Access of energetic particles to Titan׳s exobase: A study of Cassini׳s T9 flyby

Abstract We study how the local electromagnetic disturbances introduced by Titan affect the ionization rates of the atmosphere. For this, we model the precipitation of energetic particles, specifically hydrogen and oxygen ions with energies between 1 keV and 1 MeV, into Titan׳s exobase for the specific magnetospheric configuration of the T9 flyby. For the study, a particle tracing software package is used which consists of an integration of the single particle Lorentz force equation using a 4th order Runge–Kutta numerical method. For the electromagnetic disturbances, the output of the A.I.K.E.F. hybrid code (kinetic ions, fluid electrons) is used, allowing the possibility of analyzing the disturbances and asymmetries in the access of energetic particles originated by their large gyroradii. By combining these methods, 2D maps showing the access of each set of particles were produced. We show that the access of different particles is largely dominated by their gyroradii, with the complexity of the maps increasing with decreasing gyroradius, due to the larger effect that local disturbances introduced by the presence of the moon have in the trajectory of the particles with lower energies. We also show that for particles with gyroradii much larger than the moon׳s radius, simpler descriptions of the electromagnetic environment can reproduce similar results to those obtained when using the full hybrid simulation description, with simple north–south fields being sufficient to reproduce the hybrid code results for O + ions with energies larger than 10 keV but not enough to reproduce those for H + ions at any of the energies covered in the present study. Finally, by combining the maps created with upstream plasma flow measurements by the MIMI/CHEMS instrument, we are able to estimate normalized fluxes arriving at different selected positions of the moon׳s exobase. We then use these fluxes to calculate energy deposition and non-dissociative N2 ionization rates for precipitating O + and H + ions and find differences in the ion production rates of up to almost 80% at the selected positions. All these results combined show that the electromagnetic field disturbances present in the vicinity of Titan significantly affect the contribution of energetic ions to local ionization profiles.

code (kinetic ions, fluid electrons) is used, allowing the possibility of analyzing the disturbances and asymmetries in the access of energetic particles originated by their large gyroradii. By combining these methods, 2D maps showing the access of each set of particles were produced. We show that the access of different particles is largely dominated by their gyroradii, with the complexity of the maps increasing with decreasing gyroradius, due to the larger effect that local disturbances introduced by the presence of the moon have in the trajectory of the particles with lower energies. We also show that for particles with gyroradii much larger than the moon's radius, simpler descriptions of the electromagnetic environment can reproduce similar results to those obtained when using the full hybrid simulation description, with simple north-south fields being sufficient to reproduce the hybrid code results for O + ions with energies larger than 10 keV but not enough to reproduce those for H + ions at any of the energies covered in the present study.
Finally, by combining the maps created with upstream plasma flow measurements by the MIMI/CHEMS instrument, we are able to estimate normalized fluxes arriving at different selected positions of the moon's exobase. We then use these fluxes to calculate energy deposition and non-dissociative N 2 ionization rates for precipitating O + and H + ions and find differences in the ion production rates of up to almost 80% at the selected positions. All these results combined show that the electromagnetic field disturbances present in the vicinity of Titan significantly affect the contribution of energetic ions to local ionization profiles.

Introduction
With a radius of 2575 km, Titan is Saturn's largest moon and the second largest moon in the Solar System after Jupiter's Ganymede. Unlike Ganymede, Titan does not possess an internal magnetic field (Wei et al. (2010), Backes et al. (2005)) but it is the only moon in the solar system known to have a dense atmosphere, with a surface pressure of 1.5 bar (Fulchignoni et al. (2005)). The upper layers of the complex atmosphere are constantly ionized by different energy sources creating a complex ionosphere with different peaks that has been studied by several instruments on-board Cassini, both remotely and in-situ. Additionally, chemical reactions may also be induced by the precipitation of energetic particles (Vuitton et al. (2007), Krasnopolsky (2009)).
Titan's ionosphere has a complex vertical structure with different ionization sources like solar EUV radiation, precipitating energetic plasma from Saturn's magnetosphere, meteorites and galactic cosmic rays (Galand et al. (2010), Gronoff et al. (2009)). The relative importance of theses ionization sources is different for the dayside and the nightside of the moon ). Whereas on the dayside solar radiation is the main ionization source (Galand et al. (2006), Ågren et al. (2009), Cui et al. (2009a)), on the nightside impact ionization from incoming magnetospheric plasma, especially from electrons, becomes dominant (Galand et al. (2010), Richard et al. (2015). Additionally at the nightside, transport of ions coming from the dayside by horizontal winds has been shown to play an important role as well (Cui et al. (2009b)).
The main ionospheric peak, created by the incoming solar radiation, is located at approximately 1200 km. Below that altitude different peaks are located, that present significant changes in magnitude between different flybys (Kliore et al. (2008)). The production of these peaks has been attributed to different ionization sources with López-Moreno et al. (2008) suggesting that galactic cosmic rays could be responsible for ionization at altitudes around 65 km, Molina-Cuberos et al. (2001) suggesting meteoritic ablation as the source for the mid-altitude peaks near 700 km and the impinging magnetospheric plasma being suggested as the responsible for the peaks at higher altitudes. Cravens et al. (2008) studied the energy deposition from H + and O + ions for energies above 30 keV as measured by the Cassini MIMI instrument and, by estimating ionization rates, suggested that the precipitation of those ions could be related to the formation of the density peaks observed between 500 km and 900 km.
These results are in agreement with more recent results from Snowden and Yelle (2014), who calculated energy deposition rates for thermal and energetic O + and H + ions while studying the thermal structure of the upper atmosphere. They found that while the peak deposition rate for thermal O + ions occurs at approximately 1100 km altitude for bi-modal populations and 1075 km altitude for plasma sheet populations (both classifications according to Rymer et al. (2009)), energetic ions (with energies larger than 10 keV) deposit their energy below 1000 km.
More recently, Sillanpää and Johnson (2015) studied the influence of ionneutral collisions, calculating energy deposition rates at the exobase using a hybrid code with different considerations in terms of types of interactions.
There, they showed that the ion-neutral collisions greatly reduce the energy deposited in the upper atmosphere.
Titan is located at a mean distance of 20.2 Saturn radii (R S ) from the planet (1 R S = 60,268 km), placing it very close to the magnetopause stand-off distance, that Achilleos et al. (2008) described with a bi-modal distribution with peaks at 22 and 27 R S (depending on the solar wind dynamic pressure) based on a magnetopause model by Arridge et al. (2006) and observations from Cassini. This locates Titan most of the time in the outer Saturnian magnetosphere where it has been observed for most of the dedicated flybys, even though it can be located both in the magnetosheath (observed three times during the first ten years of the Cassini mission, Bertucci et al. (2008), Wei et al. (2011) and Edberg et al. (2013)) and in the unshocked solar wind (observed once, Bertucci et al. (2015)).
In addition to these variabilities, even when Titan is completely immersed in the outer magnetosphere of Saturn, the surrounding environment can be highly variable in time scales that can go from minutes to hours since the moon can be located above, below or inside Saturn's magnetodisk that, as described in Arridge et al. (2008), has a bowl shape that is dependent on the season and the solar wind conditions. Due to the fast rotation of the planet (Saturn completes a rotation around its axis in approximately 10h 34m, Read et al. (2009))) the heavier species of the plasma tend to be confined close to the equator but, as described in Arridge et al. (2011), due to the ambipolar electric fields that arise from the charge separation due to the high mobility of the electrons, lighter ion species such as H + tend to be located on a wider region around the equator than heavier species like O + . This creates a latitude-dependent difference in the plasma composition that introduces a further variability to the plasma environment on which Titan can be immersed at any given time.
All of this together determines the structure of Titan's magnetospheric in-teraction region, which typically differs from that of a moon in a north-south magnetic field configuration (Arridge et al. (2011)) and can be encountered immersed in a magnetospheric plasma flow with directions that differ from purely azimuthal corotation. The resulting structure has also implications on how particles can access the exosphere and deposit their energy into lower atmospheric layers and because of this variability, it becomes necessary to study these phenomena on a case-by-case basis. Apart from the obvious variability to be expected due to the different incoming fluxes that can significantly change from one flyby to the other (e.g. Garnier et al. (2010)), the specific electromagnetic field configuration for each flyby will guide particles with different gyroradii in a different way, accessing the atmosphere with a different latitude-and longitude-dependent probability.
In this paper we focus on the effect that the uneven access of energetic particles into Titan's atmosphere due to local electromagnetic field disturbances may have in the structure of the ionosphere. For this we study the trajectories of H + and O + ions with energies from 1 keV up to 1 MeV by means of a particle tracing software package. Charged particle tracing has been successfully used to study the interaction of magnetospheric plasma with solar system bodies in many occasions with some recent applications specifically for the Saturnian system (e.g. Wulms et al. (2010), Kotova et al. (2015)).
In general, the access of particles to the atmosphere will be determined by the local electromagnetic topology, which for Titan is highly variable as described above. For this study we selected the T9 flyby which occurred in conditions of non-azimuthal flow and magnetic field offset from the north-south direction, better illustrating the effect that the disturbances might have in the trajectories of charged particles. For the specific electromagnetic field configuration present during the flyby, reproduced by the A.I.K.E.F.  this specific flyby , Coates et al. (2007), Bertucci et al. (2007), Sittler et al. (2010)).
Among the interesting features that were studied Coates et al. (2012), using data from the Cassini CAPS/ELS instrument, reported the existence of a split signature to the tail with presence of ionospheric photoelectrons, suggesting a magnetic connection of the tail with the sunlit part of the moon.
This same tail structure, with two lobes and a central current sheet, was observed by the magnetometer (MAG) instrument, as reported by Bertucci et al. (2007). There, they suggested that this complex structure could be caused by the connection of each lobe to the dayside and the nightside respectively or, alternatively, to perturbations occurring in the upstream conditions, even though this last interpretation seems to be contradicted by the observation of the same split structure during subsequent tail flybys (Coates et al. (2012)). Szego et al. (2007) interpreted the first structure as Titan's mantle and the second one as the moon's wake, with a region in between where ambient plasma was observed.
Similar observations were made using the Cassini Radio and Plasma Wave Science (RPWS) instrument as reported by Modolo et al. (2007). Apart from the asymmetry of the wake, they also reported a displacement of the ideal corotation wake, something that has been reproduced by different models and analyses, with Bertucci et al. (2007) setting the displacement at an angle of 36°. Coates et al. (2012), based on Cassini CAPS data analysis, interpret the plasma flow as having a southward component while Szego et al. (2007) concluded that the deflection should be larger than 40°. For the simulations presented in this paper, a deflection of 34°, as used on a hybrid simulation by Simon et al. (2007) in order to reproduce the observed MAG data, is assumed.

Model and simulations
In order to map the access of energetic ions to Titan's exobase, a particle tracer is used to follow the ion trajectories in the system. As energetic ions carry low current density, their impact on the electromagnetic field topology is negligible and a simple tracing algorithm works as a reasonable approxi-mation. Still, the background electromagnetic environment upon which ions will be propagated needs to be defined.
In the following subsections, the basics of the tracing code as well as the electromagnetic field description used to obtain the plots presented in the results section are explained.

Tracing code
The basic equation of motion for charged particles in an electromagnetic field is the Lorentz force, given by Equation 1, where v is the particle's velocity, E the electric field, B the magnetic field, q the particle's charge, m the particle's mass and γ the relativistic Lorentz factor.
In order to study the access of particles to Titan's exobase, we integrate the equation of motion in a particular magnetospheric configuration using a fourth order Runge-Kutta method.
The integration can be forwards or backwards in time, depending on the chosen approach. Forward integration can be useful for studying how a system with some given initial conditions evolves in time, whereas backward integration is a more sensible approach when one wants to study how the system gets to a specific final position in phase space (Marchand (2010)).
Since we are interested in the access of particles to the exobase, the problem reduces to studying how the evolution of particles occurs to finally reach a specific position in space. By using the backward tracing approach, a great amount of computational time is saved, avoiding the calculation of trajectories of billions of particles that would never reach the exobase (and thus would be of no interest for the present study) and would still be required if forward tracing were used. Additionally, backward tracing has the advantage that, given that the simulations are non-collisional, no statistical sampling errors are introduced, leaving the approximate nature of the electromagnetic fields and integration methods used as the only sources of error (Marchand (2010)).
Thus, the approach used here to estimate the access of particles is the use of backtracing of different particles with different physical characteristics (energy, starting polar and azimuthal angles), all of them starting at the same altitude above the moon's surface but at different positions defined by latitude and longitude angles. The starting altitude is that of the exobase, taken for this study as located at an altitude of 1450 km above the surface ). The choice of this altitude and the impact that moving this boundary has on the results presented on this paper are analyzed in Appendix A.
Notice that for each starting point, depending on the characteristics of the particle being simulated (e.g. polar angle, energy, etc.), the particle may or may not collide with the moon. This is illustrated in Figure 2, where the trajectories of four hydrogen ions with different energies starting at the same initial position can either collide with the moon or escape the system, basically depending on the starting velocity vector and gyroradius.
As initial positions for the simulations, 10800 equally spaced points around the moon were chosen, covering a range in latitude values from -90°to +90°a nd in longitude from 0°to 360°, both with linear steps of 1°. The coordinate system being used is the TIIS, where 0°latitude is defined as the moon's For each of the starting points described, 6480 particles were simulated, each of them with a different combination of polar and azimuthal angles, each parameter varying from 0°to 180°and from 0°to 360°and with linear steps of 2°and 5°correspondingly.
All of the above gives a total number of particles of roughly 70 million being simulated for each energy and for each species. For the present study, two different species were included, namely hydrogen (H + ) and oxygen (O + ) ions. In terms of energy, for each species a range going from 1 keV to 1 MeV was covered.

Code validation
In order to determine whether the integrating process yields the right results or not, simple runs simulating particles with pitch angles of 90°(i.e. no parallel velocity component) assuming a vertical north-south (along the z-axis on a TIIS coordinates system) magnetic field configuration with azimuthal corotation were performed and the corresponding maps showing the access of particles were produced, yielding the expected results as shown in Figure   3, where a depletion of particles on the regions close to the magnetic tail can be observed, whereas full access is present for the rest of the local positions around the moon.
The map represents an equirectangular projection in Saturn-centered coordinates of Titan's exobase with the X-axis representing the longitude angle and the Y-axis representing the latitude angle. The color code represents the percentage of simulated particles that are able to escape the moon's environment during the backward tracing, which is the same as the regions that particles with the given characteristics would be able to reach in the moon's  with access close to the poles in the position of the tail are present because, during the simulation, particles are allowed to propagate downwards for a short distance (50 km) below the exobase and thus particles that start in the backward tracing at the exobase close the to poles are able to escape through that small region.
The idea of allowing the particles to propagate downwards is based on the selection of the boundary conditions for the simulations. Once the simulation starts, it is necessary to decide when to stop it. For this, two different boundary conditions need to be defined: 1) what happens when a particle hits the specified lower boundary and 2) when to stop the simulation assuming the particle left the interaction region.
For the first one, since we are interested in the access of particles to the exobase without considering any propagation into a collisional environment, the boundary has to be located at (or close to) the exobase. In our simulations, particles are allowed to penetrate up to 50 km in order to avoid eliminating particles that could make a small incursion into lower altitudes (e.g. due to gyroradius effects) before departing from the moon. Thus, the inner boundary for the simulations shown in this paper is not exactly the starting point (exobase at 1450 km) but a hard limit of 1400 km. This boundary is still considered a collision-free environment with many authors  2009)). Since we are running single independent particle simulations, there is no need to avoid discontinuities in the densities so particles can be abruptly removed from the simulation without affecting the overall results. So as soon as a particle reaches an altitude of 1400 km above the surface it is removed from the simulation and assumed as lost.
For the second boundary, the condition that the particle being simulated reaches a position in space with undisturbed magnetic fields needs to be fulfilled. This means that the particle has to reach a position where the magnetic field is equal to the upstream field.
However, given that particles with large gyroradii could still return to the interaction region ( Figure 4), an additional condition is applied, which consists of letting the particle travel far from the moon and coming back after one gyration. If after this first gyration the particle does not collide with the moon but rather keeps drifting away from it, then it is finally assumed as escaped.
Validating computation parameters such as the integration step is not so straightforward. The approach taken was to save the initial and final velocity of the particles being simulated and taking the mean speed variation for each starting position (longitude/latitude angle pairs). Even though variations are expected due to the presence of the electric field, these variations should not be too large, given the fact that the electric field is mostly expected to be in a direction perpendicular to the magnetic field.
In this paper, the output generated for the T9 flyby by a hybrid code named A.I.K.E.F. (Müller et al. (2011)) is used. In the model, ions are treated as individual particles while electrons are treated as a neutralizing fluid. Figure 5 shows the equatorial magnetic field (as seen from above) for the specific conditions of the T9 flyby with the colors representing the magnitude.
In the hybrid code simulation, both the magnetic and electric fields are self-consistently calculated during the production of the output and these (static) values are used during our tracings. For our tracing, a snapshot of the calculated fields was used. Titan itself is treated as an absorbing obstacle, meaning that any ion macroparticle in the code that reaches the inner boundary is removed from the simulation.
For the ionosphere, three species were included, namely H + 2 , CH + 4 and N + 2 and the massloading of the plasma was simulated by photoionization. Since we are interested only in the magnetic field perturbations and not in the ion densities, this relatively simple approach is sufficient for our purposes.
The upstream parameters used during the production of the hybrid code output for the T9 flyby are summarized in Table 1. All the upstream parameters were kept constant during the simulation run (for more details refer to Feyerabend et al. (2015) on this issue).
Given the short time scale of the studies presented here, taking the fields as invariant during the tracing is a sensible assumption. Nevertheless, the hybrid code output for this study is provided self-consistently only within a cube of 15 Titan radii (1 R T = 2575 km) side. This choice is based on the high computational times required for the hybrid code simulation. Even though the hybrid code simulation is run with an adaptive mesh with higher spatial resolution closer to the moon, the output used on this study has been re-sampled to a uniform grid with 280 sample points on each of the three directions, giving a resolution of 0.05 R T .   (Feyerabend et al. (2015) on this issue).

Parameter
Once the particles being traced leave the hybrid code cube, it becomes necessary to extend somehow the electromagnetic field model to continue with the tracing. Particles can leave the 15 R T side cube either due to their large gyroradii or due to their motion along the field lines. In the first case, particles will make a relatively short excursion outside the cube whereas in the second case they will gyrate around the field line while traveling with a parallel velocity component to their mirror point and back. For this last case, a full magnetospheric model (e.g. Khurana et al. (2006)) would be needed whereas for the former one a simpler approach can be used.
Whether particles need to be traced to their mirror points or not depends mainly on their equatorial displacement during half a bounce period. If this displacement is large enough so that the particle can be removed from the simulations once it leaves the interaction region, then a simple description can be adopted for the vicinity of the moon. This is indeed the case for all the particles studied in this paper with the minimum expected equatorial displacement being at least 3.5 times larger than the particle's gyroradius.
This can be observed in Figure 6, where the equatorial displacement and corresponding gyroradius are plotted for H + and O + ions and for each energy level covered in this study. In both cases, a minimum is reached at an energy of 20 keV, where the displacement-to-gyroradius ratio is of 3.5, allowing the particle to drift away from the moon without colliding with it after returning to its vicinity. Table 2 presents the drifts for selected energies. The drifts were calculated using the full magnetospheric model ) with 60% corotation by means of the method presented in Roederer (1967) considering pitch angles close to 90°. The calculation includes both a magnetic field-related drift and an electric field-related drift.
The magnetic drift is calculated using Equation 2, where m 0 is the particle's mass, c is the speed of light, q is the elementary charge, B eq is the equatorial In both equations λ m represents the latitude of the particle's mirror points, B(s) is the magnetic field at the position where the numerical integral is being calculated and B m is the magnetic field magnitude at the mirror points.
The electric drift is simply the E × B drift as calculated using Equation

Results
In this section, maps showing the access of particles to Titan's exobase are presented and discussed. For reasons of space, only maps for four different energies for O + and H + ions are presented in order to show the variabilities that arise from the different gyroradii.
In addition to the mentioned maps, the influence that variations in the field configuration have in the access of particles is studied by comparing the maps obtained using three different models: 1) a uniform, north-south magnetic field, 2) a uniform, rotated, magnetic field with the upstream values from the hybrid code output and 3) the full hybrid code output which accounts for the draping of the lines close to the moon.
The results are presented in the form of equirectangular projections of Titan's exobase as shown in Figure 3. The only difference between Figure 3 and the maps presented in this section is the position of the white and black lines; whereas in the map presented in Figure 3     3.2. Access of particles with the full hybrid code output Figure 9 shows the maps obtained using the full hybrid code output for O + with four different energy levels. From the color scale, it is evident how particles with higher energies have much higher access at every position around the moon, with the effect becoming less evident for particles with energy lower than 10 keV.
Additionally, a symmetry with respect to the equator is observable especially for the highest energies. This symmetry arises from the gyroradii of the particles, that are in every case larger than the moon's radius (e.g. 5.3 R T for 90°pitch angle O + ions at the equator with an energy of 100 keV and 15 R T for the 1 MeV case). This causes that, in the close vicinity of the moon, particles travel with a trajectory very close to a straight line and thus the effect of the draping of the lines caused by the moon is almost negligible.
Finally, a wave-like shape is observed surrounding the symmetric feature mentioned in the previous paragraph, especially for the middle energies (e.g. 10 keV in Figure 9). This effect is produced by the rotation of the field observed during the flyby. On a vertical magnetic field configuration, particles traveling along the magnetic field lines can reach the close vicinity of the moon either from the north or the south poles, creating an access pattern that is symmetric around the equator of the moon. If in contrast the magnetic field is rotated by a certain angle with respect to the equatorial plane, particles coming from the north will have more access at a certain longitude, while particles coming from the south will have more access at a completely different longitude, thus creating the observed structure. Figure 10 shows the maps obtained using the full hybrid code output for H + with four different energy levels. A similar effect like that observed with O + ions is present, with larger access in most regions of the exobase for higher energies. Similarly, the symmetry around the equator is also observable, even though the deviation from the symmetry arises with higher energies, showing for the 100 keV case an already noticeable wave-like shape and the symmetry completely absent for the 10 keV case. An interesting effect for both the O + and the H + case is that for the lower energies, the access of particles is larger for the region surrounding the magnetic tail than for the region from where the incoming plasma should be impinging the moon. Even though this has already been reported by other authors (e.g. Sillanpää et al. (2007)), it seems counterintuitive and has its roots on the distortions of the electromagnetic fields introduced by the presence of Titan. To help visualize this, Figure 11 shows the magnitude of the magnetic field at the exobase of Titan. In this projection it is evident that the magnetic field magnitude is much lower on the tail and much stronger at the ram direction. This helps shield the regions close to 150°while it leaves the regions close to the tail more unprotected due to the lower magnetic field magnitude. This basically affects particles with smaller gyroradii that tend to drift on curves of equal magnetic field and will thus tend to avoid the pile-up region present where the incoming plasma flow encounters the moon's ionosphere, while particles with larger gyroradii are able to access all the regions around the moon.
From the maps just presented it is possible to observe that the access of particles is not homogenous around the moon, with some areas more accessible to specific particles with specific energies. This is easier to observe in Figure 12, where the percentual access of O + and H + ions is plotted against the energy ranging from 1 keV to 1 MeV for four different selected positions around the moon (Table 3 and Figure 11). The selection of the regions was based on visual inspection of the access maps presented above. The idea was to take regions with large and regions with small variations along the analyzed energy range.
In both plots, the first thing that can be seen is that the access is the largest in every case for the higher energies. In fact, for the four selected points at the exobase, the access steadily increases with energy until a steady level that varies with particle and position is achieved. This point is located at around 10 keV for the O + case for the four points and at around 300 keV for the H + case for three of the points with the Lat: 0°, Long: 0°case being stabilized at approximately 20 keV.
Altogether, the two plots show how the access of particles is highly asymmetric all over the moon, with the asymmetry increasing with decreasing gyroradius. We interpret this asymmetry as one of the possible causes for the high variability observed in the ionospheric profiles obtained by in-situ measurements by different instruments on-board Cassini (Cravens et al. (2009b) Position Latitude (°) Longitude (°) Position 1 0 146 Position 2 50 146 Position 3 -50 146 Position 4 0 0 Table 3: Selected positions at the exobase around the moon for ionization rates analysis. and references therein). In the following subsection we derive energy deposition and ionization rates in order to explore this possibility.

Energy deposition and ionization rates
Since Titan was located below the current sheet during the T9 flyby, a strong Saturn-directed component was present in the magnetic field data. This is visible in Figure 13 that shows the three magnetic field components as detected by the MAG instrument (Dougherty et al. (2004)), as well as   By combining the O + and H + spectra shown in Figure 12 with the upstream fluxes detected by the MIMI/CHEMS , we are able to estimate the normalized fluxes of different particles at given locations of the moon's exobase. These normalized fluxes are shown in Figure 15.
For both cases a difference between the upstream fluxes and the fluxes reaching the exobase is present, with the difference being the largest for the lower energies. This is again a result of the shielding effect being stronger for particles with smaller gyroradius and thus having a larger attenuating effect on the upstream fluxes for particles with lower energies than for those with higher energies. The left panel in Figure 16 shows the integrated ionization rates by O + ions with energies higher than 10 keV on the atmosphere. The figure shows that most of the ionization by energetic O + ions occur at an altitude of approximately 900 km above the moon's surface, where a production of roughly 4 ions/cm 3 is predicted.
To get an estimate of the differences in ionization rates at the selected positions around the moon, a weighted difference between the position where the maximum rate was observed and that where the minimum rate was observed was calculated. The difference is weighted according to the local magnitude of the ionization rate, normalized to the maximum value. This gives an estimate of the difference where the ionization rates are the highest and neglects altitudes at which the differences can be higher but the ionization rates are very low.
The curve showing the weighted difference is presented on the right panel of Figure 16. A maximum difference between the peak ionization rates of 18% is calculated for this case. This difference was calculated between the position with highest ionization rate (position 4) and the one with the lowest  and closer to 2 ions/cm 3 for position 3 (-50°latitude and 146°longitude).
Also remarkable for the H + case is the higher magnitude of the weighted difference peak. Whereas for oxygen ions the peak was around 18%, for hydrogen the peak reaches almost 80%. In terms of altitudes and magnitudes, production rates for both the O + and the H + ions are in good agreement with the results derived for T5 by Cravens et al. (2008) where they present prudction rates for ions with energies above 30 keV, with only the ionization peak for H 2 occuring at slightly higher altitude in this study.
With this very simple ionization model, we are then able to estimate that the ionospheric density variations from magnetospheric ions precipitation due to the electromagnetic field disturbances observed during T9 would be range from less than 20% to more than 75% at different positions around the moon. This means that if the differences observed in the ionospheric densities for the nightside of the moon (where the precipitating plasma plays an important role on the ion production) are taken into account, part of them could be explained not just by the upstream plasma variations, but also by the difference in particle's access caused by the electromagnetic field disturbances present during the different flybys.

Summary
By means of particle tracing software and using three different magnetic field models, the effect that different disturbances present in the vicinity of Titan have in the access of particles to the exobase was studied. For this, three different simulations, namely one with a simple north-south field, a second using the upstream electromagnetic fields observed before and after the T9 flyby that includes the strong X T IIS and Y T IIS components and a third one with the full description provided by the A.I.K.E.F. hybrid code were compared for the same species and energies, showing that the importance of having a full electromagnetic field description (such as the one provided by the hybrid code) increases with decreasing gyroradii. In this sense, it was shown that for particles with gyroradii larger than few R T , a simple constant vertical field or an unperturbed field with a Saturnward component can produce very similar access maps than a full hybrid code description.
Then, by using the full hybrid code description of the electromagnetic fields specifically produced for the T9 flyby, we produced 2D projection maps However, in order to be able to link the results with observations made by Cassini, a more detailed study needs to be carried out including extra factors such as other atmospheric constituents (at least CH 4 ) as well as more complex ionization reactions. Another effect that is not considered in this study and that should play an important role is the incidence angle of the precipitating ions. This is a factor that could lead to even larger differences according to whether ions precipitate closer or farther from the vertical. This incidence angle will also be affected by the way ions are guided by the local electromagnetic fields.
by BMBF through DLR under contract 50OH1101 and by the Max Planck Gesellschaft. L. Regoli is supported by a joint Impact Studentship between UCL the Max Planck Gesellschaft.
Appendix A. Setting the collisionless boundary at different altitudes By tracing back the particles using the exobase (1450 km) as a starting point and given that no particle interactions are simulated during the tracings, it is implicitly being assumed that all the environment above the exobase is collisionless. This assumption is not necessarily true and thus a further analysis including the different interactions expected according to the densities needs to be done.
To analyze the possible impact that the inclusion of these phenomena could have on the access of particles, the same simulations presented in the previous subsections were run, this time changing the altitude of the initial position with a step of 50 km on each simulation run.
The maps showing the access of 1 keV O + ions for four different altitudes (1 R T + 1450 km, 1.2 R T + 1450 km, 1.4 R T + 1450 km and 1.6 R T + 1450 km) are presented in Figure A.18, where it can be seen that still for a variation in the setting of the exobase of up to 150 km (around 5% of Titan's radius) no significant changes are present in the particle's access maps. With these results in mind, the original choice of an altitude of 1450 km for the exobase seems to be a sensible one.