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I'm catching up on my childhood mistakes. One of them was the "nuclear flash", the enormous explosion when the sun ignited. Apparently, this did not happen as the ignition of the sun was a gradual process, not a violent one, as explained in this question.

A consequence of that childhood mistake was the idea that, through that explosion, the dust between the (proto)planets was blown away, explaining why the solar system is empty, except for the planets and their moons (the asteroid belt and Oort cloud are again other phenomena).
However, as the Sun's ignition was not an explosion, then what happened with the dust between the (proto)planets?

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    $\begingroup$ I have some info here astronomy.stackexchange.com/a/49425/16685 about the equilibrium process of asteroid / planetesimal collisions that ProfRob mentions. $\endgroup$
    – PM 2Ring
    Nov 21, 2023 at 16:50
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    $\begingroup$ There is still a lot of dust in the Solar System, as can be seen in the phenomenon called zodiacal light en.wikipedia.org/wiki/Zodiacal_light $\endgroup$ Nov 21, 2023 at 23:41
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    $\begingroup$ The Zodiacal dust is second generation and still has a relatively short lifetime of maybe tens of millions of years. It must be continuously regenerated in collisions. $\endgroup$
    – ProfRob
    Nov 22, 2023 at 14:59
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    $\begingroup$ Wait, it was your childhood mistake that there was a "nuclear flash" when the sun ignited??? $\endgroup$ Nov 23, 2023 at 4:39
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    $\begingroup$ @EndAnti-SemiticHate: as a child, I've been reading quite some books about stars and planets. Some of them called the birth of the sun a "nuclear flash" ("kernflits" in Dutch, my mother tongue), which caused my imagination to invent an enormous explosion, blowing away all particles which were not heavy enough. The idea of the sun, heating up because of gravity pressure and that heat being slowly transformed into heat, caused by nuclear fusion (so in a gradual way, not an explosive one) was too boring to me to handle at that age :-) $\endgroup$
    – Dominique
    Jan 2 at 8:49

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Dust happens in two ways. "Primordial dust" just condenses out of the protostellar material in the disc providing it gets cool enough and dense enough. "Second generation" dust is generated by collisions between planetesimals.

In both cases there are a number of mechanisms that get rid of this dust, two of the main ones being radiation pressure and Poynting-Robertson drag.

Radiation pressure (the force with which radiation from the protosun acts upon a dust particle) will vary with the flux of radiation, and falls as $r^{-2}$. This has the same dependence as gravitational force on the dust and so the ratio of the two forces will be approximately constant. The ratio will depend on the density, albedo and shape of the dust particles. However, generally speaking, anything smaller than $10^{-7}$ m will get blown out of the Solar System on a very short (ballistic) timescale.

Thus, what happens is that as soon as the Solar System becomes optically thin to the Sun's radiation then all the small primordial dust particles are blown away. Of course this dust can be regenerated by collisions between planetesimals, but again, this will be an equilibrium process in the sense that small dust particles would need to be being continuously generated in order for a population to be present, since they get blown out of the Solar System quickly.

Poynting Robertson drag is a tangential acceleration of the dust particles caused by the fact that in their frame of reference, the radiation from the Sun does not arrive radially. It slows the dust particles down and they spiral in to the Sun. Again, this will act as soon as dust particles are being illuinated by the protosun.

Poynting Robertson drag also depends on the density of the particles, their size and the distance to the Sun as $r^{-5/2}$. As a result, it gets more important for dust at smaller $r$. Poynting-Robertson drag is irrelevant for small particles, since they are blown away by radiation pressure. For larger particles, they will spiral into the Sun on a timescale that depends on their size and starting position. For dust of size $\sim 10^{-6}$ m at $r=1$ au, that timescale is only 10,000 years. It is longer for dust that is further out and for larger particles. The net result is that it is easy to clear out the inner disc of dust, less easy to get rid of it further out.

Dust in the outer Solar System that survives radiation pressure ($>10^{-7}$ m) and Poynting Robertson drag ($>$ a few au) may survive for a long time, but it will be subject to being captured by growing giant planets. It will also eventually be pushed out of the Solar System by the influence of the solar wind - an outflow that is distinct from radiation pressure. Stellar winds/outflows in young stars are probably much stronger than the weak solar wind we have today and small dust particles are well-coupled to the outflowing gas. Some of the larger particles 10-100 microns might survive for tens of millions of years, but ultimately almost all the dust seen in the Solar System after that is second generation - formed in collisions.

A further source of dust destruction is radial infall for small dust particles that are well-coupled to gas but which is being accreted onto the star during its first few million years. Larger dust particles may be less well-coupled but these can drift inwards because of friction between the dust and the gas that it moves through. This can then leave it susceptible to Poynting-obertson drag as before.

Empirically, we observe that the process of dust removal appears to be complete in 10-20 million years and any dust that is seen thereafter is episodic and probably the result of collisions between planitesimals.

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    $\begingroup$ Don't forget that an (unknown) fraction of the dust is accreted into planet-forming material. $\endgroup$ Nov 21, 2023 at 23:10
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    $\begingroup$ So, as far as radiation pressure concerns, you are basically saying that the fact that the pushing out of the dust happens gradually instead of explosively, does not mean that it doesn't happen (only not as spectacular as in my childhood mind :-) ). I must admit that the drag, caused by the electrical and magnetic fields interference , goes above my understanding capabilities. $\endgroup$
    – Dominique
    Nov 22, 2023 at 7:22
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    $\begingroup$ It is assumed that there was some planetary migration in the early days of the solar system, which has many reasons, but those phenomena have probably played a tiny bit of a role there. $\endgroup$ Nov 22, 2023 at 7:39
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    $\begingroup$ @Dominique the planets themselves are simply too big for these forces to have a noticeable effect. Both forces are basically roughly proportional to the cross section (area, so square of the object radius), but the mass goes with the cube of the radius. These affect single particles and asteroids, but planets are beyond them. $\endgroup$
    – Chieron
    Nov 22, 2023 at 9:32
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    $\begingroup$ Is there a perfect size of dust particle where the drag and the pressure exactly cancel each other out? ... On second thought, that might mean staying at the same distance but slowing down the orbit, which should give gravity a stronger hand if I'm not missing anything obvious. $\endgroup$
    – Syndic
    Nov 23, 2023 at 7:56

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