An open magnetopause model of the Earth's distant tail based on ISEE 3 evidence

Abstract

It is shown that an “open” hydromagnetic equilibrium model of the Earth's distant magnetotail can describe the gross features of the cross‐tail dimensions, the magnetic field intensity, and the average plasma density in the tail lobes, as measured by ISEE 3. The tail flaring rate changes (decreases) downstream at around X ∼ −(100–120) RE. Beyond that distance our model predicts a noncircular flattened tail whose average diameter is 2 RT = 2|yz|1/2 = 60–70 RE at down‐tail distances of X ∼ −200 RE and 2RT ∼ 70–110 RE at X ∼ −1000 RE. These values agree with measurements by ISEE 3 and Pioneer 7, respectively. The degree of flattening y/z (east‐west/north‐south dimension ratio) is related to the degree of anisotropy of the plasma pressure (p∥/p⊥ ratio) and to the degree of anisotropy of the field pressure in the solar wind. The most probable flattened tail, elongated in the east‐west direction, is obtained in our model (for p∥/p⊥ ∼ 1) with an y/z ratio of 1.4–1.7 at X ∼ −200 RE and 7–12 at X ∼ −;1000 RE. A tail cross section elongated in the north‐south direction (y/z < 1) would require a large p∥/p⊥ ratio, exceeding the threshold for the excitation of the fire hose instability in the solar wind. The magnetopause in our model is assumed to be partially open as implied by the observed electron distribution functions, by magnetic field data, and by the presence of mantle‐type plasma in the distant tail lobes. The degree of openness α, defined as the fraction of the ambient interplanetary magnetic field lines that become connected to the lobe field lines, is evaluated to be α ∼ 0.1. If the initial magnetic flux in each lobe is taken to be 0.65×109 Wb and if α = 0.1, we obtain a decrease of the average (X aberrated) component of the tail lobe field from |BT| = 7.5–8.5 nT at X ∼ −200 RE to |BT| ≲ 5 nT at X ∼ −1000 RE. The related lobe plasma density increase between these distances is from nT = 0.3–0.4 to 0.8–1.5 cm−3. The field and plasma values obtained are in reasonable agreement with the observations. The total length of the tail depends on α, and the value α = 0.1 allows the tail to reach X ∼ −(2–3) × 10³ RE as supported by the evidence of magnetospheric tail‐associated phenomena seen in Pioneer 7 data. Higher values of up to α = 0.2 cannot be ruled out on the basis of plasma data, but in that case the magnetic flux loss from the lobes becomes too fast to permit the tail to extend beyond X ∼ −(700–1000) RE.