Will No-One Rid Me Of This Turbulent Sphere ?

PROLOGUE

December, 1170 A.D. Henry II, king of England and de facto ruler of much of France, is holding court in Normandy. Though one of the most powerful men in Europe, Henry's Christmas season is about to be upset by one of the most infamous and darkest incidents of his long and successful reign. A capable warrior and masterful diplomat, even Henry is not wholly immune to mistakes, and his worst, a gnawing corrosion of his authority for much of the last decade, is reaching a climatic finale that will forever overshadow all of his achievements.

Then as now, despite a far greater direct influence of the Church in political affairs, the separation of Church and state is clear. Years before, the ambitious Henry, seeking further authority over the multitudinous subjects within his vast dominions, attempted to circumvent this by appointing his best friend as Archbishop of Canterbury. It was a rare but catastrophic misjudgement. Conscious of his own inadequacies as a bishop, Thomas Becket was unable to balance the competing demands of his energetic prince and the barely concealed sneers of his ecclesiastical flock. Henry, unwittingly, had forced his hand.

For reasons we will never fully understand, Becket sided firmly and irrevocably with the Church. Years of conflict destroyed his friendship with Henry. Finally, late in December of 1170, a relatively petty incident sealed his fate. Hearing of his latest misdemeanour, an exasperated Henry is said to have cried out one of the most famous lines in English history : "Will no-one rid me of this turbulent priest ?!?"

Henry's words, the story goes, were overheard by a group of soldiers. Dubiously interpreting this rhetoric as royal command, Becket was cruelly martyred a few days later. It seems that Henry was genuinely distraught by this and never forgave himself for what may well have been, in defiance of cynical expectations, little more than a tragic accident.


That was the prologue. Did you enjoy it ? I hope so, but now it's time to talk about science. We'll get back to Becket later.

Introduction : turbulence is still a right pain

Almost 850 years have elapsed since that dark and fateful day. Fortunately, while not itself without occasional conflict with more literal elements of the priesthood, the relationship to contemporary circumstances in astronomy is merely allegorical. Our problems with turbulence are not poetic expressions of anger : they actually are problems with turbulence itself, albeit turbulent spheres rather than priests. Although I suppose if you could find a really fat, angry priest who hated astronomy, that would count too.

Turbulence is the subject of my latest paper*, specifically regarding dark galaxies. Regular readers know that I return to this topic like an over-zealous yo-yo, so I'll be brief. Cosmological simulations predict many more galaxies than we can see. In the most recent simulations, while most clouds of dark matter eventually accrete gas and start churning it into stars, many others do not. According to these models, most galaxies are surrounded by swarms of these dark galaxies - small, sterile, stillborn clumps condemned to a perpetually starless un-life.

* It took a surprising amount of effort to get MNRAS to accept the title and the final version is long-winded and boring. At least they let us mention Henry II in the acknowledgements though.

That sounds like a very ugly scenario that's hard to test and fiendish to disprove. How do you go about finding something that, by definition, you can't see ?

Fortunately a few of these ethereal bodies might not be quite as dark as the rest. Star formation, we know, is not an inevitable consequence of gas. While it doesn't appear to be particularly difficult to start, there are conditions under which it can be suppressed. Even normal, giant galaxies have gas discs which are typically much more extended than their stellar discs - they have enormous regions, often double the size (or more) of what we can see in visible light, without any star formation at all. So, maybe some of these much smaller dark halos could have just enough gas to be detectable, but not enough to trigger that vital process that turns dead gas into a shining nuclear furnace.

Candidates for such exotic objects are rare and controversial. A few do exist, but there are rival explanations that at first glance seem more plausible and less drastic than having to invoke starless galaxies. If we're to have a chance of working out what these things really are, rather than what we'd like them to be, we need to be rather more cautious than King Henry's turbulent priest.

Key to understanding the true nature of these starless atomic hydrogen clouds are their internal velocities. The critical requirement is that their motions must be so fast that without a binding dark matter halo they would quickly disintegrate (that's why we think dark matter exists in the first place). Of course, it's also possible that we happen to detect clouds which actually are in the process of disintegration, so the velocity dispersion by itself is of limited benefit. But we can do better than that : we can map how the gas is moving throughout the galaxy. So what would be much more persuasive would is if those motions had the neat, ordered structure expected from rotation but hard to create through other processes.

From the SDSS blog. A galaxy dominated by nice, ordered rotational motion would have a velocity structure like the middle panel, whereas one dominated by random motions would look more like the right panel.

And if we really get to indulge ourselves, we'd like our candidates to be as antisocial and far away from other galaxies as possible. It's well established that many starless clouds can be produced by gravitational interactions that tear gas out of galaxies if they pass sufficiently close. Our previous works have attempted to quantify the parameters of such debris, so that we can say which clouds are more likely to be tidal debris and which might be genuine dark galaxies. The answer depends on the size, mass, isolation and velocity width of the clouds all at once.

Juggling all these parameters together is tricky, but we can simplify things. We were particularly interested in a few clouds in the Virgo cluster which I'd found during my PhD, partly out of sheer ego if I'm completely honest, and partly because of their remarkably high velocity dispersions. Velocities dispersions have to be coupled with mass and size to tell you anything about an object's total mass. That's not so easy with Arecibo, which has unrivalled sensitivity but its spatial resolution is about the same as the human eye. So those measurements can only give us an upper size limit. Even so, the velocities of the Virgo clouds seemed so high there was no way to avoid a significant unseen dark matter component at any plausible size*.

* In principle the clouds could be teeny-tiny and super dense, which would mean they wouldn't need any dark matter. But at that size they'd be so dense they ought to be undergoing an insane orgy of wanton star formation, and they're not.

So if we fix the other parameters of the clouds to be similar to the observed ones in Virgo, we can reduce things down to just the velocity dispersion as our important measurement. That means we need any clouds in simulations to be small (no more than 50,000 light years across, about half the size of the Milky Way), isolated (at least 300,000 light years from the nearest galaxy), and have enough mass to be detectable to our survey (more than about 10 million solar masses of hydrogen). These criteria are very broad ranges, so we're not restricting ourselves to impossibly specific demands.

In our simulations, we found that tidal encounters could easily explain clouds meeting these criteria if they had measured velocity dispersions less than 50 km/s. Objects with dispersions 50 - 100 km/s were unusual, but present. Features above 100 km/s were vanishingly rare. The clouds we were studying in reality were more like 180 km/s, so very unlikely to have been produced by these interactions. We also showed that this result isn't terribly model dependent : clouds of these parameters are fundamentally difficult to produce by tidal encounters.


Turbulent spheres are turbulent

So, the dark galaxy hypothesis naturally explains the properties of the observed clouds, while the tidal debris scenario has severe difficulties. In a testament to the scientific principle of dealing aggressively with confirmation bias, the dark galaxy hypothesis - which would also solve that long-standing missing galaxy problem - has proven chronically unpopular (though maybe less so these days), while the tidal debris scenario is generally accepted.

But perhaps there's a completely different explanation. In 2016, Burkhart & Loeb suggested that maybe there was another factor at work : the external pressure of the intracluster medium. Galaxy clusters, like the Virgo cluster where we found our interesting clouds, are not just great empty voids flecked with galaxies. Clusters themselves possess their own gas component :  very hot, thin, and not bound to any particular galaxy but filling most of the cluster volume.

The intracluster medium as seen through ROSAT X-ray observations.

Burkhart & Loeb's model was a simple enough calculation. The external pressure from this hot gas acts to crush any unfortunate clouds, whereas pressure from the gas in the clouds themselves acts in the opposite way, trying to blow them apart. Their model said that maybe these two forces were in (more or less) balance, keeping the clouds stable for long enough that we'd be able to observe them. They used the pressure estimated from the X-ray data to infer the size of the clouds if they were to remain stable, and found it agreed with the size constraint from the original Arecibo measurements. Hurrah !

And we should remember that there's an even more basic feature of the clouds that we often take for granted : they're made of neutral atomic hydrogen gas. Above a few tens of thousands of Kelvin, this gas becomes ionised and undetectable to our survey. The temperature of the clouds this new model demands is, if their pressure comes from ordinary thermal pressure, in excess of 100,000 K. This is much too hot to remain neutral. That means the source of the pressure can't be their internal heat, but it must be due to bulk motions of the gas moving in different directions : turbulence.

There's quite a lot of different possibilities for the clouds high velocity dispersions, then. Let me try and summarise this graphically. Click here for the image in its original format if it doesn't display correctly.

This turbulent sphere

It must be said that we weren't terribly optimistic about the turbulent sphere model. A cloud which is simultaneously trying to tear itself apart in different directions while being crushed form outside does not suggest it has a happy, balanced existence. Thermal pressure would be okay, since that could act uniformly in all directions, neatly balancing the external gas pressure since that too acts uniformly in all directions. But this dynamic, turbulent pressure simply can't do that.

So we were pretty confident that such clouds would rapidly become a big ugly mess of one sort or another. The question was how rapidly this would happen, and for how long the clouds would be compatible with the observations. The velocity dispersion and size of the clouds suggested about 100 million years, but given the complexities of two different gases with different processes acting on each, this could be an oversimplification. And it's much harder to predict how long the all-important velocity dispersion would last as the clouds simultaneously implode and explode.

Which is why we set up a series of numerical simulations. Each model contains a central sphere of neutral hydrogen with some turbulent velocity field, representing the Virgo clouds, surrounded by hot, thin gas representing the intracluster X-ray gas. We kept the intracluster gas the same in each model, since it doesn't vary all that much throughout the cluster. For the clouds, we tried varying their mass, size, and parameters of the turbulence (e.g. on what scales the velocity varies inside the cloud, the contrast between maximum and minimum velocity, etc.). And we made synthetic observations, so we could directly compare what our simulation did with what we would observe if it was a real gas cloud in the sky.

Naturally we began with a model that closely reproduced the Burkhart & Loeb calculation. What happened ? Well, it went splat. The whole thing garbled itself into a writhing mass of filaments that tore itself apart.

While the cloud did "survive", in the sense that there was still some gas left in the middle, it was no longer anything like the cloud it once was. It's a bit like if Rambo decided to cut off his penis and become a florist : he wouldn't die, exactly, but he'd hardly still be Rambo any more either.

None of our other models did any better. No matter how we varied the parameters, or what combination of values we used, we couldn't do much better than that first attempt. We think it's a fundamental property of the mechanism : bulk random motions from turbulence aren't the same as the much smaller-scale motions from temperature.

We did a bunch of simulations, and found three main behaviours. Top : the cloud just disperses, as in the gif. Middle : the cloud heats itself up through its own internal collisions, becoming undetectable. Bottom : the cloud's collisions cause it to collapse before it eventually disperses.

But it's good practise to ask not just if this model works as stated, but if there's any way it could be made to work. Simulations and observations are always limited, and, as someone once quipped, it's a terrible mistake to think that all the facts you have are all the facts there are - it's the basic mechanism we want to test, not one very specific case. Here, for example, we set up the turbulent velocity field by magic, without trying to model how it might have formed (we have really no idea how you'd get such a strong turbulence field in such a small object). We didn't model complex processes like thermal conduction or heating via the X-ray radiation from the hot cluster gas, or magnetic fields.

The problem is that even the combination of all these missing factors doesn't seem to give the model much wiggle room. The only way a cloud can remain stable is if the forces causing expansion and compression are balanced. So far as we know, there is absolutely no reason whatsoever to suppose that all of that missing physics could help solve that basic difficulty. What you'd need is some mechanism that continuously drives the turbulence but continuously, reactively adapts to how the hot gas behaves in response, constantly moving the gas around but always keeping it in the same general region. And we haven't got a sodding clue what could do that. At this stage, our model is more than sufficient to say that the basic idea just doesn't work in this case.

Which is not quite to say that it couldn't work at all. Remember that the high line width of the clouds is Rambo's penis what we're interested in here. But we're interested in this precisely because it's unusual. Most other dark hydrogen clouds have much lower widths, and for those turbulence could indeed play an important role. What we tended to find in our models - purely by accident and not design - was that our clouds generally evolved to having those lower line widths found in more "normal" clouds.

While the paper was being refereed, a certain Bellazzini et al. did their own set of simulations of one of these more typical clouds. They found it could survive for a billion years, even while moving through the cluster gas. It ended up in a unpleasantly bedraggled state, mind you, but it survived.

A Rorschach test ? No, it's a figure from Bellazzini et al. The top row shows the temperature of the cloud at three different times while the bottom row shows its density.

These simulations didn't actually use turbulence at all, just thermal pressure. Their cloud had only a very low line width, so it wouldn't need a huge amount of turbulence anyway. Unlike our high line width clouds, it's easy to imagine that stripping gas out of a galaxy might give it a little bit of turbulence as it starts its lonely journey through the cluster. Turbulence could certainly play an important and interesting role in the evolution of clouds like this. Just not in the case of clouds that we were interested in.


What's next ?

So, to wrap up, there's this problem of observations not finding enough galaxies, and an idea that maybe they exist but are made only of dark matter and gas but no stars. Objects which seem to fit the description have actually been found. But these clouds might not just be dark galaxies. The current three leading ideas are in following state :

• The clouds might be dark galaxies. In this case their high line widths would be due to rotation. Simulations show they could be stable during encounters with other galaxies, giving them a good chance of long term survival. This also fits with recent discoveries of large numbers of large but incredibly faint (dim rather than dark) galaxies.
• They could be tidal debris, gas ripped out of galaxies during interactions. Their line width would be due to streaming motions along the line of sight. Simulations show that this is possible but highly improbable - it's really difficult to produce a cloud which is small, isolated, and with that all-important very high line width in this way. Every cloud detected would be a case of us happening to observe a galaxy interaction during a very short phase of its evolution.
• They could be turbulent spheres. Random bulk motions within the clouds could be kept in check by the compression from the hot external gas pressure. This doesn't work - such clouds disintegrate very rapidly, though in a variety of interesting ways.

None of this is to imply that tidal debris or pressure confinement aren't important. In fact, I'd say most clouds probably are tidal debris, because they have low line widths which the simulations say is easy to do. And pressure confinement might well be important in those cases. Turbulence ? We're not so sure about that one. We don't know of a good way to keep injecting energy into a cloud after it's been separated from its parent galaxy.

The point is that while these processes have important roles to play for some clouds, it doesn't automatically imply that they matter very much for the particular clouds that we're interested in. So far as we can tell, turbulence and external pressure don't help in the slightest for these objects. In fact, because the clouds disperse in roughly the time predicted just based on their size and motion, it could be that it's making very little difference to most of them. Of course, some other explanation might need to use turbulent motions as well, but what we've shown so far is that by itself, turbulence simply doesn't work. And I doubt that it can be made to work without employing some fundamentally different physics.

I don't know what the clouds really are. The evidence thus far points quite clearly towards dark galaxies, but I have a sneaking suspicion that they might turn out to be some form of tidal debris after all. Oh, it won't be the sort we've tested. It'll be something more complicated, caused by a combination of tidal forces and the intracluster gas. Maybe. Of course, it's also possible that they'll turn out to be something else we haven't even thought of yet.

Finally, we should return to poor old Thomas Becket. For if his noble liege had been not a medieval prince but an astronomer, he would surely have cried out, "Will no-one rid me of this turbulent sphere ?". To which Becket, his postdoc, would have responded, "There is no need, sire, it hath destroyed itself." And they all lived happily ever after.

Conclusion : Thomas Becket should have gone in for astronomy instead. It's generally a lot less bloody.