Parker Solar Probe observations show that the young solar wind (inside roughly 0.5 au) from coronal holes, streamers, and low-Mach-number boundary layers can be largely reproduced by a spherically symmetric two-fluid isopoly model driven by proton and electron thermal pressure, but the model leaves residual fast-wind acceleration unexplained and its heating is manually tuned rather than mechanistic. The open problem is to quantitatively establish the role of Alfvén waves — the leading candidate for the missing energization — in proton heating and direct wave-pressure acceleration of each source class, in particular whether they explain the coronal-hole-wind proton heating (high initial temperature with slow decrease) and the additional coronal-hole-wind acceleration beyond about 40 solar radii that the model cannot produce. Later work has quantified pieces (slow-wind Alfvénic turbulence heating rates, coronal wave Poynting fluxes, per-class turbulence anisotropy) but has not established this quantitative per-source-class attribution.

Background

The solar wind is the continuous outflow of ionized plasma from the solar corona that fills interplanetary space. A long-standing problem of heliospheric physics is what supplies the energy that heats the corona and accelerates the wind to its observed speeds of roughly 300–800 km/s. The Parker Solar Probe (PSP) spacecraft, launched in 2018, has repeatedly sampled this plasma as close as about 13 solar radii (RSR_S) from the Sun, i.e. the 'young' solar wind soon after it leaves the corona, using its FIELDS magnetometers and SWEAP particle instruments.

The solar wind originates from distinct coronal source regions: coronal holes (CH), which are regions of open, unipolar magnetic field with low density in extreme-ultraviolet images and the source of fast wind; helmet streamers, closed-field arcades whose cusps release slow, dense wind; and the more recently identified low-Mach-number boundary layers (LMBLs), the inner boundaries of coronal holes where the radial Alfvén Mach number (the ratio of wind speed to the Alfvén speed, the characteristic speed of magnetohydrodynamic waves) is locally reduced. Earlier modeling traditions represent the wind with polytropic fluids, in which the temperature declines as a power law of density; a common two-piece 'isopoly' prescription keeps the temperature isothermal near the Sun and polytropic farther out, with the transition radius a free parameter.

Jiao et al. (2024, ApJL 975 L41) analyzed the first 17 PSP encounters, classified wind intervals into CH, streamer, and LMBL classes using in-situ thresholds, and fitted a two-fluid (separate proton and electron enthalpy) isopoly model with spherical symmetry. They found that proton and electron thermal pressures reproduce most observed speed profiles, with the difference in proton pressure primarily responsible for the difference in wind speed between classes, and obtained sonic critical points (where the flow speed equals the sound speed) at about 3.6–7.3 RSR_S. However, the model's initial temperatures and isothermal transition radii are set manually, the CH wind shows additional acceleration beyond about 40 RSR_S that the model cannot produce, and the proton heating demanded for CH wind (high initial temperature, slowly decreasing) lacks a mechanism.

Alfvén waves — transverse, incompressible oscillations of the magnetic field and plasma that propagate at the Alfvén speed — are abundant in CH wind and can both heat protons (through turbulent dissipation) and push the wind directly (through wave-pressure force). An energy-budget framework by Halekas et al. (2023) quantified steady-state contributions of proton pressure, the ambipolar electric field (the electric field set up by electron–proton separation, which transmits electron pressure to the ions), and wave energy to proton acceleration between 13.3 and about 100 RSR_S, finding that waves and the electric field together carry enough energy for both fast and slow wind; but that analysis is interval-averaged, not resolved by source class, and not embedded in a self-consistent model. The question left open is therefore the quantitative, mechanistic attribution: how much of the proton heating and of the direct acceleration of each source class is actually supplied by Alfvén waves rather than thermal pressure and the electric field, and whether a model that couples wave propagation and dissipation to the plasma can reproduce the observed per-class profiles without manually tuned heating.

Problem Statement

For the young solar wind measured by Parker Solar Probe, quantitatively establish the role of Alfvén waves in heating and accelerating the wind from the three identified source classes (coronal-hole interiors, streamers, and low-Mach-number boundary layers). Concretely, determine the quantitative contribution of Alfvén-wave energy to proton heating and to direct wave-pressure acceleration in each source class, and establish whether — and by how much — Alfvén waves account for the coronal-hole-wind proton heating (high initial temperature with slow decrease) and the additional coronal-hole-wind acceleration beyond about 40 solar radii that the two-fluid thermal-pressure model of Jiao et al. (2024) cannot produce. A solution must provide this quantitative per-class attribution for all three source classes, derived from a self-consistent model that couples wave propagation and dissipation to the plasma and reproduces the observed speed and proton-temperature profiles without manually tuned heating; answering only the two coronal-hole questions is not sufficient. The observational framework for this attribution is the proton-acceleration energy budget of Halekas et al. (2023), which partitions the required energy among proton thermal pressure, electron thermal pressure acting through the ambipolar electric field, and Alfvénic wave energy. The mechanistic attribution — how much of each class's proton heating and direct acceleration is actually supplied by Alfvén waves rather than by thermal pressure and the electric field — remains quantitatively open. The source paper further notes that its model's initial temperatures and isothermal transition radii are set manually to best fit the data, and suggests that the role of the Alfvén waves is a potentially helpful point to consider in further refinement of the model.

References

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