⊛ Several observations support idea that Alfvén waves like motion in the low corona carry an energy flux sufficient to power the solar wind.
⊛ AWs energize the solar wind via two mechanisms: heating and work. Heating involves the cascade and dissipation of AW energy. While, work involves work done by the AW pressure force, which directly accelerates plasma away from the Sun.
⊛ Perez and colleagues in their recent paper now examined which Mechanism is more effective in energizing solar wind.
⊛ They found that heating is more efficient than work in energizing solar wind. As it transfers 50-70% of AW power at coronal base to solar wind.
⊛ The reason heating mechanism is in range of 50-70% is AW power dissipates within radius of Coronal base and Alfvén critical point.
Following Parker’s prediction that the Sun emits a supersonic wind, a number of studies attempted to model the solar wind as a spherically symmetric outflow powered by the outward conduction of heat from a hot coronal base. Although these studies obtained supersonic wind solutions, they were unable to reproduce the large outflow velocities measured in the fast solar wind near Earth (700 − 800 km s¯1), and they did not explain the origin of the high coronal temperatures (∼ 106 K) upon which the models were based.
These shortcomings led a number of authors to conjecture that the solar wind is powered to a large extent by an energy flux carried by waves. Several observations support this idea, including in situ measurements of large-amplitude, outward-propagating Alfvén waves (AWs) in the interplanetary medium and remote observations of AW-like motions in the low corona that carry an energy flux sufficient to power the solar wind.
These observations have stimulated numerous theoretical investigations of how AWs might heat and accelerate the solar wind. In many of these models, a substantial fraction of the Sun’s AW energy flux is transferred to solar-wind particles by some form of dissipation. Because photospheric motions primarily launch large-wavelength AWs, and because large-wavelength AWs are virtually dissipationless, the AWs are unable to transfer their energy to the plasma near the Sun unless they become turbulent. Turbulence dramatically enhances the rate of AW dissipation because it causes AW energy to cascade from large wavelengths to small wavelengths where dissipation is rapid. One of the dominant nonlinearities that gives rise to AW turbulence is the interaction between counter-propgating AWs. Because the Sun launches only outward-propagating waves, solar-wind models that invoke this nonlinearity require some source of inward-propagating AWs. One such source is AW reflection arising from the radial variation in the Alfvén speed. Direct numerical simulations of reflection-driven AW turbulence (RDAWT) in a fast-solar-wind stream emanating from a coronal hole have shown that AW turbulence initiated by wave reflections can drive a vigorous turbulent cascade. The turbulent dissipation rates in the simulations of Perez & Chandran (2013) and Chandran & Perez (2019) are consistent with the turbulent heating rates in solar-wind models that rely on RDAWT, which have proven quite successful at explaining solar-wind observations.
In addition to solar-wind heating via the cascade and dissipation of AW energy, AWs energize the solar wind through the work done by the AW pressure force, which directly accelerates plasma away from the Sun. The relative importance of AW heating and AW work, however, is not well understood. Now, Jean Perez and colleagues used direct numerical simulations of reflection-driven AW turbulence (RDAWT) to determine the fraction of the AW power at the coronal base (PAWb) that is transferred to the solar wind via turbulent dissipation between the coronal base (rb) and radius r, denoted χH(r), and the fraction that is transferred via work, χW(r).
Their simulations solve for the evolution of transverse, non-compressive fluctuations in a fixed background solar wind whose density, magnetic-field strength, and outflow-velocity profiles are chosen to emulate a fast-solar-wind stream emanating from a coronal hole. They found that heating from the cascade and dissipation of AW fluctuations between radius of coronal base (rb) and the Alfvén critical point (rA) transfers between 50% and 70% of PAWb to the solar wind, whereas work in this same region transfers between 15% and 30% of PAWb to the solar wind. The variation in these numbers arises from the different photospheric boundary conditions imposed in our different numerical simulations.
“We found that heating is more effective than work in transferring energy to solar wind.“— told Perez, first author of the study.
The reason that χH(rA) is in the range of 50% to 70% is that a moderate fraction of the local AW power dissipates within each Alfvén speed scale height, and there are a few Alfvén speed scale heights between rb and rA. The reason that χW(rA) is small compared to 1 is that, Alfvén speed is greater than solar wind outflow velocity, (i.e. vA > U) at r < rA, so AWs in this sub-Alfvénic region are in an approximate sense speeding through a quasistationary background without doing much work. Work becomes relatively more efficient at transferring AW energy to the particles at r > rA, where vA < U and the AWs are in an approximate sense “stuck to the plasma.” However, because most of the Sun’s AW power dissipates via heating before the AWs reach rA, the total rate at which work transfers AW energy to the plasma at r > rA is a small fraction of PAWb. Although only a small fraction of PAWb survives to reach rA, the average proton magnetic moment increases robustly at r > rA (assuming that a substantial fraction of the turbulent heating rate goes into perpendicular proton heating at these radii), because heating becomes more effective at producing magnetic moment in regions of weaker magnetic field.
They concluded that the accuracy of their results is limited by their neglect of compressive fluctuations, which enhance the dissipation of AW energy via “AW phase mixing”. Plasma compressibility further enhances the rate of AW dissipation via parametric decay. Three-dimensional compressible MHD simulations of the turbulent solar wind from r = rb out to r > rA, could lead to improved estimates of χH(r) and χW(r).
Featured image: χH(r) (solid) and χW(r) (dashed) are the fractions of the Sun’s AW power injected at the base that are transferred to solar-wind particles via heating and work, respectively, between the coronal base and heliocentric distance r. PAW/PAWb (dashed-dotted) is the fraction of the power that remains at each heliocentric distance r. These fractions are evaluated for Run 1, Run 2, and Run 3 using the expressions given in Section 2.1 in their paper and for the CH09 analytic model (lower-right panel) using the expressions given in Section 3.2 in their paper. All four panels are computed using the n(r), B0(r), and U(r) profiles in (section 3.2) through (section 3.4). The green dotted lines represent the sum of the three fractions, which due to energy conservation equal one in steady state. Small deviations from one in the numerical simulations are due primarily to averaging over a finite number of realizations rather than a full ensemble representing a true statistical state. © Perez et al.
Reference: Jean C. Perez, Benjamin D. G. Chandran, Kristopher G. Klein, Mihailo M. Martinović, “How Alfvén waves energize the solar wind: heat vs work”, ArXiv, pp. 1-15, 2021. https://arxiv.org/abs/2103.09365
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