Evaluating the Ionospheric Mass Source for Jupiter's Magnetosphere: An Ionospheric Outflow Model for the Auroral Regions

Ionospheric outflow is the flow of plasma initiated by a loss of equilibrium along a magnetic field line, which induces an ambipolar electric field due to the separation of electrons and ions in a gravitational field and other mass‐dependent sources. We have developed an ionospheric outflow model using the transport equations to determine the number of particles that flow into the outer magnetosphere of Jupiter. The model ranges from 1,400 km in altitude above the 1 bar level to 2.5 RJ along the magnetic field line and considers H+ and H3+ as the main ion constituents. Previously, only pressure gradients and gravitational forces were considered in modeling polar wind. However, at Jupiter we need to evaluate the effect of field‐aligned currents present in the auroral regions due to the breakdown of corotation in the magnetosphere, along with the centrifugal force exerted on the particles due to the fast planetary rotation rate. The total number flux from both hemispheres is found to be 1.3–1.8 × 1028 s−1 comparable in total number flux to the Io plasma source. The mass flux is lower due to the difference in ion species. This influx of protons from the ionosphere into the inner and middle magnetosphere needs to be included in future assessments of global flux tube dynamics and composition of the magnetosphere system.


Introduction
reported ionospheric species at high latitudes magnetically conjugate with Jupiter's inner and middle magnetosphere using the Juno spacecraft's Jovian Auroral Distributions Experiment (JADE). In this paper, we illustrate computations of the field-aligned outflow of material from the Jovian ionosphere and the ionosphere as a source of magnetospheric plasma.
The idea of ionospheric outflow as an important element of magnetospheric physics was first theorized in the terrestrial magnetosphere as a supersonic flow of charged particles from the ionosphere in the high-latitude regions of a planet (Axford, 1968;Dungey, 1961) in analogy with the solar wind supersonic flow of charged particles from the Sun. The terrestrial polar wind, comprised of H + and O + , was first detected by Hoffman (1970).
Ionospheric outflow requires an imbalance of equilibrium to trigger plasma motion along the magnetic field line with low pressure at large distance. In the terrestrial case, the opening of a flux tube by reconnection at the magnetopause initiates the process and the outflow occurs on open flux tubes in the terrestrial polar cap. The first suggestion of Jovian ionospheric outflow being an important aspect of the Jovian system appears in Piddington (1969) (referenced by Kennel & Coroniti, 1975). The primary force leading to outflow was the centrifugal effect of the rapid planetary rotation on open field lines in the polar cap. However, these early predictions predate the Voyager Jupiter encounters. There is now known to be a major internal magnetospheric near-equatorial source of plasma at Io due to the moon's volcanism (e.g., Hill, 1979b;Pontius & Hill, 1982). Io releases 1,000 kg s −1 of SO 2 , which forms a neutral torus around Jupiter at the radial distance of Io's orbit (5.9 R S ) (Delamere & Bagenal, 2003;Delamere et al., 2005). The neutral material is ionized, predominantly by electron impact and charge exchange, picked up and accelerated to near corotation, the angular rotation velocity of the planet (Pontius & Hill, 1982;Pontius, 1995). For a thorough review of these processes, see Thomas et al. (2004).
Estimates of the total ion particle flux emanating from near Io are in the range (0.5-1.7) × 10 28 s −1 (Bagenal, 1997) or 3 × 10 28 s −1 (Saur et al., 2003). Using a model of the plasma disc, Bagenal and Delamere (2011) estimate the total ion mass flux from Io to be 260-1,400 kg s −1 . The ionized iogenic material, remaining in a plasma disc near the magnetic equator, moves outward from the inner magnetosphere in a diffusive process. The diffusion is through a flux tube interchange motion where loaded flux tubes move away from the planet while depleted tubes (which have lost material at large distance) move back in. Beyond a radial distance of 17 R J , the outward moving plasma begins to subcorotate, resulting in the magnetic field (Bagenal et al., 2016;McNutt et al., 1979) being bent back and the generation of field-aligned currents. Radial currents associated with the bent back field act to maintain plasma rotation (Hill, 1979a). Field-aligned currents associated with the bent back field couple the magnetosphere to the ionosphere with current closure occurring through Pedersen currents at the ionosphere. The rotation enforcement currents generate Jupiter's quasi steady state main auroral emission (e.g., Ray et al., 2015).
The overall flux circulation providing the iogenic material diffusive transport and loss is called the Vasyliunas cycle (see, e.g., Vasyliunas, 1983). In the cycle, reconnection takes place and plasma is lost through this process. The iogenic material is frozen to the magnetic field as it moves outward, but somewhere the frozen-in condition must be violated as magnetic flux has to be conserved overall, but steady particle transport requires loss at large distance. The plasma loss is achieved through flux tubes undergoing magnetic reconnection in the magnetotail.
Next consider what happens to the plasma in the ionosphere in the Vasyliunas cycle. Consider a tube where the cold plasma population in ionosphere and magnetosphere are initially in equilibrium. Outward flux tube motion driven by the iogenic material near the equator will also carry ionospheric material on the flux tube to higher invariant latitude. At the same time, the volume of the tube will increase and the cold plasma pressure at high altitude on the flux tube will decrease. One can thus expect ionospheric material to move upward to maintain equilibrium, initiating outflow. We see this as an explanation of the new Juno observations (Valek et al., 2019), which are on field lines between Io's orbit and the main auroral zone (and not on open flux as one might expect for a polar wind analogous with Earth).
A critical question is how far ionospheric plasma moves along the field during the flux tube outward motion. If the ionospheric material travels far enough along the field to participate in the reconnection, not only will some escape but the residual plasma in the equatorial region on the depleted closed tube will be a mixture of heavy iogenic material and light ionospheric plasma. The tube will move inward and shrink in volume with the iogenic material and ionospheric material gaining energy. If the ionospheric material in the outflow induced on the outward leg of the cycle does not reach the equatorial region where reconnection takes place, ionospheric material will not be lost but also the mixing will not occur.
The purpose of this paper is to use a simple one-dimensional model to examine outflow using appropriate ionospheric source conditions with varying background conditions in order to assess the nature of ionospheric flow possible on closed field lines. It is assumed that the overall magnetospheric background context in the equatorial regions is a Vasyliunas circulation system driven by diffusion of heavy material ionized in the Io torus region, as described above.
As noted earlier, at Earth the dominant plasma outflow process is in the Dungey cycle on open flux tubes. Any such process at Jupiter it is likely to be much less important to redistributing ionospheric plasma. Cowley et al. (2003) describe it at Jupiter mapping to a thin slice along the dayside and dawn flank of the magnetosphere. Indeed, some authors suggest that the Dungey cycle does not operate at all at Jupiter (Delamere et al., 2005;McComas et al., 2014). As our motivation is to investigate mechanisms for ionospheric outflow on closed flux tubes, our context needs be the Vasyliunas cycle.
Any ionospheric outflow introduces an electric field along the background magnetic field. It is an ambipolar electric field and a direct consequence of the different masses of electrons and ions in the ionosphere. However, the Vasyliunas cycle circulation induced by the Io material sets up a global field-aligned current system (Vasyliunas, 1983) and these currents will also introduce field-aligned electric fields (Ray et al., 2010), modifying any outflow conditions. Moreover, this current system may also introduce heat through Joule heating by the associated currents in the ionosphere (e.g., Smith & Aylward, 2009); this effect could also impact the conditions for ionospheric outflow.
In contrast, the importance of ionospheric outflow as a source of plasma at Jupiter is less well understood. At both of the gas giants, an ionospheric outflow is expected to be dominated by the main ionospheric constituents, H + and H þ 3 . Bodisch et al. (2017) discuss the relative abundance of lighter ions in Jupiter's magnetosphere during the Voyager 1 and 2 flybys. They show that protons account for up to 20% of the plasma between 5 and 30 R J and are consistent with an ionospheric source due to a high H + /He 2+ ratio (Mall et al., 1993). Further evidence comes from H þ 3 ions were also found during the Ulysses flyby (Lanzerotti et al., 1993). These results are consistent with an ionospheric particle production rate of 2 × 10 28 s −1 (Nagy et al., 1986).
Recently, Valek et al. (2019) observed that ionospheric species at high latitudes magnetically conjugate with Jupiter's inner and middle magnetosphere using the Juno spacecraft's JADE. The ionospheric species were found on flux tubes mainly at latitudes below the main auroral emission but poleward of the Io footprint location, a range approximately 10°in latitude wide (Grodent et al., 2003). No such signatures of ionospheric plasma were found at polar latitudes.
These initial observations of ionospheric outflow at Jupiter and Saturn are enticing, as the changes to the magnetospheric plasma composition and energy have consequences for magnetospheric dynamics. A better understanding of the drivers of ionospheric outflow at the giant planets requires modeling similar to the extensive efforts applied at the terrestrial system (see review by Lemaire et al., 2007). Based on Juno observations (Valek et al., 2019), ionospheric outflow may contribute to the composition of magnetospheric plasma near the auroral zone boundary, that is, in the middle magnetosphere.
The goal of this study is to describe ionospheric outflow at Jupiter, including the effects of centrifugal forces due to the rapid planetary rotation rate and field-aligned auroral currents from the coupling of the magnetosphere and the ionosphere. Section 2 describes the model, which uses a hydrodynamic approach. Section 3 evaluates ionospheric outflow at Jupiter over a range of initial conditions appropriate to the system. The implications of the ionospheric contribution to Jupiter's magnetosphere are discussed in section 4 with a summary of our analysis presented in section 5.

Model
The outflow model described here is a hydrodynamic, multifluid, 1-D model. The spatial dimension is along the magnetic field, which has a cross-sectional area, A, that increases as the reciprocal of the field strength. The model introduces contributions from gravitational forces, centrifugal forces, pressure gradients, and forces associated with the ambipolar electric field. As we are expanding the model to a number of planetary radii, the JRM09 magnetic field model (Connerney et al., 2018) is implemented to estimate the flux tube cross section.
The two major ion species, H + and H þ 3 , are evaluated through the use of the five-moment gyrotropic transport equations (Banks & Kockarts, 1973), which are based on the continuity of mass (Equation 1), momentum (Equation 2), and energy (Equation 3) in a system. The equations also include the centrifugal acceleration term (ω 2 r), where ω is the angular velocity due to corotation and r is cylindrical distance from the rotational axis resolved along the field line. Only rigid corotation is evaluated. 10.1029/2019JA027727

Journal of Geophysical Research: Space Physics
A subscript of "i" denotes that this is done for each ionic species separately, ρ is mass density, u is velocity, S is the mass production rate, P is pressure, e is electron charge, m is the mass of the ion species, g is the gravitational acceleration, κ is the thermal conductivity, T is temperature, and γ is the specific heat ratio. DM i Dt is the rate of momentum exchange, and DE i Dt is the rate of energy exchange.
We assume κ i ¼ 4:6 × 10 6 mi mp −0:5 T 5=2 e J m −1 s −1 K −1 and κ e = 1.8 × 10 8 T 5/2 e J m −1 s −1 K −1 (Banks & Kockarts, 1973), where m p is the proton mass. ∂ ∂r Aκ i ∂T i ∂r is considered negligible in this formulation. This is determined by magnitude analysis at the first iterations (<0.5% magnitude compared to the largest terms in Equation 3). The full term is removed to improve computational efficiency.
The magnetic-field-aligned components of the gravitational and centrifugal acceleration terms are evaluated along the field line. The parallel electric field, E ‖ , produced by the net charge separation is given by A subscript of "e" denotes the quantity for an electron, and n is the number density. The remaining unknowns are DM i Dt (rate of momentum exchange) and DE i Dt (rate of energy exchange), which are given by A subscript of "y" denotes the different neutral species, ν iy is the collision frequency between the ionic species and neutral species, and k b is the Boltzmann constant. We assume the neutral atmosphere is at rest (u- We use charge neutrality for singly ionized species 7 and a steady state electron velocity assumption 8 to solve for the density and velocity of the electrons. To solve for the energy of the electrons, we use an energy equation 9. Variable j is current density of field-aligned currents, which is scaled using the flux tube cross section j = j 0 A 0 /A, where j 0 is the current density at a reference altitude A 0 . The current density profile as a function of latitude (Ray et al., 2015) is applied at a height of 1,000 km, coincident with the peak in ionospheric electron density.
The temporal resolution is 0.01 s. The field line is split into 75 km wide spatial grid points, which relates to 2,400 grid points for a field line of length 2.5 R J over which the spatial derivatives are estimated using central difference Euler for first-order derivatives. This method is used as the terms are not stiff when using a time step of 0.01 s or less. We note that the results are robust for smaller spatial grid sizes (down to 20 km), and as such, we use 75 km for efficiency in computing.
Initial distributions are specified along the entire spatial domain and are derived from either the initial temperature distribution or the initial density distribution using the following formulations. Velocity is found from equating the thermal energy to the kinetic energy, Mass production is estimated as a 1% fraction of the mass density, and the results are robust against a 2 orders of magnitude change in this value. Pressure is calculated from the plasma pressure equation, P i = n i k b T i .
The neutral species evaluated within the model are H 2 , He, and H. Each species is used to calculate the mass and energy exchange rates, which require a collision frequency that is calculated using where λ y is the neutral gas polarizability, which are 0.82 × 10 −30 , 0.21 × 10 −30 , and 0.67 × 10 −30 m 3 for H 2 , He, and H, respectively (Schunk & Nagy, 2000). Initial values of density of the ionic and neutral species are extrapolated with an exponential decay, with appropriate scale height, from 1,400 km in "JIM"-the Jovian Ionospheric Model (Achilleos et al., 1998). An initial distribution of temperature is also retrieved from the JIM, which increases as an exponential to 0.5 R J and then is estimated by a logarithmic decay to a base value. Evaluation and robustness of these values is discussed later. All initial value are shown in Figure 1, along with the flux tube cross-sectional area, A. The model is run until quasi steady state is reached, or until the difference between two iterations is negligible (difference between outputs of two iterations is <0.1% for 1 s in simulation time, or 100 time steps). Number flux along a single flux rope is calculated as n e u e multiplied by the cross-sectional area A. This can also be calculated for each ionic species.

Results
Figure 2 displays the quasi steady state parallel electric field, the acceleration terms (gravitational, centrifugal, and electric field), and electron and ion fluxes, corresponding to initial values described as "Run 1" in Table 1. The electric field (Figure 2a) peaks around 10,000 km along the field line, which is the position at which the separation of the electrons and ions is largest due to the corresponding densities and temperatures. The electric field then reduces to a steady value. This pattern is followed by the acceleration due to the electric field in both the H + and H þ 3 ions (dark blue and light blue solid curves in Figure 2b). Additionally, we see the gravitational acceleration decreases with radial distance along the field line, while the centrifugal force increases (dashed teal and dashed purple in Figure 2b). At around 2 R J the centrifugal acceleration becomes dominant over the gravitational acceleration. A density depletion is expected to occur in this region.
The total particle source from the auroral oval can be estimated by multiplying the number flux of particles with the area of a 2°wide oval at 75-77°latitude around the planet, and then multiplying by 2 to give a value for both hemispheres. This is done at an altitude of 25,000 km, where the number flux becomes approximately constant. The initial conditions described for Figure 2, and the total particle and mass sources (calculated by taking the relative proportions of electrons, H + and H þ 3 ), are shown by "Run 1" in Table 1. A field-aligned current function (Ray et al., 2015) is used where the largest magnitude current used is 3 × 10 −6 A m −2 scaled from the bottom of the ionosphere.
However, we note that the density and temperature in the ionosphere may vary significantly, and the upward field-aligned currents alone may range from 1-7 μA m −2 (Ray et al., 2009). As such, we vary the field-aligned currents, temperature, and number densities of n H þ and n H þ 3 to present a range of total 10.1029/2019JA027727 Journal of Geophysical Research: Space Physics particle and mass source rates. The extremes of these ranges are presented in Table 1 as "Run 2" and "Run 3," where "Run 3" represents a more auroral-like ionosphere, and "run 2" represents a more nonauroral ionosphere. This results in a range for the total particle source of 2.4-4.9 × 10 27 s −1 , and a range in the total mass source of 4.3-8.5 kg s −1 . As the ranges of number density and temperature used to evaluate an uncertainty are large, we assume this is the largest source of uncertainty in the model and do not evaluate the intrinsic errors involved with the numerical methods used.
By mapping the ionosphere out to the magnetically conjugate area in the equatorial region (Vogt et al., 2011), the particle and mass flux that reaches the equatorial region can be quantified. We use flux equivalence, A I F I = A E F E , where A I is the area in the ionosphere, and F I is the flux through this area. A E is the area in the equatorial region that the ionospheric area maps to, and F E is the flux through the equatorial area. We then run the model over the auroral region at 75°to 77°in steps of 0.02°, where a upward current is present between 75-76°and a downward current is present between 76°to 77°. The strength and direction of the field-aligned currents in this region follow the model in Figure 9f of Ray et al. (2015). Figure 3 shows the electron, ion, and mass flux scaled to the equator from a height of 25,000 km. The electron flux is highly modified by the field-aligned currents present, where it is enhanced by a downward current and retarded by an upward current in the auroral regions. Electron flux resulting from the inclusion of FACs is shown as the solid green curve; the dotted green curve shows electron flux with FACs omitted. We extend Figure 3 to include the equatorward range of latitudes of 65-75°using a dipole field to map the field lines to the equator between 5 and 15 R J , shown in Figure 4. This is the region bounded by the Io footprint and the auroral oval described by Valek et al. (2019). The model implements no field-aligned currents in this area, and a general trend of decreasing particle flux is found due to the increasing area of which each ionospheric area maps out to the equator.
Combined with the 2°wide auroral region we discussed above, a total particle source from polar wind at Jupiter would be between 1.3 and 1.8 × 10 28 s −1 and a mass source of 18.7-31.7 kg s −1 . This is a

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Journal of Geophysical Research: Space Physics comparable number source, but a much smaller mass source than that of Io. This total mass source is also within the range of total mass sources from the solar wind discussed earlier (20 and 150 kg s −1 ).

Discussion
While our model is spatially 1-D, compounding where and under what conditions the model is run, we can describe the behavior of ionospheric outflow in Jupiter's polar regions by applying it for a range of latitudes and auroral current conditions. Figure 3 displays the results of 100 runs of the model along one line of longitude (∼0300 local time) between latitudes of 75-77°. This is done to estimate the effects of field-aligned currents on the flux that will reach the equator along each of these field lines, assuming that this latitude region is where the auroral oval at Jupiter is found. The current-latitude relationship from Ray et al. (2015) is used, and it is clear that an inverse relation is present between current and electron flux at the equator.
The latitudinal structure of the auroral currents has consequences for the total ionospheric outflow. The region of upward current causes the electron flux (solid green curve) to reduce in this area, and the region of downward current causes the electron flux to increase. This effect is due to the fact that electrons are already moving along the field line in either the opposite (upward current) direction and, as such, decreases the number of electrons moving outward or outward along the field line (downward current) and, as such, increases the number of electrons moving outward. The dotted green curve shows the relation without field-aligned currents. This relationship is dominated by the general decrease with increasing latitude, which is due to the area that each latitude is mapping out to increases at the equator.
We note that very little effect is seen in the ion flux and the mass flux due to the much smaller mass of the electrons. Hence, downward field-aligned currents increase the overall ionospheric outflow and upward field-aligned currents decrease the overall ionospheric outflow. Spatial and temporal changes in field-aligned currents are not investigated at this time. However, discussion of their effects with regard to Saturn can be found in the companion manuscript, Martin et al. (2020).
In addition to the field-aligned currents, this model also takes into account the effects of centrifugal acceleration. As shown in Figure 2b, the centrifugal acceleration (purple dashed line) increases in magnitude along the spatial domain of the model, where at around 150,000 km it becomes dominant over the gravitational acceleration. However, it has a nonzero contribution to the velocity of the particles flowing from the ionosphere. Run 4 in Table 1 excludes both the centrifugal force and field-aligned currents. As a result, the total particle source over a 2°oval at the polar region is reduced by a near factor of 2 from the range of values given when the centrifugal force is included. Thus, we conclude that the centrifugal force acts to enhance the flux of particles from the ionosphere at the giant planets. Note. Run 3 has auroral-like values with high temperature and low densities at the ionospheric end of the field line; Run 2 has nonauroral region values with low temperatures and high densities at the ionospheric end of the field line. Values for Run 1 correspond to the results presented in Figure 2; Run 4 shows an example of the same initial conditions as Run 1 but excluding both field-aligned currents and centrifugal force. Run 5 shows an example of a run for the subauroral regions.
The results from Valek et al. (2019) show an increased value of ionospheric outflow between the Io footprint and the auroral oval on average. If we assume that ionospheric outflow occurs only at latitudes between the Io footprint and the auroral oval, which is approximately 10°in latitude wide (Grodent et al., 2003), we find a total particle source of 1.3-1.8 × 10 28 s −1 , which equates to a total mass source of 14.4-23.2 kg s −1 , an example of which is shown in "Run 5" of Table 1. This range is calculated using the same ranges of input values for Runs 1 and 2, with no field-aligned currents as described for this region by Ray et al. (2015). Changes in ionospheric density over this region could be included in future development of this model to give a more accurate representation of the flux reaching the equator along the field lines. For the time being, a constant density is used, which leads to the smooth decrease in the fluxes. Valek et al. (2019) also showed that very little ionospheric plasma is found on polar cap field lines. This may indicate that the Dungey cycle does not efficiently drive ionospheric outflow at Jupiter, if the cycle is present at all. A complete picture of the sources of Jovian magnetospheric plasma will also requires eventual understanding of the entry and assimilation of solar wind material as the estimates based on incident flux by Hill et al. (1983) and Bagenal and Delamere (2011) make clear.

Summary
An ionospheric outflow model was developed to model the outflow at the auroral regions of Jupiter. The model uses the five-moment gyrotropic transport equations, along with the assumption of quasi-neutrality and a steady state electron velocity. The effects of field-aligned currents in the auroral region and the centrifugal acceleration experienced by the particles are included. The main conclusions of the study are as follows: 1. A total particle source for both hemispheres is found to be 1.3-1.8 × 10 28 s −1 when considering the auroral and subauroral source regions. 2. This corresponds to a total mass source of 18.7-31.7 kg s −1 . 3. These values are comparable to studies of Io as a source (Bagenal, 1997;Saur et al., 2003) and is close to estimates of ionospheric particle production rate by Nagy et al. (1986). 4. The total ionic mass source from Io is far larger than the ionic mass source of the ionosphere found in this study, where at Io the major ion is assumed to be SO þ 2 compared to the ionospheric H + and H þ 3 ions. 5. Centrifugal force and downward field-aligned currents act to increase the flow of electrons from the polar regions, whereas upward field-aligned currents act to decrease the flow of electrons from the ionosphere. Journal of Geophysical Research: Space Physics 6. Mapping the flux from the auroral region to the equator, we find a radially dependent mass flux with a near exponential decrease from the middle magnetosphere to the outer, with a electron flux which is highly modulated by the field-aligned currents present.
Constraints on initial conditions to improve a future model and give local time and latitudinal variation may be possible with the Juno spacecraft now in a position to measure ionospheric outflow and plasma properties in the high latitudes at Jupiter.

Data Availability Statement
The ionospheric outflow model is available on request from C. J. M. and L. C. R., and model outputs are available from a Lancaster University repository with DOI 10.17635/lancaster/researchdata/312.