JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 93, NO. All, PAGES 12,923-12,931, NOVEMBER 1, 1988 ElectronHeatingand the PotentialJump Across Fast Mode Shocks STEVEN J. SCHWARTZ Astronomer Unit, School of Mathematical Sciences, Queen Murat Gollege, London MICHELLE F. THOMSEN, S. J. BAME, AND JOHN STANSBEERY Los Alamos National Laborator•t, Los Alamos, New Mexico The electron heating and the electrostatic potential jump across collisionless shocks play an important, if not dominant, role in the electron momentum balance. We present here a survey of these two quantities over a large sample of fast mode collisionless shocks. Results for estimates of the electrostatic potential (as measured in the de Hoffmann-Tellerreference frame) based on an estimate of the jump in electron enthalpy and on Liouville's theorem correlate well with each other, although the latter are consistently higher, perhaps due to irreversible processesaffecting the shock electron dynamics. The size of the potential does not appear to be strongly controlled by any of the various upstreamparameters (shock geometry, Mach number, etc.) and represents approximately 12% of the incident ion ram kinetic energy, this figure showing some tendency to decrease with increasing Mach number. The electron contributionto the total (ion plus electron) heating across the shockvariessystematically from 50% or more at subcritical Mach numbersto lessthan 10% at the highest Mach number shocks in the sample. The electron heating showsonly modest, but systematic, departure from that which would result by preserving the ratio of the perpendicular temperature to the magnetic field strength. 1. INTRODUCTION The electron dynamics and heating at collisionless shocks have been subjects of interest for some time. However, the dominant processes and parameters controlling the electron heating have not been firmly established. A wide variety of instabilities and wave modes have been suggested as im- portant thermalizers (see, for example, Wu et al. [1984]), while reversible particle dynamics in the macroscopicquasi- steady fieldsof the shock [Feldman et al., 1983a, b] are prob- ably the dominant processes responsible for the shape (and therefore the heating) of the electrondistribution, as ele- gantly demonstratedin the detailed analysisof Scudder et al. [1986c]. Other studies [Feldman et al., 1983c; Thomsen et al., 1987a]of fast mode shock crossings have revealed that the electron heating correlates well with the incident ram energy (mostof which the fast shock mustthermalize [e.g., Schwartz el al., 1987,Table2]) but does not seem to be con- trolled by any of the other traditional upstream parameters associated with the shock (e.g., the angle 8Bn• between the upstream field and shock normal, the upstream fast magne- tosonic mach number M,•8•, the upstream plasma beta or the upstream electron to ion temperature ratio T,•/Ti•). In the present work we complement these studies by (1) utilizing a large sample of fast mode shocks including both low Mach number "subcritical" interplanetary shocks and high Mach number planetary bow shocks encountered in the outer heliosphere and (2) exploiting techniques used previ- ouslyat slow modeshocks in the geomagnetic tail [Schwartz et al., 1987]to estimate the cross-shock potential. We shall see that the distinction between subcritical and supercritical shocks is considerably less obvious in the data than it is in theoretical treatments. We concern ourselves here with the Copyright 1988 by the American Geophysical Union. Paper number 88JA03329. 0148-0227/88/88JA-03329505.00 potential as seen in the de Hoffmann-Teller frame, in which the shockis at rest and the bulk flow is field-aligned in both the upstream and downstream asymptotic states. The only nonvanishingdc electric field in this frame is the thermo- electric field, which is directed along the shock normal and confined to the shock layer itself. One benefit of working in this frame is that it obviates the need to look in detail at particle trajectories within the shock layer, provided, as is the case for most collisionlessshocks, that the electrons can be regarded as completely magnetized, and that the field profiles allow the electrons in question to traverse the shock (seeScudder et al. [1986c] for a discussion of these aspects of electron trajectories). 2. DATA SET Our data represent 66 crossingsof the terrestrial bow shock and 14 interplanetary shocks observed by the var- ious ISEE spacecraft between 1977 and 1979, along with one crossing of the Jovian bow shock [Scudder et al., 1981; Moses et al., 1985]and oneof the Uranian bowshock [Bage- hal et al., 1987] made by the Voyager spacecraft.Many of these shockshave already been discussed in previous studies [e.g.,Feldman et al., 1983a, b,c; Thomsen et al., 1987a].The basic measurementsinvolve magnetic field information, ion bulk parameters, and electron bulk parameters along with the energy associated with the edge feature of the down- stream flat-topped electron distributions in cases where this latter feature was apparent. In some cases,notably among the interplanetary shocks, the flat top is considerably less- pronounced or absent. In a few other cases this detail of the electron data was not readily available. Most of these edge velocities were based on the Los Alamos fast plasmaexperiment (seeFeldman et al. [1983a] for a more detailed description of the instrument and as- sociated observations of electron distributions at the bow shock). Of the experiment's many characteristics, the wide field of view (4-55 ø with respect to the spin plane) intro- duces the largest uncertainty in relating the measured edge 12,923