Mapping the Lunar Wake Potential Structure With ARTEMIS Data

Abstract

The refilling of the lunar wake is relatively well explained by the theory of 1-D plasma expansion into a vacuum; however, the field-aligned wake potential is not a directly measured quantity, and thus, a statistical analysis of wake potentials at high altitudes has not been previously performed. In this study, we obtain the wake potential by comparing the field-aligned electron distributions inside and outside of the lunar wake measured by the two probes of the Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) mission. The derived potentials from ARTEMIS data vary with solar wind electron temperature and bulk flow velocity as the theory predicts. We also expand the 1-D plasma theory to 2-D in the plane of the interplanetary magnetic field and the solar wind velocity to examine how a tilted interplanetary magnetic field affects the wake potential structure. As the expansion time for the two sides of the wake differs, a wake potential asymmetry is developed in our model. This asymmetry is confirmed by the data-derived wake potentials. Moreover, ambipolar electric fields are obtained from both the modeled and data-derived wake potentials and show good agreement. Lastly, we examine the effects of the solar wind strahl-electron population on the wake potential structure, which appears to cause a net potential difference across the lunar shadow. This may imply that the disturbance of the wake plasma expansion extends farther outside the wake than previous plasma-expansion theories have predicted.

Figure 1.

Geometry for a tilted interplanetary magnetic field (IMF): In a 2-D plane, the X axis points opposite the solar wind flow velocity, and the Y axis is parallel to the perpendicular component of the IMF with respect to the X axis. The IMF has an angle of θ = arccos(B_x/|B|) with the X axis. A boundary line L₁ separates regions magnetically connected (R1 and R2) and unconnected (R3) by the Moon, which is parallel to the IMF and intersects the lunar surface at a tangent point T(X_t, Y_t). The two shadowed regions, R1 and R2, are divided by another boundary line L₂, which connects T and the center of the Moon. E₁ and E₂ represent the expansion fronts of the rarefaction waves on each side. Then, at an observation point (x, y), the IMF intersects Y = ±1 R at (X₁, R_L) and (X₂, −R_L), where R_L is the lunar radius.

Figure 2.

(a) The wake potential calculated from equations (4)–(6) for R1, R2, and R3 combined, with a solar wind speed of |V_sw| = 400 km/s, an electron temperature of T_e = 24 eV, and an IMF angle of θ = 135°. (b) The averaged potential from our theory in the Y-Z plane for X = [−1.3, −1.0]. (c) The potentials at the expansion fronts E₁ and E₂. IMF = interplanetary magnetic field.

Figure 3.

An ARTEMIS probe P1 orbit example on 1 January 2014. From top to bottom, the time series of (a) the spacecraft position in the cylindrical coordinates, where the X axis points opposite to the solar wind flow velocity, r_cyl is the distance from the X axis; (b) the magnetic field strength and vector components in the SSE coordinates; (c) the magnetic angle relative to the X axis; (d) the spacecraft potential; (e) the averaged ion energy spectra; (f) and (g) the electron energy flux for pitch angles 0–15° and 165–180°, respectively, both corrected for spacecraft potentials; and (h) the deduced wake potential from electrons traveling toward the wake, parallel electrons for inbound (red) and antiparallel electrons for outbound (blue).

Figure 4.

The map of wake potentials in the X-Y′ plane in the abbreviated coordinates, averaged over Z′ = [−0.5, 0.5], for solar wind electron temperature (a) T_e > 12 eV (energy unit) and (b) T_e < 12 eV. The gray pixels are where there are less than 10 samples or no data, the same applied to Figures 5–11. (c) Wake potential as a function of electron temperature for X = [−1.5, −1], Y′ = [−0.25, 0.25], and Z′ = [−0.5, 0.5], as indicated by the green dashed box in (a). The solid line and error bars in (c) show the quartiles of each bin.

Figure 5.

The map of wake potentials in the X-Y′ plane in the abbreviated coordinates, averaged over Z′ = [−0.5, 0.5], for solar wind speed (a) |V_sw| > 370 km/s and (b) |V_sw| < 370 km/s.

Figure 6.

The maps of wake potentials in the abbreviated coordinates for perpendicular interplanetary magnetic fields (cone angle >70°): (a, b) in the X-Y′ plane averaged over Z′ = [−0.5, 0.5]; (c, d) in the Y′-Z′ plane averaged over X = [−1.3, −1.0] (as indicated by the two vertical dashed lines in a and b). (a) and (c) cases with strahl (FR > 2 or FR < 1/2). (b) and (d) cases with no strahl (1/2 < FR < 2). FR = flux ratio.

Figure 7.

The maps of derived electric fields in the X-Y′ plane for perpendicular interplanetary magnetic fields (cone angle >70°): (a) cases with strahl (FR > 2 or FR < 1/2) and (b) cases with no strahl (1/2 < FR < 2). The color shows the electric field magnitude, and the arrow indicates its direction. The arrow lengths are scaled by electric field magnitudes. FR = flux ratio.

Figure 8.

The maps of wake potentials in the abbreviated coordinates for cases with no strahl (1/2.5 < FR < 2.5): (a–c) in the X-Y′ plane averaged over Z = [−0.5, 0.5]; (d–f) in the Y′-Z′ plane averaged over X = [−1.3, −1.0] (as indicated by the two vertical dashed lines in (a)–(c). (a and d) Quasi-parallel IMFs (cone angle <50°); (b and e) Intermediate IMFs (50° < cone angle < 75°); (c and f) Perpendicular IMFs (cone angle > 75°). IMF = interplanetary magnetic field.

Figure 9.

The maps of derived electric fields in the X-Y′ plane for cases with no strahl (1/2.5 < FR < 2.5): (a) quasi-parallel IMFs (cone angle <50°), (b) intermediate IMFs (50° < cone angle < 75°), and (c) perpendicular IMFs (cone angle > 75°). The color shows the electric field magnitude, and the arrow indicates its direction. The arrow lengths are scaled by electric field magnitudes. IMF = interplanetary magnetic field.

Figure 10.

Maps of wake potentials from the data for the intermediate IMF case (a) and the model (b) in the X-Y′ plane. (a) is the same as Figure 8b. (c) The relative difference is calculated as (data-model)/model. The positive values in (c), or the red color, means the data-derived potential is more negative. IMF = interplanetary magnetic field.

Figure 11.

(a, b) Maps of electric fields derived from Figures 10a and 10b in the X-Y′ plane, respectively. (a) is the same as Figure 9b but with a different display. The color shows the electric field magnitude, and the arrow with a uniform length indicates its direction.

Figure 12.

The averaged potential over X = [−1.3, −1.0] and Z = [−0.5, 0.5] against Y′ for the strahl case (a) and the nonstrahl case (b) under perpendicular IMFs, corresponding to the data within the two dashed lines in Figures 6a and 6b, respectively. (c) The averaged potential against Y′ for quasi-parallel IMFs under a nonstrahl condition, corresponding to the data within the two dashed lines in Figures 8a. The vertical bars indicate quartiles of each bin. IMF = interplanetary magnetic field.