The question is in the title.

A bit of background info: the escape velocity at the photosphere of the Sun is ~ 620 km/s, but the mean speed of the solar plasma there (inferred from the temperature) is ~ 150 km/s. Yet not only is the solar wind able to escape the surface, reaching out to ~ 100 a.u., but it's speed there remains relatively high and constant (as Voyager 2 shows, until ~ 85 a.u. the speed is about 400 km/s: enter image description here

So basically it seems the wind gets almost twice the energy needed to escape (the half of which is spent to actually escape, and the other half remains in the form of kinetic energy) "out of nowhere".

I have read that the extra energy is supposed to somehow come from the magnetic field. How exactly? And why at the same time it does not seem that the magnetic field of interstellar plasma is attenuated because of that?

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    $\begingroup$ What have you read? The issue of the solar wind acceleration is unsolved. There are lots of ways that energy can be transported by and stored in magnetic fields. Are you looking for descriptions of Alfven waves and magneto-acoustic waves? $\endgroup$ – Rob Jeffries Nov 30 '17 at 12:21
  • $\begingroup$ I'm looking for an explanation easy enough to follow. If "the issue is unsolved" is your answer, OK, that sounds legit. $\endgroup$ – Dusty Jim Nov 30 '17 at 13:25
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    $\begingroup$ As Rob correctly points out, this is a long-standing issue and there is a new mission called Parker Solar Probe (formerly Solar Probe Plus) that is intended to try and address this issue. $\endgroup$ – honeste_vivere Nov 30 '17 at 15:14

Full understanding for this phenomenon has still not been understood. However, we do have a good idea. It is correct that magnetic field plays a major role in the phenomenon and this part is covered in magneto-hydrodynamics. However, you should start off with a more simple case in which magnetic field in absent and you can consider the whole space to be isothermal. In this case, there are two competing forces The first is the gravitation pulling the gas inwards and the second one is the density gradient which decreases as one goes outwards (mass is constant and volume is increasing). This creates an outwards push, so to say. The thing you are looking for is called the Parker's critical solution for the velocity structure of stellar winds. Note that my assumption for isothermal environment is wrong but could be approximated to a good distance in certain stars because heating takes place due to radiation pressure. However, you can also prove that if there is no energy or momentum deposition in the wind by anything, then the gas will not escape. The final equation for the velocity structure in isothermal case turns out to be (after taking some symmetry approximations) are:-

formula for velocity of winds

The proof for polytropic winds also goes along the same lines.

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  • $\begingroup$ So essentially it is the excess pressure from "below" that counteracts the gravitational attraction? $\endgroup$ – Dusty Jim Nov 30 '17 at 13:30
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    $\begingroup$ "heating takes place due to radiation pressure"? The question is about the solar wind; which is not radiation-driven. $\endgroup$ – Rob Jeffries Nov 30 '17 at 13:50
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    $\begingroup$ @DustyJim Yeah, that and the temperature gradient, if you are considering any. The particles at more temperature has more excitation and hence have more collisions on an average. $\endgroup$ – Rishabh Jain Nov 30 '17 at 17:28
  • $\begingroup$ @RobJeffries As I clearly mentioned, the approximation is valid only in certain stars. As it turns out, the radiative processes involved may be close to isothermal. I was just stating the case for isothermal. It can also be extended to arbitrary momentum and energy deposition but it is difficult to solve analytically. $\endgroup$ – Rishabh Jain Nov 30 '17 at 17:33

Just imagine the sun as continuously emitting this radiation. Thus the previous emitted radiation has more radiation behind it to provide a force.

It doesn't matter that the escape velocity is slower because the radiation force acting on it is greater than the gravitational force. Wether this force come from photons or actual particles it doesn't matter. The point is, the forces don't sum to a negative (relative to particles velocity vector) or even zero, hence 400km/s...

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