Implications of rapid planetary rotation for the Dungey magnetotail of Saturn

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 11,, doi:1.129/24ja1716, 25 Implications of rapid planetary rotation for the Dungey magnetotail of Saturn S. E. Milan, E. J. Bunce, S. W. H. Cowley, and C. M. Jackman Department of Physics and Astronomy, University of Leicester, Leicester, UK Received 3 August 24; revised 13 December 24; accepted 1 January 25; published 15 March 25. [1] Employing our current understanding of the structure and dynamics of Saturn s magnetosphere, we present a time-dependent model of the kronian Dungey cycle magnetotail, which is based upon a modification of a similar model developed for Earth s magnetotail (Milan, 24a). The major difference arises due to the rapid rotation of Saturn and the partial corotation that this imposes on the open field lines threading the polar cap. This results in twisted tail lobes, with the form of concentric cylinders of oldest to newest open flux from the inside out. The oldest, and hence longest, open field lines form the backbone of a highly extended magnetotail. Surrounding this are bundles of field lines disconnected by tail reconnection, propagating down-tail at the solar wind speed. Owing to the twisted nature of the tail, these bundles remain entangled with the lobe cores to form exterior flux ropes. In the limit that the addition and removal of open flux from the magnetosphere by magnetic reconnection can be treated as a last-in-first-out system, we formulate a description of the flux transport within the tail and drive this with estimated dayside reconnection voltages deduced from Cassini observations of the IMF made upstream of Saturn (Jackman et al., 24). Citation: Milan, S. E., E. J. Bunce, S. W. H. Cowley, and C. M. Jackman (25), Implications of rapid planetary rotation for the Dungey magnetotail of Saturn, J. Geophys. Res., 11,, doi:1.129/24ja Introduction Copyright 25 by the American Geophysical Union /5/24JA1716$9. [2] Recent studies have sketched a relatively detailed picture of the expected dynamics of Saturn s magnetosphere and the flows which would be driven in the ionosphere by these dynamics [e.g., Cowley et al., 24]. The purpose of the present paper is to discuss the ramifications of these dynamics for the more distant magnetotail, in particular building upon an understanding of Earth s magnetotail developed by Milan [24a]. The main differences between the magnetospheres of Earth and Saturn arise due to the rapid rotation of Saturn and the partial corotation that this imposes on the magnetosphere. While corotation occurs in Earth s magnetosphere also, this is mainly confined to the near-earth plasmasphere region. In contrast, corotation is thought to influence the dynamics of the whole kronian magnetosphere, even in regions where the solar windmagnetosphere interaction is also important. At midlatitudes in the ionosphere and in corresponding regions of the magnetosphere, rapid planetary rotation coupled with centrifugally driven mass outflow from the inner magnetosphere results in the Vasyliunas cycle [e.g., Michel and Sturrock, 1974; Hill et al., 1974; Vasyliunas, 1983], in which magnetic reconnection has been implicated in the release of magnetic islands down the tail. At the magnetopause, magnetic reconnection allows the capture and subsequent release of solar wind magnetic field lines. This drives Dungey cycle flow in the magnetosphere and highlatitude ionosphere [Dungey, 1961] and gives rise to an extended magnetic tail formed from stretched open magnetic field lines known as the northern and southern magnetotail lobes, as proposed by Dungey [1965; see also Cowley, 1991;Milan, 24a]andobservedatSaturnby Ness et al. [1981, 1982]. [3] The magnetotail lobes map to the ionospheric polar caps; consideration of the expansion and contraction of these polar caps in response to magnetic reconnection gives clear insights into the mechanisms which couple solar wind mass, energy, and momentum into the magnetosphere, both at Earth [Russell, 1972;Siscoe and Huang, 1985;Cowley and Lockwood, 1992;Milan et al., 23;Milan, 24b]and at Saturn [Jackman et al., 24].The proportion of magnetic flux that is open or closed in a magnetosphere is not a constant but changes in response to competition between the rate of opening of flux by reconnection at the dayside magnetopause and flux closure by reconnection occurring in the magnetotail. The amount of open flux in the system can be quantified by measurement of the size of the ionospheric polar caps, which expand when dayside reconnection is dominant and contract when reconnection is dominant on the nightside [Milan et al., 23; Milan, 24b, and references therein]. Specifically, the rate of change of the flux in the polar cap F PC is controlled by the following statement of Faraday s Law: Z d dt PC B ds ¼ df PC dt ¼ F D F N ; ð1þ 1of1

2 where F D and F N are the rates (voltages) of creation and destruction of open flux at the low-latitude (dayside) magnetopause and in the (nightside) magnetotail, respectively, and B is the planetary magnetic field at ionospheric altitudes. Correlation of the so-deduced magnetopause reconnection rate with upstream measurements of the solar wind motional electric field then allows the efficiency of magnetic reconnection to be determined. This efficiency represents in effect the proportion of interplanetary magnetic field lines that impinge on the magnetosphere which reconnect with terrestrial field lines and is found to be close to 2% [Holzer and Slavin, 1979;Holzer et al., 1986; Reiff et al., 1981; Milan, 24a, 24b]. Recently, Jackman et al. [24] turned this argument around to predict the rate of magnetopause reconnection at Saturn from measurements of the interplanetary magnetic field (IMF) made upstream of the planet by Cassini. We use the magnetic reconnection rates determined in that paper to develop a model of the magnetotail response to coupling. [4] Isbell et al. [1984] speculated that torque imposed by the ionosphere on the open field lines would cause Saturn s magnetotail lobes to become highly twisted. More recent reports [e.g., Bunce et al., 23; Cowley et al., 24; Stallard et al., 24]havesuggestedthatwhiletheconductivity of the high-latitude ionosphere is not sufficient to maintain rigid corotation of the lobes, subcorotation at a reasonable fraction (1/3) of the planetary rotation rate does indeed occur. We now discuss the implications of this twisting of the magnetotail lobes for the solar windmagnetosphere interaction and derive a simple timedependent model that allows the form and dynamics of the tail to be deduced. 2. Saturn s Tail Versus Earth s Tail [5] As stated in section 1, the main difference between the magnetotails of Earth and Saturn is that the latter is twisted, whereas the former is not. We present a schematic view of the twisted kronian magnetotail lobes in Figure 1a; sandwiched between these lobes will be flux and plasma associated with the Vasyliunas process. Owing to the rotation of the planet, the sense of twist in the northern and southern lobes is opposite. Each field line crosses the magnetopause and exits into the interplanetary medium at a distance down-tail that is related to the time elapsed since the field line was reconnected (opened) at the dayside magnetopause and the stretching of the field line at the solar wind speed; older field lines, that is field lines that were opened more distantly in the past, stretch a greater distance downstream of the planet. In other words, the antisunward ends of the field lines are anchored in the solar wind, the anchor-point propagating downstream at the solar wind speed. If the polar cap subcorotates at one third of the planetary rotation rate, then a new turn is placed on the lobes every 3 hours or so. If the solar wind speed, which is constantly stretching the open lobe field lines, is 5 km s 1, then each turn is approximately 9 R S in length. [6] Jackman et al. [24] estimated that there is approximately 35 GWb of open flux in the kronian magnetosphere and that the average dayside reconnection rate is some 45 kv. Thus it might be expected that the open flux is Figure 1. A schematic view of the magnetotail lobes of Saturn. (a) Dotted and solid curves show the twisting of old and recently opened lobe field lines. The point at which field lines exit the tail across the magnetopause depends on the age of the field line, the time since reconnection at the dayside. The possible location of a tail X-line is indicated. (b) The same field lines after reconnection in the tail. The outcome is a closed field which corotates with the planet and an exterior flux rope. replenished every 1 days, which corresponds to 7 full rotations of the polar cap flux; clearly, the dynamics of the magnetotail will be highly dominated by this corotation. In the case of Earth, flux remains open for an average of 4hours,andtheplanetrotatesevery24hours;inthiscase corotation is not a major consideration. For illustrative purposes, we can study the effect of adding the corotation component to steady-state Dungey cycle ionospheric flow, as in Figure 2. This shows the Northern Hemisphere highlatitude ionosphere, with the polar cap approximately centered on the magnetic pole, bounded by the open/closed field line boundary or OCB indicated by a dark circle; inside this, field lines are open and map to the solar wind; outside of this region, field lines are closed and map to the conjugate ionosphere. The Dungey cycle flow (Figure 2a) comprises antisunward plasma drift across the polar cap with return flow at lower latitudes, flow streamlines crossing the OCB along those portions where reconnection is occurring, known as the merging gaps, shown dotted. As we initially assume the steady-state case, the rates of dayside 2of1

3 Figure 2. Schematic representations of steady-state ionospheric convection in the polar regions associated with (a) the Dungey cycle and (b) corotation-driven flow; thin, arrowed lines are flow streamlines. The thick circular line represents the boundary between open and closed field lines, the open/ closed field line boundary (OCB) or polar cap boundary; that portion shown dotted indicates the (top) dayside or (bottom) nightside merging lines. (c) The superposition of these components, for the case where corotation dominates over the Dungey cycle. A thin dotted line indicates the boundary between open flux associated with the Dungey cycle and that which corotates continuously with the planet. and nightside reconnection are equal, and the polar cap remains of uniform size (equation (1)). The corotation flow (Figure 2b) shows concentric flow streamlines. As described above, we expect the flow to be at near-rigid corotation equatorward of the OCB, with partial corotation inside the polar cap, though we have not attempted to indicate that here. The superposition of these two components depends on their relative strengths. For the case of Earth, Dungey cycle flow dominates, and the addition of corotation results in only a small perturbation of the flow pattern shown in Figure 2a. On the other hand, if corotation is dominant, as is the case for Saturn, then the resulting pattern is that shown in Figure 2c. We see a central core of the polar cap that remains open indefinitely, subcorotating with the planet. Field lines opened by reconnection at the dayside flow antisunward across the polar cap in the dusk sector, are then closed by reconnection at the nightside, and then move sunward in a return flow region confined to the dawn sector. These were the arguments employed by Cowley et al. [24] to determine the ionospheric flow patterns shown in their paper. Although the prediction of closed flow streamlines contained within the polar cap may seem counterintuitive, we show below that this is a natural outcome of the twisting of the magnetotail lobes. In what is to follow, we will refer to the ionospheric flow pattern of Figure 2c, and the associated magnetospheric convection, as a last-in-first-out system, in that it is field lines that have recently been opened on the dayside that are subsequently closed on the nightside; other open field lines which populate the inner polar cap do not participate in the Dungey cycle, except during large departures from the steady state that will be described later. We now turn to a discussion of the nonsteady but slowly varying state that is more appropriate to the true dynamics of magnetospheres, due to the time-dependence of reconnection processes. First we describe the well-understood magnetotail structure at Earth and then discuss the ramifications of the imposed corotation at Saturn. [7] Milan [24a] showed that the Earth s magnetotail can be treated as a first-in-first-out system. That is, open field lines propagate toward the neutral sheet of the tail as new open field lines are stacked up behind (causing the polar cap to expand), and older field lines are removed from the equatorial plane of the tail during substorms (causing the polar cap to contract). To a first approximation, the field lines follow each other toward the central plane of the tail, and their footprints across the polar cap, in orderly procession, as illustrated schematically in Figure 3a. Dotted lines indicate the boundaries between regions of open flux added during different intervals of magnetopause reconnection, numbered in chronological order. As new regions of open flux are added at the dayside, for instance region 6, then the polar cap expands and plasma flow is excited in the ionosphere to maintain a roughly circular polar cap. Subsequent closure of flux on the nightside removes the oldest open flux, the polar cap contracts, and flows are once again excited to redistribute the flux and plasma in the polar regions. This process results in the familiar twin-cell ionospheric convection pattern associated with the Dungey cycle [e.g., Cowley and Lockwood, 1992] and indicated for the steady state in Figure 2. Equatorward of the high-latitude convection pattern, plasma corotates with the planet, but this corotation is slow as discussed above. In the magnetotail the oldest field lines (region 1) will be stretched the furthest down-tail; the youngest (regions 5/6) will be the shortest. Very roughly, the polar cap can be thought of as a cross section of the near-earth magnetotail lobe, with the newest open flux forming the outer portion of the lobe and the oldest open flux lying adjacent to the plasma sheet. Reconnection at the neutral sheet, once it has pinched off the closed field lines of the plasma sheet, will merge the oldest open field lines with their counterparts in the opposite lobe. These are effectively removed from the system, and newer flux sinks toward the central plane of the tail to take their place. This first-in-first-out behavior allows a simple treatment of flux conservation to provide an estimate of the profile of open flux within the tail [Milan, 24a],which will be briefly discussed in section 3. 3of1

4 Figure 3. Schematic representations of the ionospheric convection in the polar regions of (a) Earth and (b) Saturn, in response to a burst of dayside reconnection, followed by nightside reconnection. The thick circular line represents the boundary between open and closed field lines, the open/closed field line boundary (OCB) or polar cap boundary; that portion shown dotted indicates the (top) dayside or (bottom) nightside merging lines. Thin dotted lines show the boundaries between regions of open flux created by separate bursts of dayside reconnection, numbered in chronological order of creation. Thin, arrowed lines are flow streamlines, and block arrows indicate the expansion or contraction of the polar cap. Plasma flows across the OCB at the merging gaps; away from the merging gap the OCB is adiaroic (not flowing across) and moves with the plasma flow. At midlatitudes, equatorward of the convection shown, the Earth s ionosphere corotates, though this is slow and has not been indicated. Corotation is much faster at Saturn and has been shown explicitly. Corotation within the kronian polar cap occurs at 1/3 of the speed equatorward of the OCB. 4of1

5 [8] In the case of Saturn this model is not appropriate, and in fact the lobe field lines can be thought of as a lastin-first-out system, as described above in relation to Figure 2c. As new open field lines are added to the front of the polar cap, they become entrained in the subcorotation imposed by the ionosphere (indeed, this probably represents a deceleration of their motion in the ionosphere, as prior to reconnection they will be moving at closer to rigid corotation [Cowley et al., 24]),asshowninanidealizedfashionin Figure 3b. The new region of flux, added over some period of hours, will form an annulus surrounding the preexisting regions of open flux (causing the polar cap to expand). This occurs because, as discussed above, the transport of flux in the zonal direction, driven by the imposition of partial corotation, is much more significant than the transport across the polar cap from noon to midnight, which is associated with the addition and removal of flux from the system by reconnection. [9] In the magnetotail, the new annulus of open flux will form a sheath of field lines encircling the older and hence longer open field lines which map to the more central polar cap, as shown in Figure 1a. The old open flux in the center of the polar cap might be expected to exist for considerable lengths of time; these field lines, which will form the core of the magnetotail lobes, will hence be stretched to great downstream distances by the flow of the solar wind. As a consequence of the lobe twisting, it is the newest field lines which will lie adjacent to the plasma sheet (as well as the tail magnetopause) in the near-saturn magnetotail and which will be reconnected by merging in the tail neutral sheet during kronian substorms ; each burst of reconnection will shave an annulus of open flux from the outside of the polar cap inward (causing the polar cap to contract). Such a newly closed field line is indicated in Figure 1b; this field line will subsequently corotate with the planet, forming the closed field line return flow indicated in Figures 2c and 3b. Owing to the twisting of the lobe field lines, the further down-tail the X-line is located, the further dawnward this will map in the ionosphere, displacing the auroral manifestation of the kronian substorm into the postmidnight sector (this is discussed in rather more detail by Cowley et al. [25]). [1] Figure 1b also shows the fate of field lines disconnected by reconnection in the neutral sheet. Clearly, these disconnected field lines cannot disentangle themselves from the inner core of tail flux, unlike the situation at Earth where disconnected field lines are free to accelerate down-tail and return to the solar wind. At Earth, antisunward flows in the plasma sheet are greater than the solar wind speed, such that the highly distended disconnected field lines eventually straighten again. We do not think that this will be possible in the tail of Saturn, and disconnected field lines will propagate antisunward at the solar wind speed, at the same speed as the stretching of the inner connected field lines, remaining entwined around the tail as a coherent structure. We call these exterior flux ropes to contrast them with plasmoids or flux ropes ejected in the central plane of the tail by the Dungey cycle at Earth and those associated with the Vasyliunas cycle in the equatorial plane of the tail at Saturn. [11] We see then that the oldest open flux which populates the central polar cap is effectively shielded from nightside reconnection by newer open flux at the outer edge of the polar cap. The oldest open field lines remain connected to the planet for extremely long periods of time, continuously subcorotating about the pole, explaining the closed flow streamlines in Figure 2c. [12] The ionospheric dynamics can be summarized as follows: field lines corotate with the planet at all times, but whether the corotation is rigid or partial depends on whether the field lines are closed or open. As new flux is opened, the polar cap expands to lower latitude and field lines poleward of the expanding boundary slow to one third of rigid corotation; as flux is closed, the polar cap contracts and field lines equatorward of the contracting boundary are accelerated back to near-rigid corotation. 3. A Quantitative Approach [13] Having established the order in which field lines are added to the tail and subsequently removed, we can construct a model of how these field lines are stretched by the flow of the solar wind. Figure 4a shows the first-infirst-out model established for Earth by Milan [24a], appropriate for the Northern Hemisphere. The abscissa is downstream distance and the ordinate is the amount of magnetic flux within each magnetotail lobe, the connected tail. For simplicity it is assumed that the length of the tail is so great that the dayside and nightside reconnection X-lines are located at x =. Within the tail, at x =(i.e.,nearthe Earth) the amount of open flux in the tail equals that threading the polar cap F PC,whichcanbedeterminedfrom ionospheric measurements. At further down-tail distances the flux decreases as field lines cross the magnetopause and enter the solar wind. Most recently opened field lines exit the magnetotail relatively close to the Earth; older field lines are stretched to greater distances. The rate at which field lines leave the tail as a function of downstream distance depends on the rate of dayside reconnection F D at the time of their creation. At times when the reconnection rate is high, dense bundles of flux leave the tail and the flux content of the lobe decreases rapidly with distance; when the reconnection rate is low, few field lines cross the magnetopause and the flux content remains nearly uniform. The lower panel shows example rates of dayside and nightside reconnection on a scale that runs backward in time, such that the bursts of reconnection line up with the field lines that they created as they cross the magnetopause and join the IMF; if a field line leaves the tail at a distance x downstream at time t, then it was opened at x =byaburst of dayside reconnection which occurred at time t x/, where is the solar wind speed. This allows the following statement of the flux content of the distant lobe to be formulated [Milan, 24a]: F CT ðx; tþ ¼ F PC ðþ t 1 F D ðt x= Þdx; ðearthþ ð2þ where F CT is the flux in the connected tail. That is, near the Earth the connected flux is equal to that threading the polar cap, but this decreases with down-tail distance at a rate governed by the past history of the dayside reconnection rate. 5of1

6 Figure 4. A schematic representation of the field lines forming the magnetotail lobes of (a) Earth and (b) Saturn. The dark box to the left indicates the open flux in the polar cap. The open flux in the tail (dark grey region) decreases with down-tail distance at a rate governed by the dayside reconnection rate at the time that the open flux was created, F D (t x/ ). Lobe field lines disconnected by tail reconnection are shown in light grey. In the case of Earth these are sandwiched between the lobes and are free to accelerate down-tail to return to the solar wind. In the case of Saturn, these are wrapped around the lobes to form exterior plasmoids. (Note that due to the directions of the arrows on the field lines, Figure 4a is appropriate for the northern lobe of Earth, whereas Figure 4b is appropriate for the southern lobe of Saturn.) 6of1

7 [14] At Earth, when flux is removed by tail reconnection, it is the oldest, longest field lines that become disconnected to form the disconnected tail [Cowley, 1991]. In Figure 4a this removal of flux is simply effected by the decrease in F PC for F N > (equation (1)), resulting in the whole F CT curve moving downward. The point D can be thought of as the dayside merging line where new open flux is added to the system, and the point N is the nightside merging line where old open flux is removed. The disconnected field lines, now indicated below the abscissa, occupy the equatorial plane of the tail, connecting across the neutral sheet into the Southern Hemisphere. The earthward ends of these propagate down-tail at the plasma sheet speed V PS. These field lines can be thought of as forming a plasmoid ejected down the tail following substorm-associated reconnection. The earthward ends of these highly kinked field lines contract along their length to be returned to the solar wind. Cowley [1991] estimated that the speed of contraction of these field lines would be V PS 1.2 so that the disconnected tail would be approximately 5 times the length of the connected tail, the distance the solar wind ends travel before the kink catches up. [15] These facts having been recognized, it is possible to formulate the total amount of flux (connected and disconnected) in the tail F and then solely the disconnected flux F DT (see Milan [24a]): Fx; ð tþ ¼ F PC ðþ t 1 and F D ðt x= Þdx þ 1 F N ðt x=v PS Þdx; ðearthþ ð3þ V PS F DT ðx; tþ ¼ Fx; ð tþ F CT ðx; tþ; x < L CT ; ðearthþ Fx; ð tþ; x > L CT where L CT is the length of the connected tail, the point at which F CT =. [16] We now consider the structure of the kronian tail, formed by similar bursts of dayside and nightside reconnection (Figure 4b). The picture described above for Earth has to be modified for Saturn, as now both dayside and nightside merging lines add and remove open flux from the same place, the outer edge of the polar cap, shown by the colocation of D and N in Figure 4b. In other words, because of the rapid rotation of the planet, it is the most recently opened field lines that are disconnected by tail reconnection, a last-in-first-out system, as described in section 2. In this case, the origin of Figure 4b can be thought of as the center of the polar cap, with F PC increasing outward toward the OCB, or, equally, the x-axis is the central axis of the twisted lobe, with F increasing outward toward the magnetopause and the plasma sheet. Owing to the twisting of the lobe field lines (not represented in the figure), once they are disconnected, field lines from the northern lobe join into the southern lobe, not simply across the central plane of the tail, as is the case at Earth, but across the dusk flank, forming the planetward end of the exterior flux rope shown ð4þ in Figure 1b. The lightly shaded region in Figure 4b represents the flux contained within such an exterior flux rope (cf. Figure 1b); at the antisunward end field lines leave the tail and join into interplanetary space (these are the ends formed by reconnection at the dayside), whereas at the sunward end the field lines cross into the opposite hemisphere across the dusk flank (formed by reconnection in the tail). Planetward of the exterior flux rope, more field lines are shown leaving the tail, which have been formed by the most recent burst of dayside reconnection. [17] Making these assumptions, the total flux in the tail is simply (cf. equation (3)) Fx; ð tþ ¼ F PC ðþ t 1 F D ðt x= Þdx þ 1 F N ðt x= Þdx: ðsaturnþ ð5þ Of this, the disconnected portion (light grey in Figure 4b) is given by F DT ðx; tþ ¼ 1 where F Dð t x= Þ 8 1 F D ðt x= Þ; >< ¼ >: ; F N ðt x= Þdx F Dð t x= Þdx; ðsaturnþ ð6þ F N ðt x= Þdx > F N ðt x= Þdx ¼ F Dð t x= Þdx F Dð t x= Þdx : ðsaturnþ This relationship states that field lines crossing the magnetopause into the solar wind are part of the connected tail if insufficient tail reconnection has occurred to disconnect them; otherwise, they are part of the disconnected tail. In other words, the field lines belong to the light shaded region of Figure 4b if more tail reconnection has taken place recently than dayside reconnection. On the other hand, if dayside reconnection has dominated recently, the field lines are connected and belong in the dark shaded region. Explicitly, in the case presented in Figure 4b, during the most recent burst of dayside reconnection F D >but F D =,asnonightsidereconnectionhasoccurredsince;the flux leaving the tail is connected flux, and the amount of disconnected flux does not change. Further down-tail, corresponding to field lines reconnected more distantly in the past, the amount of disconnected flux in the tail increases due to a burst of nightside reconnection. At this time/distance, both F D =andf D =.Furtherdown-tail still, a previous burst of dayside reconnection means that field lines are crossing the magnetopause; these are initially disconnected field lines as F D > (the integral of F N is greater than the integral of F D), but eventually it is connected field lines that are leaving the tail as the ð7þ 7of1

8 disconnected flux is exhausted. We note that this formulation is very similar to the treatment of lobe reconnection in the terrestrial magnetosphere in the work of Milan [24a], which also can be thought of as a last-in-first-out process. Finally, the connected tail profile is simply F CT ðx; t 4. An Example Þ ¼ Fx; ð tþ F DT ðx; tþ: ðsaturnþ ð8þ [18] Having formulated a model of the structure of Saturn s distant magnetotail in response to solar wind coupling, we now drive this with realistic estimates of the dayside reconnection voltage derived by Jackman et al. [24] from measurements of the IMF made upstream of Saturn by the Cassini spacecraft as it approached Saturn prior to Saturn orbit insertion. These predicted dayside reconnection voltages, for the period day 225, 23, to day 6, 24, are shown in Figure 5a. The reconnection voltages range between and 4 kv in the main, with a few brief excursions to values as high as 6 or 8 kv; the average voltage is approximately 45 kv. The voltages have a bimodal behavior, remaining low (<5 kv) for extended periods, followed by intervals of elevated voltage (>1 kv). This behavior mirrors the occurrence of welldeveloped corotating interaction regions (CIRs) in the solar wind at 9 AU. Periods of high and low voltage correspond to intervals of compressed and rarefied solar wind, respectively. In addition, the reconnection rate is modulated by the north-south orientation of the IMF; if the IMF is directed northward (southward), the field is antiparallel (parallel) to the subsolar kronian field and reconnection is most (least) efficient. This modulation occurs on timescales much shorter than the occurrence and duration of CIRs and hence is not readily visible in Figure 5a. It should be noted that the reconnection rates shown are by no means definitive, though it is intended that they will be verified by comparison with HST observations of changes in size of the polar cap [e.g., Gérard et al., 24; Clarke et al., 25], muchas has been done at Earth [e.g., Milan, 24b]. A very preliminary analysis (E. J. Bunce et al., Cassini observations of the interplanetary medium upstream of Saturn and their relation to the Hubble Space Telescope aurora data, submitted to Advances in Space Research, 25) suggests that the reconnection rates are indeed realistic. [19] From this reconnection voltage time series, we show a plausible response of the open flux content of the kronian magnetosphere in Figure 5b. This has been constructed by integrating F D and F N (equation (1)). Initially, F N is set to zero, and equation (1) is integrated until an upper limit of F PC =45GWbisreached.Wetheninitiatetailreconnection at an arbitrary rate of F N =3kVandcontinueintegration until a lower threshold of F PC =15GWbisreached.Tail reconnection is then switched off again. These upper and lower limits are estimated from previous observations of the variability of the latitude of the kronian aurora [Jackman et al., 24]. Although the exact nature of tail reconnection onset, rate, or duration is not currently known, we feel that our estimate of F PC is representative of the expected behavior of the kronian system: 3 substorms are found in the 2-day interval or approximately 3 4 per solar rotation [Jackman et al., 24]. The repetition rate of the substorms depends on the dayside coupling rate; if the coupling rate is low, then several days can pass between substorms (e.g., days ); if it is high, many substorms can occur in a similar period (e.g., days ). [2] Figure 5c shows the profile of connected flux in each tail lobe, derived from equations (5) (8). At Saturn (x =) the amount of flux in the lobe is just that in the polar cap, F PC. As the size of the polar cap increases, the near-saturn tail inflates, and as time progresses the inflated region progresses further down-tail as the newly opened field lines are stretched downstream at the solar wind speed. This inflated region extends the greatest distance downstream when the dayside reconnection rate is relatively low, such that tail reconnection does not occur for extended periods of time (e.g., prior to day 343). At the onset of tail reconnection, however, the most recently opened field lines are disconnected to form exterior flux ropes. These bundles of disconnected flux are shown in Figure 5d, carried down-tail at the solar wind speed. The length of each flux rope will depend on the time over which dayside reconnection creates new open flux prior to it being disconnected by tail reconnection, essentially the duration between each substorm. For an intersubstorm period of 1 days, this translates to a stretching of these field lines of approximately 7 R S, in which time the field lines are twisted through eight turns. [21] In our model, the central 15 GWb of polar cap flux are never disconnected, and in essence the model assumes that these field lines are of infinite length (hence the residual connected flux of 15 GWb at X = 15, R S (6 AU) and beyond at all times). In practice, our assumption that open flux is added and removed from the polar cap in exact concentric annuli is unlikely to be valid, for instance if the closure of flux during substorms is especially rapid such that a very significant fraction of the open flux is closed in a short period of time. Even so, we expect that the oldest open field lines will exist for long periods of time, and the connected tail will often extend considerably further downstream than the 15, R S shown in Figure Conclusions [22] We have presented a simplified model of the transport of open flux within Saturn s magnetotail and formulated a means of determining the structure of the distant magnetotail in terms of dayside coupling with the solar wind and nightside reconnection. We show by consideration of both the steady-state and time-dependent cases that the flux transport in the kronian system can be approximated to a last-in-first-out system, in contrast to the first-in-firstout paradigm appropriate at Earth. As at Earth, the interaction between the solar wind and the magnetosphere of Saturn produces an extended magnetotail as open field lines are stretched in the downstream direction. However, the twisting of the lobe field lines imposed by the atmospheric torque associated with rapid planetary rotation results in this tail having a significantly modified structure. Nevertheless, a treatment of open flux transport within the tail allows the structure to be determined from a knowledge of changes in the size of the polar cap and the dayside 8of1

9 Figure 5. (a) The dayside reconnection voltage FD predicted for Saturn from upstream measurements of the IMF by Cassini, for a 2-day interval as Cassini approached SOI. (b) A possible time series of polar cap flux FPC, constructed by integration of the dayside reconnection voltage, with kronian substorms initiated when the flux reaches 45 GWb (see text for details). (c) The modeled connected flux content of one magnetotail lobe, driven by FD and FPC. (d) The same for the disconnected flux. reconnection rate, in much the same way as for Earth [Milan, 24a]. We expect that this description is appropriate for the magnetspheres of other rapidly rotating planets, for instance Jupiter, also. [23] The tail is found to inflate during periods of dayside coupling, this inflation being stretched down-tail at the solar wind speed. The length of the inflated section of tail stretches a distance down-tail governed by the time since 9 of 1

10 the last episode of tail reconnection; the lower the dayside reconnection rate, the longer duration between substorms, and hence the longer the inflated tail. During kronian substorms the newest (shortest) open field lines are disconnected and propagate down-tail at the solar wind speed while wrapped around older, longer connected field lines, forming an exterior flux rope. An inner core of connected field lines is expected to extend very great distances in the antisunward direction, only being reconnected by extreme nightside reconnection bursts which close most of the polar cap flux. Sandwiched between the two lobes will be plasmoids associated with the Vasyliunas cycle. [24] Furthermore, the twisted nature of the magnetotail lobes leads to interesting predictions regarding the nature of kronian substorms. The auroral manifestation of tail reconnection will be displaced into the postmidnight sector by an amount governed by the down-tail distance of the X-line, and the return flow will be in the same sense as corotation (see also Cowley et al. [25]). In the distant tail, plasma jets associated with acceleration at the nightside X-line will be observed not only in the plasma sheet boundary layer (PSBL), as at Earth, but also adjacent to the tail magnetopause, inside those field lines that comprise the exterior flux rope. It is possible that these predictions can be tested during Cassini s tour of the kronian magnetosphere. [25] Acknowledgments. SEM and SWHC are supported by PPARC grant PPA/N/S/2/197. EJB is supported by PPARC grant PPA/P/S/ 22/168. [26] Lou-Chuang Lee thanks James Slavin and Vytenis M. Vasyliunas for their assistance in evaluating this paper. References Bunce, E. J., S. W. H. Cowley, and J. A. 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