<p>What exactly did you google for? I googled for 'laval nozzle solar wind' and got many detailed references. Just take the <a href="http://www.physics.usyd.edu.au/%7Ecairns/teaching/2010/lecture8_2010.pdf" rel="nofollow noreferrer">first reference</a> that comes up and in Sect.8.2. the analogy between Parker's solar wind equation and the Laval nozzle equation is explained in detail.</p>
<p>However, as you are half implying already, concepts of thermodynamics are at the heart of this theory. But rather than going into details of the equations here, let me illustrate the situation through a fictitious analogy:</p>
<p>assume an outside monitoring device at the International Space Station (ISS) detects an airstream coming from station. Let's call it the ISS-wind. Now scientists are very puzzled as to the nature of the wind and develop all kinds of theories how the outside walls of the station could produce and accelerate this amount of air. It does not occur to them that the air is simply coming from the inside through a leak.</p>
<p>The situation is potentially the same for the solar wind. The point is that the photosphere is slightly leaky everywhere (in some regions more, in others less) and a few high energy particles (representing the gravitational potential energy of the Sun) are coming through from below the photosphere. And it is obvious that such a scenario can not be represented by a theory based on thermodynamics, as the concept of temperature alone does not allow to correctly model the energy distribution function over an energy range from less than 1 eV to about 1 keV.</p>

CC BY-SA 4.0
2022-07-31T07:25:29.540Z
I didn't downvote, but I think that this answer could be more helpful if you actually "went into details of the equations". I don't really get the point of your analogies with the ISS and of your argument about the solar wind.
Prallax
CC BY-SA 4.0
2022-07-31T08:51:47.313Z
@Prallax The analogy is explained in the last paragraph. I don't know how I could make it even clearer. The point is that the equations in the relevant references are based on the assumption of LTE and thus are unable to correctly deal with non-Maxwellian velocity distribution functions.
Thomas
CC BY-SA 4.0
2022-05-03T21:43:15.077Z
2022-05-03T21:43:15.077Z
Thomas
<p>Seeing <a href="https://astronomy.stackexchange.com/q/49233/7982">What determines the speed of a star&#39;s solar wind?</a> I'm having flashbacks from undergraduate days where the professor started their lecture on solar wind by writing something that they called the <a href="https://en.wikipedia.org/wiki/De_Laval_nozzle" rel="nofollow noreferrer">de Laval nozzle equation</a> on the board.</p>
<p>I don't now remember <em>which</em> equation it was, but I have a hunch it might have been related to mass flow per unit area and it was certainly more complicated than <span class="math-container">$1/r^2$</span>.</p>
<p>That certainly shows up in google searches but so far none of the answers there mention it, and instead of discussing expansion/rarefaction mostly just use <span class="math-container">$k_B T$</span>.</p>
<p>So I'd like to ask:</p>
<p><strong>Question:</strong> Can stars be thought of as nozzles? How important is thermodynamics and the de Laval nozzle equation for understanding the speed of the solar wind vs distance?</p>

CC BY-SA 4.0
2024-01-17T14:46:47.300Z
Perhaps try https://physics.stackexchange.com/a/612590/59023 or https://physics.stackexchange.com/a/524215/59023?
honeste_vivere
<astrophysics><stellar-astrophysics><solar-wind>
Stars as nozzles; how important is thermodynamics and the de Laval nozzle equation for understanding the speed of the solar wind vs distance?
uhoh
# Stars as nozzles; how important is thermodynamics and the de Laval nozzle equation for understanding the speed of the solar wind vs distance?

(Asked by: username_0 on 2022-05-02)

Seeing [What determines the speed of a star's solar wind?](https://astronomy.stackexchange.com/q/49233/7982) I'm having flashbacks from undergraduate days where the professor started their lecture on solar wind by writing something that they called the [de Laval nozzle equation](https://en.wikipedia.org/wiki/De_Laval_nozzle) on the board.

I don't now remember *which* equation it was, but I have a hunch it might have been related to mass flow per unit area and it was certainly more complicated than $1/r^2$.

That certainly shows up in google searches but so far none of the answers there mention it, and instead of discussing expansion/rarefaction mostly just use $k\_B T$.

So I'd like to ask:

**Question:** Can stars be thought of as nozzles? How important is thermodynamics and the de Laval nozzle equation for understanding the speed of the solar wind vs distance?

**Tags:** astrophysics, stellar-astrophysics, solar-wind
> **Comments:**
> **username_1**: Perhaps try https://physics.stackexchange.com/a/612590/59023 or https://physics.stackexchange.com/a/524215/59023?  

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## 1 answers

### Answer by username_2 on 2022-05-03. Score: -1

What exactly did you google for? I googled for 'laval nozzle solar wind' and got many detailed references. Just take the [first reference](http://www.physics.usyd.edu.au/%7Ecairns/teaching/2010/lecture8_2010.pdf) that comes up and in Sect.8.2. the analogy between Parker's solar wind equation and the Laval nozzle equation is explained in detail.

However, as you are half implying already, concepts of thermodynamics are at the heart of this theory. But rather than going into details of the equations here, let me illustrate the situation through a fictitious analogy:

assume an outside monitoring device at the International Space Station (ISS) detects an airstream coming from station. Let's call it the ISS-wind. Now scientists are very puzzled as to the nature of the wind and develop all kinds of theories how the outside walls of the station could produce and accelerate this amount of air. It does not occur to them that the air is simply coming from the inside through a leak.

The situation is potentially the same for the solar wind. The point is that the photosphere is slightly leaky everywhere (in some regions more, in others less) and a few high energy particles (representing the gravitational potential energy of the Sun) are coming through from below the photosphere. And it is obvious that such a scenario can not be represented by a theory based on thermodynamics, as the concept of temperature alone does not allow to correctly model the energy distribution function over an energy range from less than 1 eV to about 1 keV.

> **Comments:**
> **username_3**: I didn't downvote, but I think that this answer could be more helpful if you actually "went into details of the equations". I don't really get the point of your analogies with the ISS and of your argument about the solar wind.  
> **username_2**: @Prallax The analogy is explained in the last paragraph. I don't know how I could make it even clearer. The point is that the equations in the relevant references are based on the assumption of LTE and thus are unable to correctly deal with non-Maxwellian velocity distribution functions.  

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