Titan s near magnetotail from magnetic field and electron plasma observations and modeling: Cassini flybys TA, TB, and T3

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2006ja011676, 2006 Titan s near magnetotail from magnetic field and electron plasma observations and modeling: Cassini flybys TA, TB, and T3 F. M. Neubauer, 1 H. Backes, 1 M. K. Dougherty, 2 A. Wennmacher, 1 C. T. Russell, 3 A. Coates, 4 D. Young, 5 N. Achilleos, 2 N. André, 6 C. S. Arridge, 2 C. Bertucci, 2 G. H. Jones, 4 K. K. Khurana, 3 T. Knetter, 1 A. Law, 2 G. R. Lewis, 4 and J. Saur 1 Received 17 February 2006; revised 3 July 2006; accepted 7 July 2006; published 19 October [1] The first close Titan encounters TA, TB, and T3 of the Cassini mission at almost the same Saturnian local time 1030 and in the same spatial region downstream of Titan have enabled us to study the formation of the tail of its induced magnetosphere. The study is based on magnetic field and electron plasma observations as well as threedimensional modeling. Our most important findings are the following: (1) No crossings of a bow shock of Titan were observed, and all encounters occurred at high plasma b > 1 for transsonic and trans-alfvénic Mach numbers. (2) The magnetic draping signature of the induced magnetosphere often shows a sharp outer boundary called the draping boundary (DB) in the near-tail region. (3) The DB is often occurring as a discontinuity in magnetic field spatial derivatives, and therefore the DB is a discontinuity in the spatial distribution of plasma currents. (4) Perpendicular to the incident flow direction the DB shows an approximately elliptic cross section elongated along the incident magnetic field direction and a displacement toward the Sun. (5) We argue that the DB in the magnetic tail region corresponds to the boundary of a structure which is analogous to an Alfvén wing at very small b and in our case of larger b contains Alfvénic and slow mode features. It forms a tail like a delta wing in aerodynamics. (6) For the two less disturbed flybys, TA and T3, a polarity reversal layer has been observed with thicknesses of 320 km and 230 km, respectively. Citation: Neubauer, F. M., et al. (2006), Titan s near magnetotail from magnetic field and electron plasma observations and modeling: Cassini flybys TA, TB, and T3, J. Geophys. Res., 111,, doi: /2006ja Introduction [2] The Cassini mission with its planned 44 close encounters with Saturn s largest satellite Titan will allow the detailed investigation of the complex interaction between the satellite s dense atmosphere, a still hypothetical weak internal magnetic field and its magnetoplasma environment. It will thus greatly amplify the results from the first Titan encounter of the Voyager 1 spacecraft on 12 November The flyby altitude was 4006 km for Voyager 1 and is planned to be between about 950 km and 10,409 km for the 1 Institut für Geophysik und Meteorologie, Universität zu Köln, Cologne, Germany. 2 Space and Atmospheric Physics, Blackett Laboratory, Imperial College, London, UK. 3 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA. 4 Mullard Space Science Laboratory, University College London, Dorking, UK. 5 Southwest Research Institute, San Antonio, Texas, USA. 6 Centre d Études Spatiales des Rayonnements, Université Paul Sabatier, Toulouse, France. Copyright 2006 by the American Geophysical Union /06/2006JA targeted flybys during the primary mission of Cassini. The first results from magnetospheric field observations during the first close Cassini encounter with Titan, TA, on 26 October 2004 have been presented in a previous paper by Backes et al. [2005]. [3] Observations from the previous Pioneer 11, Voyager 1, and Voyager 2 flybys [see Schardt et al., 1984] suggest that at its orbital distance of 20 R S Titan is mostly located in Saturn s outer magnetosphere. This has been confirmed by the first Cassini encounters TA, TB, TC, T3 T10 at the time of this writing [see also Hendricks et al., 2005; Achilleos et al., 2006]. Here we use the historical nomenclature, in chronological order, of the Titan encounters that have taken place: T0, TA, TB, TC, T3, T4,..., T10 up to now. On the other hand, it is expected that conditions of strongly enhanced solar wind dynamic pressure will lead to situations where Titan is located in the magnetosheath or even in the solar wind, particularly for Saturnian local times (SLT) around The incident flow in the magnetosphere is consistent with an approximately corotational flow direction and a reduced velocity. For the Voyager 1 flyby it was estimated to be about 120 km/s compared with the full corotational velocity of 200 km/s and a small radial inward component [Hartle et al., 1982; Neubauer et al., 1984]. The 1of15

2 Table 1. Some Characteristics of Cassini Titan Flybys TA, TB, and T3 and the Voyager 1 Flyby and Solar Conditions TA TB T3 V1 SCET a of CA 26 Oct Dec Feb Nov : : : :23 CA altitude, km CA latitude CA longitude Saturn local time Subsolar latitude Subsolar longitude a Spacecraft event time in UTC. draping signature reported below is consistent with this picture. [4] The interaction is essentially atmospheric, although a small but significant internal magnetic field cannot be ruled out yet. It was shown for the Voyager 1 encounter [Neubauer et al., 1984], and is also evident for the Cassini encounters, that the incident plasma can be characterized as a high b case (b is the ratio of total thermal and magnetic pressure), where the flow is also subfast. The interaction is complex, because the angle a between the flow direction and the direction of incoming ionizing solar EUV photons varies up to 180 during one Titan orbital period of days. Photoionization is the dominant source of ionization of Titan s atmosphere, because the energy density of ionizing magnetospheric electrons is quantitatively less important [Keller et al., 1994; Backes et al., 2005]. The Voyager 1 encounter occurred at a time just after the vernal equinox with a latitude of the subsolar point of 3.8 and the three Cassini encounters occurred well after the winter solstice with subsolar latitudes of 23.2, 22.8, and 22.2 for TA, TB, and T3, respectively. Solar wind interactions at comets, Venus, and Mars with the corresponding atmospheres are all characterized by a 0. Hence a is an important independent variable at Titan. Interestingly, SLT for the first three close encounters TA, TB, and T3 was almost the same (approximately 1030). It is this serendipitous coincidence that we shall use to investigate the interaction at a fixed SLT. Table 1 gives the most important parameters for the encounters. The situation is somewhat comparable to 1330 SLT at the Voyager 1 encounter, which is symmetric with respect to local noon apart from the deviation of 20 from corotational flow at Voyager 1 [Hartle et al., 1982] referred to above. Apart from this deviation the sun was near a 90 for the Voyager 1 and Cassini encounters in this paper, i.e., the sun was shining on one of the flanks of the flow. [5] In this paper we shall investigate Titan s magnetospheric interaction and compare it with the similar Voyager 1 case. We shall use magnetic field observations and electron plasma observations obtained during flybys TA, TB, and T3. The encounter TC was not useful for this purpose because the observations during this flyby were very limited in order to not impede the delivery of the Huygens probe and occurred at a large distance far upstream. Similar SLT conditions will not recur before the end of [6] The motivation for this study is threefold. First, the formation of the magnetic tail is a particularly interesting and important aspect of the interaction. Second, for the Saturnian magnetosphere Titan s plasma interaction constitutes a possible source of plasma and neutral gas which must to some extent (to be determined in later studies) depend on the magnetic interaction. Third, we investigate an interesting case of an atmosphere-plasma interaction not found elsewhere in the solar system. [7] Finally, the study of the problem of an atmosphereplasma interaction over a wide range of conditions may turn out to be important for the huge number of cases possible in the study of extrasolar planets. [8] Experimental conditions and the flyby trajectories will be described in section 2. In section 3 we shall discuss the magnetospheric conditions under which the encounters occurred. In section 4 we shall give a brief overview of the physical basis of the interaction picture with an emphasis on the draping concept. This leads to a new type of coordinate system called draping coordinates, which as the basis for its unit vectors uses incoming flow and magnetic field vectors. More precisely, because of a nonnegligible trend in the incoming magnetoplasma characteristics, we have to use dynamic draping coordinates to be defined later. Dynamic draping coordinates will be used in section 5 for the presentation of the data with an interpretation within the draping concept and some emphasis on the formation of the tail or wake region of Titan s induced magnetosphere. The observations will be compared with the modeling results of Backes [2004; see also Backes et al. 2005] in section 6. In section 7 we shall discuss some important physical aspects of the interaction, and a summary will be given in section 8. A list of frequently used acronyms is given at the end of the paper. 2. Experiment Details and Flyby Trajectories [9] The magnetometer experiment has been described in detail by Dougherty et al. [2004]. The experiment consists of a vector helium magnetometer (VHM) and a fluxgate magnetometer (FGM). The VHM is mounted at the outer tip of the magnetometer boom and the FGM halfway along the boom of 11 m total length. In the central ±2 hour interval around closest approach (CA) and also during part of the more distant measuring intervals the magnetometers operate at an elevated measurement rate of 32 vectors per second for the FGM and 2 vectors per second for the VHM. Because of the larger distance from the spacecraft sources of magnetic interference we used the VHM data throughout most of this paper. The quantization uncertainties were 4.9 pt and 3.9 pt for the FGM and VHM, respectively. [10] The CAPS instrument [Young et al., 2004] consists of three sensors: an electron spectrometer (ELS) [Linder et al., 1998], an ion mass spectrometer (IMS), and an ion beam spectrometer (IBS). Here we use upstream electron density and temperature values derived from ELS, which has an energy range ,000 ev, energy resolution 16.7%, and a total angular range split into anodes. During the upstream region of the TA and TB encounters, this fan-shaped field of view was scanned by the CAPS actuator, which moved between angles of 80 to +104 with respect to the spacecraft -Y axis. A narrower actuator range was used near CA to 2of15

3 Figure 1. Titan flyby trajectories projected on the X, Y plane and Y, Z plane of the Titan interaction system TIIS for the TA, TB, T3, and the Voyager 1 flybys. Closest approach locations are indicated by large dots. Tick marks are 60 s apart. optimize the CAPS measurements in the ram direction (These measurements are not shown here). [11] Data from a central anode, corrected for spacecraft photoelectrons and spacecraft potential, were used for the moment calculations. A moment integration was performed on the corrected electron phase space density measurements over the energy range of the instrument, assuming isotropy of the measured spectrum over 4 steradians (a reasonable approximation for electrons in this region). The results were similar to those from an alternative technique which uses the peak of the corrected counts spectrum. [12] The flyby trajectories were all inbound and on the downstream side of Titan. Figures 1a and 1b show the trajectories for the encounters TA, TB, T3, and Voyager 1 as projections on the X, Y plane and Y, Z plane of a Cartesian Titan-centered coordinate system. The coordinate axes X, Y, Z point in the direction of ideal corotational flow, from Titan toward Saturn and along the rotational axis of Titan (i.e., in the northward direction), respectively. We refer to this coordinate system as the Titan interaction system (TIIS). The trajectories thus allow the study of the formation of the wake and the tail of the induced magnetosphere close to Titan. The flyby velocities relative to Titan were 6.1 km/s, 6.1 km/s, and 6.0 km/s, respectively. All the three trajectories are inbound and northbound in the TIIS with slightly different velocity components. In comparison the Voyager 1 trajectory occurred inbound and southbound at 17.3 km/s total velocity. [13] We finally note that throughout the paper we shall use spacecraft event time (SCET) in UTC and a Titan radius of R T = 2575 km. 3. Ambient Conditions of the Magnetosphere of Saturn Around the Encounters TA, TB, and T3 [14] In this section we briefly report the properties of the magnetic field in the Titan interaction coordinates for several hours before and after encounters TA, TB and T3. TA data have already been graphically presented in Figure 2 of Backes et al. [2005] in Kronian solar magnetic (KSM) coordinates. All the three encounters occurred well inside the magnetosphere of Saturn, i.e., at solar wind dynamic pressure not too far from average. The last magnetopause crossing of Cassini occurred 0449, 0643, and 1821 UTC before CA for TA, TB, and T3, respectively [Achilleos et al., 2006]. In all three cases the magnetic field was generally characterized by a negative component B z, in agreement with Saturn s internal field orientation and a positive B y. The fields can be explained by the superposition of Saturn s internal field, current sheet (or ring current) fields, and the fields of the Chapman-Ferraro currents in a magnetopause with a subsolar point well below Titan s orbital plane or Saturn s equatorial plane, i.e., at southern latitudes. [15] A remarkable observation has already been made by Backes et al. [2005] for the TA encounter. The magnetospheric field seemed to jump from one relatively stable level before the encounter to a different stable level after the encounter. TB did not show such a behavior on a similar timescale. The magnetospheric field was generally quite variable with only a small difference between both sides of the encounter. T3 again shows a noteworthy difference between the inbound and outbound pass. Outbound partial contact with the magnetospheric current sheet was observed. [16] A discussion of the dynamics of the outer magnetosphere on a large scale and its relation to Titan is interesting but outside the scope of this work. 4. Titan s Magnetospheric Interaction and Magnetic Field Line Draping [17] The interaction of Titan with the surrounding magnetoplasma of Saturn s magnetosphere is a special case of the many other atmospheric interactions found in the solar system, like at Venus, Mars, comets in the solar wind, and the Galilean satellites in Jupiter s magnetosphere. Flow conditions in the solar wind are characterized by a plasma b around b 1 and super-alfvénic and supersonic flow. In 3of15

4 Figure 2. Sketch of the draping of frozen-in magnetic field lines near Titan. An example of field lines is shown in which all illustrated field lines penetrate the equatorial X DRAP, Z DRAP plane on a given equatorial streamline with small Y DRAP < 0. No draping, weak draping, strong draping, and reverse draping are illustrated, where reverse draping can be considered a special case of strong draping. Field lines 1, 2, 3, and 6 are the undisturbed field line, a field line with weak draping, and simple strong draping field lines, respectively. Field lines 4 and 5 are also strong draping field lines with segments of reverse draping with B z > 0. The X DRAP, Y DRAP plane can be considered the magnetic equatorial plane in an ideal case. the Jovian magnetosphere flow conditions are characterized by Mach numbers not far from one and b varying from very small values for Io, increasing further out [Kivelson et al., 2004]. [18] In the Saturnian inner magnetosphere the flow conditions are characterized by b 1 and M A 1 at Enceladus [Dougherty et al., 2006] and increasing values further outward. The sonic Mach number M s remains near one. [19] The results from the Voyager 1 flyby at Titan have been reviewed by Neubauer et al. [1984]. The interaction occurred at transsonic and trans-alfvénic conditions and a fast Mach number M f < 1, consistent with no bow shock in front of Titan. The plasma b has been determined to be as large as [20] The interaction between the neutral atmosphere and the incoming plasma flow is mediated by the addition of mass to the plasma by photoionization due to solar EUV radiation and collisional ionization due to photoelectrons and hot magnetospheric electrons. The mass loading leads to a braking of the plasma by the neutral gas. As also shown by the modeling results of Backes [2004], elastic collisions play a significant and increasing role in the lower atmosphere of Titan. In addition momentum is redistributed by pressure forces and forces due to currents. The resulting three-dimensional flow system is intimately connected with the magnetic field via the frozen-in field theorem which is valid except for the lower regions of increasing resistivity. The resulting distortions of field lines are generally referred to as draping. Magnetic flux transport is replaced by magnetic diffusion well below 1000 km [Keller et al., 1994]. [21] The draping picture is of particular diagnostic value for the flow field when the initial magnetic field is perpendicular to the initial flow. The ion properties are not yet known accurately from observations. Recently, Ma et al. [2006, paragraph 12] still had to assume the ion composition with the caveat of on the basis of the limited information. Voyager 1 observations [Hartle et al., 1982] and the fitting to the numerical model by Backes et al. [2005] suggest that a flow in the corotational direction at a reduced speed is a good assumption. The relatively small observed B x components suggest the perpendicularity assumption to be reasonably true. [22] Figure 2 illustrates the draping picture for various degrees of field line distortion. We introduce a new draping coordinate system DRAP, in which X DRAP is along the flow direction, Z DRAP antiparallel to the magnetic field vector ~B 0 in the incident flow, and Y DRAP completes the right-handed Cartesian system. It is analogous to the coordinate system used by Kivelson and Russell [1983] in their analysis of one aspect of the Titan interaction. Since the geometry of the draped field lines depends on the kinematics of the flow, we have chosen the region close to the X DRAP, Z DRAP plane for the illustration. In this region the flow initially slows down, to later accelerate again as found in the model by Backes [2004]. The initially straight field lines are carried by plasma mass elements which, because of the slow down, lag behind the undisturbed flow near the X DRAP, Y DRAP equatorial plane, which may be called the magnetic equatorial plane of the induced magnetosphere of Titan. In general, B x and B y change sign when passing through the magnetic equatorial plane Z DRAP = 0. The layer around Z DRAP = 0, in which the variation of B x and B y through zero occurs like in the tail can be called the polarity reversal layer (PRL). We further note that the development of components B y in the draping system requires the occurrence of nonzero components v y in the flow. Slowing down of the v x component alone leads to the development of B x < 0 and a change in B z. A change in sign of B z from negative to positive requires nonzero components v z corresponding to a flow toward the magnetic equator. We shall use the term weak draping in the case of relatively small components B x, B y in Figure 2, the term strong draping in the case of large B x, B y components and the term reverse draping in the case of positive components B z in the DRAP system. If in reverse draping a northern and a southern draped field line come close together reconnection may occur [Verigin et al., 1984]. [23] We also note that the component B y describes the deviation from a straight line of a field line projected on the Y DRAP, Z DRAP plane of the draping system. A field line with an equatorial outward bulge is described by B y > 0 at Z DRAP > 0 and Y DRAP > 0, for example. An indentation at the equator corresponds to B y < 0 in the latter case. Model results [Backes, 2004] show that for the case of a 0, B y is essentially vanishing upstream of Titan in the disturbed flow. A reversal of the sign of B x is also possible but not shown in Figure 2. Plasma on streamlines at some distance from the X DRAP, Z DRAP plane experiences acceleration and a velocity maximum on the flanks after initial deceleration. This leads to B x > 0 for Z DRAP > 0 and B x < 0 for Z DRAP <0 4of15

5 Table 2. Entry and Exit From Induced Magnetosphere of Titan for Titan Flybys TA, TB, and T3 and V1 a TA TB T3 V1 Entry in SCET b 26 Oct :00 13 Dec :40 15 Feb :00 12 Nov :20 Distance at entry in R T Exit in SCET 1541: : : :40 Distance at exit in R T a The inbound and outbound draping boundaries (DB). b Spacecraft event time in UTC. as also illustrated by Backes et al. [2005] and in section 7.2. This behavior is also observed for cases of small b. [24] It is instructive to present the data of the flybys TA, TB, T3, and also Voyager 1 (V1) in a suitably chosen draping coordinate system. In this coordinate system the Z DRAP direction is chosen antiparallel to the magnetic field direction in the incident flow. If the flow is approximately perpendicular to this initial magnetic field the concepts described in Figure 2 can directly be applied. For this purpose we have first looked for the onset and termination of the draping signature near Titan in the 4 s average B x component of TIIS over a time interval of CA ± 30 min to define the extent of the induced magnetosphere. Here we have also used dips in the magnitude to define the center of the draping boundary layers. The times of onset and termination can be referred to as the draping boundaries (DB) of the inbound and outbound draping boundary layers of Titan s induced magnetosphere, respectively, if we take into account their finite thickness. In the case of Voyager 1 we use the same procedure based on the given 1.92 s averages and CA ± 10 min only, taking into account the ratio of the relative velocities of Voyager 1 and Cassini of 17.3/6.1 in an approximate way. Thus the spatial distance along the corresponding trajectory arcs is approximately the same for Cassini and Voyager 1 for these time intervals. In our view the times of onset of draping are quite well defined, whereas the exits from the draping region could also be at 1539 UTC for TA and at 0708:30 UTC for Figure 3. Four second average magnetic field vector data in the dynamic draping coordinate system for TA, where the crossings of the outer boundary of the induced magnetosphere are also shown. Orbital coordinates are Cartesian, Titan-centered components in Titan radii R T. Also shown are altitude (in R T ), solar zenith angle, and latitude (in degrees). 5of15

6 Figure 4. Four second average magnetic field vector data in the dynamic draping coordinate system for TB. For further explanation, see Figure 3. T3. The times of entry and exit of the induced magnetosphere are shown in Table 2 together with the distances from Titan s center. The time intervals are most clearly defined for TA, followed by T3, V1, and TB. Both the V1 and TB encounters occurred in a disturbed Saturnian magnetosphere. 5. Cassini and Voyager Magnetic Field Observations in the Dynamic Draping System for TA, TB, T3, and V1 and Their Interpretation [25] Figures 3, 4, 5, and 6 show the magnetic field results in a dynamic draping coordinate system for encounters TA, TB, T3, and V1, respectively. We have again used 4 s averages for the Cassini encounters and 1.92 s averages for V1. For the definition of the dynamic draping coordinate system see Appendix A. In the dynamic draping coordinate system in all four cases the sun is approximately in the magnetic equatorial plane X DRAP, Y DRAP. As a consequence, the induced magnetosphere is expected to be symmetric with respect to the magnetic equatorial plane under stationary flow conditions. [26] Because Titan may develop a bow shock at least temporarily and only limited plasma ion data are available at present, we have first inspected the magnetic field in Figures 3, 4, and 5 and also outside the intervals used in Figures 3 5 for a bow shock signature, i.e., a magnitude jump with the correct sign and an associated small directional jump. After no bow shock crossing had been seen by Voyager 1 and at Cassini TA [Backes et al., 2005] there is also no bow shock signature at TB and T3 inbound or outbound from Titan. Here we note that we would expect a hypothetical bow shock to increase in strength as X DRAP decreases, i.e., the outbound orbit should be particularly suitable for bow shock identification. The lack of a bow shock signature is in agreement with the impression by Backes et al. [2005] that the plasma conditions were not very different between the Voyager 1 and TA flybys. This also applies to flybys T3 and (to a lesser extent) TB. [27] The onset of the draping signature followed by a fast transition from weak to strong draping is clear in the three Cassini cases in the TIIS representation of B x (not shown in this paper). This onset is also clearly seen in Figures 3, 4, 5, and 6 where our choice of dynamic draping coordinates brings the B x and B y signatures down to zero before the onset. The onset is followed by a continuous increase of B z for TA and also T3 and a fast one at TB. The onset has already been called the inbound draping boundary (DB) of the induced magnetosphere. In Table 2 the inbound and outbound DBs have been collected. 6of15

7 Figure 5. Four second average magnetic field vector data in the dynamic draping coordinate system for T3. For further explanation, see Figure 3. [28] In the case of TA, the good agreement between observations and the 3-D model of Backes [2004] demonstrated by Backes et al. [2005] not only attests to the quality of the model but also to the quiet character of the magnetospheric background deduced from the data above. After starting with a brief indentation feature and draping in the X DRAP, Y DRAP plane only until 1514 UTC, the B y component shows the signs of outward bulging as the equator is approached in the northern lobe of the induced magnetosphere. A region of B y 0 occurs (slightly delayed) around Y DRAP = 0 at 1527 UTC for TA. This is almost coincident with a region of strong reverse draping. A deep minimum in B exists centered around 1528 UTC, where the field goes down to B 2 nt. These draping signatures have superimposed the weakening of the magnetic field inside the region of weak pileup. A pileup maximum may be identified around 1517 UTC with a field of 7 nt. From the comparison with the numerical 3-D model and the work by Keller et al. [1994] the subsequent minimum field region is referred to as the magnetic ionopause, which indicates the shielding by Titan s ionosphere. The transition from northern polarity to southern polarity expected at Z DRAP =0 then follows at 1535 UTC slightly early because Z DRAP is still about 320 km. Remember that here we have determined our rotated draping coordinate system strictly from the data surrounding the induced magnetosphere only, whereas in the case of Backes et al. [2005] it has been determined by a least mean squares fit of the data. During polarity reversal B x hesitates for about 30 s to reverse sign before the southern magnetic tail region, where strong draping and pileup is reached with a maximum magnetic field of 12 nt. The southern draping region is also accompanied by a strong negative B y component, expected for strong bulging. Using the interval with the fast positive slope of B x in Figure 3 for the polarity reversal, the polarity reversal (i.e., the PRL) layer extends over a time interval from 1534 to 1536 UTC with only a hint at a magnitude minimum in the center. Thus the PRL is not a neutral sheet. Only the outbound DB is associated with a magnitude minimum, although the identification is not completely unambiguous, as mentioned before. During the PRL interval Z DRAP decreases by 320 km, which can be referred to as the thickness of the PRL. [29] The flyby observations of TB show similar features with a clear inbound DB and a clear outbound DB but substantial deviations from the simple draping picture in detail. Draping rapidly becomes very strong after the inbound DB crossing. The magnetic ionopause is much better defined and much deeper than at TA. The minimum value of B 0.8 nt should be taken with caution until the 7of15

8 Figure 6. The 1.92 s average magnetic field vector data in the dynamic draping coordinate system for the Voyager 1 encounter. Note that the shorter time interval covered and the averaging interval have been chosen to partly compensate for the different flyby velocities of the Cassini and Voyager 1 encounters. For further explanation, see Figure 3. systematic measurement errors have been determined better. The magnetic ionopause lasts from 1130 to about 1135 UTC. It is remarkable that B x stays near zero for another five minutes until about 1140 UTC, when southern magnetic polarity begins to appear. Appreciable fluctuations are present which do not readily fit into a simple draping picture, e.g., the two maxima in B y around polarity reversal. However, the pronounced minima in B at the important boundaries not found at TA can be used to identify the major boundaries. The inbound DB, the outbound DB, and the PRL are associated with deep minima in the magnitude of B. Here the structure of the central PRL seems to be much closer to a neutral sheet than at TA. If we associate the dip in B of the PRL at 1140:30 UTC with the polarity reversal, then we get Z DRAP = 0.78R T for the center of the PRL in contrast to the expected Z DRAP = 0. Thus we see again that for TB the observations are far from a simple symmetric induced magnetosphere. We note that some of the deviations from a good ordering in draping coordinates can be removed if strong changes in flow direction are assumed. [30] The flyby T3 occurred at a larger distance of CA but still through the well developed neutral atmosphere. Entry into the induced magnetosphere according to Figure 5 occurs at 0632 UTC, followed by an increasing and variable draping signature. Strong draping is reached at about 0647 UTC, where the short excursion to reverse draping may be due to some nonstationary dynamics. The field lines are straightening again when the nominal symmetry plane Y DRAP = 0 is crossed at 0656:30 UTC with a southern-like strong draping signature immediately followed by a short northern interval and a strong southern draping and pileup magnetic field of total 12.5 nt (to be compared with the far surrounding field of 6 nt). Apart from these complex polarity variations we may choose 0657:40 UTC until 0659:00 UTC for the PRL. The thickness from Z DRAP would then be 230 km. In agreement with the idea of draping coordinates Z DRAP = 0 occurs nearby at 0656:45 UTC. In contrast to TA and TB there is not a sudden drop from strong draping to no draping but rather a transition to an interval of less strong draping, lasting from 0705 UTC to the outbound DB at 0710 UTC at the latest. The sudden jump in magnetic field vectors at 0708 UTC may be an alternate choice for the outbound DB. [31] Figure 6 shows the magnetic field in the dynamic draping coordinates for Voyager 1. The choice of draping 8of15

9 Table 3. Unit Vectors ^~B 0 and ^~v 0 Defining the Draping System for the Numerical Model TA TB T3 ^~B 0 (0.130, 0.656, 0.744) (0.322, 0.913, 0.250) (0.418, 0.429, 0.800) ^~v 0 (0.983, 0.015, 0.186) (0.881, 0.192, 0.433) (0.905, 0.121, 0.409) coordinates is less unique than in the other cases because of the substantial variations outside the Titan-related perturbations proper. In contrast to the Cassini encounters weak draping starts gradually before a sharp transition to strong draping associated with well defined dips in field magnitude centered at 0539 and 0544 UTC. Both the northern draping region and the southern draping region are very pronounced. Again the outbound southern draping region shows stronger components B x and a smaller extent relative to the center of the polarity reversal interval at 0542:10 UTC. Y DRAP =0 occurs at 0539:26 UTC. The associated asymmetry has been explained as due to a 20 inward deviation of the incident flow [Hartle et al., 1982]. 6. Comparison of the Magnetic Field Results with the Results of the Advanced 3-D Model of Backes [2004] [32] Backes et al. [2005] recently briefly discussed the TA magnetic field observations in comparison with the model by Backes [2004] along the flyby trajectory. A comparison between a 3-D MHD model and TA and TB observations has also been made in the recent paper by Ma et al. [2006], where the model formulation was quite different, however. The model run used by Backes et al. [2005] was performed before TA and was therefore based on Voyager 1 results as input data to characterize the properties of the incident flow [Neubauer et al., 1984]. Since the model had assumed the incident flow to be perpendicular to the magnetic field, the observation of B x 0 but B y 6¼ 0 and B z 6¼ 0 far from CA in the TA observation and the initial assumption of flow parallel to the X axis of the Titan interaction system both suggested to rotate the solution such that the magnetic field in the incident flow is parallel to the observed one. In this spirit the rotation angle of the model around the x axis was obtained by a least mean squares fit of the model data to the observed data. Note that in the model the initial magnetic field was 4 nt in contrast to the observed field around 6 nt. The resulting fit using a rotation angle of 41.7 was quite acceptable, from which it was concluded that the model describes the physics of the interaction quite well. Also, it can be concluded that the flyby observations were not affected by substantial time variations during the encounter. Table 3 shows the unit vectors ^~B 0 and ^~v 0 for the incident magnetic and velocity directions giving the best fits for time intervals of ±20 min around CA for all three encounters. We call the new coordinate system defined by ^~B 0 and ^~v 0 the model draping system. Note that ^~v0 has been assumed to be perpendicular to ^~B 0. Also, the rigid rotation of the coordinates in the least mean squares fit have led to appreciable deviations from the real Sun direction, as a comparison between Tables 1 and 3 shows. [33] TA differs appreciably from the case TB, where the magnetic field observations show a dynamic behavior as discussed in section 2 and confirmed by MIMI observations [Mitchell et al., 2005]. Figure 7 compares the best fit model magnetic fields with the observed magnetic fields for TB, based on a least mean squares fit. The main features of the magnetic signature can be seen again as the DB transitions, the magnetic ionopause, and the PRL. The comparison again shows good agreement, but not as good as for TA. For example, the magnetic field minimum associated with the magnetic ionopause is much broader but less deep than in the data. The magnetic PRL is more pronounced in the measured B z component but less in the B x and B y components. The model has pronounced pileup fields in contrast to the data. It is in agreement with our independent choice of the inbound DB. Some of the disagreement may be attributed to the substantial magnetospheric dynamics and some to remaining model deficiencies. [34] Figure 8 shows the comparison for T3. There is again general agreement although the observed data are more structured. The amplitude of the variations is greater in the observations for the B x component and the magnitude and smaller in the B y and B z components. It is remarkable that the ledge of reduced draping from 0705 to 0708 in the 4 s average B x data of Figure 5 is also indicated in Figure 8 both in the observed and the model results. This is interesting in connection with the early Voyager 1 interpretation of the weak and strong draping regions identified during the V1 encounter. It was then argued that the regions demonstrate pickup of protons and heavy ions, respectively. Since the model by Backes [2004] considers only one heavy ion species this interpretation may have to be revised, i.e., the ledge can be explained as a dynamical phenomenon not necessarily implying a change in ion chemistry. On the other hand the sharp structure bounding the weak draping region may indicate the involvement of light ions, like protons. [35] The model predictions can also be compared with electron densities observed by the Langmuir probe of the RPWS experiment which has been presented by Wahlund et al. [2005] for TA and TB. It turns out that the electron peak of the model occurs one minute too early at TA and TB and at an electron density which is too low by a factor of about three. The major features of the electron density data are also seen in the model predictions in the vicinity of the peaks. The model electron densities fall off much too fast away from the peak region, however. We suggest that this problem may be solved by further improvements in the energy equation of the model, even after a sensitivity analysis has shown that the good agreement of other observed features is due to the detailed treatment of the electron energy balance. [36] In general, the comparison between the model results and the TA, TB, and T3 observations shows very satisfactory agreement in the main features but also in some more 9of15

10 Figure 7. Comparison of 60 s average magnetic field observations (solid lines) in TIIS and modeling results (dashed lines) after rotation of the model results from the model draping system into the TIIS coordinate system for Titan encounter TB on 13 December detailed features. There are differences in the timing and the amplitude of the features as reported above. 7. Discussion [37] In section 5 we have shown that the magnetic field observations at flybys TA, TB, T3 and the Voyager 1 flyby can be well understood by a combination of geometrical and draping considerations. This is particularly true for the quiet flybys TA and T3 and somewhat less for the disturbed flyby TB. The Voyager 1 case is intermediate. Only for the identification of the magnetic ionopause we have used numerical modeling results. Section 6 has shown that the observations, except perhaps for TB, are well explained qualitatively and to some extent quantitatively by the advanced 3-D model of Backes [2004; see also Backes et al., 2005]. [38] In this section we discuss some important physical aspects of the problem which have been postponed not to interrupt the flow of the paper in previous sections Incident Magnetoflow Conditions [39] We have seen in sections 4 6 that the magnetic field conditions of the incident magnetospheric flow were quiet during TA, more disturbed during TB, and somewhat disturbed during T3. The observation of the individual DB crossings suggests that the average flow conditions were not too far from the Voyager 1 conditions. Disturbances during TB were mostly temporal variations with a timescale of several minutes. This is in agreement with the electron plasma data as also the average electron densities and temperatures shown in Table 4 together with some derived quantities. [40] The most important of the Mach numbers for purposes of the discussion in this section is the Alfvén Mach number M A, which is given together with the sonic fast Mach number for TA and TB in the recent paper by Ma et al. [2006]. Because of the caveats concerning the ion data mentioned in section 4 we choose an average ion mass of A = 7 amu more toward the Voyager value and a velocity of v = 120 km/s in Table 4 for the flybys TA, TB, and T3. Since the ion temperatures seem to be relatively poorly constrained by observations and the numerical model is quite successful with the large Voyager ion temperatures we tend to consider b > 1 but well below the Voyager value, a good choice for TA and TB and also T3 before improved CAPS results become available, which fully exploit the capabilities of the experiment Asymmetry Between Y < 0 and Y >0 [41] The observations of the draped magnetic field in the tail-forming region very close to Titan are characterized by strong asymmetry relative to the PRL for all encounters, where the induced magnetosphere seems much more extended on the sunward side than on the opposite one (see Table 2). The cross section of the induced tail together with the projection of the trajectory on the Y, Z plane shown in Figures 3a and 3b of Backes et al. [2005] suggests that the asymmetry is partly due to the trajectory in which the 10 of 15

11 Figure 8. Comparison of 60 s average magnetic field observations (solid lines) in TIIS and modeling results (dashed lines) after rotation of the model results from the model draping system into the TIIS coordinate system for Titan encounter T3 on 15 February spacecraft approached the PRL from the north through the region of the magnetic ionopause around CA with its reduced magnetic field magnitude. The same situation can be seen in Figures 9 and 10 for TB and T3, respectively, in which the model cross sections at the X coordinate of the PRL crossings is also shown. The three figures (for TA, see Backes et al. [2005]) of the cross section in the Y, Z plane indicate nevertheless that the tail close to Titan is characterized by a sizable asymmetry with respect to the X, Z plane, where the induced magnetosphere is much more extended on the sunward side than on the opposite side. It has been suggested by Hartle et al. [1982] that this is due to the finite gyro radius effects on newly born pickup ions running into the denser neutral atmosphere on the night side and away from it on the sunward side. The effect is strongest for R g,pu /H > 1, where R g,pu is the gyroradius of a pickup ion and H the atmospheric scale height. The good agreement between the data and the model by Backes et al. [2005] suggests that the effect is not very important inside the induced magnetosphere, because the model does not Table 4. Plasma and Magnetic Field Parameters From the Averages of the Combined Time Intervals Before and After the Encounter Proper TA TB T3 V1 Averaging interval, before Averaging interval, after Electron density, a m Mass density, amu/m Electron temperature, a ev Magnetic field magnitude, nt Electron pressure p e, b Pa Ion pressure p i, Pa??? Magnetic field pressure p m, Pa b =(p e + p i )/p m >1 >1 >1 11 Alfvén Mach number Sonic Mach number??? 0.57 Fast Mach number <1 <1 < a From CAPS-ELS observations. b Computed from average kt e N, where T e and N are single observations. 11 of 15

12 Figure 9. Magnetic field model results [Backes, 2004; Backes et al., 2005] in model draping coordinates for TB with B x shown in color coding and the projections of the magnetic field vectors on the Y DRAP, Z DRAP coordinate system at X DRAP = 1.25 R T. The trajectory projection is also shown with the crossing of the plane indicated by a diamond. The PRL is indicated by a dark gray box. take into account finite gyroradius effects. The description is nevertheless accurate in most of the induced magnetosphere, because the pickup ion gyroradius is reduced due to the strongly reduced flow velocity. Thus the remaining asymmetry is a consequence of the asymmetry in the plasma production rate due to the day-night asymmetry in the photoionization rate. The effect will be enhanced by a possible day-night asymmetry in the exosphere of Titan. The Hartle effect will still play an important role in the outer induced magnetosphere and beyond the draping boundary DB in three dimensions Deviations From a Simple Draping Picture and the Role of Fossil Fields [42] By discussing the magnetic field observations in Figures 3 6 we have been able to interpret most of the features in terms of the straightforward application of the draping concept developed with the aid of Figure 2 which was based on stationary, quiet flow. This was particularly successful for TA and T3. However, even during these encounters there were features not readily explainable, like some fluctuating fields in TA and T3 and the jerk of 30 s around 1535 UTC during flyby TA. TB had strong deviations from the simple picture which can be explained by nonstationary and particular variations in the velocity direction. Thus temporal variations in the magnetoplasma incident on some fiducial plane at X DRAP 2 3 R T, say, combined with transverse spatial variations can basically be used as an explanation. However, fields observed at very low altitudes of Titan will have traveled a long time from the fiducial plane. We call them fossil fields. [43] For example, for TA the altitude varies from 1400 to 1700 km during the PRL. Although no velocity information has been reported yet at these altitudes, theoretical modeling [Keller et al., 1992; Backes et al., 2005] suggests vertical components of tens to at most hundreds of m/s at these altitudes. Assuming 100 m/s then the difference in age of the plasma encountered at 1700 km and 1400 km together with its frozen-in magnetic field can be estimated to be about 50 minutes. The time of passage from a fiducial plane upstream of Titan will take at least an hour as the interpretation of model results shows. The age of the field lines is even longer below the altitude range of the PRL down to CA at 1530:04 UTC. Thus from about 1524 to 1536 UTC the magnetic field lines connected into the vicinity of Titan have entered Titan s interaction volume one to several hours ago and thus do not necessarily have to do with the incident field on which the dynamic draping field coordinate system is based. In spite of substantial variations, the fossil fields still confirm the general stability of the large-scale incident field because the broad magnitude minimum around about 1527 UTC is not severely distorted. The jerk mentioned above and observed around 1550 km altitude may be a fossil feature. [44] The concept of fossil fields has interesting consequences for the physical interpretation of flyby data and modeling projects: Below 1600 km altitude, say, physical quantities tend to depend on the inflow parameters which flowed into Titan s neighborhood more than an hour ago and hence are difficult to reconstruct in a dynamic magnetospheric environment Shape and Physical Nature of the Draping Boundary [45] An interesting property of the DB of the induced magnetosphere is the shape in three dimensions. A complete Figure 10. Magnetic field model results [Backes, 2004; Backes et al., 2005] in model draping coordinates for T3 with B x shown in color coding and the projections of the magnetic field vectors on the Y DRAP, Z DRAP coordinate system at X DRAP = 1.35 R T. The trajectory projection is also shown with the crossing of the plane indicated by a diamond. The PRL is indicated by a dark gray box. 12 of 15

13 Table 5. Approximate Cross Section of the Draping Boundary by a Displaced Ellipse After Backes et al. [2005] for TA in Draping Coordinates Semimajor axis along ±Z Semiminor axis along ±Y Displacement of center along Y X coordinate of cross section study would require many more observations, preferably under constant solar and incident flow conditions. However, even with the limited data the cross section of the draping boundary of the near tail of Titan can be characterized. Among the three encounters, TA has the smallest S/C velocity component V x and thus moves less in the X direction than in the Y, Z plane of our draping coordinates. Figures 3, 4, and 5 indicate for the time intervals , , and on encounter day for TA, TB, and T3, respectively, the following displacements DX relative to the Y, Z plane: DX qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:304; :0415; 0:608: ðdyþ 2 þðdzþ 2 Value 3.5 R T 2.0 R T 0.2 R T 1.2 R T From the TA results, which are clearly most suitable, we can approximate the tail cross section as an ellipse with the properties given in Table 5, combining Table 2 and the numerical model of Backes et al. [2005]. The numerical modeling results are in approximate agreement with the entry and exit locations of the draping boundary observed. [46] It is interesting to consider the physical nature of the DBs by comparing theoretical concepts and observations. The observations clearly indicate the onset of increased spatial gradients toward Titan, if the temporal variations are generally considered as mostly spatial variations. At TA we note that the inbound DB is characterized by the immediate onset of a steep gradient. We can call this a first-order discontinuity as in other fields of physics. The sequence of gradients is more complex inward of the outbound DB, where in Figure 3 steep gradients in B z are followed by a steep gradient in all components particularly B x as one goes inward. If we assume that the onset of steep gradients further inward is not fortuitous on just these trajectories and if therefore the same variation can be expected on hypothetical, offset, parallel trajectories, one arrives at an important conclusion: Then the DB corresponds to the outward boundary of a region with strong current densities inside and at most weak currents outside, i.e., a zero-order discontinuity in the current density. The current density just inside the boundary must then be parallel to the DB. The DB therefore constitutes the outer boundary of a global distribution of currents associated with the draping and due to mass loading. Importantly, mass loading does not have to be active everywhere on the DB. [47] A quantitative physical model of the Titan DB follows from the extension of the physical considerations of Neubauer [1998] from the case of b 1 to cases with b > 1. Here the disturbance field is viewed as a superposition of the different MHD modes. Because the flow is subfast, fast magnetoacoustic waves are radiated in all directions, almost isotropically for b > 1. However, in contrast to the case of b 1, Alfvén wings and slow mode wings form in the same region for b!1and with strong overlap at moderate b > 1 downstream of Titan [see, e.g., Jeffrey and Taniuti, 1964, Figure 4.5c]. The outer boundary of the MHD wings is then given by the envelope of the Alfvén characteristics issuing from all parts of the atmosphere of Titan interacting with the plasma. The DB observed corresponds to the MHD wing boundary cross section at X = 1.2 R T for the ellipse approximation described in Table 5. The wing is fan shaped in any plane parallel to the X, Z plane and of slowly varying width in the X, Y plane. The opening angle of the fan is given locally by the Alfvén Mach numbers M A, or in terms of the standard angle Q A between the external magnetic field and the wing boundary in any plane parallel to the X, Z plane and not too far from that plane, tan Q A ¼ M A [48] We now understand quantitatively why the model results of Backes et al. [2005] agree well with the observations at TA. The reason is the similar Alfvén Mach number at the Voyager 1 encounter and at TA after Table 4. Since the magnetic field becomes strongly distorted inside the DB it could also be called the outer boundary of the magnetotail of the induced magnetosphere of Titan. Outside the DB, MHD wing boundary or the tail boundary the plasma is essentially disturbed by the fast mode only, with much weaker disturbance levels because energy is carried away by the fast mode much more effectively. Because of these fast disturbances equation 1 is exactly true locally and approximately for the Alfvén Mach number M A based on far upstream parameters. We note finally that because of the large heavy ion gyro radii near Titan a more accurate description than by MHD may be necessary Magnetic Ionopause [49] It is by comparison with the modeling results of Keller et al. [1994] and, particularly, Backes [2004] that we have identified the magnetic ionopause of TA and TB as a feature characterized by a broad minimum in the magnetic field magnitude near but not exactly centered at CA. Comparison with the modeling diagnostics of the 3-D model by Backes [2004] shows that it is characterized by force equilibrium between the electric current force (~j ~B force) and the frictional force acting on the slowly flowing plasma. As expected it is most pronounced for the lowaltitude flybys TA and TB, whereas at T3 there is at most a weak signature overlapping the PRL signature. The magnetic ionopause shields the lower atmosphere-ionosphere system from the Saturnian magnetospheric field if the ionosphere is sufficiently well developed. 8. Summary [50] Cassini magnetic field and electron plasma measurements from the three Titan encounters TA, TB, and T3, as well as 3-D modeling have been used to study the draped magnetic field structure in the near tail of Titan s induced magnetosphere under different Saturnian magnetosphere ð1þ 13 of 15