A Fast Bow Shock Location Predictor‐Estimator From 2D and 3D Analytical Models: Application to Mars and the MAVEN Mission

Abstract

Historically, planetary bow shocks, their position, size, and shape, have been characterized statistically with the use of (empirical) analytical fitting models in two-dimensional (2D) or three-dimensional (3D) spatial coordinates. A classical starting point for characterizing the Earth's bow shock in 3D includes the seminal work of Formisano (1979), who investigated the asymmetry of the shock with respect to the apparent solar wind flow direction, with the use of quadratic surface fits with nine free parameters. In parallel, other studies, such as that of Slavin and Holzer (1981) relied on a simple polar equation assuming axisymmetry along the Sun-planet line, corrected by the apparent motion of the solar wind in the rest frame of the planet, the so-called aberrated X axis. The 2D approach has the merit of needing only three free parameters but ignores the potential asymmetries of the shock as, for example, seen at Earth's bow shock (e.g.

Statistical distribution of mirror mode-like structures in the magnetosheaths of unmagnetised planets: 1. Mars as observed by the MAVEN spacecraft

“…CMa, SRM, GSW, YF, JH, DRC, CB and JE contributed to the data validation and interpretation, numerous ideas and science discussions, but also helped with the writing of the main text. (Simon Wedlund et al, 2022b, between low and high EUV conditions) and the range of subsolar IMB positions, R ss,imb (Trotignon et al, 2006;Edberg et al, 2008) EUV conditions, and negative values towards low EUV conditions. 'Full magnetosheath' considers the detection probabilities outside of the average IMB (defined by the fit of Edberg et al, 2008), whereas 'Deep magnetosheath' only considers P in the narrow region delimited by the two black continuous lines in Fig.…”

“…We start with spacecraft coordinates expressed in the Mars Solar Orbital (MSO) coordinate system (sometimes called "Sun-state" coordinates), where the X MSO axis points towards the Sun from the centre of Mars, Z MSO points towards Mars' North pole and is perpendicular to the orbital plane defined as the X MSO -Y MSO plane passing through the centre of Mars, with Y MSO completing the right-hand triad. We then transform this system into aberrated MSO coordinates by rotating the X MSO -Y MSO plane 4 • counterclockwise around the Z MSO axis in order account for the apparent "aberration" of the orbital motion of Mars with respect to the average direction of the solar wind (Simon Wedlund et al, 2022b). The new aberrated coordinate system, aligned with the average apparent solar wind direction, is noted…”

“…3 as maps for the full dataset considered here, with a bin resolution of 0.1 R M . For reference, we also indicate the bow shock (BS) and the induced magnetospheric boundary (IMB, sometimes referred to as 'magnetic pileup boundary') from several previous works (Edberg et al, 2008;Hall et al, 2019;Simon Wedlund et al, 2022b). Because these boundary positions were determined statistically and represent an average over an extensive range of geophysical conditions, their exact position may vary by a few grid cells for individual observations and should only be taken as a rough indicator of the shape of the boundaries around that point.…”

“…With the predicted position of the IMB from Edberg et al (2008) for the comparatively higher solar conditions encountered by MGS, MM-like structures seem to "leak" into the magnetosphere, although we cannot say for sure if these detections are in fact inward of the IMB or not. For example, an appreciable part of the detections seemingly present in the solar wind upstream of the average shock position (Hall et al, 2019;Simon Wedlund et al, 2022b) are in fact just behind the actual shock, whose position continuously varies with the solar wind upstream conditions. A cursory examination of individual detections for a reduced dataset in Dec. 2014 and Sept. 2016 pleads in favour of this latter idea (see for example Fig.…”

“…4). By modifying the global energy input to the Martian atmosphere-ionosphere-exosphere system, both aspects lead to variations in Mars' exospheric extent and ionisation levels, and are among the key drivers of the bow shock and IMB positions (Hall et al, 2016;Gruesbeck et al, 2018;Simon Wedlund et al, 2022b;Garnier et al, 2022).…”