MFB2 Temperature anisotropy

We analyze the time period during the wave signature measured by the PWI search coil magnetometer spanning 23/06/2022 9:45 to 9:51 denoted with the pink lines.
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The trajectory of the spacecraft at the time is shown below in the MagnetoSpheric Mercury (MSM) Frame.
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We can get the magnetic field and its direction across this trajectory through the KT17 Model in the MagnetoSpheric Mercury (MSM) Frame and transform it in the MPO frame using SPICE kernels.

Parametrize to correct solar wind conditions
Test with Giulio's magnetic field

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We can also get the direction of the P0,P1,P2 SIXS detectors in the MPO frame by transforming a $z = (0, 0, 1)$ vector from 'MPO_SIXS-P-0' frame to 'MPO_SPACECRAFT'. By taking the vector product with the direction of the magnetic field we can compute the pitch angle $θ$ :

\cos θ = \frac{\vec{a} \cdot \vec{b}}{| \vec{a} | | \vec{b} |}

Here we plot the differential flux of the high energy electrons during the whistler signature in one axes, and the calculated pitch angle of the detector on the other.
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To keep the same scale we can plot it in one figure, where green refers to the P0 detector, blue to P1 and red to P2.
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We can notice some variations in the measurement of each viewing direction, however small since the detectors happen to be in quasi-oblique angles. Assuming an anisotropic Maxwellian distribution we can derive a measure of the parallel and perpandicular heating, although sparsely sampled.

T_{∥} \propto \sum_{E, θ} \cos^{2} θ \cdot F_{E} (θ, E)

T_{⊥} \propto \sum_{E, θ} (1 - \cos^{2} θ) F_{E} (θ, E)

A bounded measure of the anisotropy $\in [- 1, 1]$ where -1 is fully perpandicular, +1 is fully parallel and 0 is isotropic can be derived through:

A = \frac{T_{∥} - T_{⊥}}{T_{∥} + T_{⊥}}

The physical signal begins around 9:48 where A is consistently negative, meaning

F_{⊥} > F_{∥}

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The hypothesis of a monotonically anisotropic shape of the distribution function is a strong one, and therefore this cannot conclude a definite answer on the heating mechanism. We can expand by including measuremnts and pitch angles from the 2 available viewing direction of the Mercury Electron Analyser (MEA) instruments.

We can also simulate an anisotropic maxwellian and test this metric over a known function.

To-do

Include MEA counts and pitch angles
MEA2-SIXS measurements at high energies comparison
Sample Giulio's distribution
Sample anisotropic maxwellian
CAD SIXS