# Global structure of Jupiter's magnetospheric current sheet

## Abstract

[1] Jupiter's magnetosphere contains a gigantic sheet-like structure located near its dipole magnetic equator that contains most of the plasma and energetic particles swirling in Jupiter's magnetosphere. Called the “current sheet,” it behaves like a rigid structure inside a radial distance of ∼50 *R*_{J} where the periodic reversals of the *B*_{r} component are highly predictable. Beyond a radial distance of ∼25 *R*_{J}, the tilted current sheet lags behind the dipole magnetic equator in proportion to the radial distance of the observer. On the nightside, at radial distances >50 *R*_{J}, the current sheet is seen to become parallel to the solar wind flow direction. In this work, we analyze magnetic field observations from all six spacecraft that have explored Jupiter's magnetosphere (Pioneers 10 and 11, Voyagers 1 and 2, Ulysses, and Galileo) to determine the global structure of Jupiter's current sheet. We have assembled a database of 6328 current sheet crossings by using an automated procedure which utilizes reversals in the radial component of the magnetic field to identify current sheet crossings. The assembled database of current sheet crossings spans all local times in Jupiter's magnetosphere under differing solar wind conditions. The new model is based on a further generalization of the hinged-magnetodisc models of Behannon et al. (1981) and Khurana (1992). Four new features of the improved model are that (1) close to Jupiter, the prime meridian of the current sheet (the azimuthal direction in which it attains its highest inclination) is found to be shifted by 2.2° from the VIP4 model current sheet (Connerney et al., 1998). (2) In addition to the delay caused by the wave travel time, the location of the current sheet is further delayed because of the sweep-back of the field lines. (3) The signal delay associated with wave propagation is seen to vary both with radial distance and local time, and (4) the current sheet is allowed to become parallel to the solar wind direction at large distances in the magnetotail in agreement with the observations. The new model is much superior at predicting current sheet crossing times than previously published models (especially in the midnight and dusk sectors). The RMS error of fit between the modeled and observed current sheet crossing longitudes is 19.3°. A comparison of the new model with previous models is presented.

## 1. Introduction

[2] Magnetic field and energetic particle observations from Pioneer 10 and Pioneer 11 [*Smith et al.*, 1974, 1976; *Van Allen et al.*, 1974, *Van Allen*, 1976; *McDonald and Trainor*, 1976] showed the presence of a thin (half thickness ≈2.5 *R*_{J}) equatorial current sheet in Jupiter's dawn magnetosphere. Further observations from Voyager 1 and Voyager 2 [*Ness et al.*, 1979a, 1979b, 1979c; *Bridge et al.*, 1979a, 1979b] established that the current sheet also contains low-energy plasma and showed that it merges into the magnetotail current system on the nightside. Analyses using pressure balance argument showed that the average energy density of ions is ≥30 keV in the current sheet [*Walker et al.*, 1978; *Lanzerotti et al.*, 1980].

[3] The structural studies of the current sheet from Pioneer and Voyager data revealed that at radial distances >25 *R*_{J}, the current sheet crossings do not coincide with the expected location of the dipole magnetic equator but are delayed in time [*McKibben and Simpson*, 1974; *Carbary*, 1980]. Following a lead provided by the theoretical works of *Northrop et al.* [1974] and *Eviatar and Ershkovich* [1976], the delay was modeled by researchers as an information propagation lag time that increased linearly with radial distance [*Kivelson et al.*, 1978; *Carbary*, 1980; *Goertz*, 1981; *Behannon et al.*, 1981].

[4] Seven spacecraft (Pioneer 10, 11; Voyager 1, 2; Ulysses, Galileo, and Cassini) have now visited the magnetosphere of Jupiter. Figure 1 shows an equatorial view of the trajectories of these spacecraft. Cassini skimmed the boundaries of Jupiter's magnetosphere in January 2001 but did not come close enough to provide useful information on Jupiter's current sheet. The other six spacecraft have between them sampled the Jovian current sheet over all longitudes and local times over a broad range of radial distances and solar wind conditions. We use magnetic field observations from these six spacecraft to locate all of the current sheet crossings and develop a global model which is in better agreement with the physics of the problem and is valid over all local times.

## 2. Coordinate Systems

[5] In this work, we use two different coordinate systems, a right-handed Jupiter centered spherical coordinate system rotating with Jupiter and a nonspinning Cartesian coordinate system that uses Sun direction as a reference. Traditionally, for observations from Jupiter, astronomers and planetologists have used a left-handed Jupiter-centered spherical coordinate system (*R*, θ, λ) called system III (see *Dessler* [1983] for a definition), where *R*, θ, and λ are the radial distance, colatitude, and west longitude of the observation. System III (sIII) is a left-handed coordinate system. In the pre-Galileo era, the space physics community adopted sIII for use with spacecraft and planetary trajectories. However, in accordance with the SI convention, the magnetic field data were presented in a right-handed spherical coordinate system. In this work, we have rationalized the use of the coordinate systems and use a right-handed coordinate system (*R*, θ, ϕ) for both data and trajectories. The sIII right-handed coordinate system used by us is identical to the sIII system except that its azimuthal coordinate ϕ(= 360° − λ) increases toward east. In order to minimize confusion, we have also reexpressed the equations from previous publications in the sIII right-handed coordinates.

[6] The second coordinate system used is called Jupiter-Sun-orbit (JSO) coordinate system (*x*, *y*, *z*) which has its *x* axis pointing to the Sun and its *z* axis is perpendicular to the orbital plane of Jupiter. The *y* axis is normal to *z* and *x* axes and completes the triad. This coordinate system is useful for studying structures and phenomena that are influenced by the solar wind.

## 3. Data

[7] A dominant feature of the magnetic field observations from a low-latitude spacecraft in Jupiter's magnetosphere (see Figure 2) is the periodic reversal of the radial component at the rotation rate of Jupiter. This periodicity caused by the up and down motion of the tilted magnetic dipole equator and the Jovian current sheet over the spacecraft can be used to determine the location of Jupiter's current sheet. When the spacecraft is above (below) the current sheet, the radial component of the magnetic field is positive (negative). Thus a change of sign of *B*_{r} from positive to negative marks a north to south (N → S) crossing where the spacecraft moves from north of the current sheet to its south. Similarly, a change of *B*_{r} from a negative value to a positive value marks a south to north (S → N) crossing. In an average sense, the *B*_{θ} component is always positive in the equatorial plane and because the Jovian current sheet is thin, the relation ∇ · **B** = 0 implies that *B*_{θ} does not change appreciably across the current sheet. Modeling of data from the dawn/midnight sector shows [*Khurana*, 1992] that the half thickness of the current sheet is ∼2.5 *R*_{J} in that sector. In much of the magnetosphere, the azimuthal component of the magnetic field is seen to be out of phase with the radial component (see Figure 2) giving the magnetic field lines a swept-back configuration. *Hill* [1979] and *Vasyliunas* [1983] showed that the sweepback of the field lines results from a radial current flowing in the equatorial plane which reinforces corotation on the outflowing plasma. *Khurana and Kivelson* [1993] analyzed the radial currents in the Jovian equatorial plane and concluded that the plasma corotation in the postmidnight quadrant of Jupiter's magnetosphere could be maintained up to a radial distance of ∼50 *R*_{J} if the outflow rate in that quadrant does not exceed 2.5 × 10^{29} amu/s. Recent works have explored the relationship between the Jovian aurora and the equatorial radial currents [*Hill*, 2001; *Cowley and Bunce*, 2001; *Khurana*, 2001].

[8] In this work we have used all of the magnetic field data available from Pioneers 10 and 11, Voyagers 1 and 2, Ulysses, and Galileo to understand the global structure of the Jovian current sheet. For Pioneers and Ulysses, the available data set resolution was 1 min. For Voyagers we used the 48 s averaged data. For Galileo, the data from all three telemetry modes (LPW, Δt = 0.333 s; RTS, Δt = 24 s; and MRO, Δt = 32 min) were used. To determine the current sheet crossings, the data from all of the spacecraft were first averaged over running windows of 32 min duration. We identified magnetopause crossings visually and excised the data collected from the magnetosheath and the solar wind regions. Next, a computer program identified 6328 current sheet crossings from the reversals of the *B*_{r} component.

[9] The current sheet behaves like a rigid structure inside a radial distance of ∼50 *R*_{J} where the periodic reversals of the *B*_{r} component are highly predictable. Figure 3 shows magnetic field data from the dawn and dusk sectors of the Jovian magnetotail over a radial distance range of 40–85 *R*_{J}. Inside of ∼50 *R*_{J}, the current sheet crossings are regular, with only a few crossings qualifying as multiple crossings where the spacecraft encounters *B*_{r} = 0 more than once during its traversal from one lobe of the magnetosphere to the other. However, as the observations from Figure 3 show, beyond 50–60 *R*_{J} the current sheet becomes “floppy” where multiple crossings of the current sheet are common. The main reason for these oscillations of the current sheet at large distance is that because of the reduced field strength, the equilibrium location of the magnetotail changes strongly in response to changes in the solar wind conditions. In addition to the magnetotail motions, we find that the *B*_{r} component of the magnetic field becomes extremely irregular in the dusk sector beyond a radial distance of ∼60 *R*_{J} (see Figure 3, right). We do not fully understand the reason for the irregular nature of the *B*_{r} component on the duskside, but a part of the answer may lie in the fact that the current sheet becomes much thicker (half-thickness > 6 *R*_{J}) on the duskside so that the spacecraft spends more of its time in the high β current sheet where natural waves and fluctuations are large. The large thickness of the current sheet on the duskside can be gauged from the facts that the *B*_{θ} component is stronger on the duskside and the lobe-like quiet field regions are absent. In this work, we have excluded such chaotic periods from our database of current sheet crossings.

## 4. Current Sheet Description

*Z*

_{cs}is the height of the current sheet in sIII (right-hand) coordinates, ρ is the cylindrical radial distance of the observer from Jupiter's spin axis, θ

_{cs}is the tilt of the magnetodisc with respect to the planetary equator, and ϕ′ is the azimuthal direction (called the prime meridian) in which the elevation of the current sheet is maximum. From the VIP4 model of Jupiter's internal field [

*Connerney et al.*, 1998], θ

_{cs}= 9.52° and ϕ′ = 339.4° (east longitude).

*R*

_{J}are delayed from the expected dipole equator crossings in proportion to the radial distance of the observer (see Figure 4, where we show current sheet crossing longitudes from Voyager 1). This has been traditionally understood in terms of a signal delay required for the information about the motion of the dipole to propagate to the outer magnetosphere.

*Northrop et al.*[1974] provide a more accurate description of the situation by using the concept of a wave packet traveling in a subcorotating magnetosphere in the presence of a radial outflow (

*u*

_{ρ}). Northrop et al. showed that the incremental delay

*d*δ/

*d*ρ in the arrival of information about the magnetic equator at a radial distance ρ is given by

_{J}and Ω

_{m}are the angular rotation rates of Jupiter and the magnetosphere, respectively, and

*V*

_{A}is the local Alfven wave velocity. Northrop et al. used

*Mestel*'s [1961, 1968] MHD solution to relate the magnetic field configuration to the plasma flow:

*m*is a constant along a field line. In the ionosphere of Jupiter,

*B*

_{ϕ}is close to zero; therefore

*m*can be identified as the angular velocity of the ionospheric plasma (Ω

_{i}). Following

*Goertz*[1981], equation (2) can then be rearranged with the help of (3) as

*u*

_{ρ}> 0) plasma in the magnetosphere (the second term on the right-hand side). Integrating (4) over ρ, we get

_{r=1}is the prime meridian of the current sheet near Jupiter and

*Kivelson et al.*[1978] put forward the first computational model for the current sheet structure that included wave delay for current sheet crossings observed beyond a radial distance of 14

*R*

_{J}

*.*Later, models by

*Behannon et al.*[1981],

*Goertz*[1981],

*Khurana and Kivelson*[1989], and

*Khurana*[1992] generalized the model for use with both Pioneer and Voyager data. However, all of the previous models have ignored the delay, δ

_{B}, arising from the bend-back of the field lines.

[12] In addition to the systematic delay seen in all of the current sheet crossings, it was observed that for spacecraft located north of Jupiter's equatorial plane, the N→S crossings are delayed more than the south to north (S → N) crossings. This effect has been understood to be related to the hinging of the current sheet, as illustrated in Figure 5. A spacecraft located at a fixed Jovian latitude and radial distance is initially north of the fully tilted current sheet. As Jupiter rotates, the current sheet moves over the spacecraft and the spacecraft finds itself south of the current sheet (a N→S crossing). As the figure shows, the hinged current sheet would arrive later than the fully tilted current sheet. The figure also shows that the S→N crossing would be observed sooner for the hinged current sheet than for the fully tilted current sheet. The hinging model also predicts that the situation is reversed for a spacecraft located south of Jupiter's equatorial plane. For such a spacecraft, the S→N crossings would be delayed more than the N→S crossings.

*Behannon et al.*[1981], who rewrote equation (1) as

_{D}− Ω

_{J}ρ/

*U*, ϕ′

_{D}is the prime meridian of the dipole,

*a*

_{0}is the hinging distance, Ω

_{J}is the angular velocity of Jupiter, and

*U*is the wave propagation speed. Near Jupiter, in the prime meridian (where ϕ = ϕ′ and the current sheet achieves its highest elevation),

*Z*

_{cs}= ρ tan θ

_{cs}, but for ρ ≫

*a*

_{0},

*Z*

_{cs}approaches a constant value,

*a*

_{0}tan θ

_{cs}.

*Goertz*[1976, 1979] and

*Kivelson et al.*[1978] have shown that for Pioneer 10 observations, the current sheet did not appreciably bend away from the dipole equator. Another problem with equation (8) is that different hinging distances are required for Voyager 1 and Voyager 2 flybys to obtain good fits. These inconsistencies were resolved by

*Khurana*[1992], who suggested that the hinging was caused by solar wind forcing and not by the centrifugal force acting on the plasma. He chose to hinge the current sheet at a fixed

*x*(JSO) distance rather than at a fixed radial distance. He generalized equation (8) to

*Khurana*[1997]). However, in the dusk sector, the predicted current sheet crossings are systematically delayed compared with the observations. We have therefore generalized the

*Khurana*[1992] model further by including three additional effects. First, in the determination of prime meridian, ϕ′, we now explicitly include its dependence on the field line geometry (see equation (5) above). Second, we let the wave velocity

*v*be a function both of radial distance and local time, Ψ. Finally, we let the current sheet become parallel to the solar wind direction and not the Jovian equator at large distances. The equation describing the new model is given by

*x*

_{H}is the hinging distance and θ

_{sun}is the angle between the Sun-Jupiter line and the Jovigraphic equator. The functional form of the prime meridian longitude, ϕ′, is described in the next section. Figure 6 plots the location of the current sheet obtained from equation (13) in three pseudo-meridians in which the tilt of the current sheet is maximum, zero, and minimum, respectively, with respect to the Jovian equator (ϕ = ϕ′, ϕ = ϕ′ + 90° and ϕ = ϕ′ + 180°). For comparison, we also show the locations of the dipole magnetic equator and the current sheet of

*Khurana*[1992] in the same meridians. For this simulation, we chose θ

_{sun}positive, i.e., the solar wind flow has a southward component and

*x*

_{H}= −47

*R*

_{J}

*.*As shown in the figure, the hinging variable

*x*

_{H}acts in such a way that for

*x*<

*x*

_{H}, the current sheet is collocated with the dipole magnetic equator but becomes parallel to the solar wind flow for

*x*≫

*x*

_{H}.

## 5. Determination of the Prime Meridian Longitude

[16] As discussed above, new observations show that both the prime meridian and the elevation angle of the current sheet vary with radial distance and local time in a nonlinear fashion. Therefore a direct inversion of equation (13) is not possible. We solve the problem by using a two-step procedure. In step one, we determine the prime meridian as a function of radial distance and local time by exploiting the fact that for any two consecutive current sheet crossings, the prime meridian and latitude of the current sheet do not change appreciably. In step two, we use direct substitution to determine the hinging distance of the current sheet.

*x*and

*y*of the JSO system can be assumed to be constant in equation (13) for the two crossings. In addition, over the small radial distance and local time covered by the spacecraft over this time, the prime meridian ϕ′ of the current sheet, which is a slowly varying function of radial distance and local time, can also be assumed to remain constant. Equation (13) shows that any two neighboring current sheet crossings occur where the vertical location of the spacecraft equals that of the current sheet, i.e.,

*Z*

_{sc1}=

*Z*

_{sc2}. Thus equating (14) and (15), we get

*n*is either 0 or 1. Thus there are eight different solutions depending on the signs used in the left-hand and right-hand sides of equation (17) and the value chosen for

*n*. Four of the solutions are trivial and arise when the same sign is used on both sides of (17) (and correspond to situations when both chosen current sheet crossings are either N→S or S→N crossings). However, when one considers a pair in which a N→S current sheet crossing precedes a S→N current sheet crossing, she gets

_{1}is numerically always greater than the cyclic variable ϕ

_{2}by adding 360° to ϕ

_{1}, if needed (because in sIII right-hand system, the longitude of a slow moving spacecraft must decrease with time). Figure 7 shows the observed ϕ′ calculated from equations (18) and (19) used on the complete database of current sheet crossings. Only consecutive nonmultiple crossings were used in this procedure. In case of a data gap, we ensured that the two crossings in the pair were not separated by more than 11 hours. We found 4343 viable pairs which were used in equations (18) and (19). As expected, the observed prime meridian decreases with radial distance for all local times (i.e., the prime meridian is delayed). However, we also see that the radial gradient is not uniform over all local times. At a fixed radial distance, the delays are much more pronounced in the dawn sector compared with their values in the dusk sector. To understand this puzzling behavior, let us turn to equation (5), which states that the delays in current sheet result from a combination of two effects, namely, the field line bend-back (δ

_{B}) and wave propagation time delay (δ

_{wave}). Observations [

*Khurana*, 2001] show that the bend-back of the field lines is a strong function of local time. Therefore it is possible that some or all of the asymmetry in the observed ϕ′ is caused by the asymmetry of the field line configuration. Figure 8 (left) shows a global plot of the ratio

*B*

_{ϕ}/(ρ

*B*

_{ρ}) observed by the six spacecraft in Jupiter's magnetosphere. The ratio clearly shows that the field is more swept-back in the dawn sector than it is in the dusk sector. Noting that the ratio approaches zero near Jupiter and attains a weak radial and strong local time dependence at large radial distance, we selected the following functional form to fit the ratio:

*a*

_{0}, ρ

_{0}, ρ

_{1},

*a*

_{m}, and α

_{m}are model parameters. We used a quasi-Newton technique with line search [

*Kahaner et al.*, 1989] to optimize the fit for the nonlinear equation (20). The best fit model coefficients are shown in Table 1. The RMS error of fit was 0.002

*R*

_{J}

^{−1}. Figure 8 (right) shows a color plot of the best fit model. We next integrated equation (20) with respect to the radial distance to get δ

_{B}(model) (see equation (6) above):

_{B}is shown in Figure 9. As expected, the delays are close to zero near Jupiter and attain large values in the dawn sector in the outer magnetosphere. The δ

_{B}delays are quite small (<10°) in the dusk sector.

^{a}

δ_{B} Parameters |
Value | δ_{wave} Parameters |
Value |
---|---|---|---|

a_{0}, R_{J}^{−1} |
−0.0056 | V_{0}, R_{J}/Hr |
39.4 |

ρ_{0}, R_{J} |
33.0 | ρ_{2}, R_{J} |
83.4 |

ρ_{1}, R_{J} |
52.8 | ||

b_{0}, degrees |
2.2 | ||

a_{1}, R_{J}^{−1} |
0.0056 | b_{1} |
0.7489 |

a_{2}, R_{J}^{−1} |
0.0031 | b_{2} |
0.6144 |

a_{3}, R_{J}^{−1} |
0.0036 | b_{3} |
0.5414 |

a_{4}, R_{J}^{−1} |
0.0061 | b_{4} |
0.0703 |

α_{1}, degrees |
−77.0 | β_{1}, degrees |
119.9 |

α_{2}, degrees |
23.7 | β_{2}, degrees |
−112.2 |

α_{3}, degrees |
167.2 | β_{3}, degrees |
108.1 |

α_{4}, degrees |
−24.5 | β_{4}, degrees |
−71.9 |

ρ_{3}, R_{J} |
26.2 |

- a
Hinging distance,
*x*_{H}= −47 R_{J}.

_{wave}(observed) from the equation

_{wave}delay. The wave delay is similar in magnitude to the delay caused by the sweep-back of the field lines. Close to Jupiter, the wave delay is seen to be small and independent of local time. At large distances, the wave delay displays a pronounced local time dependence. In order to model δ

_{wave}, we generalized the wave delay function of

*Khurana*[1992] to include a local time dependence at large distances (see equation (12) above):

*b*

_{0},

*V*

_{0}, ρ

_{2},

*b*

_{j}, β

_{j}, and ρ

_{3}are model parameters. The parameter

*b*

_{0}is a measure of the difference between the prime meridians of the VIP4 magnetic equator and the new model near Jupiter. For ρ ≪ ρ

_{3}, the term inside the bracket reduces to 1, and the wave delay becomes independent of local time. However at large ρ, the bracketed term introduces a local time dependence to the delay. The wave velocity

*V*is related to δ

_{wave}by

*ds*is a segment of the field line. An inversion of (24) for wave velocity

*V*requires a knowledge of global magnetic field (to define the relationship between

*ds*and ρ), which is not yet possible. We will therefore not try to determine the Alfven wave velocity profile in the magnetosphere.

[19] Figure 10 (right) shows the modeled δ_{wave}. The RMS error of the fit is 11.9 degrees. In order to reduce the effect of outliers on the fit, any data points that differed from the fit by more than 2.5*RMS were excised from the database. This procedure further eliminated another 1252 data points from our database. A physical examination of the excised crossings revealed that most of them occurred during times when the magnetosphere and the current sheet were highly disturbed. The best fit coefficients obtained from the remaining 3091 current sheet crossings are shown in Table 1. The model successfully reproduces both the local time and the radial distance variations of δ_{wave}.

## 6. Determination of the Current Sheet Tilt

*x*

_{H}, called the hinging distance (see equation (13)). As the prime meridian, ϕ′, is now known through equation (25), we can compute the longitude of a current sheet crossing, ϕ

_{cs}(model), directly by substituting a range of values of

*x*

_{H}in the following equation:

*Z*

_{cs}=

*Z*

_{sc}. In the above equation the plus (minus) sign is used for the N→S (S→N) crossings. The

*x*

_{H}that minimizes the RMS difference between ϕ

_{cs}(observed) and ϕ

_{cs}(model) is −47

*R*

_{J}(see Figure 12). The best fit model has an overall RMS error of fit of 19.3 degrees in predicting the current sheet crossing longitudes.

## 7. Best Fit Model

[22] Table 2 compares the RMS error of fit of the new model with those of the previous models. It is seen that the new model performs much better than the existing models in fitting the current sheet database. When compared with the previous models, which were constructed from data derived exclusively from the dawnside, it is seen that the current model performs as well as or better than the existing models in that local time sector. However, the real improvement in the modeling is observed when comparisons are made in the midnight, dusk, and postnoon sectors from new data derived from Galileo.

Model Applied to Data From | Kivelson et al. | Behannon VG1 | Behannon VG2 | KK 1992 | New Model |
---|---|---|---|---|---|

Current Sheet Crossing Data Derived From All Distances |
|||||

Pioneer 10 | 21.3 | 20.2 | 26.1 | 19.9 | 14.8 |

Voyager 1 | 21.7 | 27.5 | 38.3 | 22.3 | 16.9 |

Voyager 2 | 16.4 | 18.4 | 16.4 | 19.6 | 12.5 |

Galileo | 32.7 | 32.3 | 25.6 | 33.0 | 19.4 |

All spacecraft | 32.4 | 32.0 | 25.6 | 32.7 | 19.3 |

Data Derived From R < 70 |
|||||

Pioneer 10 | 17.1 | 17.2 | 19.7 | 18.2 | 13.3 |

Voyager 1 | 11.0 | 11.8 | 17.9 | 11.6 | 13.8 |

Voyager 2 | 15.5 | 18.8 | 14.6 | 12.2 | 12.7 |

Galileo | 21.7 | 24.3 | 19.3 | 20.5 | 14.9 |

All spacecraft | 21.5 | 24.1 | 19.2 | 20.3 | 15.0 |

Data Derived From R < 60 |
|||||

Pioneer 10 | 18.0 | 17.0 | 20.6 | 18.6 | 14.0 |

Voyager 1 | 10.3 | 10.1 | 12.1 | 10.3 | 13.9 |

Voyager 2 | 14.1 | 18.7 | 14.9 | 12.5 | 11.3 |

Galileo | 18.6 | 21.9 | 17.4 | 17.3 | 12.9 |

All spacecraft | 18.4 | 21.8 | 17.4 | 17.2 | 13.1 |

Data Derived From R < 50 |
|||||

Pioneer 10 | 20.3 | 18.4 | 23.2 | 20.8 | 15.7 |

Voyager 1 | 8.4 | 9.3 | 8.0 | 8.0 | 11.1 |

Voyager 2 | 13.5 | 18.7 | 15.1 | 12.5 | 10.9 |

Galileo | 14.6 | 18.8 | 14.8 | 13.5 | 10.4 |

All spacecraft | 14.6 | 18.7 | 14.9 | 13.5 | 10.6 |

[23] Another informative way of assessing the new model is to plot the observed and modeled sIII right-hand longitude of the spacecraft during current sheet crossings. These are shown in Figure 13 for four representative orbits (G2 outbound, G7 outbound, C22 outbound, and I33 outbound) selected to highlight dawn, midnight, dusk, and noon sectors of the magnetosphere. A good agreement is seen between the observations and the new model in all local time sectors.

## 8. Summary and Discussion

[24] By using a new analysis technique, we have developed a global model of the structure of Jupiter's current sheet. The new model form shows that the fast Jovian rotation and the supersonic solar wind provide equally important contributions to the equilibrium location of the Jovian current sheet. Four new features make our model robust and add new physics to it. These are (1) near Jupiter, the prime meridian longitude of the current sheet is larger by 2.2° than that in the VIP4 model, (2) the delay in the current sheet location caused by field line bend-back is found to be significant and is now properly modeled, (3) the wave propagation velocity is allowed to be a function of both radial distance and local time, and (4) the current sheet is made parallel to the solar wind direction at large distances in the magnetotail.

[25] The results of this study would be of interest for many future studies. The 5 and 10 hour periodicities observed in many spacecraft measurements like local plasma density, electric current density, particle distribution functions, plasma wave intensity, and total charge on dust grains are caused by the relative motion of the spacecraft with respect to the current sheet. The structural models of the current sheet can therefore be used to organize and further understand these observations. The current sheet models are also required in building global models of the magnetospheric field. In addition, works that require estimates of the thickness of the current sheet in the magnetosphere will benefit from this study because magnetic field and particle density data can be fitted to models like the Harris neutral sheet model using equation (13).

[26] Finally, we would like to comment on the 2.2° shift required in the prime longitude of the current sheet near Jupiter. The shift implies that VIP4 model does not adequately represent the orientation of the Jovian dipole during the Galileo epoch. The dipole tilt and longitudinal orientation of the VIP4 model are 9.5° and 159.2°, respectively. We find that even though the VIP4 dipole tilt agrees with our model, a more realistic value of its longitudinal orientation is 161.4°. There is an obvious explanation for this longitudinal shift. It is quite likely that the Jovian rotation period used to calculate the spacecraft longitudes needs a small revision (requiring a change of 2.2° over the 2 1/2 decades that separate Galileo measurements from Voyager and Pioneer observations). Recently, Z. Yu et al. (Rotation period of Jupiter from the observations of its magnetic field, submitted to *Icarus*, 2005) performed a singular value decomposition analysis of the internal field of Jupiter to determine its secular variations and to better define the rotation period of Jupiter. Even though they used a different data set (vector magnetic field from Galileo inside of 20 *R*_{J} rather than the current sheet crossing locations used by us) and also used a completely different technique (least squares fit to the internal magnetic field) to determine the dipole's longitudinal orientation, our value of ϕ′ = 341.6° is virtually identical to the value obtained by them (341.9°) for the Galileo epoch. This suggests that the rotation period of Jupiter as defined by IAU (= 9 hours 55 min 29.71 s) requires a very minor correction (−6 ms) to be compatible with the Galileo magnetic field observations. The new rotation period consistent with our observations is 9 hours 55 min 29.704 s.

## Acknowledgments

[27] We gratefully acknowledge many discussions with Margaret Kivelson, which helped us to greatly improve the paper. We would like to thank Steven Joy and Joe Mafi of the Magnetospheric Node of the Planetary Data System for preparing the magnetic field data sets used in this work. We also thank Dianne Taylor for her contribution to this work. This work was supported by the National Aeronautics and Space Administration through Jet Propulsion Laboratory under contract 1238965, and by NASA grants NAG5-8945 and NAG5-9546. UCLA-IGPP publication 6206.

[28] Lou-Chuang Lee thanks Aharon Eviatar and another reviewer for their assistance in evaluating this paper.