Solar wind at 33 AU: Setting bounds on the Pluto interaction for New Horizons

1 Introduction

After a journey of over 9 years the New Horizons spacecraft flies past Pluto on 14 July 2015. A scientific objective of the New Horizons mission is to quantify the rate at which atmospheric gases are escaping the planet [Stern, 2008; Young et al., 2008]. At Pluto, the properties of the interaction of the escaping atmosphere with the solar wind depend not only on the rate at which the atmosphere is escaping from Pluto but also vary with the solar wind conditions (e.g., flow, density, ram pressure, and temperature). Key to estimating Pluto's total atmospheric escape rate is measurements of the size of the solar wind interaction region.

The two New Horizons instruments that measure charged particles are the Solar Wind Around Pluto (SWAP) instrument [D. McComas et al., 2008] and the Pluto Energetic Particle Spectrometer Science Investigation (PEPSSI) instrument [McNutt et al., 2008]. The SWAP and PEPSSI instruments (a) measure the deceleration of the solar wind from mass loading by ionized atmospheric gases; (b) detect a shock upstream if the boundary to the interaction region is sufficiently abrupt; and (c) measure fluxes of Pluto ions when they are picked up by the solar wind. A specific challenge we face with New Horizons is that the spacecraft does not carry a magnetometer so that we will need to rely on monitoring of the interplanetary magnetic field (IMF) near Earth and propagating the field magnitude, field polarity (sector boundary) from measurements near 1 AU out to 33 AU.

New Horizons flies past Pluto at a distance of 32.9 AU from the Sun when the spacecraft is 31.9 AU from Earth with a one-way light time of 4 h 25 min. At the time of encounter, Pluto is 1.9° above the ecliptic plane on its eccentric orbit. New Horizons is heading nearly toward the nose of the heliosphere, in a direction toward the Galactic center. After the flyby, there are options of targeting other objects in the Kuiper Belt within the following ~3 years at ~40 AU. Moving at 2.9 AU/year, the New Horizons spacecraft has enough fuel and communications capability to continue measuring the solar wind out to ~100 AU.

The Sun and the out-flowing solar wind vary on a wide range of timescales. The ~11 year solar cycle is associated with reversals of the polarity of the Sun's magnetic field. The solar cycle has a major impact on the coronal structure, which in turn drives the three-dimensional solar wind that fills and inflates the heliosphere. Around solar minimum, fast, steady wind arises at high latitudes from large circumpolar coronal holes and more variable, slow wind flows at lower latitudes from the streamer belt, coronal hole boundaries, and transient structures [e.g., McComas et al., 1998]. Around solar maximum, this simple structure breaks down with smaller coronal holes, streamers, and transients arising in the corona and leading to a complicated and highly variable solar wind structure at all heliolatitudes. The July 2015 New Horizons flyby of Pluto occurs as the Sun is in the descending phase of the solar cycle.

In 2 of this paper, we summarize the Voyager data obtained around the distance of Pluto's orbit. In 3, we discuss the long-term, multidecadal variability of the solar wind that needs to be taken into account when scaling the Voyager data to the New Horizons epoch. In 4, we present examples of particle data obtained by New Horizons in the solar wind. In 5, we make predictions for the scale of the region of the interaction of the solar wind with Pluto's atmosphere. We briefly discuss these modeling results and list our conclusions in 11.

2 Voyager Data

To survey solar wind conditions that the New Horizons spacecraft (and Pluto) could encounter in mid-2015, we have taken two approaches: (1) we have taken data obtained by Voyager 2 between 25 and 39 AU, and (2) looked at data from the New Horizons instruments on its trajectory to Pluto. We chose Voyager 2 because it has magnetic field data as well as reliable plasma. We took Voyager 2 data from 1988 to 1992 when it traversed from 25 to 39 AU at ecliptic latitudes of ~ +4° to −8°. The maximum of solar cycle 22 was in ~1990, around the middle of our sample period. Voyager observations of the outer heliosphere are reviewed by Richardson et al. [1996a, 1996b] and Richardson and Burlaga [2013].

We show the trajectories of the two Voyagers and of New Horizons projected onto the ecliptic plane in Figure 1, highlighting the region of Voyager 2 data used (thick blue line). Figure 2 shows daily averages of solar wind flow speed (V), proton number density (n), proton temperature (T), and magnetic field magnitude (B) measured by Voyager 2 during this period. The solar wind flow is nearly radial. The average E-W angle from 20 to 40 AU is 0.75° and the average N-S angle is 1.5°. In a large interplanetary coronal mass ejection at about 35 AU in 1991, these angles reached 5°, but that was only in one very unusual event [Richardson et al., 1996c]. Densities and dynamic pressures are normalized by a 1/R² factor to 32 AU. We note that at 32 AU pickup ions have a noticeable effect, decreasing the speed of the solar wind by several percent and increasing T, counteracting adiabatic cooling on expansion, resulting in a relatively flat temperature profile [Richardson et al., 2008].

The values of n, T, and B show short-term (t ~ day-week) variations of a factor of 5–10 about a fairly steady average value. The solar wind speed shows smaller variations over days-weeks but shows a semiperiodic variation on a ~1.3 year timescale observed throughout the heliosphere [Richardson et al., 1994; Gazis et al., 1995]. These oscillations have not been reported in the current solar cycle. On a smaller scale, plasma changes were predominately due to Corotating Interaction Regions (CIRs), with speed increases roughly once per solar rotation. When Voyager 2 was near 32 AU (mid-1991), the solar wind speed jumped from 370 to 600 km/s and the density increased by more than a factor of 10. The effects of this Merged Interaction Region persisted for about 30 days. Only a few shocks were observed per year at this distance by Voyager 2. More common are CIRs, which are typically observed once per solar rotation at this distance in the declining phase of the solar cycle [Lazarus et al., 1999]. Typical speed increases at a CIR at this distance are 30–50 km/s, and these are often associated with energetic particle increases. The New Horizons spacecraft will take only a few hours to pass through the interaction region at Pluto, so we are hoping that the solar wind is relatively steady through this time.

We took the Voyager data shown in Figure 2 and made histograms of the parameters (Figure 3) and derived statistical quantities listed in Table 1. In Figure 3a, the solar wind speed shows limited variation (± ~ 10%), while the density distribution has a significant tail to higher densities. The derived quantities of solar proton flux (nV) and dynamic pressure (P = ρV² = n m_p V² where m_p is the mass of a proton) also exhibit significant tails (which is why we show median, 10th percentile, and 90th percentile values in Table 1 in addition to mean and standard deviation). Figure 3b shows distributions of magnetic field strength (B) and proton temperature (T) as well as derived quantities: Alfvén Mach number (M_alf = V/V_A where V_A = B/(μ_oρ)^1/2) and ratio of particle thermal pressure to magnetic pressure (β = nkT/[B²/2 μ_o]). The high Mach number and low β values indicate that at these distances the solar wind is a very cold, fast flow carrying the solar magnetic field. Note that these Voyager plasma data do not include interstellar pickup ions which can make a significant contribution to the total thermal pressure at these distances, as discussed below.

Energetic particles in the vicinity of Pluto's distance in the solar wind were detected by the Low-Energy Charged Particle Experiment instruments at Voyager 1 and Voyager 2 in the late 1980s and early 1990s. Decker et al. [1995] reported on 28 keV–3.5 MeV ions detected at Voyager 2 from 33 to 42 AU. From 1991.5 to 1993.5, they observed energetic intensities that were recurrent with roughly the ~26 day solar rotation period, similar to the variations in the bulk plasma speed seen by the Voyager 2 PLS instrument. There was also a long (~1 year) intensity increase associated with a pair of large-traveling interplanetary shocks in 1991. At shorter timescales, nonstatistical variations of order 6 h were also seen in the energetic particles. Such multiscale variations and correspondences between energetic particle and plasma measurements are typical in the solar wind, although structure tends to evolve at greater distances from the Sun.

To partially compensate for the lack of a magnetometer on New Horizons, we look for a relationship between solar wind ion properties and the local interplanetary magnetic field (IMF). We have examined several years of Voyager 2 data spanning both different heliocentric distances and solar wind conditions in the hope of resolving some reliable proxy measurement but have had only limited success. We can characterize that effort by describing three different conditions. First, the spacecraft observed typical solar minimum conditions in 1984 when it was at 14 to 15 AU from the Sun. Second, when the spacecraft reached 32 AU in 1990, it was experiencing solar maximum conditions. Third, when it saw declining phase conditions in 1993, the spacecraft was at 40 AU. It may be possible to use observations such as these to infer a reasonable value for the unmeasured magnetic field once the solar wind conditions surrounding the encounter are known. The fundamental problem with finding a proxy measurement for B is the merging of fast and slow streams along with ejecta that produces MIRs at solar maximum and CIRs at solar minimum. Fast wind and slow wind close to the Sun have established correlations between flow conditions and the average magnetic field, but merging modifies these properties.

As an example of what may be possible, Figure 4 shows the correlation between the Voyager 2 solar wind proton flux and the magnetic field intensity for the period day of year (DOY) 90 to 220 of 1984. This was solar minimum or low solar activity levels. New Horizons encounter with Pluto during the declining phase after a weak solar maximum, so we are expecting relatively low solar activity. The correlation is helpful and can be refined once we better understand the encounter conditions.

3 Long-Term Variations

Conventional wisdom has suggested that the basic solar wind output is primarily tied to the phase of the solar cycle, similar to the behavior of the three-dimensional structure. However, D. J. McComas et al. [2008] demonstrated that a much longer-term trend currently dominates over any smaller solar cycle effect. This multidecade trend exhibits significantly reduced solar wind density, dynamic pressure and energy, and interplanetary magnetic field (IMF).

The most recent solar minimum (end of cycle 23) stretched into 2009 and was particularly deep and prolonged. In cycle 24, sunspot activity rose to a very small double peak. Meanwhile, the heliospheric current sheet developed large tilt angles, similar to prior solar maxima. McComas et al. [2013] recently extended their 2008 study and showed that the solar wind and IMF properties continued to drop through the prolonged solar minimum and maintained low values through the ~2012 “mini” solar maximum, illustrated in Figure 5. Figure 6 shows that the sunspot numbers went through a second maximum in early 2014 and that we expect New Horizons to be at Pluto as the Sun is on the declining phase of cycle 24.

From 2009 through DOY79 of 2013, the proton parameters are lower on average (compared to values typically observed from the mid-1970s through the mid-1990s) by the following factors [McComas et al., 2013]: density ~27%, temperature ~40%, solar wind speed and beta ~11%, thermal pressure ~55%, and IMF magnitude ~31%; and radial component of the IMF ~38%, mass flux ~34%, dynamic pressure ~41%, and energy flux ~48%. With the proton dynamic pressure persisting near the lowest values measured in the space age (~1.4 nPa compared to ~2.4 nPa typical from the mid-1970s to mid-1990s), these results have important implications for the solar wind's interaction with planetary atmospheres and magnetospheres.

The results of D. J. McComas et al. [2008, 2013] indicate that the weak solar maximum and low solar wind output are driven by an internal trend in the Sun that is longer than the ~11 year solar cycle. For the purposes of this study, these results mean that the Voyager-based estimates from when Voyager 2 was around 30 AU (1988–1992) have to be scaled down significantly for predictions for New Horizons' flyby of Pluto in July 2015, as listed in Table 2.

Of particular importance for estimating the size of the interaction with an escaping atmosphere is the solar wind flux, nV. It is the solar wind momentum (strictly speaking ρV = n m_p V) that is tapped to pick up ions that are created by photoionization and charge exchange of atmospheric molecules. We are particularly interested, therefore, in how the Voyager 2 values of nV scale down by a factor of (1–0.34) = 0.66, giving a mean value scaled down from 3.24 to 2.14 km s⁻¹ cm⁻³ (or 2.14 × 10⁹ m⁻² s⁻¹). The median value scales down to 1.55 km s⁻¹ cm⁻³ with 10th/90th percentile values of 0.55/4.6 km s⁻¹ cm⁻³ (Table 2).

New Horizons reaches 33 AU in July 2015 when the Sun is expected to be in the declining phase of an unusually low-activity solar maximum (Figure 6). Between 2012 and 2013, the monthly sunspot number exhibited an apparent peak at ~60, but late in 2013 and into the first half of 2014, the solar activity rose to peak sunspot numbers of ~100, declining through 2014–2015, suggesting that the IMF intensity at 33 AU will be lower than experienced by Voyager at these distances.

4 New Horizons Data

Since New Horizons flew past Jupiter in spring 2007 (for a gravity assisted en route to Pluto), the spacecraft has been in hibernation with annual periods of activity. The SWAP and PEPSSI instruments were initially turned off during hibernation but since 2012 have been taking data semicontinuously. By the time New Horizons encounters Pluto in July 2015, we will have 3.5 years of solar wind data between 22 and 33 AU.

Figure 7 shows an energy-time spectrogram of SWAP data (20 eV/q to 8 keV/q) plus fluxes of tens of keV to MeV particles measured by the PEPSSI instrument. We have picked a time that illustrates active behavior of the solar wind. Figure 7 (top and bottom) shows 168 days of data in the latter half of 2012 (DOY 189 to 357 where DOY = day of year) when New Horizons moved from 23.5 to 25 AU. The SWAP spectrogram shows the cold beam of solar wind protons (with a kinetic energy of ~1 keV) with lesser (few percent) fluxes of alpha particles, comoving with the protons at twice the kinetic energy per charge. The ion energy distribution also shows a clear signal of interstellar pickup H⁺ ions extending to four times the energy per charge of the proton beam [Randol et al., 2012, 2013].

5 Predictions for Solar Wind Interaction With Pluto's Atmosphere

Having gathered a sense of the solar wind at Pluto's current distance from the Sun, we next address what is known about Pluto's escaping atmosphere and how the solar wind might interact with it.

5.2 Solar Wind—Atmosphere Interaction

As the atmosphere escapes Pluto's gravity and expands into space, the molecules are slowly ionized by solar UV photons and charge exchange with solar wind protons. The timescale for photoionization of N₂ is in the range of 1.2 to 3.3 × 10⁹ s depending on the UV activity of the Sun [Wegmann et al., 1999]. This is 38–105 years, a significant fraction of the 248 year orbital period of Pluto. The charge-exchange rate [ ] depends on the flux of solar wind protons and is nearly an order of magnitude lower than the photoionization rate [Wegmann et al., 1999]. Thus, the timescale for removal of the neutral, escaping atmosphere is on the order of a few decades (by which time the escaping molecules have spread out thousands of Pluto radii), so that most of the atmosphere escapes into interplanetary space. Photodissociation of N₂ and dissociative ionization of N₂ also contribute to loss but on even longer timescales [Huebner and Mukherjee, 2015; Solomon and Qian, 2005]. The small number of molecules that become ionized, however, can have a substantial effect on the solar wind. Once ionized, the molecule begins to gyrate around the ambient magnetic field and is immediately accelerated to the bulk speed of the solar wind. For a nominal solar wind speed of 380 km s⁻¹ the initial gyroenergies of N₂⁺, C⁺, N⁺, and O⁺ are 12–30 keV. For a typical ambient magnetic field of 0.1 nT, the gyroradii of pickup N₂⁺ ions are 1.3 × 10⁶ km or 1000 > R_P. The momentum imparted to the picked up ion comes from the solar wind, which is correspondingly slowed down, stagnating the flow upstream of the planet, and potentially forming a shock [Galeev et al., 1985].

Initial studies of the solar wind interaction with Pluto's atmosphere [e.g., Bagenal and McNutt 1989; Bagenal et al., 1997] suggested that the solar wind interaction with Pluto's atmosphere would depend on whether the atmospheric escape flux is strong (producing a “comet-like” interaction) or weak (producing a “Venus-like” interaction). In both of these descriptions, it is assumed that the planet's atmosphere/ionosphere and the solar wind could be considered as fluids. For many solar system bodies, fluid descriptions of a plasma-obstacle interaction are often sufficient. Global-scale magnetohydrodynamic (MHD) models have been successful in capturing the basic structure of such plasma interactions. With the IMF being very weak at Pluto's orbital distance (Table 1), the length scales on which the plasma reacts are large compared with the size of the interaction region. For instance, at 33 AU the gyroradius of solar wind protons is ~23 R_P, and the pickup ion gyroradius is ~1000 R_P [Bagenal and McNutt, 1989; Kecskemety and Cravens, 1993]. Furthermore, the upstream ion inertial length is comparable to the size of the obstacle (2–4 R_P) which could significantly alter the nature of the momentum transfer from the solar wind flow to the atmospheric ions.

The extended region of mass loading far from Pluto makes it a “soft” obstacle to the supersonic solar wind. We contrast this with the expected “hard” obstacle created by a planetary magnetic field. However, inside the bow shock, in a region called the sheath, the plasma density increases as the decelerating flow approaches Pluto's presumably dense and bound atmosphere. The magnetic field, “frozen” to the flowing plasma, is compressed in the decelerating flow and correspondingly increases in strength. As some point, the pickup ions form a dense and “hard” obstacle to flow. In the cometary literature there is considerable confusion in the naming of the boundary (e.g., “cometopause,” “ionopause,” “collisionopause,” “magnetic pileup boundary,” and “contact surface”) and its exact location (see discussions in Neugebauer [1990], Cravens [1991], and Gombosi et al. [1996]). We will adopt the term “interaction boundary” from here forward.

5.2.1 Cometary Model

The ions picked up in the unperturbed solar wind upstream of Pluto in an IMF of ~ 0.1 nT have large gyroradii (~600,000 km ~500 R_P). Predicting the location of the bow shock in the large ion gyroradius limit is difficult. Nevertheless, we compare the distance to the bow shock directly upstream of Pluto with predictions using the cometary models of Biermann et al. [1967] and Galeev et al. [1985] for partially mass loaded solar wind flow. In the fluid limit (or semikinetic if nonthermal pickup ion pressure is included), pressure balance considerations provide the distance to the bow shock as the standard Galeev formula for solar wind stagnation point (normalized to Pluto's radius) as

(1)

where Q_o is the neutral escape rate, V_esc is the neutral outflow velocity, τ is the ionization time constant, n_sw and V_sw are the unperturbed solar wind density and flow velocity, and (ρV)_c is the critical loaded mass flux normalized to the upstream mass flux.

Biermann et al. [1967] showed that the solar wind flow is continuous until a value of (ρV)_c = 4/3 is reached (see also Flammer and Mendis [1991] for a more detailed treatment). This would make the factor ζ = [(ρV)_c − 1]⁻¹ = 3. From comparisons of models of comets (within the fluid regime) with models in the kinetic regime, Delamere [2009] argues that the kinetic case at Pluto is more consistent with (ρV)_c ~8/3 giving ζ = 3/5 = 0.6. In the fluid limit, each pickup ion in the mass-loaded upstream flow remains in the given fluid element. But in the large ion gyroradius limit, the pickup ion exits the solar wind fluid element laterally and the momentum transfer is far from complete on timescales less than the gyroperiod. In the hybrid simulations of Delamere [2009], the momentum transferred to the pickup ions in the upstream region is only a small fraction of the total pickup momentum. So the contamination to the flow is initially relatively small. As a result, the bow shock moves closer to Pluto. With these limitations in mind, we apply two approaches to calculating the location of the interaction boundary: a cometary model where the gravity of Pluto is basically ignored above the exobase, and a coronal model where the gravity is included (more similar to the coronas of Mars and Earth).

For the cometary model, we apply the Galeev formula and take the following nominal values: a neutral escape rate of Q_o = 3 × 10²⁷ s⁻¹ [Zhu et al., 2014]; pickup ion mass of m_i(N₂) = 28 amu; neutral escape speed V_esc = 10 m/s; solar wind density n_sw ~ 0.006 cm⁻³ = 6000 m⁻³; solar wind speed V_sw ~ 380 km/s = 3.8 × 10⁵ m/s; and R_P = 1184 km = 1.184 × 10⁶ m. By plugging in these nominal values for photoionization timescale of τ ~ 1.5 × 10⁹ s, we get

(2)

Note that this formulation is only a rough approximation of where we could expect to see the standoff distance of the solar wind upstream of Pluto. We aim to use New Horizons SWAP measurements of the upstream density n_sw and speed V_sw of the solar wind and its detection of the upstream boundary location (Rs) to estimate the net neutral escape rate (Q_o).

5.2.2 Adding Finite Gravity of Pluto

The situation at Pluto has the potential for being more complex due to the deviation of the density above the exobase from a strict inverse square law due to Pluto's gravitational field. If we reexamine Galeev's approach, it is convenient to define a “pickup ion column density”

(3)

where τ is the total ionization time and all of the other quantities are as defined before with N₂ taken as the dominant pickup ion which slows the flow. A generalized standoff equation can be written as

(4)

For a simple inverse square density behavior, we obtain the previous result for comets

(5)

Note there is an implied relation in this case of

(6)

but this presupposes that the escaping component dominates both the ballistic and, potentially, satellite, component which is probably not the case with the finite gravity of Pluto.

To provide standoff estimates, we require the neutral density as a function of altitude above the exobase (assuming that the standoff will occur above that level). For the limit in which λ_c ~ 0, the free molecular flow asymptotic limit results in a cubic equation with one real root in λ^1/2 if all the density components are included. However, the satellite component—if fully populated—dominates and we obtain

(7)

For the numbers discussed here, this yields Rs ~1200 R_P, a distance from Pluto reached by New Horizons just over a day from closest approach for the nominal conditions. Even at such a large scale, the correction for ionization loss of the neutrals (the Haser correction in the cometary literature [Haser, 1957] but also discussed in the appendix of Galeev et al. [1985]) is not required. For bound molecules, the correction approach is more complicated in any event (see equation (121) in Chamberlain [1963] and the accompanying discussion).

The significant difference between the case of comets and the case of a gravitationally bound, evaporative exosphere is the presence of the ballistic component. For the conditions here, simply zeroing out the coefficient of the satellite component still leaves a cubic equation for λ_standoff^1/2, but the solution is no longer consistent with the asymptotic limit of the expression for the integrated column density. The asymptotic limit (with equation (95) of Chamberlain [1963]) yields a standoff distance of ~26 R_P. The numerical value is closer to ~35 R_P and the ballistic component only would yield ~ 30 R_P. New Horizons will reach 35 R_P at ~50 min prior to closest approach to Pluto.

5.2.3 Numerical Simulation

To advance beyond a 1-D analytic description of the subsolar standoff distance, we need to turn to numerical simulations. Simulation of the solar wind interaction with comets is one of several instances where the fluid description is not appropriate and application of MHD is limited. The DS1/Plasma Experiment for Planetary Exploration instrument measured a surprisingly asymmetric plasma environment near Comet Borrelly at 1.3 AU which Delamere [2006] attributed to large ion gyroradius effects. The pickup ion gyroradius in this case was comparable to the size of the interaction region, driving the plasma boundaries northward in the case of a northward directed convection electric field. Delamere [2006] and Hansen et al. [2007] found that beyond 1.3 AU, the fluid MHD approach is very limited.

While solar wind conditions at 30–50 AU dictate a kinetic treatment of all ion species, a hybrid approach is reasonable where the electrons are treated as a massless fluid, given that the electron inertial length is small (~50 km) compared to the gradient scale lengths of the extensive interaction region. To simulate conditions at Pluto, we have applied the hybrid code first proposed by Harned [1982] and developed by Delamere et al. [1999]. The code assumes quasi-neutrality and is nonradiative. We have developed a 3-D hybrid simulation for modeling the solar wind interaction with Pluto. Since our preliminary efforts [Delamere and Bagenal, 2004; Delamere, 2009], the code has been further developed to make significantly larger spatial domains feasible. Figure 8 shows three simulations of the solar wind (density n = 0.006 cm⁻³, flow speed V = 380 km s⁻¹) interaction with an escaping atmosphere where Q_o = 3 × 10²⁷ molecules s⁻¹ and the outflow speed is taken to be 50, 25, and 10 m s⁻¹. The corresponding standoff distances are 50, 90, and 170 R_P.

6 Discussion and Conclusions

Figure 9 shows the location of this stagnation distance versus solar wind flux (n_swV_sw) for the various atmospheric escape models discussed in this paper for a range of values for Q_o and V_esc. The median and 10th /90th percentile values of flux, scaled down from Voyager 2 values to the 2015 era, are shown as vertical lines. These models suggest that we can expect the New Horizons spacecraft to cross the upstream boundary anywhere from about 7 to ~1000 R_P. The models A–D apply the comet model shown in equation 2 to the Strobel atmospheric models listed in Table 3. Models E–H correspond to the same cases A–D but with V_exobase = 100 m/s. The triangles are for the atmospheric models discussed above that include the effects of Pluto's gravity and correspond to exosphere populations of escaping (blue), ballistic (orange), and satellite (green) molecules. The green, orange, and blue stars correspond to the interaction distances from the numerical simulations discussed above and presented in Figure 8.

Measurements from the SWAP and PEPSSI instruments on New Horizons will characterize the solar wind interaction with the ionized escaping atmosphere and quantify the mass loading of the solar wind. Furthermore, comparison with these analytic and numerical models allows us to explore the sensitivity of the location of the interaction boundary to model conditions.