Radial dependence of temperature of solar wind?

Question

How does the temperature of the solar wind plasma depend upon radial distance from the Sun?

Answer 1

The only species of which we can actually measure a temperature are the electrons, protons, and alpha-particles. Parker Solar Probe (PSP) measurements show that the proton core temperature does not change isotropically with increasing radial distance [e.g., Huang et al., [2020]]. The parallel, perpendicular, and total temperatures change as:

• $T_{\parallel, p} \propto r^{-0.98}$
• $T_{\perp, p} \propto r^{-0.48}$
• $T_{total, p} \propto r^{-1.21}$

in what is called fast solar wind (i.e., $V_{sw}$ > 450 km/s) while in slow solar wind (i.e., $V_{sw}$ $\leq$ 450 km/s), these go as:

• $T_{\parallel, p} \propto r^{-0.99}$
• $T_{\perp, p} \propto r^{-1.94}$
• $T_{total, p} \propto r^{-1.34}$

The solar wind electrons are comprised of a cold, dense core, a hot, tenuous halo, and a magnetic field-aligned, anti-sunward beam called the strahl [e.g., Wilson et al., [2019]]. The total electron temperature of the entire velocity distribution function (VDF) goes as $T_{total, e} \propto r^{-0.59}$ in the slow wind and $T_{total, e} \propto r^{-0.31}$ in the fast wind [e.g., Maksimovic et al., [2020]; Stverak et al., [2015]]. Technically, the power-law index for $T_{total, e}$ is a function of $V_{sw}$, but these are just meant to illustrate that the radial dependence of temperature for electrons is not fixed.

The core and suprathermal (i.e., both halo and strahl combined) electrons tend to have very different slopes than each other and the total electron temperature. The core tends to go as $T_{total, ec} \propto r^{-0.74}$ and the halo as $T_{total, es} \propto r^{-0.06}$ to $r^{-0.03}$ within ~100 solar radii of the Sun [e.g., Moncuquet et al., [2020]]. When viewed over larger radial distances, these go to $T_{total, ec} \propto r^{-0.5}$($r^{-0.6}$) and $T_{total, eh} \propto r^{-0.5}$($r^{-0.3}$) for slow(fast) solar wind [e.g., Stverak et al., [2008]].

In fact, things get even more interesting. The power-law index for all particle species and subcomponents can change with radial distance as well. The point being, the solar wind is not controlled by typical thermodynamic assumptions (i.e., because the solar wind is a non-equilibrium, ionized kinetic gas called a plasma).

I discuss the limitatiions of typical thermodynamic assumptions as well at https://physics.stackexchange.com/a/527527/59023.