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My daughter asked me last night: What is the hottest thing in the universe?

The first thing that sprang to mind was the core of a fresh neutron star (this question agrees: What is the hottest thing in the universe?), so I told her that and then tried to verify it on the Internet. Unfortunately, most of the articles online claimed that the hottest things in the universe are quasars, since they have a "brightness temperature" of 10 trillion kelvin. That sounded fishy, and a review of the literature revealed that brightness temperature has no direct relationship to actual temperature.

Poor journalistic practice aside, what is our best estimate of the temperature of these objects?

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  • $\begingroup$ What is temperature by your definition if you exclude brightness temperature? Is kinematic also excluded? Do you require (quasi) equilibrium? $\endgroup$ – planetmaker Mar 6 at 16:17
  • $\begingroup$ @planetmaker Yes, I think quasi-equilibrium is what I want. Perhaps the answer is that the detectable radiance-producing part of a quasar has no well defined temperature and the rest of the quasar is not detectable, so we have no idea what the temperature is. $\endgroup$ – Xerxes Mar 7 at 17:07
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A question/answer over at physics.se discusses the issue of quasar spectral output. Part of one answer says,

The percentage of radiation that is thermal versus non-thermal varies from quasar to quasar, and for a single quasar is going to be different at different wavelengths, so there isn't one simple answer (and also it depends on what angle you are viewing the AGN from relative to the jet axis)

And similarly, there isn't a single value you can quote for the accretion disk temperature. Different AGN have different black hole masses, different matter infall rates and generally different environments. And a single accretion disk doesn't have a single temperature either: the temperature is higher towards the center, but to the details of what the emission spectrum looks like depends a lot on what parameters you put in to the model and what assumptions you make about energy transfer within the disk etc.

So it's not really accurate to estimate quasar thermal temperature from the "Brightness temperature," because the latter only applies to objects closely fitting Planck's black body law.

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