Icarus 305 (2018) 186–197 Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Energy deposition and ion production from thermal oxygen ion precipitation during Cassini’s T57 ﬂyby Darci Snowden∗, Michael Smith, Theodore Jimson, Alex Higgins Department of Physics, Central Washington University, 400 E. University Way, Ellensburg, WA 98926, United States a r t i c l e i n f o Article history: Received 24 January 2017 Revised 7 June 2017 Accepted 10 January 2018 Available online 11 January 2018 Keywords: Titan Atmosphere Aeronomy a b s t r a c t Cassini’s Radio Science Investigation (RSS) and Langmuir Probe observed abnormally high electron densities in Titan’s ionosphere during Cassini’s T57 ﬂyby. We have developed a three-dimensional model to investigate how the precipitation of thermal magnetospheric O+ may have contributed to enhanced ion production in Titan’s ionosphere. The three-dimensional model builds on previous work because it calculates both the ﬂux of oxygen through Titan’s exobase and the energy deposition and ion production rates in Titan’s atmosphere. We ﬁnd that energy deposition rates and ion production rates due to thermal O+ precipitation have a similar magnitude to the rates from magnetospheric electron precipitation and that the simulated ionization rates are suﬃcient to explain the abnormally high electron densities observed by RSS and Cassini’s Langmuir Probe. Globally, thermal O+ deposits less energy in Titan’s atmosphere than solar EUV, suggesting it has a smaller impact on the thermal structure of Titan’s neutral atmosphere. However, our results indicate that thermal O+ precipitation can have a signiﬁcant impact on Titan’s ionosphere. © 2018 Elsevier Inc. All rights reserved. 1. Introduction Cassini has discovered that most of the O+ and other water group ions (e.g. H2 O+ , OH+ ) in Saturn’s magnetosphere originate from the plumes of Enceladus. Once ionized, these particles are conﬁned to a region near Saturn’s magnetic equator known as the plasma sheet. Eventually, the water group ions are transported to Saturn’s outer magnetosphere where Titan orbits. Near Titan, Saturn’s plasma sheet is only a few Saturn radii thick and the tilt of Saturn’s magnetic axis causes the plasma sheet to be morphed into a bowl shape by the pressure of the solar wind. Therefore, depending on the season, the average position of the plasma sheet is above or below Titan’s orbital plane. However, the plasma sheet does not stay in its average position, rather it is highly dynamic and is observed oscillate with a period similar to Saturn’s rotational period (around 10.7 h). The motion of the plasma sheet causes it to periodically move past Titan, exposing Titan’s atmosphere to the water group ions that are conﬁned there (Arridge et al., 2008). Hörst et al. (2008) showed that the oxygen containing ions that originated from Enceladus’s interior have a signiﬁcant and lasting impact on the chemistry and composition ∗ Corresponding author. E-mail address: [email protected] (D. Snowden). https://doi.org/10.1016/j.icarus.2018.01.014 0019-1035/© 2018 Elsevier Inc. All rights reserved. of Titan’s atmosphere. Despite this, there are relatively few studies that quantify how thermal O+ precipitation affects Titan’s thermosphere and ionosphere. We have developed a three-dimensional ion precipitation model to quantify the ﬂux of magnetospheric thermal (1 eV to 10 keV) O+ into Titan’s atmosphere. We use this model to investigate how precipitating oxygen affects Titan’s thermosphere and ionosphere by calculating global ionization and energy deposition rates. In particular, we examine the O+ precipitation during Cassini’s T57 ﬂyby. Titan was observed to be in Saturn’s plasma sheet both before and after T57 (Rymer et al., 2009; Nemeth et al., 2011); therefore, Titan’s atmosphere should have been exposed to thermal O+ precipitation while Cassini was making in situ measurements. Also, during T57, Cassini’s Radio Science Investigation (RSS) and Langmuir Probe observed abnormally high electron densities in Titan’s ionosphere near 1200 km altitude suggesting enhanced ionization from thermal ions or electrons from Saturn’s magnetosphere (Kliore et al., 2011; Richard et al., 2015). The ﬂux of oxygen through Titan’s exobase calculated here is in agreement with other recent simulations of O+ precipitation at Titan (e.g. Sillanpaa and Johnson, 2015); however, our model is unique in that we also calculate how this ﬂux affects Titan’s atmosphere. We ﬁnd that, in limited regions, ionization rates from magnetospheric O+ in the thermal energy range are high enough to explain ionospheric density enhancements on the order of D. Snowden et al. / Icarus 305 (2018) 186–197 187 2. Cassini’s T57 ﬂyby Cassini’s T57 ﬂyby took place at 18:32 UT on 2009 June 22. Fig. 1 shows the trajectory of the ﬂyby and the solar zenith angles traversed in Titan’s atmosphere. Cassini entered Titan’s atmosphere on the anti-Saturn/night side, downstream of the corotational magnetospheric ram direction. Cassini then traveled toward the ram direction and exited on the day side of Titan’s ionosphere. During T57, Titan was on the night side of Saturn’s magnetosphere at 22 h Saturn local time. The average ambient magnetic ﬁeld was [2.27, 4.77, −1.05] nT and the By component of the magnetic ﬁeld indicates that Titan was below Saturn’s magnetic equator (Simon et al., 2010). Moments derived from Cassini Plasma Spectrometer (CAPS) data show that the upstream density, temperature, and velocity was variable for several hours before T57 (see Fig. 2). Rymer et al. (2009) and Nemeth et al. (2011) have classiﬁed this ﬂyby as a mix of bi-modal and plasma sheet types. A bi-modal classiﬁcation means that the oxygen ions have a higher density and are colder than what is typically observed in the plasma sheet and is most likely correlated with Titan passing through Saturn’s current sheet. Finally, as previously discussed, occultation data has been used to calculate the electron density during this ﬂyby and Kliore et al. (2011) showed that it was abnormally high compared to previously observed densities on the solar limb. The peak electron density measured by the Langmuir Probe was also high for Titan’s nightside ionosphere at 1380 cm−3 (Snowden and Yelle, 2014b; Richard et al., 2015; Agren et al., 2009). Both observation suggest signiﬁcant ionization from magnetospheric particles. 0.1 W + Temperature (eV) 0.05 W + Velocity (km s -1) 10 0 0 cm−3 . The precipitation of O+ into Titan’s atmosphere occurs over a limited region of Titan’s ionosphere. For a magnetic ﬁeld conﬁguration similar to the T57 ﬂyby, we ﬁnd that the region of enhanced ionization is close to but does not overlap with the area where RSS observed enhanced densities in Titan’s ionosphere. However, high ionization rates do overlap with the area that Cassini’s Langmuir Probe measured enhanced densities. Our results suggest that both thermal O+ precipitation and thermal magnetospheric electron precipitation can be important ionization sources in Titan’s atmosphere above 10 0 0 km. We ﬁnd that the energy deposited by thermal O+ is similar to the energy deposited by other magnetospheric particles, but less than the energy deposited by solar EUV. W + Density (cm -3) Fig. 1. The trajectory during Cassini’s T57 ﬂyby as seen from above the equatorial plane and looking toward Saturn. Cassini’s altitude (dashed) and solar zenith angle (solid) versus altitude. Results are displayed in the TIIS coordinate system with the x-axis pointing in the nominal magnetospheric ﬂow direction, the y-axis pointing toward Saturn, and the z-axis completing the right handed system. The arrow labeled T57 shows the average upstream magnetic ﬁeld direction. 0 15:30:00 16:00:00 16:30:00 17:00:00 15:30:00 16:00:00 16:30:00 17:00:00 15:30:00 16:00:00 16:30:00 17:00:00 500 400 300 200 100 200 150 100 50 Time (UTC) Fig. 2. Ion moments derived from CAPS/IMS (ion mass spectrometer) data taken before closest approach during the T57 ﬂyby (Young et al., 2004). The top panel shows W+ ion density, which is an ion group that includes the density of H2 O+ , OH+ , and O+ . The center panel shows W+ group temperature and the bottom panel shows W+ bulk velocity. 3. Model 3.1. 3D model of Titan’s plasma interaction Titan does not have an intrinsic magnetic ﬁeld and the plasma and electromagnetic ﬁelds that make up Saturn’s magnetosphere interact directly with Titan’s atmosphere. In Saturn’s outer magnetosphere, where Titan orbits, the plasma densities vary between about 0.01 and 0.1 cm−3 depending on the relative location of Saturn’s plasma sheet. The bulk magnetospheric plasma velocity is about 100 km/s and the direction can vary signiﬁcantly from corotation (Thomsen et al., 2010). The magnetic ﬁeld near Titan has a strength of about 5 nT and the convective electric ﬁeld, which nominally points away from Saturn, has a strength of about 0.3 mV/m (Arridge et al., 2011a; Arridge et al., 2011b). The slowing of the magnetospheric plasma causes a pile-up and enhancement of the magnetic ﬁeld upstream of Titan. The perturbation of the magnetic and electric ﬁeld near Titan’s atmosphere affects the cy- 188 D. Snowden et al. / Icarus 305 (2018) 186–197 Fig. 3. Results of two-dimensional particle tracing simulations. The background magnetic ﬁeld is 5 nT into the page and the electric ﬁeld is 0.5 mV/m in the negative ydirection. The magnetic ﬁeld around a circular obstacle increases with a cosine function with maximum magnitudes of either 10 nT (a, c) or 20 nT (b, d). Colored lines show the trajectories of 16 amu ions with a bulk velocity of 100 km/s and thermal energies of 100 eV (green), 1,000 eV (red), and 10,000 eV (cyan). (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.) cloidal trajectory of oxygen ions with gyroradii that are on the order of the scale size of the gradients in the magnetic ﬁeld (about one Titan radius, RT = 2575 km) or in the thermal energy range below about 10,0 0 0 eV. If a southward ambient magnetic ﬁeld is assumed, the draping and enhancement of the magnetic ﬁeld tends to prevent oxygen ions from impacting the anti-Saturn and wake sides of Titan’s atmosphere. In other regions, oxygen ions are not completely deﬂected and can reach altitudes near Titan’s exobase where neutral collisions begin to dominate. Results from simple two-dimensional simulations that illustrate how the magnetic pile-up region upstream of Titan might affect the trajectories of oxygen ions with different energies are shown in Fig. 3. In each simulation, the magnetic ﬁeld is 5 nT in the negative z-direction (into the page) except in a torus region where the magnetic ﬁeld strength is either doubled or quadrupled over a region of 1 or 3 RT . In the center of each region of enhanced magnetic ﬁeld is a circular obstacle (or “atmosphere”) with a radius of 4075 km (1.58 RT ), where particles are absorbed. Particles with energies of 10, 10 0 0, and 10,0 0 0 eV (with gyroradii equal to 0.46, 1.5, and 4.6 RT , respectively) are injected with a drift velocity of 100 km/s at the left hand boundary. In Fig. 3(a) all of the ions directly upstream of Titan’s atmosphere are absorbed, as evident by the empty wake region behind Titan. In this case, the magnetic enhancement is so weak and spatially limited it does not have a strong effect on the O+ trajectories. In Fig. 3(b), the stronger enhancement of the magnetic ﬁeld means that the trajectory of all ions is affected. The shrinking of the O+ gyroradii in the region of enhanced ﬁelds causes the ions to drift around the atmosphere. This prevents some ions from impacting the anti-Saturn side of the atmosphere and more ions populate Titan’s wake. Fig. 3(c) and (d) shows the effect of expanding the region of enhanced magnetic ﬁeld. Increasing the spatial scale of the gradient in the mag- D. Snowden et al. / Icarus 305 (2018) 186–197 netic ﬁeld strongly affects the trajectories of the 10,0 0 0 eV ions. About the same number of 100 eV and 10 0 0 eV particles hit the atmosphere in panels (a) and (c), but more 10,0 0 0 eV particles are deﬂected in panel (c). Panel (d) shows that enhancing the ﬁeld strength means that many more 10,0 0 0 eV particles are deﬂected around the atmosphere. The possible deﬂection of thermal magnetospheric oxygen ions due to the enhanced magnetic ﬁeld near Titan means that a threedimensional model that includes realistic electromagnetic ﬁelds and plasma ﬂow near Titan is needed to calculate the ﬂux of ions crossing Titan’s exobase. Here we used a three-dimensional multiﬂuid model of Titan’s interaction with Saturn’s magnetosphere to calculate magnetic and electric ﬁelds near Titan. Previously, the results of this model were shown to be in good agreement with observations from Cassini’s TA, TB, T3, and T55 ﬂybys (Snowden et al., 2007; Snowden and Winglee, 2013). The multiﬂuid model solves the generalized Ohm’s law, the induction equation, and the continuity, energy, and momentum equations for 4 ion ﬂuids (1 amu, 16 amu, 28 amu and 52 amu) and an electron ﬂuid, assuming isotropic temperatures and quasi-neutrality. Ionospheric ions are produced by photoionization, photoelectron ionization, and lost through dissociative recombination. Equations are solved on a 3D rectangular nested Cartesian grid with ﬁve boxes and the total simulation size is 44 × 35 × 35 RT . In this study, we used the electric and magnetic ﬁeld calculated by the multiﬂuid model to form a 10 × 10 × 10 RT data grid with a maximum resolution of 120 km near Titan. A more detailed description of this model can be found in Snowden and Winglee (2013). Many previous studies have shown that the plasma density, magnetic ﬁeld, and plasma velocity are highly variable near Titan (e.g. Rymer et al., 2009; Nemeth et al., 2011). The variability means that the properties of induced ﬁelds around Titan, and their affect on the precipitation of magnetospheric particles, is also highly variable. In this study, we are trying to reproduce the ion precipitation for T57; therefore, the upstream parameters of the model have been selected to be in agreement with the upstream parameters observed by Cassini. Fig. 5 shows the magnetic ﬁeld observed before and after the ﬂyby. The W+ velocity, temperature, and density observed by CAPS/IMS are shown in Fig. 2. We do not show H+ /H+ density and temperature but H+ /H+ CAPS/IMS mo2 2 ments exhibit similar variability with densities between ∼ 0.005 and 0.2 cm−3 and temperatures between ∼ 100 and 1,0 0 0 eV over the same time period. In the multiﬂuid simulations, the magnetospheric plasma was initialized upstream of Titan and was assumed to be composed of H+ (1 amu) and O+ (16 amu). Two simulations were run, the ﬁrst “nominal ﬂux” simulation represents average magnetospheric values measured near Titan. The second “high ﬂux” simulation represents the maximum density and velocity observed. The nominal ﬂux simulation had the following upstream parameters: H+ density of 0.05 cm−3 , O+ density of 0.05 cm−3 , upstream velocity of [90, 0, −30] km/s, upstream ion temperature of 500 eV, and upstream magnetic ﬁeld of [2, 4, −2] nT. The high ﬂux simulation had the following upstream parameters: H+ density of 0.09 cm−3 , O+ density of 0.09 cm−3 , upstream velocity of [150, 0, 0] km/s, upstream ion temperature of 500 eV, and upstream magnetic ﬁeld of [2, 4, −2] nT. Fig. 4 shows the total simulated magnetic and electric ﬁeld in the equatorial plane. In both simulations, the magnetic ﬁeld strength is enhanced in a region roughly 5–7 RT upstream of Titan. The maximum ﬁeld strength in the pile-up region is about 5 nT greater in the high ﬂux simulation due to the greater upstream density and ﬂow speed. The magnetic and electric ﬁeld in this simulation also have a bow wave upstream because magnetospheric plasma ﬂow is super-alfvénic, whereas the ﬂow in the nominal ﬂux simulation is sub-alfvénic. 189 We verify the results of the model by comparing the magnetic ﬁeld from our nominal simulation to that measured by Cassini and Fig. 5 shows a comparison between the simulated magnetic ﬁeld and the magnetic ﬁeld measured by Cassini’s magnetometer. This ﬁgure also shows the tilt of the ﬂow-induced magnetosphere due to the signiﬁcant y-component of the upstream magnetic ﬁeld, which is not apparent in Fig. 4. The magnetic ﬁeld simulated by the nominal simulation along the T57 trajectory is similar to the measured magnetic ﬁeld; however, the model does not accurately reproduce the data before closest approach. The magnetometer data indicates that the ambient magnetic ﬁeld was variable before this ﬂyby and it is likely that at least some of the disagreement between the simulation and the data is due to fossilized remnants from a different ambient magnetic ﬁeld. 3.2. Ion precipitation model We use a particle tracking model to study the precipitation of thermal (1–10,0 0 0 eV) O+ into Titan’s upper atmosphere. The model has two parts. First, the trajectory of 16 amu superparticles in Saturn’s magnetosphere are calculated by solving the Lorentz equation of motion, m ddtv = q(E + v × B ) using the Boris method with a ﬁxed time step of 0.1 s (Boris, 1970). The model interpolates the E and B ﬁelds from the three-dimensional multiﬂuid simulation to the position of the particle. Fig. 5 shows a few of the two million cycloidal trajectories simulated. Only a small fraction (4932 or 0.25%) of the initialized particles intercepted Titan’s atmosphere, and we show the trajectory of a few intercepting particles in red. Nearly all the particles that intercepted Titan’s atmosphere were initialized nearly directly upstream of Titan in a similar region as these particles. Around 1600 km altitude, the collision frequency between O+ and N2 becomes comparable to the gyrofrequency of an oxygen ion with energy less than 10 keV. If a superparticle reached this altitude, we assumed that it continued to move through Titan’s atmosphere along a straight path as shown in Fig. 6. This ﬁgure indicates that most particles hit Titan’s exobase at a grazing angle and traveled horizontally through the atmosphere relative to the surface. Fig. 7 shows that the incidence angles, measured from the 1600 km surface normal, follow a smooth distribution centered on 60°. Therefore, it is not appropriate to assume that magnetospheric ions penetrate the atmosphere with a normal angle relative to the exobase, as is often done in one-dimensional models. The range and energy deposition rates of the particles were calculated using the continuous loss approximation, i.e.: dE ∼ −2n(Sn + Se ), dx (1) where n is the neutral gas density and Sn and Se are the nuclear and electronic stopping loss cross sections for O+ interacting with N gas, respectively. The factor of 2 accounts for the fact we are modeling the interaction with N2 rather than N. The nuclear cross sections were calculated using the universal potential (Johnson, 1990) and the electronic stopping cross sections are from the mstar program (Paul and Schinner, 2001) and both are shown in Fig. 8. We only included collision with N2 because it is by far the most dominant molecule below the exobase and assumed a spherical shape for Titan’s atmosphere. We used the N2 density proﬁle from Strobel (2012), which is an average of the density measured by Cassini’s ion neutral mass spectrometer (INMS). Using an average N2 density proﬁle introduces some error; however, the INMS density from T57 does not accurately describe the neutral density all latitudes and longitudes. Snowden and Yelle (2014b) also used this method to estimate the energy deposition rates of magnetospheric ions in Titan’s ‘plasma sheet’ and ‘bi-modal/heavy-rich’ plasma environments. However, the model used here is different 190 D. Snowden et al. / Icarus 305 (2018) 186–197 Fig. 4. The total magnetic ﬁeld and electric ﬁeld calculated by the multiﬂuid simulation in Titan’s equatorial plane. The two left panels show results from the nominal ﬂux simulation and the two right panels show results from the high ﬂux simulation. from the model in Snowden and Yelle (2014b) because that model did not take into account how the ﬁeld structure near Titan affects the energy ﬂux, incidence angle, or the spatial distribution of precipitating O+ at the exobase. The continuous slowing down approximation is a macroscopic approach to simulating the effect of ion precipitation on the atmosphere. The nuclear and electronic stopping loss cross sections can be used to calculate the energy lost by an ion moving through a gas due to the collective effect of elastic collisions and various inelastic collisions, respectively. Continuous loss calculations are not as precise as a Direct Monte Carlo (DSCM) models (Michael and Johnson, 2005; Michael et al., 2005; Shah et al., 2009) or twostream/multi-stream ion transport models (e.g. Michael and Johnson, 2005; Shah et al., 2009; Luhmann and Kozyra, 1991). For example, DSCM simulations account for both the angular scattering of particles after collisions and the partitioning of energy between internal heat and kinetic energy. This can be particularly important near Titan’s exobase because a signiﬁcant amount of the energy deposited by precipitating ions with energies of several keV is lost due to sputtering (Michael and Johnson, 2005). The continuous loss approximation also assumes that precipitating particles follow a linear trajectory. Measurements of O+ collision cross sections at the energies we are considering (10’s to several keV) indicate that the collisions are forward scattering (Schafer et al., 1987). However, this method still overestimates the penetration depth of the particle to some degree. Despite these drawbacks, the continuous loss calculations are informative and comparisons between continuous loss calculations and Monte-Carlo calculations at other planets (e.g. Kallio and Barabash, 20 0 0) show that the two different methods result in only small differences in the energy deposition rates or ionization rates. We also report the global O+ ﬂux and the distribution of incidence angles at the exobase so these results could be used in more sophisticated models to precisely quantify energy deposition and sputtering rates. Fig. 9 shows the range or depth of penetration in Titan’s atmosphere versus the oxygen ion’s energy when it crosses the exobase. As expected, higher energy ions have a larger range and ions with larger incident angles have a shorter range. This ﬁgure also shows that nearly all the thermal O+ incident on Titan’s atmosphere are stopped above 1100 km altitude. This ﬁgure does not show that a D. Snowden et al. / Icarus 305 (2018) 186–197 191 Fig. 5. The total magnetic ﬁeld calculated by the nominal ﬂux multiﬂuid simulation. The trajectory of several of the simulated superparticles are also shown and the red trajectories show particles that hit Titan’s atmosphere. The straight red line indicates the T57 trajectory. The right panel shows the components of the magnetic ﬁeld calculated by the multiﬂuid simulation (green) compared with Cassini magnetometer data (blue). (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.) Fig. 6. The simulated trajectory of thermal O+ that cross Titan’s exobase. The shading of the lines corresponds to the incident energy of the particles, with darker shades of blue corresponding to higher energy particles. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.) Since we are focused on thermal magnetospheric O+ nearly all of the ions that hit the atmosphere had energies less than 5 keV. In this energy range both charge exchange and ionization reactions are relevant, with the latter becoming more important at larger energies and the former being dominant at low energies. We used average total ion production cross sections, which includes both dissociative and non-dissociative impact ionization and charge exchange, (σ ion ) and charge exchange cross sections (σ cx ) from Shah et al. (2009). At each altitude level, the fraction of the incident ion ﬂux that remained in the charged state was tracked using, Fion = σion (E ) − σcx (E ) σion (E ) (2) The ion fraction is used to reduce the ﬂux of ions entering the next atmospheric layer, (E, zi ) = (E, zi−1 )Fion , Fig. 7. A histogram showing the distribution of incident angles of thermal O+ crossing a surface at 1600 km altitude. The angle is measured from the surface normal. signiﬁcant number of ions that entered Titan’s atmosphere with high incidence angles exited the atmosphere before being stopped. (3) where i indicates the altitude level starting from the top of the atmosphere. This reduced ﬂux was used to calculate ionization rates in subsequent layers; however, the full ﬂux of oxygen particles (now assumed to be a mix of ions and energetic neutrals) was used to determine the energy deposition rates and the range of the oxygen atoms in Titan’s atmosphere. 192 D. Snowden et al. / Icarus 305 (2018) 186–197 Table 1 Magnetospheric parameters used to weight the simulated O+ superparticles and the resulting energy and number ﬂuxes through a surface at 1600 km. Simulation High ﬂux Nominal ﬂux Magnetospheric O+ density (cm−3 ) Magnetospheric O+ bulk velocity (km s−1 ) Magnetospheric O+ temperature (eV) Magnetospheric O+ energy ﬂux (GeV cm−2 s−1 ) Total number ﬂux (s−1 ) Average number ﬂux (cm−2 s−1 ) Max number ﬂux (cm−2 s−1 ) Total power (MW) Average energy ﬂux (MeV cm−2 s−1 ) Max energy ﬂux (MeV cm−2 s−1 ) 0.09 150 200 145 1.4 × 1024 4.7 × 105 4.8 × 106 516 1010 1300 0.05 110 200 24 2.7 × 1023 9.0 × 104 8.7 × 105 76 160 1800 3.3. Initialization and weighting of particles in the ion precipitation simulation We injected two million superparticles into the simulation at random locations along a half-sphere 8 RT upstream of Titan. The particles were started with a drifting Maxwellian distribution on a discrete energy grid from 10 to 10,0 0 0 eV with smoothly varying logarithmic spacing. The number of particles in a given energy bin is given by the integral N ( E ) = 4π v1 v2 f ( v )v2 d v, where f (v ) = Fig. 8. (top) The nuclear (Sn ) and electronic (Se ) stopping loss cross sections for O+ interacting with N. (bottom) Total ion production and charge exchange cross sections due to O+ impacting N2 . The total cross sections are a sum of several dissociative and non-dissociative reactions, see Shah et al. (2009) for details. 1450 exp − ( v − vb )2 . v2 (5) J , N (E )/A (6) where N(E) is the number of particles initialized in each energy bin and A is the area of the surface that we initialized the particles on, in this case a half-sphere with a radius of 8 RT . The value of w(E) varies with energy but was on the order of 1023 particles/s. 80 1400 ( π v ) 2 3/2 The bulk velocity of each particle was initialed with the same magnitude and direction as the oxygen ﬂuid at that location in the multiﬂuid simulation, and we assigned a random thermal velocity according to the particles temperature. By assigning a random thermal velocity we are also assumed a uniform pitch angle distribution. For atmospheric calculations, we weighted the superparticles by comparing the initialized energy spectrum to a differential particle 2 ﬂux distribution, J = vm f, computed with CAPS/IMS moments derived before the T57 ﬂyby. The particle ﬂux distribution was discretized on the same energy grid used to inject the particles. The weight for each superparticle, with units of particles/seconds, was determined by w (E ) = 1500 n (4) 70 1350 50 1250 40 1200 30 1150 1100 20 1050 10 1000 0 1000 2000 3000 4000 5000 Incident Energy (eV) Fig. 9. The range of thermal O+ in Titan’s atmosphere. Incident Angle (deg) Altitude (km) 60 1300 4. Results As shown in Fig. 2, ion moments calculated from the CAPS data before T57 were variable. Therefore, we report results from a high ﬂux case and a nominal ﬂux case to show the range of how oxygen ion precipitation might affect Titan’s atmosphere. Table 1 summarizes the parameters used to weight the superparticles and the resulting ﬂuxes at 1600 km altitude. In the high ﬂux simulation, we weighted the particles using a differential energy spectrum similar to what CAPS observed at 16:50 UT (Fig. 2). The O+ energy distribution was assumed to be a Maxwellian with a density of 0.09 cm−3 , a temperature of 200 eV, and a velocity of 150 km/s, giving a total magnetospheric energy ﬂux of 1.5 × 1011 eV cm−2 s−1 . Titan would be exposed to an energy ﬂux this high in a bi-modal environment or when there is D. Snowden et al. / Icarus 305 (2018) 186–197 Fig. 10. The number of superparticles hitting Titan’s exobase versus the energy of the ion when it is injected into the simulation. an unusually high density of O+ and an exceptionally large ﬂow velocity. In the nominal simulation, the O+ energy distribution was assumed to be Maxwellian with a density of 0.05 cm−3 , a temperature of 200 eV, and a velocity of 110 km/s giving a total magnetospheric energy ﬂux of 2.4 × 1010 eV cm−2 s−1 . This energy ﬂux is closer to the average value observed upstream during T57 or similar to what was seen by CAPS at 15:45 UT (Fig. 2). It representative of Titan being in Saturn’s plasma sheet with a relatively high density of O+ ions (Nemeth et al., 2011), but not as high as in the high ﬂux simulation. Ledvina et al. (2005) showed that strong gradients in the magnetic ﬁeld near Titan shield low energy O+ ions from entering Titan’s atmosphere similar to what was shown in Fig. 3; however, our results indicate this is not always the case. Fig. 10 shows the number of ions that hit Titan’s exobase versus the energy each ion was injected into the simulation with. Qualitatively, this distribution is very similar to the energy distribution initialized 8 RT upstream. Most of the ions that hit Titan’s atmosphere had energies near 1 keV. Few ions with high energies ( > 5 eV) hit Titan’s atmosphere, simply because very few of these high energy ions were injected into the simulation.Therefore, unlike the simulation of Ledvina et al. (2005), we do not see a signiﬁcant shielding of ions below energies of 2 keV. The lack of shielding is probably due to differences in upstream parameters used in the threedimensional multiﬂuid simulation that calculated the electric and magnetic ﬁelds. Compared to earlier work that used upstream parameters that were similar to those observed by Voyager 1, the plasma environment during T57 results in a smaller increase in the magnetic ﬁeld strength in the draping region resulting in less effective shielding. Therefore, it is not always appropriate to assume that lower energy oxygen ions, with energies less than about 2 keV, will be deﬂected away from Titan before precipitating into the atmosphere as was done in Snowden and Yelle (2014b). However, in agreement with earlier work (Ledvina et al., 2005; Sillanpää et al., 2007; Regoli et al., 2016), we ﬁnd that the energy ﬂux incident is not spatially uniform. This can be seen in Fig. 11, which shows the inward energy ﬂux and the inward particle ﬂux at 1600 km altitude. Most of the O+ ions hit the ram side of Titan’s atmosphere (between 135° and 225°) with a slight shift toward the Saturn-facing side (between 225° and 315°). The ﬂuxes are qualitatively similar in both the nominal and high ﬂux simulation. This indicates that the direction of the magnetic ﬁeld, which was the same in both simulations, strongly determines where ions cross Titan’s exobase. Table 1 lists the total power; average and max en- 193 ergy ﬂux; and the total, average, and max particle ﬂux across the 1600 km surface calculated by each simulation. The model continued to track the particles as they moved through Titan’s atmosphere and to determine ionization, energy deposition, and charge exchange rates. Fig. 12 shows the globally average altitude proﬁles and the altitude proﬁles for the ram (longitudes between 135° and 225° with the sub-ram point at 180°), anti-Saturn (between 45° and 135°), wake (between 315° and 360° and 0° and 45°), and Saturn-facing (between 225° and 315°) sides of Titan’s atmosphere. The proﬁles have the form of a Chapman production function, although they are not as smooth as what would be theoretically predicted due to poor statistics in some regions. The proﬁles are especially discontinuous on the wake side, where few particles entered the atmosphere. Running the simulation with fewer or more particles changes how smooth the curves appear, but does not signiﬁcantly change the values. It is worth noting that injecting particles downstream of Titan does not increase the energy deposition and ion production rates on the wake side because the ions drift downstream before they impact Titan’s atmosphere. As expected, energy deposition rates and ion production rates are highest in the ram quadrant of Titan’s atmosphere. They are also signiﬁcantly greater in the high ﬂux simulation compared to the nominal simulation. Ion production is dominated by charge exchange for O+ atoms with energies less than 5 keV; therefore, the ion production curves shown are almost entirely due to charge exchange reactions. In either simulation, the peak rates occur near 1150 km altitude. Table 2 show the results of ﬁtting the Chapman production function to globally averaged and ram side proﬁles and an example of one ﬁt is shown in Fig. 13. Fig. 14 shows the ionization rate calculated at 1150 km for the high ﬂux simulation. For the upstream parameters assumed here, we ﬁnd that the ionization rates peak in a limited region centered at about 0° latitude and 200° longitude. The area of peak ionization shifts depending on the magnetospheric ﬂow direction and the upstream magnetic ﬁeld. In this case, the counterclockwise tilt of the region of high ionization is due to the y-component of the upstream magnetic ﬁeld (By > 0) used in the three-dimensional multiﬂuid simulation. The cycloidal drift motion of the ions is parallel to the convective electric ﬁeld and a signiﬁcant By tilts the convective electric ﬁeld out of the equatorial plane, which affects which ions impact Titan’s exobase. As Fig. 9 shows, most of the particles that reach 1150 km altitude had a small incident angle; therefore, the region of maximum ionization looks similar to the area of maximum particle ﬂux at the 1600 km altitude surface. At higher altitudes, the ionization rates are smaller but more spread out due to the horizontal motion of the particles. 5. Discussion 5.1. Comparison to T57 The peak electron density measured on the nightside of Titan’s ionosphere during the inbound portion of T57 was abnormally high at about 1380 cm−3 near 1100 km (Snowden and Yelle, 2014b; Richard et al., 2015). A similar enhancement in the solar limb electron density above 10 0 0 km altitude was observed in the RSS data (Kliore et al., 2011). Richard et al. (2015) and Sagnières et al. (2015) used a chemical model based on CH+ densi3 ties to derive ion production rates for N+ directly from INMS taken 2 during T57. Their results imply that the ion production rates along the inbound portion of Cassini’s trajectory were close to 1 cm−3 s−1 near the peak of the ionosphere. Fig. 1 shows the orientation of T57 relative to the dayside of Titan’s ionosphere. Cassini traveled through the peak of the ionosphere around −30◦ latitude and 170° longitude at altitudes 194 D. Snowden et al. / Icarus 305 (2018) 186–197 Fig. 11. The inward energy ﬂux (left panels) and number ﬂux (right panels) of O+ ions hitting a surface at 1600 km altitude for the high and nominal ﬂux simulations. The sub-ram point is at 180° and the Saturn-facing point is at 270°. The subsolar point is at 300°. Table 2 Chapman production function ﬁt to average and ram-facing altitude proﬁles shown in Fig. 12. High ﬂux simulation Fit of Qe 1− z−z0 H −e − z−z0 H Nominal ﬂux simulation to Global average energy deposition Ram energy deposition Global average ion production rate Ram ion production rate Q z0 H Q z0 H 75 212 0.83 2.3 1170 1157 1188 1177 72 65 78 74 10 23 0.10 0.21 1196 1178 1210 1193 74 67 80 74 near 1100 km, which is near where we calculated high ionization rates from precipitating O+ . In the high ﬂux simulation, we ﬁnd that the ion production rates, including ionization and charge exchange, can be as high as 2 cm−3 s−1 . Ionization rates at 1150 km in the nominal simulation look qualitatively similar to Fig. 14 but the rates are lower, with a maximum total ion production rate around 0.4 cm−3 s−1 . Therefore, O+ impact ionization rates could be similar to those calcuated by Richard et al. (2015) and Sagnières et al. (2015) (∼1 cm−3 s−1 ) at mid-latitudes on the ram side of Titan’s atmosphere for upstream energy ﬂuxes between our nominal and high ﬂux simulation. RSS observed high electron densities around 76° latitude and 280° longitude, which is close to but does not overlap the area where we calculate high ionization rates. However, it is possible that the region of high ionization rates shifted due to changes in the upstream ﬂow direction or magnetic ﬁeld direction. As we discuss in the next section, the enhanced ionospheric densities may also be caused by magnetospheric electron precipitation suggested by Kliore et al. (2011) and Richard et al. (2015). 5.2. Comparison to previous work The results of this model can be compared to previous calculations of ionization and energy deposition from thermal O+ precipitation in Titan’s upper atmosphere. Sillanpää et al. (2007) used a hybrid model to calculate the energy and number ﬂux of O+ ions across Titan’s exobase. For Voyager 1 conditions, they calculated a global power input of 310 MW measured at an altitude of 1625 km and an average energy ﬂux of 2 GeV cm−2 s−1 . This model has been updated to include ion-neutral interactions near Titan’s exobase and more recently Sillanpaa and Johnson (2015) calculated the energy and particle ﬂux for upstream parameters observed during Cassini’s T15 ﬂyby. They found that including ion-neutral interactions below 20 0 0 km had a signiﬁcant effect on the energy and particle ﬂux measured at 1400 km altitude. In the simulation that included slowing of particles approximated by stopping power cross sections and the possible removal of particles through inelastic collisions, they calculated a global energy input of 61 MW and a particle ﬂux of 1.95 × 1023 ions s−1 at an altitude of 1400 km. In the high ﬂux simulation, we calculate a total power of 516 MW and an average energy ﬂux of 1010 MeV cm−2 s−1 incident on a surface at 1600 km altitude. For the nominal case, the total power was signiﬁcantly smaller at 76 MW with a global energy ﬂux of 160 MeV cm−2 s−1 . The particle ﬂux for the high and nominal simulations were 1.4 × 1024 ions s−1 and 2.7 × 1023 ions s−1 , respectively. Therefore, for our high ﬂux case, we ﬁnd that the energy incident on Titan’s atmosphere is higher than that calculated in previous work. This simulation used an abnormally high magnetospheric energy ﬂux distribution near Titan. As Fig. 2 shows, Titan was exposed to this high energy ﬂux for less than 10 minutes at a time. The nominal ﬂux simulation uses an upstream ﬂux that is more typical of Titan’s environment in Saturn’s plasma sheet. The energy and particle ﬂux calculated by this simulation are in good agreement with the most recent result of Sillanpaa and Johnson (2015), especially since we report the total power at an alti- D. Snowden et al. / Icarus 305 (2018) 186–197 195 Globally Averaged Energy Depostion Rate (cm -3 -1 s ) Fig. 12. The energy deposition and total ion production rates averaged over the globe or over the Saturn-facing, ram, anti-Saturn-facing, or wake side of Titan’s atmosphere. Left panels show results from the high ﬂux simulation and right panels show the results from the nominal ﬂux simulation. 70 60 50 40 30 Fig. 14. The ionization rate calculated in the high ﬂux simulation at 1150 km altitude. 20 10 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550 Altitude (km) Fig. 13. The globally average energy deposition proﬁle for the high ﬂux case ﬁt with the Chapman production function. The results for this ﬁt and others can be found in Table 2. tude of 1600 km rather than 1400 km, where ion-neutral collisions signiﬁcantly slow the plasma. The total power and energy ﬂux resulting from thermal magnetospheric O+ precipitation can also be compared to other relevant energy sources in Titan’s upper atmosphere. The total power from solar EUV during the 20 07–20 09 time period was about 1 GW (Woods, 2005), which is greater than what we calculate 196 D. Snowden et al. / Icarus 305 (2018) 186–197 for thermal O+ even in our high ﬂux simulation. The energy ﬂux from thermal O+ is similar to other magnetospheric particles. Shah et al. (2009) found that large ﬂuxes of high energy O+ (∼200k) resulted in energy ﬂuxes at Titan’s exobase around 6 GeV cm−2 s−1 . Brandt et al. (2012) found that precipitating energetic neutral atoms, with energies between 24 and 55 keV, resulted in energy ﬂuxes at Titan’s exobase around 5 GeV cm−2 s−1 . In Snowden and Yelle (2014a), the global energy input from magnetospheric electrons was found to be between about 13 and 150 MW. Locally, we calculate maximum energy deposition rates in Titan’s atmosphere as high as 200 eV cm−3 s−1 for our high ﬂux simulation and 10 eV cm−3 s−1 for our nominal ﬂux simulation. These energy deposition rates correspond to total ion production rates around 2 cm−3 s−1 and 0.4 cm−3 s−1 , respectively. Energy deposition rates were highest around 1150 km, which is near the solar EUV peak. The local energy deposition rates reported here are within the range of those calculated by Shah et al. (2009) for higher energy O+ ( > 10 keV) ions. However, O+ with energies greater than 10 keV deposit most of their energy below 10 0 0 km, where they would have less of an impact on Titan’s atmosphere due to the higher neutral density. Similarly, the ionization rates calculated in our high ﬂux case are close to the ionization rates that Regoli et al. (2016) calculated for O+ precipitation with energies greater than 10 keV. However, again they found that the peak ionization rate of about 4 cm−3 s−1 occurred at altitudes below 10 0 0 km. The temperature of Titan’s upper atmosphere is highly variable (Westlake et al., 2011; Snowden and Yelle, 2014b) and it is possible that some of the variability is due to heating from magnetospheric particle precipitation. Results of various thermal models (e.g. Westlake et al., 2011; Bell et al., 2011; Snowden and Yelle, 2014b) suggest that heating rates on the order of 20 to 40 eV cm−3 s−1 result in 10 to 20 K increases in the temperature of Titan’s atmosphere. If we assume a 50% heating eﬃciency, the results here imply that heating rates due to thermal O+ precipitation over limited areas of Titan’s atmosphere vary between about 5 and 100 eV cm−3 s−1 when Titan is in Saturn’s plasma sheet, with the more common value being closer to 5 eV cm−3 s−1 . Heating rates near 100 eV cm−3 s−1 imply that O+ precipitation may have a signiﬁcant effect on the temperature in regions experiencing O+ precipitation. However, the thermal inertia of Titan’s atmosphere means that Titan must be exposed to the O+ precipitation for at least several Earth days and Cassini data indicates that Titan is only periodically exposed to Saturn’s plasma sheet for tens of minutes to hours. Relatively short periods of enhanced ion precipitation can have a signiﬁcant effect on the density of Titan’s ionosphere. In fact, Edberg et al. (2015) found that, on average, the density of Titan’s ionosphere was enhanced by a factor of 1.4 when Titan was observed in Saturn’s plasma sheet where it would be exposed to thermal magnetospheric particle precipitation. For example, T5 is another ﬂyby that occurred when Titan was in Saturn’s plasma sheet and ionization rates from magnetospheric particle precipitation rates were large. This ﬂyby occurred on the night side of Titan’s ionosphere, near 135° solar zenith angle and the electron density observed in Titan’s ionosphere was around 10 0 0 cm−3 . Similar to T57, Cravens et al. (2009) showed that you could explain the nightside ionospheric density with ionization rates between 1 and 2 cm−3 s−1 in agreement with the more recent work of Richard et al. (2015) and Sagnières et al. (2015) who used chemical models to determine ionization rates from CH+ measured by 3 Cassin’s Ion Neutral Mass Spectrometer. Magnetospheric electrons are usually assumed to be the dominant ionization source in Titan’s night side. For example, both Kliore et al. (2011) and Richard et al. (2015) invoked magnetospheric electron ionization to explain the enhanced densities ob- served during T57. However, there is a lot of uncertainty in simulations of magnetospheric electron ionization rates in Titan’s atmosphere due to assumption about the magnetic ﬁeld line conﬁguration. In addition, Snowden et al. (2013) has shown that the inward ﬂux of electrons should be reduced overtime because Titan’s atmosphere depletes the electrons in Saturn’s ﬂux tubes. Sagnières et al. (2015) avoids these complications by calculating the electron ionization rates from the electron spectrum measured by CAPS at the same altitude. They calculated ionization rates due to magnetospheric electrons and compared them to the ionization rates derived from a chemical model for T5, T50, T57, and T59 and found that the electron impact ionization rates are 2 to 3 times too small to explain the observed electron density. The results of our model suggest that some of the discrepancy could be explained by including thermal O+ precipitation. Determining which magnetospheric particle is responsible for enhanced densities in Titan’s ionosphere is challenging because both electron and ion impact ionization is non-uniform and depends on the conﬁguration of Titan’s induced magnetosphere. In general, the results of this global ion precipitation model and the global electron precipitation model in Snowden and Yelle (2014a) suggest that ion impact ionization and energy deposition is largest on Titan’s ram-side, while magnetospheric electron impacts dominate the wake-side or in regions closer to the ‘poles’ of Titan’s induced magnetosphere. 6. Conclusion We present results of three-dimensional simulations of thermal magnetospheric O+ precipitation into Titan’s upper atmosphere. The three-dimensional model builds on previous work because it calculates both the ﬂux of oxygen through Titan’s exobase and the energy deposition and ionization in Titan’s atmosphere. Here we have simulated upstream conditions similar to those observed during Cassini’s T57 ﬂyby. We ﬁnd that thermal O+ precipitation results in ionization and energy deposition rates that are quantitatively similar to thermal magnetospheric electrons when Titan is in Saturn’s plasma sheet. The highest ionization and energy deposition rates occur on the ram side of Titan’s atmosphere but will shift depending on the upstream ﬂow direction and magnetic ﬁeld direction. Overall, the total power deposited by magnetospheric O+ is lower than that contributed by solar EUV even during T57, which occurred when Titan was in a relatively dense part of Saturn’s plasma sheet. Therefore, we expect the precipitation of thermal O+ to have a smaller impact on the energetics of Titan’s neutral atmosphere. We compare simulation results to ionization rates derived from the electron density observed by Cassini. We ﬁnd that the simulated ionization rates are suﬃcient to explain the abnormally high electron densities observed by RSS and Cassini’s Langmuir Probe during T57. 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