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Traveling solar-wind bulk-velocity fluctuations and their effects on electron heating in the inner heliosphere

Ambient plasma electrons undergo strong heating in regions associated with compressive traveling interplanetary solar-wind bulk-velocity jumps due to their specific interactions with the jump-inherent electric fields. After thermalization of this energy gain per shock passage through the operation of the Buneman instability, strong electron heating occurs that substantially influences the radial electron temperature profile. We describe the reduction of the jump amplitude due to energy expended by the traveling jump structure. We consider three effects; namely energy loss due to heating of electrons, energy loss due to work done against the pick-up-ion pressure gradient, and an energy gain due to nonlinear jump steepening. Taking these effects into account, we show that the decrease in jump amplitude with solar distance is more pronounced when the initial jump amplitude is higher in the inner solar system. Independent of the initial jump amplitude, it eventually decreases with increasing distance to a value of the order of $ΔU/U\simeq 0.1$ at the position of the heliospheric termination shock, where $ΔU$ is the jump amplitude, and $U$ is the average solar-wind bulk velocity.The electron temperature, on the other hand, is strongly correlated with the initial jump amplitude, leading to electron temperatures between 6000 K and 20 000 K at distances beyond 50 AU. We compare our results with in-situ measurements of the electron-core temperature from the Ulysses spacecraft in the plane of the ecliptic for $1.5\, \mathrm{AU}\leq r \leq 5\,\mathrm{AU}$, where $r$ is the distance from the Sun. We find a very good agreement between our results and these observations, which corroborates our extrapolated predictions beyond $r=5\,\mathrm{AU}$.