# How can solar wind be supersonic?

I was reading this Wikipedia article on Heliosphere and was confused a bit:

this supersonic wind must slow down to meet the gases in the interstellar medium

How can sonic speeds exist in space? The space is almost vacuum and sound cannot exist there. Also, isn't the heliosphere about electromagnetic wind, not atomic wind?

• Space is indeed almost vacuum, but that's the keyword. Also, can you clarify what you mean by an electromagnetic wind? – Nathan Tuggy Oct 24 '15 at 23:19
• This is actually pretty tricky to explain. See Eugene Parker’s model of hydrodynamic expansion and the solar wind theory (PDF), or Justin C. Kasper's (CfA) The Solar Wind (PDF) presentation for the 2012 Heliophysics Summer School. The latter is the most intuitive way of explaining it that I've come across. And no, solar wind is not merely EM radiation, you're probably confusing it with radiation pressure. Solar wind is a charged particles flux. – TildalWave Oct 24 '15 at 23:33
• @NathanTuggy I mean that Sun emits in space mostly electrons and protons, not heavy particles like Helium, Hydrogen. Am I wrong? – yanpas Oct 24 '15 at 23:39
• @yanpas: Hydrogen is only fractionally heavier than a single proton, you know. About .05%, give or take. – Nathan Tuggy Oct 24 '15 at 23:41

The speed of sound in space has multiple meanings because space is not a vacuum (though the number density of Earth's magnetosphere can be ~6-12 orders of magnitude more tenuous than the best vacuums produced in labs), it is full of ionized particles, neutral and charged dust.

In the interplanetary medium or IPM, there are five relevant speeds that can all be considered a type of sound in a way, because each are related to the speed of information transfer in the medium.

# The "speeds of sound"

## Sound Speed

Since a plasma can act collectively like a fluid, it can have a sound speed in the classic form of $C_{s}^{2} = \partial P/\partial \rho$, where $P$ is the thermal pressure and $\rho$ is the mass density. In a plasma, this takes the slightly altered form of: $$C_{s}^{2} = \frac{ k_{B} \left( Z_{i} \ \gamma_{e} \ T_{e} + \gamma_{i} \ T_{i} \right) }{ m_{i} + m_{e} }$$ where $k_{B}$ is Boltzmann's constant, $Z_{s}$ is the charge state of species $s$, $\gamma_{s}$ is the adiabatic or polytrope index of species $s$, $m_{s}$ is the mass of species $s$, and $T_{s}$ is the average temperature of species $s$. In a tenuous plasma, like that found in the IPM, it is often assumed that $\gamma_{e}$ = 1 (i.e., isothermal) and $\gamma_{i}$ = 2 or 3, or that $\gamma_{e}$ = 1 and $T_{e} \gg T_{i}$. The above form of the sound speed is known as the ion-acoustic sound speed because it is the phase speed at which linear ion-acoustic waves propagate. Thus, $C_{s}$ is a legitimate type of sound speed in space.

## Alfvén Speed

The Alfvén speed is defined as: $$V_{A} = \frac{ B_{o} }{ \sqrt{ \mu_{o} \ \rho } }$$ where $B_{o}$ is the magnitude of quasi-static, ambient magnetic field, $\mu_{o}$ is the permeability of free space, and $\rho$ is the plasma mass density (which is roughly equivalent to the ion mass density unless it's a pair plasma). This speed is typically associated with transverse Alfvén waves, but the speed is relevant to information transfer in plasmas.

## Magnetized Sound Waves

In a magnetized fluid like a plasma, there are fluctuations that are compressive whereby they compress the magnetic field in phase with the density, called magnetosonic or fast mode waves. The phase speed for a fast mode wave is given by: $$2 \ V_{f}^{2} = \left( C_{s}^{2} + V_{A}^{2} \right) + \sqrt{ \left( C_{s}^{2} + V_{A}^{2} \right)^{2} + 4 \ C_{s}^{2} \ V_{A}^{2} \ \sin^{2}{\theta} }$$ where $\theta$ is the angle of propagation with respect to $\mathbf{B}_{o}$.

## Thermal Speeds

There are also the thermal speeds one often thinks about in regards to gases. In a plasma, there is a thermal speed for each particle species, e.g., electrons and ions. The one-dimensional rms speed is given by: $$V_{Ts}^{rms} = \sqrt{\frac{ k_{B} \ T_{s} }{ m_{s} }}$$ where $s$ can be $e$(electrons) or $i$(ions). The three dimensional most probable speed, which is given by: $$V_{Ts}^{mps} = \sqrt{\frac{ 2 \ k_{B} \ T_{s} }{ m_{s} }}$$

The reason the solar wind becomes supersonic is actually a bit of a mystery and a large part of the motivation for the Solar Probe Plus mission. One of the original theories was that the change in the ratio of the $B_{o}/n_{o}$ with increasing distance from the solar surface caused an effect similar to that of a de Laval nozzle. There are several other aspects that complicate things (i.e., multiple non-Maxwellian particle distributions), but more recently, Alfvén waves have been proposed as the possible acceleration mechanism.