On the dynamics of the jovian ionosphere and thermosphere.

On the dynamics of the jovian ionosphere and thermosphere.

Icarus 173 (2005) 200–211 www.elsevier.com/locate/icarus On the dynamics of the jovian ionosphere and thermosphere. IV. Ion–neutral coupling George M...

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Icarus 173 (2005) 200–211 www.elsevier.com/locate/icarus

On the dynamics of the jovian ionosphere and thermosphere. IV. Ion–neutral coupling George Millward a,∗ , Steve Miller a,b , Tom Stallard a , Nick Achilleos c , Alan D. Aylward a a Department of Physics and Astronomy, University College London, Gower Street, London WC1 6BT, UK b Visiting Research Scientist, Institute for Astronomy, Woodlawn Drive, Honolulu, Hawaii HI 96822, USA c Space and Atmospheric Physics Group, Imperial College, London SW7 2AZ, UK

Received 25 March 2003; revised 23 June 2004

Abstract We use the fully coupled, three-dimensional, global circulation Jovian Ionospheric Model (JIM) to calculate the coupling between ions in the jovian auroral ovals and the co-existing neutral atmosphere. The model shows that ions subject to drift motion around the auroral oval, as a result of the E × B coupling between a meridional, equatorward electric field and the jovian magnetic field, generate neutral winds in the planetary frame of reference. Unconstrained by the magnetic field, these neutral winds have a greater latitudinal extent than the corresponding ion drifts. Values of the coupling coefficient, k(h), are presented as a function of altitude and cross-auroral electric field strength, for different incoming electron fluxes and energies. The results show that, with ion velocities of several hundred metres per second to over 1 km s−1 , k(h) can attain values greater than 0.5 at the ion production peak. This parameter is key to calculating the effective conductivities required to model magnetosphere–ionosphere coupling correctly. The extent to which angular momentum (and therefore energy) is transported vertically in JIM is much more limited than earlier, one-dimensional, studies have predicted.  2004 Elsevier Inc. All rights reserved. Keywords: Aurora; Ionospheres; Jupiter, atmosphere; Jupiter, magnetosphere; Modelling

1. Introduction For two decades or more, there have been suggestions that the energy input into the auroral regions, resulting from the precipitation of particles accelerated from the magnetosphere, could contribute to the high temperatures measured in the jovian ionosphere (e.g., Waite et al., 1983). The calculated exospheric temperature of Jupiter, relying only on solar inputs to heat the atmosphere, is around 200 K (Strobel and Smith, 1973; Yelle and Miller, 2004). However, measured temperatures are between 700 and 1150 K (Drossart et al., 1989; Lam et al., 1997), depending on the exact location and date of observations. Jupiter’s auroral zones are known to receive some 1013 to 1014 W from particle pre* Corresponding author. Fax: +44-(0)-20-7679-9024.

E-mail address: [email protected] (G. Millward). 0019-1035/$ – see front matter  2004 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2004.07.027

cipitation (e.g., Clarke et al., 1987; Prangé and Elkhamsi, 1991). In recent years, there have been a number of important advances in understanding the processes by which Jupiter’s aurorae are formed. These have centred on the magnetic coupling between an equatorial plasma sheet within the middle magnetosphere, and the planet’s upper atmosphere. According to earlier work by Hill (1979) and co-workers (Hill et al., 1983), the jovian magnetic field, rotating with the planet, also brings this equatorial plasma sheet into corotation. However, at sufficiently large radial distances from the planet, this mechanism begins to break down and the plasma sheet lags behind corotation. The result is a current system flowing along magnetic field lines from the plasma sheet and closing in the auroral ionosphere. The currents are carried mainly by high-energy electrons, which precipitate into the jovian atmosphere, and ionise it. Recent work by Hill (2001)

Jovian ion–neutral coupling

and Cowley and Bunce (2001) has refined the theory of this mechanism.

2. Ion–neutral coupling Huang and Hill (1989) looked at one of the consequences of the Hill mechanism from the perspective of the auroral upper atmosphere (ionosphere–thermosphere). Here collisions between ions, magnetically connected to sub-corotating regions of the magnetosphere, and neutrals produces a “rotational slippage” of the jovian upper atmosphere. They parameterised this with a height-dependent function: f (h) = 1 − δΩn /δΩM ,

(1)

where δΩn = ΩJ − Ωn , the difference between the angular velocities of Jupiter and of the neutral gas at height h, and δΩM = ΩJ − ΩM , the difference between the angular velocities of Jupiter and of the plasma in the region of the equatorial plasma sheet that is magnetically connected to the auroral oval. Clearly, at the top of the auroral neutral atmosphere, the ion lag to corotation is also δΩM . Cowley and Bunce (2001) introduced a parameter K, also related to the coupling between the sub-corotating ions and the neutrals, and given by: K = (ΩJ − Ωn )/(ΩJ − ΩM ).

(2)

Here ΩJ is the angular velocity of Jupiter, Ωn is the angular velocity of the relevant neutral atmosphere, and ΩM is the angular velocity of the plasma (again at the top of the auroral neutral atmosphere). Leaving aside the height dependence of f , it can be seen that f ∼ 1 − K. Viewed in a corotating frame of reference, the magnetosphere generates an equatorward-pointing electric field, E, causing ions in the auroral oval to drift clockwise as viewed from above the north rotational pole, with a velocity:   v = E × B/B 2 , (3) where B is the jovian magnetic field at auroral latitudes. In this viewpoint, K corresponds to the fraction of the ion velocity, at the top of the atmosphere, imparted to the neutrals by collisions. The auroral upper atmosphere is thus characterised by a counter-rotating ionospheric wind accompanied by a more slowly counter-rotating thermospheric wind, the latter driven by collisions. This neutral wind, driven mechanically (rather than thermally), has been suggested as a further source of energy for heating the thermosphere (Miller et al., 2000). In three previous papers (Stallard et al., 2001, henceforth Paper I; Stallard et al., 2002, henceforth Paper II; Millward et al., 2002, henceforth Paper III), we looked at infrared observations of the jovian auroral regions, and modelling of effects in the ionosphere of electron precipitation. This paper looks specifically at the dynamics of the coupling between the auroral ionosphere and the co-existing neutral thermosphere, using the Jovian Ionospheric Model (JIM) (Achilleos et al., 1998).

201

3. Electric fields and particle precipitation in the Jovian Ionospheric Model (JIM) Achilleos et al. (1998, 2001) have given the basic details of the Jovian Ionospheric Model (JIM). In order to understand this work clearly, however, it is useful to recap on three key characteristics of the model: • The jovian auroral oval is generated by a flux of precipitating electrons incident on the top of the atmosphere and covering all surface points with magnetic dipole L values of between 7 and 15 (where L value denotes the distance, in units of the jovian radius, at which a dipole field line intersects the magnetic equator; see Appendix A of Achilleos et al., 1998). This produces an auroral oval roughly 5000 km wide, equating to roughly two latitudinal grid elements. The incident electron energy and number flux are input parameters to the model and can be varied from run-to-run. • An equatorward voltage (VE ) across the auroral oval is used to simulate the electric field resulting from the corotation-lag of the plasma sheet. In what is presented here, this field is the dominant field in the model. Given the width of the oval, it can be seen that an equatorward voltage of 1 MV corresponds to an electric field of 0.2 V m−1 , 5 MV to 1.0 V m−1 , 10 MV to 2.0 V m−1 , and so on. • The electric field poleward of the auroral oval is represented by a two-cell potential, giving rise to a (relatively insignificant, in this work) Dungey cycle (see Appendix A of Achilleos et al., 1998). It is clear that the polar cap potential in JIM is not realistic, in the light of recent theoretical considerations (Cowley et al., 2003) and observations (Stallard et al., 2003). These studies show that the Dungey cycle is confined to the polar dawn sector of Jupiter, and that there is a region around the magnetic pole where the ionospheric plasma drift is almost static in the inertial frame of reference. However, for this study, which focuses on the main auroral oval, the exact pattern of ion drifts in the polar cap, poleward of the main oval, is of little importance. It should also be noted that the exact location of our electron precipitation is not the same as the now-available footprints of jovian auroral IR and EUV emission (Satoh and Connerney, 1999; Grodent et al., 2003). Thus our model should be thought of as Jupiter-like, insofar as the magnetic dipole is both offset and tilted, rather than being an exact spatial replica of the planet. As stated in Paper III, the inputs to JIM consist of a monoenergetic field-aligned flux of high-energy electrons. Although this is less realistic than more sophisticated 1D models (e.g., Grodent et al., 2001), it is ideally suited to looking at the relationships between ionisation levels, crossauroral potentials and ion–neutral coupling, as well as test-

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ing the extent of the three-dimensional transport of energy and momentum in the jovian atmosphere.

4. Model calculations In much of what follows, we present our results in terms of profiles as a function of pressure, since JIM works on a grid of constant pressure levels rather than altitude. To help orientate the reader, Fig. 1 shows how pressure in the model relates to altitude above the jovian 1 bar level, and also to the pressure level number (Figs. 1a and 1b, respectively). Most of the details of the JIM calculations are given in Paper III. To recap briefly, a series of model runs were carried out for electron precipitation fluxes equivalent to energy fluxes of 0.1 to 1000 mW m−2 , and for electron energies of 1 to 100 keV, although the results for all flux/energy combinations are not presented in that paper. It was found that the resulting height-integrated conductivities could be parameterised as a function of energy flux (this was done explicitly only for 10 keV electrons), and that electrons with 60 keV incident energy produced the highest local and height-integrated conductivities per electron in the model. The model runs carried out for Paper III were then further analysed and augmented to investigate ion–neutral momentum coupling, the focus here. Additional runs were undertaken for different values of the applied equatorward, transauroral voltage, VE , and for electron precipitation energies of 10, 30, and 60 keV. In most of the runs, ion and neutral velocities were output from the model after about 1 hour of jovian time. This was discovered to be long enough for local winds within the auroral oval to readjust to the new ion

(a)

(b) Fig. 1. Pressure vs. (a) altitude and (b) pressure level, for the Jovian Ionospheric Model (JIM).

forcing and therefore sufficient for the ion–neutral coupling to be adequately assessed. In addition, for this paper, we have carried out two important longer model runs, each lasting for 1.1 jovian rotations (1 jovian rotation = 9 hr 55 min 27 s). In these, different values of the equatorward, trans-auroral voltage, VE , have been applied, to produce different auroral ion velocities. Thus the model was run, from the same starting configuration, for VE = 0 and VE = 3 MV, in order to look at the changes brought about on a global scale by a relatively extended period of ionospheric forcing. In both cases the precipitating particle flux was 6.25 × 1012 m−2 s−1 of 60 keV electrons. (Note that in Paper III, this figure is incorrectly given as 6.25 × 1012 cm−2 s−1 .) This particle flux is equivalent to a current of 1 µA m−2 , comparable to that proposed by Cowley and Bunce (2001) in their analysis of the auroral EUV emissions of Jupiter, and an energy flux of 60 mW m−2 . By utilising two model runs, identical except for the values of VE , and then calculating differences between the two, we can assess changes in parameters such as neutral temperatures and winds on a global scale. This technique effectively cancels any effects due to the model not having fully attained thermal equilibrium. Figures 2 and 3 show ion and neutral parameters over the southern and northern polar regions respectively. Figure 2a shows the ion velocity vectors resulting from a transauroral voltage, VE , of 3 MV. Figures 2b, 2c, and 2d show the neutral temperature differences between the VE = 0 and VE = 3 MV runs (colour scale) and also the neutral wind vectors for the VE = 3 MV run at 3 times after the 3 MV field is switched on (27, 53, and 160 min, respectively). Here the temperature difference and neutral winds are at the pressure level corresponding to the maximum in ion production (1.34 µbar, pressure level 2 in the model). Figure 3 shows exactly the same results, but for the northern hemisphere. When the electric field in the model is switched on (e.g., the equatorward potential is changed instantaneously from zero to 3 MV, equivalent to a change in the electric field from zero to 0.6 V m−1 ), the ions respond immediately and drift at a velocity determined by the local value of E × B/|B|2 . However, the neutrals take some time to accelerate to their terminal velocity. Figure 4 shows how the neutral gas, at the height of the peak in the electron density, responds to this instantaneous change in the auroral ion velocity. The zonal neutral velocities plotted in Fig. 4 are from a jovigraphic latitude of 58◦ N and an SIII longitude of 180◦ E, a typical point within the JIM auroral oval. Figure 4a indicates that the neutral gas is accelerated to a terminal velocity within about 50 min, as ion–neutral collisions impart momentum to the neutrals and overcome drag forces due to the surrounding atmosphere. Figure 4b shows the reverse process, the rate at which neutrals decelerate once the equatorward field is reset to zero. At this point the ions no longer drift around the oval and act, again via ion–neutral collisions, to decelerate the neutral

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Fig. 2. View of the southern polar region of the JIM model, showing temperature differences (K) between runs carried out with VE = 0 and VE = 3 MV at various times, t. Also shown are the ion and neutral velocity vectors. (a) Ion velocity vectors resulting from a trans-auroral voltage, VE , of 3 MV; resulting temperature difference and neutral wind vectors at (b) t = 27 min; (c) t = 53 min; (d) t = 160 min. In all four panels the longest arrows corresponding to roughly 500 m s−1 . Winds with a magnitude of less than 50 m s−1 are not shown.

gas. This deceleration takes roughly 40 min. We will look in more detail at the acceleration of the neutral gas again later. The effect of Joule heating within the auroral oval is almost immediate with neutral temperature differences of greater than 25 K evident within 27 min (Figs. 2b and 3b). By the end of 160 min (Figs. 2d and 3d), the 3 MV run shows temperatures up to 70 K hotter than for the case where there is no equatorward voltage across the oval, and heating effects are clearly discernible both equatorward of the oval and throughout the whole region poleward of the oval. By the same time, the neutral winds (shown by the arrows) are well developed throughout the heated regions.

5. Ion–neutral coupling parameter Representative results of the further analysis of the runs carried out for Paper III are given in Figs. 5, 6, and 7. The three rows of each figure show results for three separate experiments in which the thermosphere was subjected to a monoenergetic field-aligned electron precipitation flux of energy 10, 30, and 60 keV, respectively. In each of the three experiments the applied equatorward voltage across the auroral oval was 1 MV, for Fig. 5, 3 MV for Fig. 6, and 10 MV for Fig. 7. These voltages are equivalent to an electric field

of ∼ 0.2, ∼ 0.6, and 2.0 V m−1 , respectively. The incoming electron number flux was 6.25 × 1012 m−2 s−1 in all cases. The three columns show respectively the resultant electron density, ion and neutral zonal velocity, and k(h) (i.e., here shown as a height dependent quantity, k(h) = 1 − f (h)). Once more, the velocities shown are from a typical auroral location of 58◦ N (jovigraphic latitude) and 180◦ E (SIII longitude). The first column of Figs. 5–7 are clearly very similar. In short, the applied voltage makes little difference to the amount of ionisation in the atmosphere. Nor does it affect the altitude at which the ionisation peak occurs. The ion velocity (middle column, dashed line, in Figs. 5–7) increases strongly with altitude in the lower ionosphere and attains an approximately constant value of around 150, 500, and 1600 m s−1 above 0.4 µbar, for the 1, 3, and 10 MV cases, respectively. The neutral velocities shown (middle column, solid line) represent the situation of relative equilibrium that ensues after the initial period of acceleration (see Fig. 4a). What is clear from all three figures is that, for a given voltage/individual electron energy, the neutral velocity is largest at the height at which the electron density is a maximum. In essence the altitude dependence of the neutral velocity profile is determined by a combination of the zonal ion velocity and the ionospheric electron density. In each of the three figures, the peak in the neutral velocity profile shows increases

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Fig. 3. As for Fig. 2, but showing the northern hemisphere.

for increasing electron energy (in turn the result of larger peak electron densities caused by an increasing incoming energy flux of the precipitating particles, see Paper III). This behaviour is reflected in the values of k(h) shown in Figs. 5–7. This function reaches a maximum of 0.65–0.7 for the 60 keV electrons at the pressure/altitude corresponding to the peak of ionisation, ∼ 0.6 for 30 keV electrons, and 0.4–0.5 for 10 keV electrons. Figure 8 compares neutral velocities for our three precipitating electron energies. Fig. 8a shows the value of the peak in the neutral velocity profile (corresponding to the peak ionisation level) as a function of the applied voltage, for incoming electron precipitation of particle energy 10 keV (solid line), 30 keV (dotted line), and 60 keV (dashed line). In each of the three cases shown, the neutral velocity shows a linear increase with the applied voltage. What is also noticeable is that, with regard to the peak in the neutral velocity profile, the dashed line, for 60 keV electrons, is not significantly steeper than that for the 30 keV electrons, despite a twofold increase in the incoming precipitation energy flux, and a similar accompanying increase in the peak electron density (Figs. 5–7). Figure 8b is similar to Fig. 8a but shows the neutral velocity at a constant pressure of ∼ 1 nbar, in the upper thermosphere, and at the top of the profiles shown in Figs. 5–7. In this case the velocity of the neutral gas is much larger for 10 and 30 keV electrons (solid and dotted lines respectively) than for the 60 keV electrons.

(a)

(b) Fig. 4. Acceleration (a) and deceleration (b) curves at 58◦ N 180◦ E for neutrals at the pressure level of maximum ionisation (0.90 µbar) as a result of ion–neutral coupling. The run corresponds to 60 keV electrons and VE = 3 MV (E = 0.6 V m−1 ).

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Fig. 5. Profiles of electron density (left-hand column), zonal velocity (middle column) and K(h) (right-hand column) at 58◦ N 180◦ E, for (a) 10 keV electrons (top row), (b) 30 keV electrons (middle row), and (c) 60 keV electrons (bottom row). In the middle column, ion velocities are shown as a dashed line and neutral velocities as a solid line; ion and neutral velocities are terminal velocities for VE = 1 MV (E = 0.2 V m−1 ).

6. Momentum transfer

Cowley and Bunce (2001) define their coupling parameter K so that:

Huang and Hill (1989) investigated the vertical transfer of momentum in the jovian upper atmosphere as a result of ion– neutral coupling, defining the parameter, f (h) (see Eq. (1)). In their model, both the auroral oval ions and neutrals corotated with the planet at the base of the conducting layer. The angular velocities of both then decreased monotonically with increasing altitude (i.e., both ions and neutrals sub-corotating). At the top of the neutral atmosphere the ion lag to corotation, δΩι , was equal to δΩM (the lag to corotation of the plasma sheet at the point linked magnetically to the auroral oval), while δΩn reached a limiting value, less than δΩM . The result was that the Pedersen conductivity used to calculate the spatial scale for plasma sheet corotation breakdown (Hill, 1979) had to be replaced by an effective conductivity:  ΣP = αΣP = σP (h)f (h) dh, (4)

K = 1 − α.

where σP (h) is the local, height dependent, Pedersen conductivity. Huang and Hill’s (1989) model was later developed by Pontius (1995), and used by Hill (2001) to redetermine the point at which corotation breaks down in the magnetosphere. Hill (2001) makes the point that ΣP can be several times less than ΣP itself.

(5)

Our k(h) is height dependent and relates to Huang and Hill’s model via: k(h) = 1 − f (h).

(6)

The form and values of f (h) depend on an upward transfer of angular momentum from the layers in the neutral atmosphere where the ion densities are large (Huang and Hill, 1989; Pontius, 1995). To achieve this upward transfer of momentum, Huang and Hill (1989) required large values of the eddy diffusion coefficient (from 1012–1016 × [n]−1/2 m1/2 s−1 , where [n] is the local neutral density). With a coefficient of 1013 × [n]−1/2 m1/2 s−1 , 20 times that proposed for the equatorial upper atmosphere (Atreya, 1986), the neutrals and ions drifted at essentially the same rate. As a result, f (h) varied from 1 at the base of the conducting layer to 0 at higher altitudes, around 200 km above this base. For the higher eddy diffusion values, ∼ 1015 × [n]−1/2 m1/2 s−1 , f (h) tended to ∼ 0.2 at the top of the atmosphere. Although Pontius (1995) did introduce non-zero values of δΩM and δΩn at the base of the conducting layer, this modification did not qualitatively alter the altitude variation of f (h). The altitude profile of our parameter, k(h), is

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Fig. 6. As for Fig. 4, for VE = 3 MV (E = 0.6 V m−1 ).

Fig. 7. As for Fig. 4, for VE = 10 MV (E = 2.0 V m−1 ).

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(a) Fig. 8. Neutral zonal velocities (westward, counter-rotational) at 58◦ N 180◦ E as a function of applied voltage VE at (a) the pressure level at which peak ionisation occurs (levels 9, 5, and 2 for 10, 30, and 60 keV electrons, respectively) and (b) at pressure level 20 (= 1 nbar). Full line, 10 keV electrons; dotted line 30 keV electrons; dashed line 60 keV electrons.

not consistent with the form of f (h) outlined above, however. Instead it is sharply peaked at the level of maximum ionisation and conductivity, and cannot be represented by the analytical form deduced by Huang and Hill (1989), even though it does tend to a roughly constant value at higher altitudes. The JIM profiles of k(h) indicate that, although above the ionisation peak the neutral gas is accelerated at all levels, the vertical transport of angular velocity from the height of the ionisation peak itself, is relatively inefficient, particularly where the ion density peak is lowest in the atmosphere (i.e., for the 60 keV electrons). The result is that, as ion– neutral collisions become less efficient at accelerating the neutrals (i.e., with increasing altitude) the neutral angular velocity returns towards—but does not quite reach—that of full corotation with the planet. One possible reason for the discrepancy between this present study and that of Huang and Hill (1989) is that the atmospheric region covered by JIM is above the homopause, by definition a region in which eddy diffusion is relatively insignificant compared with molecular diffusion. Thus the situation simulated by JIM may be inappropriate to the modelling carried out by Huang and Hill (1989). However it is also significant that Huang and Hill’s (1989) one-dimensional model could not account for horizontal transfer of angular momentum. In our Figs. 2 and 3 it is clear that this is considerable, once the neutrals have had an opportunity to respond to the forcing by the drifting ions. For instance, after 160 min of forcing by the ions (Figs. 2d and 3d), there are clearly strong zonal winds at all locations poleward of the main oval. Outside (equatorward) of the oval, wind patterns are also affected strongly and there is clearly equatorward transfer of momentum from the auroral oval. This leads to an interesting result: With large neutral winds developing both equatorward and poleward of the main auroral oval, and with ion winds constrained (beyond the oval) by relatively small values of electric field, we have a general situation in which the retrograde neutral velocities exceed ion velocities. This is seen clearly in

(b) Fig. 9. Values of k(h), at the height of the maximum in ionospheric density, for 60 keV electrons and VE = 3 MV: (a) southern hemisphere; (b) northern hemisphere.

Fig. 9 which plots k(h), at the height of the maximum in the ion density profile as a colour contour plot across both northern and southern polar regions. In Figs. 9a and 9b the auroral oval is clearly visible: the oval ‘ring’ where the k value is roughly 0.6. However, this auroral value of k is a local minimum and k values both equatorward and poleward are much larger. Figure 9 saturates at a k value of 1.0 but the results show values of up to 5 (i.e., zonal neutral winds up to 5 times the value of the zonal ion wind). The internal atmospheric electrodynamics of this configuration (as opposed to the magnetospheric electrodynamics), with the neutral gas acting as a dynamo and driving the ions, is intriguing. However, this lies beyond the scope of the current paper and is the subject of ongoing research.

7. Calculation of effective Pedersen conductivity Values of the effective Pedersen conductivity, ΣP as defined in Eq. (4) can be calculated by numerically integrating the product of σP (h), the local Pedersen conductivity, and (1 − k(h)) over the altitude range of our model. We carried out model runs at three equatorward voltages, 1, 3, and 10 MV (equivalent to E ∼ 0.2, 0.6, and 2.0 V m−1 ), for the flux of 10 and 30 keV electrons. For the 60 keV electrons, there were additionally runs at lower voltages of 0.03, 0.1, and 0.3 MV. The results are presented in Table 1, for vari-

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Table 1 Effective height-integrated Pedersen conductivity and ion–neutral parameters at latitude 58◦ N and SIII longitude 180◦ E Electron energy (keV)

ΣP (mho)

VE (MV)

ΣP (mho)

K = 1 − (ΣP /ΣP )

10

0.111

1.0 3.0 10.0

0.060 0.072 0.076

0.452 0.349 0.313

30

1.024

1.0 3.0 10.0

0.493 0.522 0.529

0.519 0.490 0.483

60

5.836

0.03 0.1 0.3 1.0 3.0 10.0

0.903 1.906 2.280 2.416 2.451 2.621

0.845 0.673 0.609 0.586 0.580 0.550

ous values of the incident electron energy and equatorward auroral voltage. The results show two clear trends: • For each of the three electron precipitation energies, the value of ΣP increases and the value of K decreases with increasing VE . • For constant VE , the value of K increases with increasing electron energy (as might be expected from inspecting Figs. 5–7). For values of VE  1 MV, our modelling predicts ΣP / ΣP ∼ 0.4 to 0.7. In their work, Huang and Hill (1989) predict similar ΣP /ΣP (= α, in their notation) for values of the eddy diffusion coefficient of between 1014 and 1015 × [n]−1/2 m1/2 s−1 , with values of ΣP /ΣP lower for smaller coefficients. They calculate the ratio ΣP /ΣP ∼ 0.01 for an eddy diffusion coefficient of 1012 × [n]−1/2 m1/2 s−1 , for example.

8. Varying the precipitation number flux at constant energy So far, we have investigated the ion–neutral dynamic coupling for a single value of the incoming electron precipitation number flux (namely 6.25 × 1012 m−2 s−1 ). Additional model runs were undertaken to study the effect of changing this number flux, for a constant electron energy of 30 keV and an applied auroral voltage of 3 MV (an electric field of ∼ 0.6 V m−1 ). In seven separate runs, the incoming electron number flux was set to 2.08 × 1011 , 6.25 × 1011 , 2.08 × 1012 , 6.25 × 1012 , 2.08 × 1013 , 6.25 × 1013 , and 2.08 × 1014 m−2 s−1 . Resulting profiles of electron density, Pedersen conductivity, zonal wind velocity and k(h) are shown in Figs. 10a and 10d, respectively. Figure 11a plots the associated values of integrated conductivity (ΣP , solid line) and effective conductivity (ΣP , dotted line), as

a function of the incoming electron number flux, with K (= 1 − (ΣP /ΣP )) plotted against number flux in Fig. 11b. In Fig. 11a we see the integrated conductivity rising to a value of around 20 mho for the largest fluxes. The effective conductivity rises much more slowly with largest values of around 3 mho. This is reflected by the steadily rising value of K (Fig. 11b). In Fig. 4a earlier, we looked at acceleration of the neutral gas after an instantaneous change in the auroral voltage from 0 to 3 MV. Figure 4a showed the situation for incoming electrons of 60 keV with a number flux of 6.25 × 1012 m−2 s−1 . In Fig. 12 we show the acceleration response for 30 keV electrons. Figure 12a is in the same format as Fig. 4a and plots neutral zonal velocity against time, here at pressure level 5 (0.4 µbar), the level at which the electron density is at a maximum for the 30 keV electrons (see Fig. 10a). The seven lines on Fig. 12a (with steadily increasingly negative asymptotic values of velocity) show the response for the seven increasing values of electron number flux detailed above. Clearly, for larger precipitation number fluxes (and therefore larger peak electron densities) the neutral velocity attains higher values (larger negative) and the terminal velocity is reached in a shorter duration. This latter point, the time taken to reach terminal velocity, is demonstrated by plotting it against number flux in Fig. 12b. Here we have defined the time to terminal velocity as being the time taken until the velocity attains 99.9% of its value after 90 min. Fig. 12b shows this time, indicative of the general ion– neutral coupling time, to vary from around 70 min for the smallest fluxes, to less than 20 min when subjected to the highest fluxes. The same data is plotted again in Fig. 12c, but this time as a function of the peak electron density (taken, for each value of incoming flux, from Fig. 10a). Finally, Fig. 12d is a scatter plot in which the time to terminal velocity is plotted as a function of electron density for all heights in the model (i.e., not just at the height of the peak electron density, as in Fig. 12c), and for all seven of the number fluxes. The points plotted here thus give a more general view of how the ion–neutral coupling time varies throughout the thermosphere as a function of ionospheric electron density.

9. Conclusions The parameter k(h) is both important and convenient for understanding the dynamics of magnetosphere–ionosphere– thermosphere coupling in the frame of reference of the rotating planet, since it is a measure of what fraction of the ion velocity is imparted to the neutrals. Our results show that this can be quite large, in excess of 70% in some cases. For 60 keV electron precipitation the neutrals reach a velocity (clockwise when viewed from above the north pole) around the auroral oval of ∼ 1 km s−1 , for a 10 MV equatorward voltage. The column mass of jovian air entrained in this neutral wind is ∼ 4 × 10−2 kg m−2 . If one assumes an averaged auroral oval colatitude of 16◦ (cf. Cowley and Bunce, 2001)

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209

(a)

(b)

(c)

(d)

Fig. 10. Profiles of (a) electron density, (b) Pedersen conductivity, (c) neutral zonal velocity, and (d) k(h) at 58◦ N 180◦ E for 30 keV electrons and VE = 3 MV. The seven lines on each plot show results for incoming number fluxes of 2.08 × 1011 (solid line), 6.25 × 1011 (dotted line), 2.08 × 1012 (dashed line), 6.25 × 1012 (dash–dot line), 2.08 × 1013 (dash–dot–dot line), 6.25 × 1013 (long dashed line), and 2.08 × 1014 (dotted line with + marks) m−2 s−1 . The extra dotted line at the left-hand side of panel (c) shows the zonal ion velocity, for comparison.

(a)

(b)

Fig. 11. (a) Integrated Pedersen conductivity (solid line) and effective integrated Pedersen conductivity (dotted line) as a function of electron number flux at 58◦ N 180◦ E. (b) Associated value of K as a function of electron number flux.

of width ∼ 1000 km, the kinetic energy imparted to the auroral thermosphere by ion–neutral coupling is 2.5 × 1018 J, and it may be that this can provide a source of heating for the jovian upper atmosphere if large scale motions can be converted into heat (see Miller et al., 2000). The form of k(h) obtained from our calculations shows a well-defined maximum at the altitude of the ionisation peak. At the higher altitudes in our model the value of k(h) declines monotonically with altitude; its value at the very top of the atmospheric region covered by JIM depends on

both the precipitating electron energy and the equatorward voltage applied. This altitude profile is not that predicted by Huang and Hill (1989) and shows that vertical transport of angular momentum is not very efficient in the altitude/pressure regime covered by JIM. It is worth noting that a less peaked k(h) profile would probably be produced if JIM incorporated the precipitation profiles used by 1D models such as that of Grodent et al. (2001). However, that would be due more to the electron precipitation/conductivity profiles being less peaked than to vertical transport of angular

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(a)

(b)

(c)

(d)

Fig. 12. (a) Zonal neutral velocity at 58◦ N 180◦ E and at the height of maximum electron density (pressure level 5) as a function of time. The seven lines correspond to the seven values of incoming number flux as given in Fig. 10. (b) Time taken to reach terminal velocity as a function of electron number flux at pressure level 5. (c) as (b) but plotted against electron density. (d) as (c) but for all heights in the atmosphere (not just level 5).

momentum. Our results show, as predicted by Huang and Hill (1989), that there can be large reductions in the effective Pedersen conductivity, ΣP , resulting from ion–neutral coupling. Acknowledgments G.M. and T.S. thank the UK Particle Physics and Astronomy Research Council for postdoctoral fellowships. The JIM model results presented in this paper were achieved using the Miracle Supercomputer, which is operated by the UCL HiPerSPACE centre and funded by PPARC. References Achilleos, N., Miller, S., Tennyson, J., Rees, D., 1998. JIM: a timedependent, three-dimensional model of Jupiter’s thermosphere and ionosphere. J. Geophys. Res. Planets E 103, 20089–20112. Achilleos, N., Miller, S., Prangé, R., Dougherty, M., 2001. A dynamical model of Jupiter’s auroral electrojet. New J. Phys. 3, 3.1–3.20. Atreya, S.K., 1986. Atmospheres and Ionospheres of the Outer Planets and Their Satellites. Springer-Verlag, Berlin. Clarke, J.T., Caldwell, J., Skinner, T., Yelle, R., 1987. 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, DC, 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. Cowley, S.W.H., Bunce, J.E., Stallard, T.S., Miller, S., 2003. Jupiter’s polar ionospheric flows: theoretical interpretation. Geophys. Res. Lett. 30, 1220. Drossart, P., Maillard, J.-P., Caldwell, J., Kim, S.J., Watson, J.K.G., Majewski, W.A., Tennyson, J., Miller, S., Atreya, S.K., Clarke, J.T., Waite Jr., J.H., Wagener, R., 1989. Detection of H+ 3 on Jupiter. Nature 340, 539–541. 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. Grodent, D., Clarke, J.T., Kim, J., Waite Jr, J.H., Cowley, S.W.H., 2003. Jupiter’s main auroral oval observed with HST-STIS. J. Geophys. Res. 108, 9921–9937. 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, 8101–8107. Hill, T.W., Dessler, A.J., Goertz, C.K., 1983. Magnetospheric models. In: Dessler, A.J. (Ed.), Physics of the Jovian Magnetosphere. Cambridge Univ. Press, Cambridge, pp. 353–395. Huang, T.S., Hill, T.W., 1989. Corotation lag of the jovian atmosphere, ionosphere and magnetosphere. J. Geophys. Res. 94, 3761–3765. 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 aurorae of Jupiter. Icarus 127, 379–393. Miller, S., 10 colleagues, 2000. The role of H+ 3 in planetary atmospheres. Philos. Trans. R. Soc. London Ser. A 358, 2485–2502.

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