The Trebuchet Challenge Script (Patreon)

What do the first stars in the universe, dark matter, and superior siege engines have in common? It’s that I’m about to blow your mind talking about all three. 

Sometimes space news sneaks by without getting much attention. Not everything wows like gravitational waves or spacefaring sportscars. That’s the case with the recent discovery of earliest stars in the universe. In a Nature paper published a few weeks ago, Judd Bowman and collaborators report a signal from the very first stars to form in our universe. The same result also hints at brand new physics that may help explain the nature of dark matter. This result flew under the radar in part because it’s a subtle and clever result that requires a bit of interpretation. Today we’re doing a Space Time Journal Club to explain this discovery. We’ll follow that with the solution to our recent trebuchet challenge question.

So the very early universe was full of hydrogen gas and light. That light was the left-over heat-glow from before those first hydrogen atoms formed. This is the cosmic microwave background radiation, or CMB. This is the oldest light we can see, and we explain it in detail in a previous episode. We can also try to the light signature from that very early hydrogen gas. We do that by looking for a very particular type of photon: the one that is released or absorbed when the ground-state electron in hydrogen flips its spin direction. That photon has a wavelength of 21cm, which is radio light. In the early universe, the rate of hydrogen spin flip was in equilibrium with the CMB – meaning that for every CMB photon that was absorbed by the spin flip, another one was emitted. We say that the electron spin temperature was couple to the CMB temperature. The upshot is that the earliest 21cm radiation is hopelessly mixed with the CMB, which means it’s impossible to distinguish.

At least to start with. Before long, some of the early hydrogen gas collapsed to form the very first stars, before the first galaxies formed. The ultraviolet light from those stars shifted the equilibrium so that the electron spin temperature became connected to the temperature of the gas instead of the CMB. That change in equilibrium meant the gas was suddenly absorbing more 21cm photons than it was emitting.  After a while, the first black holes formed and started to spew out X-rays as they gobbled up hydrogen. This heated the gas, and eventually it became too hot to emit or absorb 21cm photons at all.

The TLDR is that there should have been this brief period of time when the universe was eating up 21cm photons from the CMB. That should look like a dip in the CMB spectrum. Now remember also that the universe was expanding back then, just like it is now. Absorption at 21cm would now look like absorption at a much longer wavelength. In fact, there should be a broad dip at a range of wavelengths representing the epoch of the universe in which this absorption was occurring.

And that’s exactly what Bowman and team saw. Their EDGES experiment is part of the Murchison Radio-astronomy Observatory (MRO) in Western Australia. This is one of the most radio-quiet locations on the planet, far from any human-made interference. That’s because it’s remote, not because Australians don’t have radio yet, despite the rumours. So the research team added together the CMB light from the entire visible sky and recorded this spectrum. The dip shows the drop in CMB light due to 21cm absorption. The wavelength range of the dip corresponds to the epoch between 180 to 270 million years after the Big Bang. That period represents the time between the very first stars to the onset of very active black hole growth. Measuring this range in itself is a stunning discovery that will really help us understand the early universe.

It was also expected. The absorption dip was predicted by our cosmological models, and it was right where we thought it would be. But there IS one big discrepancy between model and observation. The dip is about twice as deep as expected. Absorption is happening WHEN we thought it would, but much MORE of the CMB is being absorbed than we expected. This suggests that the hydrogen doing that absorbing is a lot COLDER than we thought – colder gas is better at absorbing 21cm photons.

However our cosmological models can’t explain how this early hydrogen gas could possibly be this cold. We know exactly its temperature at the moment of the creation of the CMB, so there’s a limit to how much it could have cooled since then. This is where the new physics comes in. In order to cool something down, you need to expose it to something even colder than itself – or expand the universe, but that’s already taken into account. The only thing colder than this ambient hydrogen at the time was dark matter. So maybe the hydrogen lost some of its heat to dark matter. Yet in order for that to happen, hydrogen would actually need to interact with dark matter. The whole thing about dark matter is that it doesn’t interact with regular matter except through gravity. But in order to cool the early hydrogen gas, there must be another type of interaction. This is getting physicists excited. It’s only a hypothesized explanation for the relative coolness of this gas, but it’s the one the authors seem to like. More time and more data will help sort this out.

OK, so now for a complete change of topic. Let’s do the answer to our recent trebuchet challenge. You were a medieval warlord. Well, maybe early renaissance. As you prefer. We looked at a couple of scenarios in which you trebuchet’d your enemies fortress wall and I asked you to use energy methods to figure some stuff out.

First I asked you the following: you fire your trebuchet at the enemy’s wall twice. In the first case the projectile flies upwards on a shallow path to strike the top of the wall, and in the second the projectile flies high in the air to fall again, striking the same location. In both cases the trebuchet counterweight started at the same height, and also reached the same height at the end of its swing. My question was: which shot was the most damaging; assuming damage only depends on the kinetic energy of the projectile at impact?

To answer this we need to know how much of the counterweight’s starting potential energy ends up in the projectile. We know that the counterweight’s height in both shots was the same at the start and at the end of the swing. At both of these points the weight is momentarily still - it has no kinetic energy and so all of its energy is in potential energy. So the energy it lost to the projectile is just the difference in these potential energies. That's the same in both shots so both gave the projectile the same total energy. We don’t know anything about the kinetic or potential energies at the moment of release, but we know the final potential energies of the projectile in both shots were the same because they hit the wall at the same height. That means the projectile’s kinetic energies at the point of impact must also be the same. And as long as they had the same mass, their speeds were the same too.

OK, for the extra credit  question: I asked for the speed of impact of the projectile, assuming the parameters you see on the screen now. Some of these were red-herring parameters. The only things you needed to know were the starting and final heights of the counterweight and projectile and the mass of the counterweight and projectile. This is the power of using energy in calculations – so many irrelevant complications melt away. Like I just explained, we can equate the energy lost by the counterweight with the energy gained by the projectile. Subtract the potential energy of the projectile at its point of impact and we have its kinetic energy. Then 1/2 mv^2 gives us its velocity - around 80 m/s. The kinetic energy of that 90kg stone is about that of a third of a stick of dynamite. Hey, it’s not bad for a medieval rock-slinger.

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