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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?

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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.

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    $\begingroup$ 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 $\endgroup$
    – vengaq
    Commented Aug 11 at 22:44
  • $\begingroup$ @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. $\endgroup$
    – Thomas
    Commented Aug 12 at 18:05
  • $\begingroup$ @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. $\endgroup$
    – Thomas
    Commented Aug 12 at 18:05
  • $\begingroup$ @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? $\endgroup$
    – vengaq
    Commented Aug 12 at 18:09
  • $\begingroup$ @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, $\endgroup$
    – Thomas
    Commented Aug 12 at 18:18
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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.

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  • $\begingroup$ 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 $\endgroup$
    – vengaq
    Commented Aug 12 at 14:15
  • $\begingroup$ @vengaq In principle yes, but in practice no. The ionization fraction is an equilibrium that can be calculated from the Saha 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. $\endgroup$
    – pela
    Commented Aug 13 at 10:40

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