<p>The amount of free electrons in the interstellar medium (ISM) depends on its  temperature, the ambient radiation field, and the chemical composition of the gas. Hot gas (<span class="math-container">$T\sim10^6\,\mathrm{K}$</span>) is completely ionized, warm gas (<span class="math-container">$T\sim10^4\,\mathrm{K}$</span>) is typically partly ionized, while cold gas (<span class="math-container">$T\sim10^2\,\mathrm{K}$</span>) is neutral.</p>
<p>The duration for a given electron in an ionized medium that it stays free, before meeting an electron-hungry ion, depends on the density <span class="math-container">$n_e$</span> of the electrons and the temperature (since a hotter gas means faster particles which recombine less easily). This temperature dependency is captured in the quantum mechanical &quot;recombination coefficient&quot; <span class="math-container">$\alpha_\mathrm{rec}(T)$</span>.</p>
<p>At <span class="math-container">$T\sim10^4\,\mathrm{K}$</span>, the recombination coefficient is roughly <span class="math-container">$3\times10^{-13}\,\mathrm{cm}^3\,\mathrm{s}^{-1}$</span>, so for instance for a <span class="math-container">$n_e = 1\,\mathrm{cm}^{-3}$</span> gas, typical of the warm medium, the recombination timescale amounts to
<span class="math-container">$$
t_\mathrm{rec} = \frac{1}{n_e \alpha_\mathrm{rec}} \sim 3\times10^{12}\,\mathrm{s},
$$</span>
or some 100,000 years.</p>
<p>Since the recombination coefficient decreases with <span class="math-container">$T$</span>, and (more importantly) since the density also does, free electron stay free longer in hotter gas. Once an electron is captured, it may be &quot;freed&quot; again by a collision with a fast-moving particle, or by energetic radiation.</p>

CC BY-SA 4.0
2024-08-12T14:15:28.140Z
and even in cold gas can there be a small probability of having a free electron (for example if we have a low density diffuse gas and the atoms are near the ionizing temperature due to the Boltzmann factor)? @pela
vengaq
CC BY-SA 4.0
2024-08-13T10:40:03.410Z
@vengaq In principle yes, but in practice no. The ionization fraction is an equilibrium that can be calculated from the [Saha equation](https://en.wikipedia.org/wiki/Saha_ionization_equation). It only asymptotically reaches zero ionization for T → 0, but the decrease is exponential, so already at T = 100 K, the ionization fraction is virtually zero. If the atoms are near the ionization temperature, then yes, but in that case the gas isn't cold, but several thousands degrees.
pela
CC BY-SA 4.0
2024-08-12T14:03:34.883Z
2024-08-12T14:03:34.883Z
pela
<p>Any individual free electron will never stay free individually indefinitely. It will recombine with a free ion if it meets one. It may take a long time in interstellar space, but eventually it will. But as there are always some sources of ionization (be it photoionization or collisional ionization) new free electrons will be created. The ratio of the ionization rate to the recombination probability determines the net free electron (and ion) density that we observe.</p>
<p>Free electrons would normally not be gravitationally bound by the galaxy as they are too fast (they are for instance not bound by the Sun's gravity either), but on  a large scale they are bound by the electric field of the ions. They are also bound by magnetic fields that exist within the galaxy.</p>

CC BY-SA 4.0
2024-08-11T22:44:04.073Z
thanks! So there would be an equilibrium between the free electrons and the recombined ones? Also, can there be electrons that have sufficiently slow velocities to be gravitationally bound to their host galaxies as well? Finally, as the interstellar gas/plasma containing these electrons is contained in the galaxy, it has angular momentum as it rotates the center of the galaxy, right? @Thomas
vengaq
CC BY-SA 4.0
2024-08-12T18:05:02.040Z
@vengaq Yes, if the conditions are constant, there is a net equilibrium between ionized and neutral plasma, depending on the ionizing energy input.

Sufficiently slow electrons will be gravitationally bound, but they will not stay at the same speed forever as occasionally they will suffer elastic collisions and may speed up in the process to become gravitationally unbound.
Thomas
CC BY-SA 4.0
2024-08-12T18:05:40.930Z
@vengaq The mass of gas in a galaxy is generally much smaller than that of the stars, so also the angular momentum, especially for the ionized component. During galaxy formation (when stars have not formed yet) on the other hand, the gas will obviously carry all of the angular momentum, although this will initially all be neutral until the temperature has increased enough for ionization.
Thomas
CC BY-SA 4.0
2024-08-12T18:09:01.967Z
@Thomas would a cloud of free electrons have a low angular momentum even if its low mass is compensated by the distance to the center of the galaxy?
vengaq
CC BY-SA 4.0
2024-08-12T18:18:30.330Z
@vengaq The angular momentum of the ionized gas will almost completely be due to the ions, as their mass is about 1800 times that of the electrons,
Thomas
CC BY-SA 4.0
2024-08-12T18:28:38.567Z
@ScienceSnake Ionizing hydrogen from the ground state requires an energy of 13.6 eV. The probability for a particle even at room temperature (300K) to have this energy is about exp(-500), so practically zero.
Thomas
CC BY-SA 4.0
2024-08-12T18:29:14.133Z
@ScienceSnake would this that you described be the same mechanism which could cause the ionization of matter described here: https://math.ucr.edu/home/baez/end.html ?
vengaq
CC BY-SA 4.0
2024-08-12T18:43:21.537Z
@Thomas even if we account for all ions besides electrons, if that ionized gas is at a great distance of the center of the galaxy, shouldn't it compensate for their low mass?
vengaq
CC BY-SA 4.0
2024-08-13T17:45:10.977Z
@vengaq Gas rotates around the center of galaxies at all distances. Initially, when the galaxy formed, there was indeed only rotating gas. Stars were only formed later from the gas. The gas we see today (whether neutral or ionized) is only some leftover. It is actually usually gas that is oberved to determine the rotation of galaxies, because for large distances there are not many stars anymore that you could measure. Ionized gas though will be affected by magnetic fields, which could complicate the intepretation.
Thomas
CC BY-SA 4.0
2024-08-11T20:58:58.960Z
2024-08-11T20:58:58.960Z
Thomas
<p>If I'm not mistaken, in interstellar gas, there can be clouds of free electrons (not &quot;attached&quot; to any atomic nucleus)</p>
<p>But can they stay like that indefinetely? Or will they inevitably end up in atoms?</p>
<p>(For example, electrons roam free in these gases due to photoionization. But in the future, when stars will die out, will then electrons re-combine with atoms? Or can there be cold plasma made from electrons so that they will still be free?)</p>
<p>And how are they holding in interstellar gas inside of galaxies? Are they gravitationally bound to them?</p>

<astrophysics><interstellar-medium><gas><particles><nebulae>
Can there be free electrons in interstellar gas in the long term?
vengaq
# Can there be free electrons in interstellar gas in the long term?

(Asked by: username_0 on 2024-08-11)

If I'm not mistaken, in interstellar gas, there can be clouds of free electrons (not "attached" to any atomic nucleus)

But can they stay like that indefinetely? Or will they inevitably end up in atoms?

(For example, electrons roam free in these gases due to photoionization. But in the future, when stars will die out, will then electrons re-combine with atoms? Or can there be cold plasma made from electrons so that they will still be free?)

And how are they holding in interstellar gas inside of galaxies? Are they gravitationally bound to them?

**Tags:** astrophysics, interstellar-medium, gas, particles, nebulae

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## 2 answers

### Answer by username_2 on 2024-08-11. Score: 8 | Accepted answer

Any individual free electron will never stay free individually indefinitely. It will recombine with a free ion if it meets one. It may take a long time in interstellar space, but eventually it will. But as there are always some sources of ionization (be it photoionization or collisional ionization) new free electrons will be created. The ratio of the ionization rate to the recombination probability determines the net free electron (and ion) density that we observe.

Free electrons would normally not be gravitationally bound by the galaxy as they are too fast (they are for instance not bound by the Sun's gravity either), but on a large scale they are bound by the electric field of the ions. They are also bound by magnetic fields that exist within the galaxy.

> **Comments:**
> **username_0**: thanks! So there would be an equilibrium between the free electrons and the recombined ones? Also, can there be electrons that have sufficiently slow velocities to be gravitationally bound to their host galaxies as well? Finally, as the interstellar gas/plasma containing these electrons is contained in the galaxy, it has angular momentum as it rotates the center of the galaxy, right? @Thomas  
> **username_2**: @vengaq Yes, if the conditions are constant, there is a net equilibrium between ionized and neutral plasma, depending on the ionizing energy input.  Sufficiently slow electrons will be gravitationally bound, but they will not stay at the same speed forever as occasionally they will suffer elastic collisions and may speed up in the process to become gravitationally unbound.  
> **username_2**: @vengaq The mass of gas in a galaxy is generally much smaller than that of the stars, so also the angular momentum, especially for the ionized component. During galaxy formation (when stars have not formed yet) on the other hand, the gas will obviously carry all of the angular momentum, although this will initially all be neutral until the temperature has increased enough for ionization.  
> **username_0**: @Thomas would a cloud of free electrons have a low angular momentum even if its low mass is compensated by the distance to the center of the galaxy?  
> **username_2**: @vengaq The angular momentum of the ionized gas will almost completely be due to the ions, as their mass is about 1800 times that of the electrons,  
> **username_2**: @ScienceSnake Ionizing hydrogen from the ground state requires an energy of 13.6 eV. The probability for a particle even at room temperature (300K) to have this energy is about exp(-500), so practically zero.  
> **username_0**: @ScienceSnake would this that you described be the same mechanism which could cause the ionization of matter described here: https://math.ucr.edu/home/baez/end.html ?  
> **username_0**: @Thomas even if we account for all ions besides electrons, if that ionized gas is at a great distance of the center of the galaxy, shouldn't it compensate for their low mass?  
> **username_2**: @vengaq Gas rotates around the center of galaxies at all distances. Initially, when the galaxy formed, there was indeed only rotating gas. Stars were only formed later from the gas. The gas we see today (whether neutral or ionized) is only some leftover. It is actually usually gas that is oberved to determine the rotation of galaxies, because for large distances there are not many stars anymore that you could measure. Ionized gas though will be affected by magnetic fields, which could complicate the intepretation.  

---

### Answer by username_1 on 2024-08-12. Score: 8

The amount of free electrons in the interstellar medium (ISM) depends on its temperature, the ambient radiation field, and the chemical composition of the gas. Hot gas ($T\sim10^6\,\mathrm{K}$) is completely ionized, warm gas ($T\sim10^4\,\mathrm{K}$) is typically partly ionized, while cold gas ($T\sim10^2\,\mathrm{K}$) is neutral.

The duration for a given electron in an ionized medium that it stays free, before meeting an electron-hungry ion, depends on the density $n\_e$ of the electrons and the temperature (since a hotter gas means faster particles which recombine less easily). This temperature dependency is captured in the quantum mechanical "recombination coefficient" $\alpha\_\mathrm{rec}(T)$.

At $T\sim10^4\,\mathrm{K}$, the recombination coefficient is roughly $3\times10^{-13}\,\mathrm{cm}^3\,\mathrm{s}^{-1}$, so for instance for a $n\_e = 1\,\mathrm{cm}^{-3}$ gas, typical of the warm medium, the recombination timescale amounts to
$$
t\_\mathrm{rec} = \frac{1}{n\_e \alpha\_\mathrm{rec}} \sim 3\times10^{12}\,\mathrm{s},
$$
or some 100,000 years.

Since the recombination coefficient decreases with $T$, and (more importantly) since the density also does, free electron stay free longer in hotter gas. Once an electron is captured, it may be "freed" again by a collision with a fast-moving particle, or by energetic radiation.

> **Comments:**
> **username_0**: and even in cold gas can there be a small probability of having a free electron (for example if we have a low density diffuse gas and the atoms are near the ionizing temperature due to the Boltzmann factor)? @pela  
> **username_1**: @vengaq In principle yes, but in practice no. The ionization fraction is an equilibrium that can be calculated from the [Saha equation](https://en.wikipedia.org/wiki/Saha_ionization_equation). It only asymptotically reaches zero ionization for T → 0, but the decrease is exponential, so already at T = 100 K, the ionization fraction is virtually zero. If the atoms are near the ionization temperature, then yes, but in that case the gas isn't cold, but several thousands degrees.  

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