There's a Hole in my Model...

When you assume, you make an ass of U and Me, or so they say.

Yesterday, I was alerted to a discovery that has the potential to challenge some of our assumptions, by somebody who wanted to know what I thought about it. To be honest, it presents something of a puzzle.

The discovery in question was a black hole. Well 'so what?', you might be tempted to ask; after all, black holes are hardly an Earth-shattering (pun intended) revelation. So what's all the hoo-ha about?

Well, it isn't the black hole itself that's remarkable. What's really remarkable is how far away it is, and its size. To show just how remarkable, I'm going to break with tradition somewhat and go over some previously-covered ground.

We've talked a fair bit about the Big Bang in quite a few other posts. We've noted that, in the popular understanding, the Big Bang is a theory dealing with the beginning of the universe. Despite the fact that this model is still talked about as the standard for the evolution of the universe, it hasn't actually been that for several decades, not least because of some fatal flaws, which we've looked at in some detail in previous posts. I'll include links to these posts at the bottom, along with any other whose subject matter crops up during the course of what follows, as these observations would take us too far afield for our purposes today. What I will do is to note that the Big Bang as we use it now doesn't actually deal with the beginning of anything. These days, the term 'Big Bang' is really nothing more than the name we give to the observed fact that the universe is expanding and was therefore smaller in the past.

It does, however, still contain some implications, not least in terms of what we observe when we look back through time at the light coming to us from the earliest times we can observe. It's certainly the case that the popular conception isn't far off the mark in some respects, and observations in the last few decades have reinforced some of them.

One of the things that all of our models have, aside from a Big Bang, is a time when our universe was extremely hot and dense. We've previously discussed the earliest observations we have of the cosmos, in a post about biological evolution in the context of entropy. In that outing, we noted that:
...one of our best current sources of information about the early universe is the cosmic microwave background radiation (CMBR), discovered serendipitously by Penzias and Wilson in 1964. What the CMBR actually represents is not, as I've seen suggested, the glow of the big bang, but the photons that come to us from the 'last scattering surface'. This is going to serve as a useful pointer to what we're discussing here, so it's worth spending a little time on.

For about the first 380,000 years or so after the Planck time - a theoretical construct dealing with the smallest useful amount of time after the 'beginning' of expansion - the cosmos was opaque to photons. The reason for this is that, after the onset of expansion, the cosmos was extremely hot and dense. So hot, in fact, that it was basically a white-hot plasma of photons and ionised hydrogen, which consists of protons and free electrons. Because of the abundance of free electrons at such temperatures, the distance that photons could travel freely was massively restricted due to Compton scattering.

Now, anybody who likes to smell nice knows what happens when a body of particles expands, because we've all felt the deodorant can cool down as we let out the smellies. The same thing happens with the cosmos. As expansion continues, the cosmos cools. Prior to a certain low temperature, electrons remain free, not bound to protons, because of a quirk of entropy, namely that, in the environment they find themselves in, there's nowhere for energy to go to become unavailable. As the termperature gets below about 4,000 Kelvin, however, something interesting happens; there's somewhere for energy to go, so the free electrons begin to bind to protons, forming the first neutral atoms. The reason they do this is because it's energetically favourable for them to do so. This is just another way of saying that, once they can shed some energy, their lowest available energy state consists of being bound to protons.

As an aside, this is where the CMBR comes to us from. By the time the temperature gets as low as 3,000K, most of the free electrons have become bound, and the photons from the last bit of Compton scattering are now free to travel through the cosmos, and it's these photons that we detect as the CMBR. Due to the expansion of the cosmos, these photons are hugely red-shifted, meaning that their wavelengths are stretched out, until their temperature is about 2.7K, or -270 degrees Celsius, a smidge less than three degrees above absolute zero.
Here's one of the latest images from the Planck satellite, the most recent generation of satellites imaging the CMBR.

So, as we can see, barring some variation, representing temperature differences of a few ten-thousandths of a degree between the hottest (red) spots and the coldest (blue) spots, it's pretty homogeneous.

Let's jump forward now, and deal with what's actually been discovered, and then we'll look at why it's a problem, as well as looking at some potential solutions.

The object that's been observed is a quasar, or 'quasi-stellar object'. A quasar is an active galactic nucleus consisting of a central black hole with an accretion disc of gas. As the gas spirals into the black hole at huge velocities, it emits enormous amounts of electromagnetic radiation. The name itself is a contraction of 'quasi-stellar radio source', as their earliest discoveries were as sources of radio waves which, in the visible part of the electromagnetic spectrum, looked an awful lot like stars. In any event the electromagnetic radiation they emit has huge luminosity, with the brightest ones giving off on the order of $1 \times 10^{40}$ W of radiation across the spectrum. When you compare that with the estimated luminosity of the Milky Way at around $1 \times 10^{36}$ W*, that's a future so bright that you've gotta wear shades. Or, at least, you would, if this were all visible light, and if we weren't talking about the past, rather than the future.

So, this quasar, known affectionately to its friends as $J1342+0928$, comes to us with a redshift of $z=7.54$. "Fascinating!" you might say. "What does that mean?" Well, as we've discussed previously, the universe is expanding. Because it's expanding at approximately the same rate everywhere - known as metric expansion - this means that objects further away are receding from us at a greater rate.

As we know from earlier discussions, when something is moving away from us, the light we receive from it is shifted toward the red end of the frequency spectrum, as the light-waves we receive get stretched out, making them look redder than their intrinsic colour. Thus, the further away something is, the faster it recedes, and the more its light is shifted toward the red.

What this means is that we can tell by how far the light has shifted from its intrinsic colour how far away it is, as in the image on the left from the European Space Agency.

This is very similar to what we all know as the Doppler Effect, in which passing sirens have their sound frequency shifted as they pass you, and it's what we now know as Hubble's Law, after Edwin Hubble, the American astronomer who first discovered extra-galactic sources and the expansion of the universe in the 1920s.

In this, what that redshift figure is telling us is that this quasar is a very, very long way away. In fact, it's at a comoving distance with Earth of just a smidgen over 29 Gly (giga-lightyears, or billion lightyears). That figure in turn means that, when the light we see from it left its source, it was about 13.1 Gly from us.

Now, this quasar is big. Really big. Not on the scale of those really bright ones discussed earlier, but still absolutely huge, on the order of 800 million times the mass of the sun, and with a luminosity of about $4 \times 10^{14}$ the luminosity of the sun.

And this is where the problems lie. We know, or we think we know, how black holes form. Now, it's certainly true that stars with larger mass exhaust their fuel much quicker than stars with low mass. Indeed, there's a direct proportionality to the mass of the star and the speed with which it runs out of fuel. Going back to the Planck image above, we know that the universe was pretty isotropic (the same in all directions) to within a few ten-thousandths of a degree, and we know that temperature relates to density. How, then, can we have a black hole of 800 million solar masses within only a few hundred million years (about 690 million, but who's counting)? In fact, although the CMBR comes to us from just shy of 690 million years before, that CMBR is itself part of a process, and electron bonding would have been continuing for some time afterwards, which means this is even closer than that.

This is a puzzle, and no mistake.

Now, there are some possible ways to resolve this. The first is that this is the merger of several smaller black holes that formed fairly early on after the last scattering. This seems statistically unlikely, though we can't rule it out as yet and, since this is the first observation of a large black hole at such a distance, and since this comes from a survey of only a very small portion of the sky, it may be that we find that this isn't anything like as uncommon as we think. It does seem to put a bit of a spanner in the works in terms of obtaining such high density from such a smooth distribution only a short time before, so this is going to be fruitful ground for research, not only in further observing this quasar itself, but also in the search for similar objects at commensurate redshifts.

Another possibility, but possibly a somewhat more troubling one in terms of our models, is that this started forming during the rebonding epoch, although how it would do this without leaving any evidence in the CMBR creates even more problems.

And the final possibility, though not one I'd give a huge amount of credence to, is that this black hole actually formed while the universe was still a plasma. Again, I'd expect evidence of this to be pretty obvious in the CMBR, so it causes more problems than it solves.

We can't really rule out either of these two scenarios, despite the lack of observed evidence in the CMBR, until we rule out the possibility that we've actually observed and corrected for it without realising it. It's certainly been the case in the past that announcements have been made of this or that thing in the CMBR when we've failed to correct for something that accounts for it, like that BICEP2 discovery that hit the world with some fanfare a few years ago, so it would be hubris to suppose that there was no possibility that we've over-corrected, or that some other assumption has been making an ass of you and me.

As always, thanks for reading, and a special thanks to my donors and patrons. You are awesome.

Corrections, nits and crits always gratefully received.

Arxiv pre-print server upload of the full paper.
Nature publication of the paper.
All Downhill From Here Evolution and entropy, featuring a potted history of the universe.

It Wasn't Big, and it Didn't Bang Before the Big Bang Part I
You Must Be Off Your Brane! Before the Big Bang Part II
The Certainty of Uncertainty Before the Big Bang Part III
Scale Invariance and the Cosmological Constant Dark matter, dark energy, and the Lambda term in General Relativity