The Drivers of the Martian Bow Shock Location: A Statistical Analysis of Mars Atmosphere and Volatile EvolutioN and Mars Express Observations

Abstract

The Martian interaction with the solar wind leads to the formation of a bow shock upstream of the planet. The shock dynamics appear complex, due to the combined influence of external and internal drivers. The extreme ultraviolet fluxes and magnetosonic Mach number are known major drivers of the shock location, while the influence of other possible drivers is less constrained or unknown such as crustal magnetic fields, solar wind dynamic pressure, or the Interplanetary Magnetic Field (IMF) intensity, and orientation. In this study, we compare the influence of the main drivers of the Martian shock location, based on several methods and published datasets from Mars Express (MEX) and Mars Atmosphere Volatile EvolutioN (MAVEN) missions. We include here the influence of the crustal fields, extreme ultraviolet fluxes, solar wind dynamic pressure, as well as (for MAVEN, thanks to magnetic field measurements) magnetosonic Mach number and Interplanetary Magnetic Field parameters (intensity and orientation angles). The bias due to the cross-correlations among the possible drivers is investigated with a partial correlations analysis. Several model selection methods (Akaike Information Criterion and Least Absolute Shrinkage Selection Operator regression) are also used to rank the relative importance of the physical parameters. We conclude that the major drivers of the shock location are extreme ultraviolet fluxes and magnetosonic Mach number, while crustal fields and solar wind dynamic pressure are secondary drivers at a similar level. The IMF orientation also plays a significant role, with larger distances for perpendicular shocks rather than parallel shocks.

Keywords: Akaike information criterion; LASSO; Mars; bow shock; solar wind.

Figure 1

Schematics of the possible drivers of the Martian shock location considered in the paper (see text for explanations). B _IMF refers to the interplanetary magnetic field (IMF) intensity, θ _bn to the angle between the normal of the bow shock (BS) and the IMF vector, θ _vn between the normal of the BS and the SW velocity vector, θ _bv between the solar wind (SW) velocity vector and the IMF vector. The signs + (with red color) and − (blue color) refer to the known or expected impact of the driver, with increased crustal fields and Extreme UltraViolet fluxes pushing the BS further from the planet, while increased SW dynamic pressure and magnetosonic mach number push it closer to the planet. The background figure is a drawing by Anastasia Grigoryeva.

Figure 2

R _TD terminator altitude of the Mars Atmosphere Volatile EvolutioN (MAVEN) (panels a to d) and Mars Express (panels e to g) shock crossings as a function of: the solar wind dynamic pressure (panels a and e), angular distance of the spacecraft from the strongest crustal source region (panels b and f), Extreme UltraViolet fluxes (panels c and g), magnetosonic Mach number (for MAVEN only, panel d).

Figure 3

Comparison of the influence of a number of physical parameters on the shock R _TD terminator altitude as measured by Mars Atmosphere Volatile EvolutioN (diamonds; dataset published by Gruesbeck et al. [2018] and Fang et al. [2017]) and Mars Express (stars; dataset published by Hall, Lester, Nichols, et al. [2016]). See text for details.

Figure 4

Schematic showing the complex inter‐correlations of a number of possible parameters of influence for the Mars Atmosphere Volatile EvolutioN (upper panel) and Mars Express (lower panel) shock terminator altitude. Blue and red lines correspond respectively to negative and positive Pearson linear correlation factors. The thickness of the lines is proportional to the Pearson correlation factor. Dashed lines represent non‐significant (p‐value above 5%) correlations. The background figure was adapted from a drawing by Anastasia Grigoryeva.

Figure 5

Residuals of the R _TD terminator altitude (in km) of the MAVEN (upper panels) and Mars Express (lower panels) shock crossings versus the possible drivers of the shock location, after removing the linear dependance versus the main drivers. The main drivers considered to calculate the residuals are the magnetosonic mach number (only available for MAVEN) and the Extreme Ultraviolet fluxes. Numbers above the panels correspond to p‐values associated with the linear partial correlations (where <10⁻⁵ refers to negligible p‐values).

Figure 6

R _TD terminator altitude (in km) of the MAVEN shock crossings in the Mars Sun Electric field coordinate system, as a function of the angle between the projection in the terminator plane of the crossing and of the IMF vector (90° points toward the convection electric field). Individual crossings are given by black dots. (Upper panel) The averaged binned profile (red line) is compared with a constant profile at the overall mean value (blue circle). The radial axis starts from 5000 km altitude to focus on the variability around the mean. (Lower panel) Averaged mean profiles are superimposed for only large (>60°, red line) or low (<30°) cone angle values of the Interplanetary Magnetic Field. Both panels correspond to direct analysis as performed by previous authors, but can be biased due to cross correlations.

Figure 7

(left) R _TD terminator altitude (in km) of the MAVEN shock crossings versus the sine of θ _bn the angle between the IMF direction and the shock normal; contour (thick red) lines of the occurrence frequency and a linear regression (dashed line) are added, as well as the Pearson correlation coefficient between both parameters. (right) Histogram of the number of crossings as a function of the ratio between the fast mode magnetosonic wave velocity and.$\sqrt{c_s^2+v_A^2}$.

Figure 8

Coefficients of the Lasso regression of the MAVEN (left) and MEX (right) drivers of the Martian shock extrapolated terminator altitude, as a function of the regularization parameter Lambda.