Electrostatic Solitary Waves in the Earth's Bow Shock: Nature, Properties, Lifetimes, and Origin

We present a statistical analysis of >2,100 bipolar electrostatic solitary waves (ESWs) collected from 10 quasi-perpendicular Earth's bow shock crossings by Magnetospheric Multiscale spacecraft. We developed and implemented a correction procedure for reconstruction of actual electric fields, velocities, and other properties of ESW, whose spatial scales are typically comparable with or smaller than spatial distance between voltage-sensitive probes. We found that more than 95% of the ESW are of negative polarity with amplitudes typically below a few Volts and 0.1T_e (5–30 V or 0.1–0.3T_e for a few percent of ESW), spatial scales of 10–100 m or λ_D–10λ_D, and velocities from a few tens to a few hundred km/s that is on the order of local ion-acoustic speed. The spatial scales of ESW are correlated with local Debye length λ_D. The ESW have electric fields generally oblique to magnetic field and they propagate highly oblique to shock normal N; more than 80% of ESW propagate within 30° of the shock plane LM. In the shock plane, ESW typically propagates within a few tens of degrees of local magnetic field projection B_LM and preferentially opposite to N × B_LM. We argue that the ESW of negative polarity are ion holes produced by ion-ion streaming instabilities. We estimate ion hole lifetimes to be 10–100 ms, or 1–10 km in terms of traveling distance. The revealed statistical properties will be useful for quantitative studies of electron thermalization in the Earth's bow shock.