> That's hotter than the Hagedorn temperature, there could be some very interesting stuff going on.

Unfortunately it's not made clear in the article, but the temperature they quote is not an actual temperature, but instead a way of describing the specific intensity of the radiation. In this case the emission they're measuring is non-thermal (synchrotron emission), so the "brightness temperature" of the radiation field is not the same as the thermodynamic temperature. I'd put in a top-level comment about it too: https://news.ycombinator.com/item?id=17898224

However, any matter in the way of the emissions would still reach something like that temperature, right? There's got to be some dust out there that's over the hagedorn temperature.

Not likely, since the intervening material probably lets most of the radio emission through. So the radiative coupling between the synchrotron emission and that material is too weak to raise the temperature by much (if any).

> There's got to be some dust out there that's over the hagedorn temperature.

Interstellar dust grains are thought to be destroyed at temperatures of 1500-2000 K (depending on composition). And their absorption cross-section for absorbing radio waves is fairly small.

Hagedorn temperature on Wikipedia: https://en.wikipedia.org/wiki/Hagedorn_temperature

I don't understand a lot of that article. I recently read about the Planck temperature, beyond which the material would emit radiation smaller than Planck length, and which is therefore sort of an upper limit of temperature beyond which we don't know what would happen. For the Hagedorn temperature, it says that beyond this temperature, things will turn into "quark matter" (linking to another article explaining that this means "any of a number of theorized phases of matter whose degrees of freedom include quarks and gluons.", which isn't very helpful), but not why that would happen. I don't understand why beyond this point, matter should suddenly turn into other 'theorized' particles.

Basically, as particles approach the Hagedorn temperature they bleed off energy in the form of matter (hadrons). This process prevents the temperature from increasing, unless it is a quark plasma - in which case there is a second and much higher temperature. The plasma would arise due to degrees of freedom (which is what temperature actually measures) - matter would have an overwhelming freedom to break apart (which it does normally all the time: see nuclear radiation).

So far as I understand it.

I don't understand a lot of it either, however my intuition tells me that it can be interpreted like just another state change.

My understanding of the transitions of matter between solid, liquid, and gaseous states is that it is primarily due to the amount of energy in the system. The more energy a particle has, the more likely it is to break its bonds with other particles around it and transition to another state. We tend to think of individual atoms being in some way the 'final' state once we reach some gaseous form, however it is not that great a leap to consider putting so much energy into the nucleus of an atom that its nucleus 'evaporates' into protons and neutrons (hadrons), and from there putting so much energy into those hadrons that they too evaporate into their constituent quarks. The difference in each case being that enough energy must be present to overcome each necessary nuclear force.

To be fair though, this is all very theoretical from what I've just read, and we don't truly know what happens yet.

Not sure why you were downvoted, I guess someone thought you were wrong? Anyway, I think it was a helpful explanation -- if anyone thinks it's wrong, they should (briefly) comment instead of downvoting.