Impact of heat flux and suprathermal electrons on steady-state solar wind modelling with Icarus

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Abstract
Context. Suprathermal electrons significantly contribute to the heat flux in the solar wind (SW), making their treatment essential for improved SW modelling. The still-significant presence of suprathermal electron populations (halo and strahl), recently revealed by the Parker Solar Probe in the young SW, makes their involvement in energy transfer between plasma populations highly plausible. Aims. We aim to quantify the impact of suprathermal electrons on steady-state SW solutions by incorporating their contribution to thermal conduction in a macroscopic magneto-hydrodynamic (MHD) framework. Methods. The Icarus heliosphere modelling tool implemented within the MPI-AMRVAC framework was used to simulate a steady-state SW. The effect of heat flux carried by free-streaming electrons was included through a source term in the energy equation. We adopted the collisionless heat flux prescription of Hollweg (1974, J. Geophys. Res., 79, 3845), ordered by a structural parameter ( α H ) that has now been adjusted ( α H → α κ ) to incorporate the influence of kinetic processes that shape the electron velocity distribution. The new, still simplified version proposed here ( α κ ) accounts for not only the skewness determined by the strahl but also the Kappa suprathermal tails of halo populations. The SW is driven with the semi-empirical Wang-Sheeley-Arge (WSA) coronal model. Our computations use the WSA maps as the inner boundary (IB) in Icarus, but also apply modified-IB conditions to reduce interactions between fast and slow wind streams and to adjust the IB pressure (and hence temperature) to the data recently reported by the Parker Solar Probe (PSP). Results. Including collisionless heat flux can considerably reduce the rate of temperature decrease with heliocentric distance, preventing cooling as rapidly as that dictated by adiabatic expansion. As expected, heat is deposited primarily in lower-temperature regions, tending to level out the structured temperature(-velocity) distribution. Furthermore, heat flux contributes to accelerating the SW, exerting a less significant yet concrete influence on radial velocity compared to temperature variations. These effects persist for both the original WSA and modified-IB conditions and can be markedly amplified by an enhanced heat flux associated with suprathermal Kappa-distributed electrons. Consistent with PSP observations, higher pressure at the IB further enhances SW acceleration, magnifying the impact of the heat flux. Conclusions. The implications of collisionless heat flux depend, to a large extent, on the IB conditions, particularly on the pressure and bulk speed of the young SW. For example, a lower thermal pressure (or temperature) at the IB can be compensated for by a heat flux input. The improved agreement between modelled and observed radial profiles in fast SWs is consistent with the enhanced electron strahl that is more specific to higher bulk speeds.

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