Electron Heat Flux and Whistler Instability in the Earth's Magnetosheath

Abstract

Despite heat flux's role in regulating energy conversion in collisionless plasmas, its properties and evolution in the magnetosheath downstream of the Earth's bow shock are scarcely explored. We use MMS in situ measurements to quantify and characterize the electron heat flux in the magnetosheath. We find that the heat flux is shaped by the magnetosheath magnetic field as it drapes around the magnetosphere. While it is affected by solar wind upstream conditions and increases with magnetic field strength, it is not substantially changed by local magnetosheath processes. Also, the heat flux is limited by whistler instability thresholds.

Figures (3)

• Figure 1: Three-minute interval from the MSH. MMS measurements of the magnetic field $\boldsymbol{B}$ (a) and the electron moments: (b) density $n_e$, (c) bulk velocity $\bm{V}_e$, (d) temperatures parallel ($T_{e\parallel}$) and perpendicular ($T_{e\perp}$) to $\boldsymbol{B}$, (e) heat flux $\boldsymbol{q}_e$ in field-aligned components. (f) and (g) show 2D eVDFs $f_e(v_\parallel,v_{\perp1})$ (averaged over 1 second) taken from 13:19:35 and 13:20:33, respectively, where $v_\parallel=\bm{v}\cdot \bm{\hat{b}}$ and $v_{\perp1}=\bm{v}\cdot (\bm{\hat{b}}\times(\bm{\hat{e}}\times\bm{\hat{b}}))$, and $\bm{\hat{b}}=\bm{B}/B$ and $\bm{\hat{e}}=\bm{E}/E$ are the magnetic and electric field directions, respectively.
• Figure 2: Electron heat flux across the MSH. (a) MMS location in each 3-minute burst interval in the GSE $XY$ plane ($Z_{\rm GSE}{\sim}(-7,-5)R_{\rm E}$). Color indicates $\langle q_{e}\rangle_{\rm 3min}$ and arrows the projected $\langle\bm{q}_e\rangle_{\rm 3min}$. Orbits are labeled chronologically 1-14 with blue numbers. (b) $\langle q_{e}\rangle_{\rm 3min}$ versus $B_{\rm MSH}$; the color scale shows $B_{\rm SW}$. Black curve shows the fit $q_e\approx 3\times10^{-4}B^{1.3}$ based on the orbit-average values (black crosses). Red circles show approximate values of $B$ and $q_e$ from the SW, obtained by reading off the axes in Fig. 13 in Scime+ 1994 (S94) scime_regulation_1994. (c) Evolution of $\langle q_{e}\rangle_{\rm 3min}$ (normalized to the mean in each orbit) with the fractional distance $d_{\rm MP-BS}$. Solid curve shows the median in bins of width 0.2, and dashed curves show the $25^{\rm th}$ and $75^{\rm th}$ percentiles in the bins. Individual orbits are shown in red. (d) Overall $q_{e}$ in the MSH; median value in solid, $25^{\rm th}$ and $75^{\rm th}$ percentiles in dashed and dash-dotted. Dotted line indicates the estimated uncertainty $0.01\,\rm mW/m^2$ (see Supplementary material). (e) GSE components of $\bm{q}_e$. (f) alignment of $\hat{\bm{q}}_e=\bm{q}_e/q_e$ with the local magnetic field direction $\hat{\bm b}_{\rm MSH}=\bm{B}_{\rm MSH}/B_{\rm MSH}$ (black) and the upstream solar wind magnetic field direction $\hat{\bm b}_{\rm SW}=\bm{B}_{\rm SW}/B_{\rm SW}$ (red).
• Figure 3: Whistler heat flux instabilities. (a) 2D histogram of $|q_{e\parallel}|/q_{\rm max}$ and $\beta_{e\parallel}$ with each count corresponding to one $30\,\rm ms$ electron measurement. (b) Whistler wave occurrence in the $\beta_{e\parallel}-|q_{e\parallel}|/q_{\rm max}$ parameter space. We show two whistler instability thresholds: the parallel heat flux instability (solid: Gary+ 1994 gary_whistler_1994: $|q_{e\parallel}|/q_{\rm max}=0.10\beta_{e\parallel}^{-0.90}$ for a growth rate $\gamma=10^{-3}\Omega_p$, where $\Omega_p$ is the angular proton cyclotron frequency) and the oblique heat flux fan instability (dashed: Vasko+ 2019 vasko_whistler_2019: $|q_{e\parallel}|/q_{\rm max}=0.20\left[\beta_{e\parallel}+0.25\right]^{-0.50}$). (c) Poynting flux of low-frequency whistler waves ($f/f_{{\rm c}e}<0.3$) versus $q_{e\parallel}/q_{\rm max}$. (d) Same as (c) but for high-frequency ($f/f_{{\rm c}e}>0.3$) whistler waves.