Flux transfer event observation at Saturn's dayside magnetopause by the Cassini spacecraft

We present the first observation of a flux rope at Saturn's dayside magnetopause. This is an important result because it shows that the Saturnian magnetopause is conducive to multiple X‐line reconnection and flux rope generation. Minimum variance analysis shows that the magnetic signature is consistent with a flux rope. The magnetic observations were well fitted to a constant‐α force‐free flux rope model. The radius and magnetic flux content of the rope are estimated to be 4600–8300 km and 0.2–0.8 MWb, respectively. Cassini also observed five traveling compression regions (remote signatures of flux ropes), in the adjacent magnetosphere. The magnetic flux content is compared to other estimates of flux opening via reconnection at Saturn.


Introduction
Flux transfer events (FTEs) are twisted flux tubes first observed at Earth's magnetopause by the ISEE 1 and 2 spacecraft [Russell andElphic, 1978, 1979]. FTEs consist of a flux rope (FR), which have been postulated to form as a result of simultaneous magnetic reconnection occurring at multiple X-lines  sandwiched between compressed draped interplanetary magnetic field (shown in Figure 1a) and the dayside magnetospheric field [Zhang et al., 2012;Zhong et al., 2013]. Other flux rope generation mechanisms include a change in the reconnection rate at a single X-line [Southwood et al., 1988;Scholer, 1988] and bursts of reconnection at a spatially narrow site that produce two "elbow-shaped" FTEs .
The twisting of a flux tube leads to a bipolar signature observed in the direction normal to the axis of the flux rope (the basic observational signature) in the magnetic field measurements. This is detected alongside an increase in magnetic field strength in the axial direction at the center of the flux rope (due to its structure, shown Figure 1b). If the spacecraft does not cross through the FTE, but passes near the edges, then only magnetic flux draped about the FTE is observed (shaded red in Figure 1a). This signature is termed a traveling compression region or TCR [Zhang et al., 2008;Slavin et al., 2012]. The observation of FTEs is common at the terrestrial planets, and they have been studied at the magnetopause at Earth [e.g., Russell and Elphic, 1978;Fear et al., 2005Fear et al., , 2008Owen et al., 2008;Varsani et al., 2014], Mercury [e.g., Russell and Walker, 1985;Slavin et al., 2009Slavin et al., , 2010Imber et al., 2014], and Jupiter Huddleston et al., 1997]. They have also been observed in the ionospheres of Venus and Mars [Elphic et al., 1980;Vignes et al., 2004] and downstream of Mars' large crustal anomalies [Brain et al., 2010].
The role of reconnection in driving the magnetosphere, and the extent to which it opens and closes magnetic flux at Saturn, is a controversial topic. Theory indicates that the occurrence and rate of reconnection are determined by the magnetic shear between the two magnetic fields and the plasma (the thermal to magnetic pressure ratio) [Quest and Coroniti, 1981;Swisdak et al., 2003Swisdak et al., , 2010Scurry et al., 1994]. The relatively low plasma of ∼1, typical of the Earth's magnetosheath, results in reconnection occurring at shear angles of ∼90 ∘ -270 ∘ [Trenchi et al., 2008], with the highest reconnection rates observed with antiparallel fields [Burton et al., 1975;Mozer and Retinò, 2007]. Large differences in plasma across the magnetopause tend to occur during high Alfvénic Mach number (M A ) conditions in the solar wind, which produce high-magnetosheaths [e.g., Slavin et al., 1984;Gershman et al., 2013]. In comparison, lower M A in the solar wind at Mercury greatly reduces the Figure 1. Illustrations of (a) a cross section of a flux rope showing the TCR region (shaded red) and (b) a three-dimensional representation of the layers of a flux rope, where the outer flux is perpendicular to the core axial field. The core axial field is pointed in the right-to-left direction here, which is the intermediate variance direction from MVA, whilst the tangential direction is in the minimum-maximum plane. (c-f ) The MAG data for the TCRs ("T"; red shading) and the FTE ("F"; blue shading). in the magnetosheath. For low-conditions, reconnection is possible for very low shear angles [Slavin et al., 2009DiBraccio et al., 2013].
At Saturn, Masters et al. [2012] investigated Cassini magnetopause crossings and found that for the majority of the observations, the conditions at the magnetopause, were not conducive to reconnection. This is supported by the lack of any dayside FTE observations to date after over 11 years of Cassini orbiting Saturn. Evidence for FTEs at Jupiter has been reported [Russell, 1995;Huddleston et al., 1997] but not at Saturn where a statistical search for FTEs found none [Lai et al., 2012]. The low-latitude boundary layer between the magnetopause and the magnetosphere at Saturn has been observed not to vary in thickness for different interplanetary magnetic field (IMF) orientations [Masters et al., 2011a[Masters et al., , 2011b, unlike at Earth where it is found to be thinner when the IMF is antiparallel to the magnetospheric field (due to the erosion of the open magnetic field lines) [e.g., Šafránková et al., 2007]. The magnetopause position at Saturn was not found to depend upon the IMF direction [Lai et al., 2012], unlike at Earth and Jupiter [Aubry et al., 1970;Kivelson and Southwood, 2003].
However, this is not to say that reconnection does not occur at all at Saturn, but it is not as common as at Earth, is not triggered under the same conditions, and that its effect on the dynamics of the Saturnian magnetosphere may not necessarily be analogous to the terrestrial system. Modeling of the possible areas where reconnection can occur has shown that reconnection is favored in regions away from the subsolar point and at higher latitudes with a range of local times [Desroche et al., 2013]. This is supported by independent global MHD simulations [Fukazawa et al., 2007].

10.1002/2016GL069260
Although no FTE signatures have been reported at Saturn, there is observational evidence for reconnection. Entry of magnetosheath plasma into Saturn's magnetospheric cusp via "bursty" or "pulsed" reconnection has been observed [Jasinski et al., 2014;Arridge et al., 2016]. In situ observations of heated electrons near the dawnside magnetopause suggest the occurrence of reconnection [McAndrews et al., 2008]. Poleward moving bifurcations in the aurora are evidence for magnetopause reconnection [e.g., Radioti et al., 2011Radioti et al., , 2013. Bursts of magnetospheric electrons on reconnected field lines in the magnetosheath coincident with auroral reconnection signatures have also been reported [Badman et al., 2013]. Similarly, Fuselier et al. [2014] presented 18 events where magnetospheric electrons present in the magnetosheath show evidence for reconnection and the associated magnetic shear angles were estimated to be >104 ∘ .
No comprehensive search was undertaken to find FTEs in this report. Here we investigate a single dayside magnetopause crossing on 2 February 2007 at Saturn by the Cassini spacecraft. This crossing contains evidence that an FTE-type flux rope was observed in a region of newly opened flux tubes adjacent to the magnetopause. First, we present a brief summary of the instrumentation used and Cassini's trajectory. Secondly, we present an overview of the observations, including minimum variance analysis of the data and a comparison to a flux rope model. Finally, we discuss the implications of these new observations for Saturn's magnetosphere.

Instrumentation
In situ electron and proton observations are presented from the Low-Energy Magnetospheric Measurement System (LEMMS) [Krimigis et al., 2004] and the Electron and Ion-Mass Spectrometers (ELS and IMS, respectively) from the Cassini Plasma Spectrometer (CAPS) [Young et al., 2004].
The Magnetometer (MAG) data are presented in the Kronographic Radial-Theta-Phi (KRTP) coordinate system (spherical polar coordinates) which is spacecraft centered for the magnetic field and planet centered for the position of the spacecraft . The radial (R) vector is directed in the planet-spacecraft direction, the azimuthal vector ( ) is positive in the direction of Saturn's rotation, and completes the right-hand set ( = R × ) and is in the colatitudinal direction, positive southward. For readers who are used to a Cartesian coordinate system, due to the location of the spacecraft during this interval being close to the subsolar point, the KRTP vectors at low latitudes are directed similarly to a solar magnetospheric system, with R approximately in the X (i.e., planet-Sun) direction, approximately in the −Z direction (i.e., southward), and approximately in the duskward direction (i.e., Y).

Spacecraft Trajectory
The highly inclined trajectory of Cassini ( Figure 2) shows that it passed over the southern pole on the dawnward side of the planet, crossed near the subsolar point of the bow shock, followed by passing over the northern pole on the duskward side. The average location of the magnetopause at the subsolar position has a bimodal distribution at ∼22 R S and ∼27 R S [Achilleos et al., 2008]. Therefore, the magnetopause crossing at ∼17.3 R S during this interval shows that Saturn's magnetosphere was significantly compressed. This is supported by results from a solar wind propagation model [Zieger and Hansen, 2008] which forecasts the arrival of a significant increase in the dynamic pressure at this time (see the supporting information), which compressed the magnetosphere.
Earlier in the trajectory (and on the same day as the event we present) while in the high-latitude magnetosphere, Cassini encountered the cusp where magnetosheath plasma was observed [Arridge et al., 2016]. During our event, Cassini was traveling in an equatorward direction and was located at a radial distance of ∼17.3 R S from the planet, a latitude of ∼−24 ∘ and a local time of 12:50.

Overview
At 23:22-23:33 UT Cassini was located in the magnetosphere where the magnetic field was strongly dipolar (i.e., predominantly in the B direction; Figure 1d). While in the magnetosphere, five TCRs were observed (shaded red). TCRs are observed when the spacecraft passes near but does not penetrate a flux rope. Instead, a region of compressed magnetic field lines is observed which drapes around the flux rope ( Figure 1a). Hence, a TCR is a two-dimensional compression wave which passes over the spacecraft. They are observed via rotations in the magnetic field in a single plane, coincident with an increase in magnitude (Figure 1f ) [e.g., Zhang et al., 2010;Slavin et al., 2012]. The first two TCRs had bipolar signatures in the radial direction, while all had increases in the colatitudinal direction and in magnitude.
An overview of the observations is shown in Figure 3. While in the magnetosphere, energetic electrons, ∼10 2 to 10 4 eV, were observed (Figures 3a-3c), and the electron number density was low (Figure 3d). At ∼23:33 UT Cassini entered a boundary layer. The drop in observed ion counts (Figure 3e, 23:33-23:42 UT) just after the vertical blue line occurred because the IMS field of view (FOV) moved out of the peak ion flow direction. At ∼23:44 UT, Cassini entered the magnetosheath where electrons with lower energies, ∼10 to 10 3 eV and the highest electron number densities, ∼1.5 cm −3 (both characteristic of the magnetosheath), were observed. The electron number density was approximately an order of magnitude higher than the statistical average ion number density in the magnetosheath , consistent with the interpretation that the magnetosphere was being compressed by an increase in the solar wind dynamic pressure. There was a very large decrease in magnetic field magnitude including a rotation across the boundary. At ∼23:53 UT, Cassini crossed the bow shock and entered the solar wind.
The region between the magnetosphere and magnetosheath is interpreted to be a region of open flux (grey shading in Figure 3) which had just undergone reconnection (with an embedded FTE-type flux rope). This is supported by the following observations. First, the magnetic field magnitude decreased from ∼7 nT (in the magnetosphere) to ∼4 nT; also, the magnetic field direction was observed to rotate from a magnetospheric dipolar configuration (positive ) to an oppositely orientated direction, including an increase (and a rotation) in the azimuthal direction, . Therefore, the spacecraft was no longer traversing closed field lines as the field was no longer in a direction consistent with the magnetospheric magnetic field. Secondly, the plasma instruments observed magnetosheath-like plasma throughout, as well as magnetospheric plasma present in the first half of the open region. This shows that the spacecraft observed a mixed plasma population from both adjacent regions. The magnetosheath-like plasma (higher in energy due to energization from reconnection and lower in density than the adjacent magnetosheath) is similar to plasma observed in Saturn's cusp and (f-i) the three components (in KRTP) and magnitude of the magnetic field (MAG)."SW" stands for the solar wind and "M'sheath" for the magnetosheath. The "Open" region is shaded in grey. "DEF" and "DNF" stand for differential energy and number flux, respectively. [Jasinski et al., 2014;Arridge et al., 2016] which is also located on open field lines. At the beginning of this open region at ∼23:34 UT an increase in the magnetic field magnitude was observed including a bipolar signature in the radial direction which we have identified to be an FTE (blue line). A comparison of the electron energy distributions between the different regions can be seen in the supporting information.

Minimum Variance Analysis
Minimum variance analysis (MVA) was performed on the FTE-type flux rope and the boundary crossing between the open region and magnetosphere, to further characterize these events and understand their magnetic structure. MVA can be used to determine the orientation of the flux rope axis by transforming the magnetic field data into a new orthogonal coordinate system with unit vectors in the maximum, minimum, and intermediate variance directions [Sonnerup and Cahill, 1967]. This method has been used extensively at various planetary magnetospheres to analyze magnetic structures [e.g., Huddleston et al., 1997;Eastwood et al., 2002;Knetter et al., 2004;Steed et al., 2011;Jackman et al., 2014;Slavin et al., 2014]. If the spacecraft passed near the center of the FTE, then the magnetic field in the minimum direction will be small (or approach zero) throughout the flux rope observation. If the flux rope is force free, then the intermediate vector corresponds to the axis [e.g., Xiao et al., 2004] of the FTE (Figure 1b).
MVA from the boundary crossing between the magnetosphere and the open region at 23:32:09-23:33:03 UT resulted in a minimum variance direction (in KRTP) of (0.98, −0.13, −0.14), predominantly in the radial direction. This is very similar to the normal direction calculated from the Kanani et al. [2010] magnetopause model of (0.98, 0.18, −0.09), showing that the boundary is similarly aligned to the magnetopause.
The FTE observation in the magnetopause normal (LMN) coordinate system can be seen in the supporting information. Figure 4 shows the MVA results for the FTE with a model flux rope shown in blue (discussed below). The calculated eigenvector (x) for each direction is shown in KRTP coordinates, as well as its corresponding eigenvalue ( ). The eigenvalue ratios were greater than 4, and so the vectors were well determined [Sonnerup and Cahill, 1967;Collier and Lepping, 1996]. The flux rope had a very strong bipolar signature in the maximum direction, which is the basic flux rope signature. B min ∼ 2 nT, is not zero, so the spacecraft did not pass through the center of the flux rope, but it did penetrate deeply into the structure. The minimum variance vector (predominantly in the radial and latitudinal directions) shows the direction the spacecraft passed through the flux rope (in its rest frame). In reality, the spacecraft speed is negligible (∼7 km/s) in comparison to the flux rope (hundreds of km/s) and is considered stationary, so the flux rope passed over the spacecraft in 10.1002/2016GL069260 a planetward and southward direction, consistent with a multiple reconnection X-line located equatorward of Cassini. This motion of the FTE-type flux rope is supported by the angular distribution of the ions which showed bulk flow to be in a similar direction.

Flux Rope Modeling
The flux rope was compared to a force-free flux rope model first put forward by Lundquist [1950] and developed by Lepping et al. [1990Lepping et al. [ , 1995. In a force-free magnetic field, the current density J is parallel to the magnetic field B (i.e., J × B = 0). Therefore, where is a constant proportionality factor and determined to be 2.405 so that the magnetic field is purely axial and tangential at the center and the edge of the flux rope, respectively (Figure 1b). Taking the curl of both sides gives The solution in cylindrical coordinates to equation (2) was shown to be a function of the Bessel functions of the first kind [Lundquist, 1950]: where H is the helicity of the structure and is equal to ±1. B 0 is the magnetic field magnitude at the center of the rope. r∕R FR is the impact factor to flux rope radius (R FR ) ratio and represents the distance of closest approach to the center of the FTE. J 0 and J 1 are the zeroth-and first-order Bessel functions. B 0 and r∕R FR are unknowns and estimated in this process. The MVA intermediate vector was used to form the axial direction of the FTE-type flux rope. The maximum and minimum directions formed the tangential direction of the flux rope, whereby the minimum eigenvector formed the trajectory direction through the FTE. The model was fit using a least squares minimization algorithm for r∕R FR in MVA coordinates. The value of B 0 was scaled accordingly after this process (see Slavin et al. [2003] for more details).
The value of the best fit impact factor was ∼0.3 R FR , with a B 0 of ∼7 nT. Figures 4c-4e show a comparison of the flux rope model (in blue) to the data. B min was very well modeled throughout the FTE, while most of B int was well modeled at the center. The bipolar signature of B max was also found to match the observations.
The magnetic flux content (Φ) of the FTE-type flux rope was calculated using To calculate flux rope radius, the transit time and velocity of the flux rope passing through the spacecraft (calculated from the CAPS-IMS ion observations) were used. The restricted FOV of IMS is not amenable to the standard moment integration techniques [e.g., Thomsen et al., 2010;Wilson et al., 2008] as they require the instrument to see the peak flow to calculate the flow velocity. However, the peak flux can be constrained to anodes 5-7 of IMS. Ion distributions can be well modeled as the sum of two comoving proton distributions with different temperatures, a hot and cold distribution, with temperatures of 1 keV and 100 eV, respectively [Richardson, 1987]. The model distribution consisted of the sum of two drifting Maxwellians (one each for the hot and cold proton distributions) and were fitted with nonlinear least squares. From the model, the peak flow was found to be located 0-20 ∘ outside the FOV of IMS (flowing southward). The resulting ion flow speeds were calculated to be 473 ± 9 to 540 ± 6 km/s, where the uncertainty in each measurement comes from the uncertainties from the nonlinear fit and the range originates in the assumed angle between the sensors and the ion flow direction.
Using the lower and upper estimates of the velocity (mentioned above), the size of the FTE is approximated to be ∼6500 and ∼7400 km (∼0.1 R S ). However, there are errors associated with the force-free fitting technique including the assumption of a force-free cylindrically shaped structure. In reality, nonnegligible plasma gradients will be present in any FTE, and FTEs will not be completely cyclindrical. This will make the assumptions not completely valid, because flux ropes are usually observed while in the process of evolving to become near force free [Kivelson et al., 1993;Zhang et al., 2010]. Errors associated with the selection of the FTE time duration will have the biggest effect on the calculated size of the flux rope and Φ, while the uncertainty on the impact factor is an order of magnitude smaller. The start-stop times were chosen to coincide with the peaks in the bipolar signature, but an increase or decrease of 3 s would result in a flux rope radius value to lie between ∼4600 and ∼8300 km and a magnetic flux content between ∼0.2 and ∼0.8 MWb.

Discussion and Conclusions
We have presented the first detection of an FTE-type flux rope at Saturn's dayside magnetopause. The Cassini spacecraft passed from the magnetosphere, where it observed five TCRs and then passed into an open flux region where energized magnetosheath plasma was observed as well as the FTE-type flux rope. The observation of TCRs in the magnetosphere and the flux rope in the open region all support the interpretation that Cassini passed from the magnetosphere onto newly reconnected open magnetic field lines, which are adjacent to the magnetopause and therefore would map at higher latitudes to the cusp. Cassini then crossed into the magnetosheath, where the plasma increased in density, before finally traversing the bow shock and into the solar wind.
An estimation of the plasma yielded values of ∼1, ∼5, and ∼19 for the magnetosphere, the open region, and the magnetosheath, respectively. These calculations were made by adding the plasma pressures from the MIMI and CAPS instruments [Sergis et al., 2009;Thomsen et al., 2010], for the entire open region and magnetosheath and for 9 min within the magnetosphere (23:20-23:29). The difference in between the magnetosphere and the open region is quite low in comparison to some magnetopause crossings at Saturn analyzed by Masters et al. [2012].
However, the in the observed magnetosheath (adjacent to the open region) is quite high. The assumption that the conditions that formed the open region were similar to the observed magnetosheath would require a high magnetic shear for magnetic reconnection. Either the magnetic shear that prompted reconnection was very high or the dependence models [Swisdak et al., 2010;Masters et al., 2012] do not provide a complete picture of the conditions required for reconnection onset. However, we do know that reconnection had occurred and formed the observed FTE and open region, and further analyses of the reconnection conditions are beyond the scope of this paper.
MVA was performed on the flux rope magnetic field measurements. The axis of the FTE (i.e., the intermediate variance direction) was found to be predominantly in the azimuthal direction (i.e., east-west), and it was found to be moving southward. Both of these characteristics are consistent with the high-shear, multiple X-line model for FTE generation Raeder, 2006], which is well supported by observations at Earth [e.g., Fear et al., 2008].
A force-free cylindrical constant-flux rope model was fit to the FTE magnetic field measurements. The result shows that Cassini's closest approach to the flux rope core was ∼0.3 R FR , and the core field strength was ∼7 nT. Using the observed ion flow velocities, the flux content of the FTE was estimated to be between ∼0.2 and ∼0.8 MWb. Terrestrial FTEs have been observed to contain similar amounts of magnetic flux, e.g., 0.3 MWb [Lui et al., 2008] and 0.4 MWb [Zhang et al., 2008].
Assuming that the five observed TCRs in this event are attributed to FTEs would give an FTE occurrence of ∼2 min (six FTEs are observed in 9 min), which is less than the ∼8 min and more than the ∼8 s observed at Earth and Mercury, respectively [Rijnbeek et al., 1984;Slavin et al., 2012]. Six FTEs in 9 min would result in a reconnection voltage of ∼2-9 kV (attributed solely to FTE generation).
In a comprehensive auroral study, Badman et al. [2013]  Modeling of the reconnection voltage at Saturn revealed an average of ∼40 kV, with an upper estimate of ∼100 kV [Masters, 2015]. The event presented here is during a magnetospheric compression, and the upper value from Masters [2015] and Badman et al. [2013] is more likely for our interval. Therefore, it could conceivably be estimated (assuming that six FTEs are generated every 9 min, and the associated resulting reconnection voltage is ∼2-9 kV) that FTEs at Saturn contribute ∼1-9% to the opening of flux during solar wind compressions. However, our observations are local to Cassini, and these estimates could be conservative because more FTEs might be generated elsewhere along Saturn's huge magnetopause, which are not sampled on Cassini's trajectory. Although this is the first reported event, this FTE may not be representative of FTEs at Saturn and a statistical survey will provide a better understanding of the variability in flux opened in FTEs.
It is not possible from this study to determine whether the flux rope reconnection voltage is the same during quiescent solar wind conditions. It is more than likely that FTE-type flux rope generation is negligible at Saturn when the overall dayside reconnection rate is very low, with fewer multiple X-lines occurring during less stressed magnetospheric conditions. This would explain the general lack of FTE observations to date. However, we have shown that there are events at the Saturnian magnetopause where reconnection occurs in an Earth-like manner and an FTE can be formed. A reexamination of the magnetopause crossings should be undertaken to search for flux rope signatures in the data.