculating the threedimensional ion concentrations and Pedersen and Hall conductivities within the auroral region of Jupiter for varying conditions of incident electron precipitation. Using the jovian ionospheric model, we present results that show the auroral ionospheric response to changing the incoming flux of precipitating electrons (for constant initial energy) and also the response to changing the initial energy (for both constant flux and constant energy flux). The results show that, for expected energy fluxes of precipitating particles, the average auroral integrated Pedersen conductivity attains values in excess of 1 mho. In addition, it is shown that electrons with an initial energy of around 60 keV are particularly effective at generating auroral conductivity: Particles of this energy penetrate most effectively to the layer of the jovian ionosphere at which the auroral conductivity is at a maximum. c 2002 Elsevier Science (USA) Key Words: aurorae; ionospheres; Jupiter, atmosphere; Jupiter, magnetosphere; modelling.

INTRODUCTION

Recent theoretical studies (Cowley and Bunce 2001, Hill 2001, Southwood and Kivelson 2001) and analyses of data from in situ spacecraft (Kivelson et al. 1997, Khurana 2001) and remote observing (Clarke et al. 1998, Prang´e et al. 1998, Satoh and Connerney 1999, Dols et al. 2000) have enormously advanced our understanding of the upper atmosphere (ionosphere and thermosphere) of Jupiter and the way in which it couples to the magnetosphere, particularly within the auroral regions. Taken together, these works help form the basis for un1 Visiting Research Scientist, Institute for Astronomy, Woodlawn Drive, Honolulu, Hawaii 96822.

95 0019-1035/02 $35.00 c 2002 Elsevier Science (USA)  All rights reserved.

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(1999) detected an auroral electrojet, predicted indirectly from Hill (1979), in 1997. In addition, Khurana’s (2001) analysis of Galileo data found field patterns compatible with the breakdown of plasmasheet co-rotation and maybe even its reestablishment for large radial distances from the planet. In the work of Cowley and Bunce (2001), the extent of plasmasheet co-rotation, the strength of the field-aligned currents, and the ionospheric conductivity are linked in a self-consistent way. One could, in theory, predict how changes in the plasmasheet could produce ionospheric alterations, which would, in turn, feed back into the magnetosphere, over a period of time. As yet, however, there is no time-dependent model that makes this link explicitly. Such a model would be extremely useful; many studies have shown that there are auroral variations over time scales that range from minutes to months and years (e.g., Baron et al. 1991, 1996, Livengood et al. 1992, Pryor et al. 2001, Waite et al. 2001, Papers I and II), without being able to identify clearly the mechanisms producing them. The purpose of this paper is to take an important first step along the route to a fully coupled jovian magnetospheric and atmospheric model, by calculating the ionisation produced by various fluxes of energetic particles and the resultant conductivity. Another important aspect, under current investigation, is the coupling of momentum within the auroral region. Results showing the associated ion and neutral winds are beyond the present scope and will be presented in a forthcoming companion paper.

THE JOVIAN IONOSPHERIC MODEL

The jovian ionospheric model (JIM; Achilleos et al. 1998) is a time-dependent, three-dimensional model of Jupiter’s thermosphere and ionosphere based on the terrestrial coupled thermosphere–ionosphere model (CTIM). The basis for CTIM was a global thermospheric model described originally by Fuller-Rowell and Rees (1980). This was enhanced by the inclusion of a fully dynamic ionospheric model at high latitudes (Quegan et al. 1982, Fuller-Rowell et al. 1987). Subsequently, the model was further enhanced to include a fully dynamic model of the mid- and low-latitude ionosphere and plasmasphere, in the process becoming CTIP (coupled thermosphere–ionosphere plasmasphere model). Fuller-Rowell et al. (1996) and Millward et al. (1996) have given full descriptions of CTIM and CTIP, respectively. For the jovian model, JIM, we use a similar numerical grid to that of the terrestrial model: a spherical, co-rotating coordinate grid which divides the model planet into 40 elements in longitude (9◦ resolution), 91 elements in latitude (2◦ resolution), and 30 elements in pressure (used, instead of altitude, to define the vertical location of a grid cell). The vertical grid spacing is uniform with respect to the logarithm of pressure, so that the value of pressure for the nth layer may be written Pn = P1 exp(−γ (n − 1)).

(1)

We take P1 = 2 × 10−6 bar as our lower boundary and γ = 0.4 as the vertical spacing between levels in units of local pressure scale height. Our upper boundary is at pressure P30 ≈ 2 × 10−11 bar. The horizontal wind velocity, total energy density, neutral composition, and ionospheric composition are evaluated at each grid point using explicit time stepping applied to finite-difference versions of the appropriate equations of continuity, energy transport, and momentum transport. Using these solutions, the vertical wind, temperature, and altitudes at each pressure level can then be reevaluated after each time step. Figure 1 shows JIM predicted altitude profiles of thermospheric parameters. All of the results are averages of separate profiles around the equatorial noon region. The vertical scale is atmospheric pressure. Figure 1a gives the mass densities of the three major constituents; atomic hydrogen, molecular hydrogen, and helium. Figure 1b shows the resulting mean molecular weight. The thermospheric temperature is shown in Fig. 1c, whilst Fig. 1d plots altitude above the 1 bar pressure level against atmospheric pressure, for reference. Chemical reactions between the species are also carried out at all time steps to update the composition. We use a time step of 4 s in our calculations, to sample the minimum time scale ≥10 s associated with the recombination of H+ 3 ions in Jupiter’s auroral ionosphere. Achilleos et al. (1998) and Millward et al. (2002) have given a full description of the JIM. Since, in what follows, some of our arguments depend on the changing chemical composition of the jovian thermosphere with altitude, it is worth recalling the key reactions that govern ionisation and neutralisation of the upper atmosphere: (A)H + hν → H+ + e− (photoionisation), (B)H + e− → H+ + e− + e− (electron impact ionisation), − (C)H2 + hν → H+ 2 + e (photoionisation), − − (D)H2 + e− → H+ 2 + e + e (electron impact ionisation),

(E)H+ + H2 (v ≥ 4) → H + H+ 2 (charge exchange), + (F)H+ 2 + H2 → H + H3 (protonisation),

(G)H+ + e− → H + hν(radiative recombination), − (H)H+ 3 + e → H2 + H

→ H + H + H(dissociative recombination). The reaction rates for these reactions are given in Achilleos et al. (1998). (In these equations, though not in the model, we have left out helium reactions, since He+ is a minor constituent of the ionosphere.) Of importance to our subsequent discussions are the following facts: (a) H+ tends to be the dominant ion at high altitudes (P < 1 × 10 bar), since there are higher concentrations of hydrogen atoms there. But at lower altitudes, where molecular hydrogen predominates, H+ 3 is the major ion. −9

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(c)

(b)

(d)

FIG. 1. Average dayside equatorial vertical profiles of neutral parameters calculated by the JIM: (a) neutral mass density of the constituents H (solid line), H2 (dotted line), and He (dashed line) plotted against pressure; (b) the resulting mean molecular mass profile; (c) neutral temperature profile, showing an exospheric temperature of around 1200 K; (d) plot of altitude above the jovian 1-bar level against pressure.

(b) Reaction F can be considered to be instantaneous, given the high concentrations of H2 in the jovian thermosphere. Thus no appreciable concentration of H+ 2 develops. (c) Reaction G is slow (kG ∼ 10−10 cm3 s−1 ) whereas Reaction H is fast (kH ∼ 10−7 cm3 s−1 ). Thus H+ ions live ∼1000 times longer than H+ 3 ions, for a given electron concentration.

lowest two pressure levels:

Hydrocarbons may be important at the base of the thermosphere, but their density is not explicitly included in JIM. Instead, a “canonical” hydrocarbon reaction is introduced for the

The hydrocarbon ions are then assumed to be “instantaneously” neutralised by electron recombination (within one JIM time step of 4 s).

+ XH + H+ 3 → XH2 + H2 .

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MODEL RUNS

A series of model runs was undertaken to investigate the effect of varying electron precipitation on the jovian auroral ionosphere. Separate experiments were concerned with the effect of changing the incoming number flux for constant electron energy, changing the electron energy for constant number flux, and changing the electron energy for constant energy flux. For each simulation values of the three-dimensional concentrations of the + ions H+ , H+ 3 , and He and electrons were output, in addition to the Pedersen and Hall conductivities. Average auroral profiles were calculated from 80 individual profiles: 40 spaced evenly around the northern auroral oval and similarly 40 from the southern hemisphere. In addition average profiles were calculated for the dayside and nightside equatorial regions. Column densities for the ions and integrated conductivities were also calculated by vertical integration of the diurnally averaged profiles. In what follows we took a starting model that had aged for six jovian rotations and had attained a good thermal equilibrium, and we allowed them to develop for a further six simulated minutes with the new inputs. This was enough time for the chemical compositions to equilibrate under the influence of the new flux and energy inputs, for most of the cases. It was, however, discovered that, for the cases of precipitation by the lower energy electrons (1–10 keV), the reaction of the ionosphere was considerably slower, with increases in the density of H+ ions still evident after 4 h. Results showing the “time development” of the plasma are given in the following. First, we investigated the effect of increasing the incoming electron energy flux, whilst maintaining an initial electron energy of 10 keV. In nine separate runs the auroral thermosphere was subjected to incoming electrons with an energy flux of 0.1, 0.3, 1.0, 3.0, 10.0, 30.0, 100.0, 300.0, and 1000.0 ergs cm−2 s−1 (equivalent to mW m−2 ). The results are shown in Fig. 2, which plots vertical profiles of the predicted concentrations for the ions H+ (dashed line), H+ 3 (dotted line), and electrons (solid line) against atmospheric pressure. Figures 2a and 2b show profiles for the equatorial local midnight and local noon respectively. The results show maximum ionospheric concentrations of ∼1 × 104 cm−3 . A comparison of Figs. 2a and 2b also clearly demonstrates how the jovian nightside ionosphere is maintained at higher altitudes by the longevity of the H+ ions. Figures 2c–2g are auroral ionospheric profiles, averaged over the latitudinal and longitudinal extent of the main auroral oval, as defined within the JIM (Achilleos et al. 1998). They show the ionosphere responding to an increasing flux of precipitating electrons, with energy fluxes of 0.1, 1.0, 10.0, 100.0, and 1000.0 ergs cm−2 s−1 respectively. As expected, the incoming precipitation leads to enhanced densities of both H+ and H+ 3 ions, with the largest increases occurring at lower altitudes, around the 1 × 10−7 bar level (an altitude of roughly 700 km above the jovian 1-bar level). Here, for a precipitation energy flux flux of 10–100 ergs cm−2 s−1 , the ionosphere reaches maximum concentrations of around 1 × 106 cm−3 . Figure 3 shows the resulting Pedersen

(solid line) and Hall (dotted line) conductivities for the same conditions as in Fig. 2. As expected the largest ionospheric conductivities occur at lower altitudes, around the 1 × 10−7 bar level. A vertical integration of these auroral parameters yields predictions of auroral column densities and associated integrated conductivities. Results are shown in Fig. 4, with the column densities of H+ and H+ 3 (Fig. 4a) and integrated Pedersen and Hall conductivities (Fig. 4b) plotted against electron precipitation energy flux. The H+ 3 column densities predicted by JIM, for both auroral and nonauroral latitudes (the latter not shown), are consistent with measurements by Lam et al. (1997) and Miller et al. (1997). Figure 4b shows that for large, though realistic, fluxes of precipitating electrons (say, 100 ergs cm−2 s−1 ) the auroral integrated Pedersen conductivity attains a value of around 1 mho. Over the incident electron energy flux range of 0.1 to 100 ergs cm−2 s−1 , the JIM prediction of auroral H+ 3 column density can be approximated by the equation log10 N(H+ 3 ) = a log10 Fe + b,

(2)

+ −2 where N(H+ 3 ) represents the column density of H3 (cm ) and −2 −1 Fe is the incident electron energy flux (ergs cm s ). For the results presented here, we find a = 0.435 and b = 12.280, in close agreement with preliminary values quoted by Rego et al. (2000). This equation is, of course, only valid for the idealised situation in which the ionosphere is subject to a monochromatic, 10-keV, source of electrons. In reality the auroral source will consist of a whole spectrum with electrons of different energies. Following the parameterisation of N(H+ 3 ), we fitted the values of the height-integrated Pedersen and Hall conductivities (P and H respectively, in units of mho) as quadratic functions of the incident energy flux (in ergs cm−2 s−1 ):

log10 P = αP log10 Fe + βP (log10 Fe )2 + γP , log10 H = αH log10 Fe + βH (log10 Fe )2 + γH .

(3)

We find αP = 0.437, βP = 0.089, and γP = −1.438 and αH = 0.244, βH = 0.121, and γH = −3.118. To investigate the effects of varying electron energy a second series of runs was undertaken in which the initial energy of the incoming electron precipitation was altered, while the number flux was kept constant at 6.25 × 1012 cm−2 s−1 . This number flux is equivalent to an electron energy flux of 10 ergs cm−2 s−1 for electrons of energy 10 keV. Figure 5 shows vertical auroral profiles for the ions H+ (dashed line), and H+ 3 (dotted line) and electrons (solid line), as before. Figures 5a–5h give results for electron precipitation of initial energies of 1, 3, 10, 20, 40, 60, 80, and 100-keV respectively. Clearly, as the energy increases, the electrons precipitate to lower altitudes. For instance, electrons of energy 1-keV are seen to penetrate to the 10−8 bar level (Fig. 5a), whilst electrons of 20-keV penetrate to ∼3 × 10−7 bar and also lead to larger concentrations of ions and electrons. However, this latter trend is not continuous. Once

JOVIAN AURORAL CONDUCTIVITIES

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(e)

(b)

(f)

(c)

(g)

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(d)

FIG. 2. Predicted concentration profiles for the ions H+ (dashed line), H+ 3 (dotted line), and electrons (solid line). (a) and (b) Equatorial nightside and dayside results respectively. (c) to (g) Average auroral profiles for simulations in which the auroral region is subject to electron precipitation of initial energy 10 keV and incident energy flux of 0.1, 1.0, 10.0, 100.0, and 1000.0 mW m−2 respectively.

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(e)

(b)

(f)

(c)

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FIG. 3.

Same as Fig. 2 for Pedersen (solid line) and Hall (dotted line) conductivities.

the individual electron energy is greater than ∼60 keV, lower ion and electron concentrations result. The reason for this is clear: A significant proportion of electrons with energies greater than 60 keV penetrate the thermosphere completely, moving into lower atmospheric regions in which any ionisation generated is

almost immediately reneutralised via H+ 3 dissociative recombination (Reaction H). A recent 1-D model study by Perry and co-workers (1999) has indicated that within the lower thermosphere, below the level at which H+ 3 is destroyed, conductivity may be produced by the ionisation of hydrocarbons, producing

JOVIAN AURORAL CONDUCTIVITIES (a)

(b)

FIG. 4. JIM predictions of height-integrated auroral ionospheric parameters as a function of the incident auroral electron precipitation flux. (a) Average auroral column densities of the ions H+ (dashed line) and H+ 3 (dotted line); (b) the associated integrated Pedersen and Hall conductivities (solid and dotted lines respectively).

+ species such as CH+ 5 and C3 Hn . We do not consider such species in JIM and therefore our results should be understood accordingly. However, the degree to which such hydrocarbon ions are important remains unclear. For instance, for the concentrations of CH+ 5 predicted by Perry et al. (1999), it might be expected that this ion would have been observed. It is of note that even the highest resolution spectra (e.g., Maillard et al. 1990) have failed to reveal such hydrocarbon ions. Figure 6 plots the accompanying Pedersen and Hall conductivities. These also peak strongly for 60-keV electrons. As before, these parameters can be integrated vertically to yield auroral column densities and integrated conductivities. These are plotted as a function of the initial electron energy in Fig. 7. Figure 7a shows column densities of the ions H+ and H+ 3 and electrons. At all energies the column density of H+ is significantly larger than that for H+ . The largest amount 3 + of H results from precipitating electrons with lower energies, around 10 to 20 keV. This is what we would expect since such lower energy particles lead to ionisation in the upper thermosphere, where the H+ ion is prevalent. This contrasts with the situation for H+ 3 . Here the largest column densities are again achieved for electron energies of around 60 keV. Electrons with

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these higher energies penetrate deeper into the thermosphere to altitudes at which H+ 3 is readily produced. As the electron energy increases above 60 keV there is a sharp drop in the ionospheric H+ 3 column density, for the reasons already discussed. Figure 7b shows the integrated Pedersen and Hall conductivities as a function of initial electron energy. The most striking feature here is the strongly peaked nature of the integrated conductivities. This plot shows that, as the electron energy increases (for constant flux), the resulting auroral conductivity increases as the electrons penetrate closer into the region of high conductivity (i.e., the lower thermosphere). However, as with the H+ 3 column density, there is a limit around about 60 keV. These particles of energy 60 keV are correctly “tuned” to penetrate optimally to the level at which the largest ionospheric conductivity naturally occurs. This result has important implications for experimental studies attempting to establish causal links between magnetospheric “activity” and observable auroral behaviour. For instance, one can imagine a hypothetical situation in which active magnetospheric processes lead to a monotonic increase in the mean precipitating electron energy from (say) 10 to 100 keV. Our results imply that the observed brightness of infrared H+ 3 emission will itself also increase, but up to a limiting point, somewhere around 60 keV. Beyond this energy the H+ 3 emission will decrease as the dominant electrons penetrate to levels where this ion is instantly destroyed. In essence, the H+ 3 emission will follow the dotted line in Fig. 7a. Thus far, our modelling of the ionospheric response to changing electron precipitation energy has been conducted for a constant incoming number flux. However, to further elucidate the atmospheric response it is also informative to consider the response for constant energy flux. To this end another set of model runs was conducted in which the incoming electron precipitation energy was varied (in separate experiments) from 1 to 100 keV, as before, but this time while keeping the energy flux constant at 10 ergs cm−2 s−1 (10 mW m−2 ). The resulting ionospheric column densities and conductivities are shown in Figs. 8a and 8b respectively. From Fig. 8a it is clear that if we are considering a constant electron energy flux with variable initial electron energy, then the largest ionospheric column densities result from electrons of lower energies. This contrasts with the results plotted in Fig. 7a (in which the H+ 3 and electron densities are at a maximum for an input of around 60 keV). However, the same cannot be said of the integrated Pedersen and Hall conductivities (Fig. 8b). Here we note that the conductivities are still strongly peaked for electron energies of about 60 keV (as before in Fig. 7b). Thus electrons of energy 60 keV are particularly effective regardless of whether we consider the input in terms of constant number flux or constant energy flux. This can be understood by looking at the formulas that give these quantities,

   σP = n e e2 /m i × νin νin2 + ωic2 ,    σH = n e e2 /m i × ωic νin2 + ωic2 ,

(4)

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(a)

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FIG. 5. Predicted auroral concentration profiles for the ions H+ (dashed line) and H+ 3 (dotted line) and electrons (solid line). Panels (a) to (h) show the effects of incident electrons with a constant number flux of 6.25 × 1012 cm−2 s−1 and initial electron energy of 1, 3, 10, 20, 40, 60, 80, and 100-keV respectively.

JOVIAN AURORAL CONDUCTIVITIES (a)

(e)

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(f)

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FIG. 6.

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Same as Fig. 5 for Pedersen (solid line) and Hall (dotted line) conductivities.

where σP is the Pedersen conductivity, σH is the Hall conductivity, n e is the concentration of electrons (all three as a function of altitude), e is the charge of the electron, m i is the ion mass, νin is the ion–neutral collision frequency (also as a function of altitude), and ωic is the ion cyclotron frequency. For any given

electron energy, conductivity, as a function of altitude, is related to the numbers of electrons and ions produced at that altitude. The term in square brackets, however, is sharply peaked at the altitude where νin = ωic . This occurs (averaged over the location and field strength of the auroral oval) at precisely the altitude that

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energy 1, 3, 10, 20, 30, and 50 keV. Similarly, Figs. 9d–9f are respectively identical to Figs. 9a–9c but for the higher electron flux of 6.25 × 1013 cm−2 s−1 . Whereas most of the lines plotted in Fig. 9 reveal only modest changes over the 250 min of jovian time plotted, the exception is for precipitating electrons of energies 1 keV (solid line) and 3 keV (dotted line). Figures 9a and 9d reveal that the column density of H+ ions increases significantly over this time period for these lower energies. The result is that at the end of this 250-min time period the column density of H+ ions is much larger, for these low electron energies, than for the other, higher energies. DISCUSSION

(b)

Our JIM simulations have all used a monochromatic source of precipitating electrons. We feel this is justified, in terms of analysing the processes that give rise to ionisation and conductivity. In reality, however, the ionising source will consist of a full spectrum of energies and this will probably result in a good deal of “blurring” of the effects discussed here. Additionally, JIM has to start with a model atmospheric composition, which—while as close to the true jovian atmosphere as possible—may not fully represent it. This will have a bearing on precisely which electron energy is most effective at ionising the atmosphere; for example, it might be the case that the maximum H+ 3 densities occur for FIG. 7. JIM calculations of integrated auroral ionospheric parameters as a function of precipitating electron energy and for a constant number flux of 6.25 × 1012 cm−2 s−1 . Panel (a) shows column densities for the ions H+ (dashed line) and H+ 3 (dotted line) and electrons (solid line); panel (b) shows the accompanying integrated auroral Pedersen and Hall conductivities (solid and dotted lines respectively). The figure shows how electrons with energies of around 60 keV penetrate into the lower thermosphere, leading to a large Pedersen conductivity response (and a peak value of around 8 mhos). As the electron energy increases above 60 keV the electrons penetrate the thermosphere fully and have a smaller effect on conductivity.

coincides with the maximum ion production for 60-keV electrons. Since this altitude is one where H+ 3 is the predominant ionospheric species, it is the production and mobility of this ion that controls the integrated conductivities.

(a)

(b)

TIME DEVELOPMENT OF THE PLASMA

As discussed previously, in most of the cases studied, the ionosphere reacted quickly to the newly applied precipitation inputs, allowing representative model output after only a few minutes of simulated time. However, our results revealed some important exceptions to this, partiularly in the case of precipitation by lower energy electrons. Results showing the time development of the ionospheric column densities to the newly applied precipitation inputs are given in Fig. 9. Figures 9a–9c show the average auroral column density of H+ , H+ 3 , and electrons, respectively, for an incoming electron number flux of 6.25 × 1012 cm−2 s−1 . In each panel the results shown are for incoming electrons of

FIG. 8. Same as for Fig. 7 but for a separate experiment in which the energy flux of the incoming electrons is held constant (at 10 ergs cm−2 s−1 ) while the incident electron energy is changed.

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FIG. 9. Ion column densities as a function of time after the onset of auroral precipitation. Panels (a), (b), and (c) respectively show results for H+ , H+ 3, and electrons for an incoming electron precipitation flux of 6.25 × 1012 cm−2 s−1 . Similarly, panels (d), (e), and (f) show the same respective constituents for a precipitation flux of 6.25 × 1013 cm−2 s−1 . In all panels the six lines give results for electron precipitation of 1 keV (solid line), 3 keV (dotted line), 10 keV (dashed line), 20 keV (dot-dashed line), 30 keV (dot-dot-dot-dashed line), and 50 keV (long dashed line).

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an input electron energy of 50 or 70 keV, rather than our value of 60 keV. This suggests that in analysing actual jovian events and data— particularly if one is trying to determine the dominant electron energies giving rise to observed auroral phenomena—it will be necessary to specify which model has been used to make the comparisons. As well as JIM, a sophisticated one-dimensional model, due to Grodent et al. (2001), is now available. This uses three components for its ionisation source, produces excellent fits to IR and UV emission data, and is applicable to regions of diffuse auroral emission as well as the discrete oval emission modelled here. The Grodent et al. (2001) model produces a somewhat higher (by about 100 K) exospheric temperature than that of JIM, suggesting a greater net influx of energy than we have used. There is also a new 3-D global circulation model, JTGCM, due to Bougher and co-workers (2001). This differs from JIM in having a lower boundary below the homopause, as well as in other particulars. As yet, neither of these models has been used to probe the input energy/flux parameter space that this study has investigated. But “benchmarking” comparison between the models, when there is the opportunity to do so, is likely to be useful. CONCLUSIONS

This study has produced a simple parameterisation of H+ 3 column densities and integrated conductivities against input flux for a monochromatic source of precipitating electrons. It has also looked at the effects of changing the electron energies, for both constant flux and also constant energy flux. We can list four major findings that should be useful for analysing IR data, and for theoretical studies of magnetosphere–upper atmosphere coupling: First, for a given electron energy (in our case 10-keV + electrons), H+ 3 and H column densities and integrated conductivities increase with increasing flux. The relationships, however, are not linear, and care has to be taken when directly relating observed H+ 3 emissions to precipitation fluxes. Second, there is an electron energy of around 60 keV in the JIM model that is maximally efficient at ionising the jovian upper atmosphere and is particularly effective in producing conductivity. This result holds true whether we consider the electron precipitation energy varying for constant number flux or for constant energy flux. For energies greater than 60 keV, electrons penetrate too deeply into the atmosphere to be increasingly effective. Third, the ion H+ 3, rather than H+ , dominates the Pedersen and Hall conductivities. Finally, the time development of the auroral ionosphere is dependent on the energy of the incoming electron precipitation. Lower energy electrons lead to increases in H+ ions in the upper thermosphere which continue to develop several hours after the onset of the precipitation. ACKNOWLEDGEMENTS The authors acknowledge the encouragement and advice given to us in the preparation of this paper by Professor Stan Cowley. JIM calculations referred to

in this article were carried out on the Miracle supercomputer at the HiPerSPACE centre at University College London, supported by PPARC.

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