Ten Trillion-Degree Quasar Astonishes Astronomers (2016)
iflscience.com
iflscience.com
See equation 2.32 of: https://www.cv.nrao.edu/~sransom/web/Ch2.html
While I get it that we can't always be persnicketty about the definition of (thermodynamic) temperature I find these alternate, phenomenological temperatures often do more harm than good. It's not just that it results in misleadingly juicy press releases.
In my experience, physicists themselves forget that they are talking about what is little more than a fiction and start sticking their "temperature" into equations where it doesn't belong.
This has more to do with phrasing it as the "surface" of the Sun rather than the temperature being ill-defined. The proper term would be the temperature of the photosphere of the Sun, which is where the physical conditions finally become such that optical light can escape. The temperature at that layer sets the blackbody emission that we observe.
That stellar spectra (ignoring absorption lines) are broadly consistent with blackbody emission suggests that the size of the photosphere changes slowly with wavelength (i.e., that the opacity isn't a strong function of wavelength, otherwise there'd be a strong temperature gradient in the optically emitting regions). So from the standpoint of optical emission it's within the precision of measurements to think about it as as a single radius/surface. Or to put it another way, the change in photosphere size across the UV/optical/NIR is, for most stars, a small fraction of the radius. Thus the relative change in the size is small compared to the overall size. So while you're technically correct, "accepting defeat" won't be of significant practical importance to our understanding of the basic properties of stars (at least when discussing the continuum; absorption lines may have larger "sized" photospheres due to their increased optical depth at larger distances). Thus while talking about a single photosphere is not technically correct statement, it's nonetheless a useful way to describe the physical system.
Furthermore, this is a discussion of the sun and not some far away "star" nobody ever even resolved to a disk.
On the sun we see the convection zones plainly, and thus speaking of a single temperature of what is clearly a feature with structure could be wery misleading (in certain specialised circumstances).
My understanding is that there's a historical reason for this convention. Many telescope observations are calibrated by comparing the sky measurements against measurements of thermal loads with known temperatures. Since the calibration sources are specified with a temperature, it's straightforward to measure the source brightness in units of a pseudo-temperature. But I agree that it's not intuitive for those familiar with it.
Another layer on this is fact that doppler broadening of emission lines from molecules means they cover a finite width. Since typical velocities in astronomy range from fractions of a km/s to hundreds of kilometers per second, line widths are typically given in km/s. Since these line widths originate due to doppler motions, a width in km/s is equivalent to a width in Hz (for a given reference frequency for the spectral line).
The combination of these two things means people often report integrated flux measurements in units of K * km / s! It seems bizarre at first, but this is equivalent to specifying it as power / unit area (again, when there's a reference frequency specified). But these units are often convenient in their own way.
In my field we sometimes liked to quote frequencies in Kelvins. What's and Planck-over-Boltzman between friends?
> But I agree that it's not intuitive for those familiar with it.
It's worse than that. The convention of using temperature usually arises from some such instrument-calibration where the temperature more-or-less exists, and is accurate. Then the same instrument gets used for things where temperature doesn't exist at all and sometimes doesn't even give a fair description of the energy scales. Yet people keep blithely reporting these things as temperatures.
https://www.iflscience.com/space/seven-trillion-degree-quasa...
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.
So far as I understand it.
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
> 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.