Twelve Mile Tall Tales

If you haven't seen it yet, I suggest you first read one of the press releases about the Thoth Tower, a proposed "space elevator" system that's supposed to be able to cut the cost of access to space. As I shall show, it won't.

Image from TechInsider.

Getting To Space Is Cheaper Than You Think

Probably not this cheap though.

Space, they say, is only an hour's drive away - straight up. The energy required to travel 100 vertical kilometres is actually extremely modest : for a hefty 100 kg individual it's about the same as 100 kWh... which costs all of £3 ($5 US). Why, then, does it take the incredible power and expense of a rocket to launch stuff into space ? Why does it actually cost something like $4,000 per kilo to get into space ?

Well, the 100 kWh is the theoretical minimum you need to overcome gravity. Any launch system is going to be less than 100% efficient, so you'll always need to put in more energy than that. Rockets in particular have to carry all their own fuel, and the fuel is heavy, so they need to carry enough to lift both the weight of the fuel and the payload. And merely reaching 100 km altitude is far easier than going into orbit at 100 km altitude.

To hurl something up to 100 km altitude, you'd have to give it a staring speed of about 1.4 km/s (3,100 mph), ignoring air resistance. But if you did that, it would simply go straight up and then fall straight back down again.

More on this at the excellent xkcd.

To get something to stay in orbit you need to go very much faster, about 7.8 km/s (17,000 mph). Although that's "only" about 5.6 times faster, energy scales as speed squared... so you'll need to give it over thirty times as much energy. Let's say you could float a balloon up to 100 km altitude (you can't, but let's pretend). If you threw something off the side, it would still simply plummet to the ground - unless you threw it at 7.8 km/s sideways. The point is your starting altitude makes almost no difference at all to the huge amount of energy you need to go into orbit. You need just as big a rocket at 100 km as you do on the ground.

Or you can just troll physics.

Wouldn't it be nice if, instead of having to deal with complicated rockets and the need for vast, explosive energies, we could just take the stairs ?

Maybe. Maybe not.

Space Elevators

Source.

The idea of a space elevator is nothing new, but traditionally it's very different to Thoth's "plan". A more typical space elevator is a cable stretching 36,000 km out from the surface of the Earth (with a counterweight station on the end to keep it in tension). At that altitude, it so happens that an orbiting object would take 24 hours to orbit the Earth. Since the Earth takes 24 hours to rotate, objects orbiting at that distance never move in the sky : they are geostationary satellites. Below this distance orbiting objects have to move more quickly, so they take less than 24 hours to orbit and aren't always visible overhead.

The dashed lines show the line of sight from each of the satellites to the ground. Watch carefully and you'll see that the satellite at 36,000 km is always above the same point on the Earth, whereas the others move.
And no, I don't know why the background is that yucky grey colour instead of its original pristine white.

Here's the thing. The station at the end of the tether is in orbit, just like any other satellite. "Drop" something from the end station and it won't fall, because it's already in orbit. At lower levels, this isn't true. The tension in the tether forces it to stay up, but the speed of the tether at all points below the station isn't high enough for it to be orbiting. So if something fell off from halfway up, it would simply drop to the Earth below.

Source.

... except that it's a bit more complicated than that. You don't simply fall straight down like you would from a very tall building or a mountain, staying parallel to the tower. This thing is so tall that we're out of the realm of everyday experience and into orbital mechanics. Gravity at the top of the tower is much weaker than at the base (more on that soon), so as you fall not only does your speed increase, but your acceleration also increases. And the linear speed at which the cable is moving forwards increases with height.

All of which means that, unlike falling off a cliff, if you fell off a space elevator from a high enough altitude you'd actually move forwards relative to it. And if you were high enough up, you wouldn't hit the ground at all - you'd go into orbit. Not a nice circular obit like at the top of the tether, but a hair-raising elliptical orbit (which in the example shown here would probably graze the atmosphere so you'd die a horrible fiery death).

Note that all the little spheres drop at the same time. But gravity
is so much weaker at the top that it takes them much longer to fall.
The Python code used to generate this is available here.

Anyway, the neat thing about this kind of space elevator is that you don't need a rocket to reach the tremendous speeds necessary for orbit. Instead of an incredibly complicated rocket system, which has to carry all its fuel onboard to travel in the vacuum of space, you can just use an electrically-powered lift. That would get you to orbit for the princely sum of £150 per person. Roughly the price of an EasyJet return ticket from Bristol to Prague. Of course it won't be this good in practise, because nothing is perfectly efficient, but clearly it's many orders of magnitude cheaper than using conventional rockets.


What About Thor ?

He isn't relevant at all. Check your spelling.


Err, OK, what about Thoth ?

I'm so very glad you asked. Thoth's design is completely different. At just 20 km tall, it's not something most people would recognize as space elevator - more of a conventional building. The thing is, 20 km just isn't high enough to convey any advantage whatsoever. At that height gravity is only about 1% less than at sea level. You need to go to altitudes of thousands of kilometres before gravity really drops significantly. Here are some numbers in handy gif form, because maths.

1 g is the gravity we experience : 9.81 m/s/s. The times shown are how long it would take to fall 1 metre under those accelerations, at the altitudes shown at the top. Earth's gravity at 5,000 km is roughly the same as the surface gravity of Mars, while at 10,000 km it's about the same as on the Moon.
Yes, I know this isn't my most sophisticated graphic, but my computer is dying. Gotta keep it simple.

Clearly, you need to go to much, much greater distances than 20 km to get any advantage over gravity. But according to Tech Insider, which gives a critique of the massive engineering challenges of building the tower :

Finally, Quine claims that since rockets eat up about 30% of their fuel during the first 12-mile ascent, the tower will offer the same savings in fuel compared to conventional rockets launched from the ground.

Oh, really ?

I think not. Rockets use more of their fuel in the early stages because that's just how rockets work. The initial mass of the rocket is very large. So if you want to accelerate that large mass against gravity, you have to eject a correspondingly large mass out the other end. Moving the rocket 20 km up makes absolutely no difference to the size of the rocket needed whatsoever, if you still want to reach the same final speed with the same payload with the same gravity.

There's one possible escape for Thoth : the tower would be so tall it would be above quite a lot of the atmosphere. At 20 km the atmosphere is about 13 times less dense than at sea level. Except there's just no way that's going to save you anything like 30%, as this NASA engineer describes, and this helpful random person on the internet explains using maths. Atmospheric drag accounts for slowing the rocket by maybe a few tens of metres per second, compared to the required velocity of several thousands of metres per second. Basically, no.

But Thoth have compounded error upon error. Even if their 30% figure was correct, it's dubious if it would help. It would be like having a 30%-off sale at Harrods : the wealthy are so rich they won't care, and the rest of us still couldn't afford it.

OK, so it would help for those people in the narrow band for whom a space mission was just about out of reach. But the cost of the tower is claimed by Thoth as $5 billion, and others at more like $500 billion, as well as the engineering challenges of its construction being formidable to say the least. So it's a case of one of the most stupendous engineering projects in history for the sake of saving 30% on very expensive rocket launches. Doesn't seem like a great deal to me - and remember, that 30% saving looks wildly optimistic.

Thoth's plan for how the tower would be used looks even worse :

"Astronauts would ascend to 20 km by electrical elevator. From the top of the tower, space planes will launch in a single stage to orbit, returning to the top of the tower for refueling and reflight,” said Dr. Brendan Quine, the inventor.

Righto, first off - when did "inventor" start to mean, "someone who had an idea" ? I've got this idea for a genetically engineered fire-breathing horse that can ride a unicycle - if I patent it do I get to call myself an inventor ? How about a robot that can procrastinate ? Some sort of swimming couch... ?

THEY SAID I WAS MAD !!!!

Anyway, space planes. They don't exist. Well, the Shuttle did, but that certainly wasn't a single-stage-to-orbit vehicle*, and to land it needed a runway 4.5 km long. So Thoth's idea, in summary is to build a tower twenty times higher than any other existing structure using techniques that might not work for optimistic fuel savings for planes that don't exist on a tower that will be too small and cost too much money.

* If it wasn't already clear : being 20 km further up doesn't make it any easier to develop a single-stage-to-orbit vehicle.

All I'm saying is that no-one with an ounce of sense will put a shred of money into this.

There are space planes in development, and they do have the capacity to transform space flight. The British company Reaction Engines is developing the Skylon vehicle, to be powered by hybrid jet-rocket engines. This has been in development for a long time, but finally the technologies appear to be maturing. It would make a much more dramatic saving in launch costs compared to a giant tower - more like 75% by some estimates. That's nowhere near the savings slash a real space elevator might bring, but enough to make a real difference.

So as far as I can tell, Thoth's plan relies on some absurdly fundamental misunderstandings of high school physics. It just won't work.


Bur let's end on a positive note. Private companies have been making ludicrous proposals for decades - Thoth's is nothing new. The difference now is that these absurdities notwithstanding, private space ventures are finally starting to make a difference. Space tourism is a reality - albeit only for the super-rich, but with the prospect of a dramatic price fall no longer a pipe dream. Space X and Orbital Sciences (now known by the less inspiring name of Orbital ATK) have already delivered cargo to the International Space Station, while Scaled Composites claimed the first astronaut launched by a privately-built rocket. And let's not forget : though Thoth's idea is very silly, someday a proper space elevator might really open up the road to the stars.

Seven Very Good Reasons To Be A Little Bit Suspicious Of Dark Matter, But Let's Not Go Nuts

This is the concluding and most important in a trilogy of posts about why dark matter is probably real, but might not be. In part one we looked at how dark matter may be important for forming galaxies, but might not be, and in part two we saw how there's absolutely no compelling philosophical reason to prefer dark matter to its main alternative explanation, modifying gravity.

While we saw a few examples in part one, in this post I want to take a more detailed look at the arguments against dark matter. While I tend toward the view that it does exist, let's not pretend that it doesn't have problems. And I find it very strange indeed when people claim that rival theories can't be correct because of their problems, knowing full well that the dark matter paradigm is hardly without difficulties. What I'm aiming to show is why I think dark matter is the best explanation, but not yet beyond reasonable doubt, as well as some of the successes and failures of the main alternative :  "MOND" (or Modified Newtonian Dynamics, though this is really just one of several proposed modifications of gravity).

1) Halo conspiracy

Dark matter halos always seem to be setup just so as to make the rotation curves of galaxies flat, which is a bit weird. Why don't they come in a wider variety of shapes ? Actually I'm not at all convinced this a problem because curves aren't always truly flat. Often they are, but sometimes they're weakly declining or even always rising.

Source.

Neither MOND not dark matter have any problems explaining the shape of the rotation curves. Their flatness is only a problem for dark matter if you really think they're surprisingly flat, which I don't. No more surprising than a surprise birthday party, at any rate... unless you're the kind of person who forgets their own birthday, in which case cosmology is not for you.

2) Rotation curve wiggles

Much more interestingly, rotation curves aren't smooth. I've heard the claim previously that MOND predicts these wiggles very well, whereas dark matter doesn't. But I'd only seen curves with small wiggles in them, and as an observer I know only too damn well not to trust error bars too much. As a rule of thumb, double the size of the error bars and you're closer to reality. So itty-bitty wiggles like these aren't very interesting.

Original source.

However, what Milgrom showed that was far more interesting was a curve with a much more dramatic wiggle in it :

Source.

What the hell is that ? The curve goes down and then back up again ? But dark matter halos are supposed to be smooth. The height of the curve should tell you how much mass is within that particular radius. If dark matter density is smoothly decreasing with radius, how can the curve drop ?

But let's not get too excited. Remember we probably shouldn't trust those teeny-weeny error bars too much. It's almost always better to get repeat observations - not because the rotation curve itself changes with time (that takes tens of millions of years), but because instruments get better. Here's a rotation curve from twenty years later of the same galaxy.

From Stacy McGaugh's MOND pages.

Quite different, isn't it ? Instead of a distinct dip, the curve now flattens off before rising again. The difference, in my opinion, is quite worrying. What might we find with the next set of observations ? True, MOND fits the data very well - so it should, because the MOND fit relies on the density profile. Assuming, though, that this curve is accurate, is it really good evidence against dark matter ?

Weeeell... it's intriguing. You might wonder if maybe this galaxy is interacting (or something) that might have disturbed the motions of its stars and gas. If it is, it isn't obvious.

Looks like NGC 1560 is quietly minding its own business to me.

Milgrom and the other MOND supporters admitted that this is the most interesting rotation curve going against the predictions of dark matter. Personally, after seeing the later observations, I can't describe this as anything more than intriguing - certainly not great evidence against dark matter, in my opinion. Admittedly, I was rather captivated at the time, but in the cold grey light of dawn* it doesn't look nearly so interesting.

* Actually the warm sticky twilight of an unpleasant summer's evening.

3) Surface brightness conspiracy

The Tully-Fisher relation is simply an observed relation between how fast a galaxy is rotating and how massive it is. Except for galaxies which have lost a lot of gas, pretty much every galaxy - no matter how red or blue, bright or faint, big or small - obeys the same relation.

From cosmoportal. "Linewidth" just means rotation speed, "I band magnitude" is basically just stellar mass.

... except that they shouldn't. It's possible to show that the surface brightness of a galaxy - how bright it is given its size - should make a difference, and low surface brightness galaxies should follow a different relation. They don't. MOND deals with this very well, and to my mind this is one of its most interesting predictions. Even if MOND is proven wrong, we should try and explain why it gets this right.

4) Lack of dark matter on small scales

Dark matter appears to be dominant over very large scales, like the entire Universe. The most striking example of the success of dark matter theory is its ability to reproduce very similar structures to what we observe in the Universe in the correct time. MOND, according to Milgrom, may be able to account for this as well - possibly even produce more structure than we actually see... but that's not yet known.

From the Millennium Simulation.

But as we go down to smaller scales, dark matter is less and less important, yet, paradoxically, more and more dominant. Galaxies in clusters are moving too fast, so the clusters should just fly apart without them. Similarly, individual galaxies are rotating too fast - same problem. But some galaxies are much, much smaller than others. Dark matter appears to utterly dominate the smallest galaxies... but is totally unimportant in similar-sized structures within larger galaxies.

For example some globular clusters are as (or more) massive than dwarf galaxies, but don't appear to contain any dark matter (i.e. they don't have flat rotation curves). In fact most people would define a galaxy as something that contains dark matter.

Now, maybe it's a bit strange that dark matter apparently dominates some tiny galaxies, but isn't present in globular clusters - but that could be down to the incredibly complex process that is galaxy formation. Yet we also don't see much (if any) evidence of dark matter when looking at motions of stars around the Sun, in contradiction to what simulations predict. It's certainly a little suspicious that dark matter appears to only affect rotation curves.

On the other hand, you might wonder how such similar-looking systems with such different rotation curves can co-exist if MOND is correct. Surely gravity is gravity, so big clouds of stars should either all have flat rotation curves, or not ?

THIS PROBLEM VEXES ME

As usual it's more complicated than that. MOND is nowhere near as simple as just making gravity a bit stronger or weaker (read that link, you won't regret it). Elliptical galaxies are also basically just big balls of stars, and MOND can explain their internal motions very well. But it's running into difficulties with the much smaller globular clusters, and even the MOND evangelicals admit this may be a severe problem. The results aren't yet decisive though.

Just to make sure you're really confused, spiral galaxies are dominated by dark matter, having about ten times as much dark as luminous matter. Interestingly, this fraction appears to be more-or-less constant and doesn't vary depending on the brightness or colour of the spiral. Yet elliptical galaxies apparently possess little or no dark matter, despite being supposed to form from the merging of spiral galaxies ! And that's very odd indeed. Probably, methinks, this whole "merging" business is massively over-rated.

5) Missing satellite problem

This is one of the biggest problems in cosmology today. Simulations predict many times more smaller satellite galaxies around our own Milky Way than are actually observed. Interestingly, on larger scales (like whole clusters of galaxies) this problem doesn't appear, with simulations predicting the correct number of galaxies. Could it be that the tremendously complicated gas physics has something to do with it ?

The Virgo Cluster.

Maybe. One explanation, which periodically goes in and out of favour, is that perhaps the smaller dark matter halos never accrete enough gas to form any stars at all. This idea is very much in vogue again right now, with a nearby starless gas cloud thought to require dark matter to survive its (apparent) passage through the Milky Way, a whole population of clouds discovered that could fit the bill, and complex simulations suggesting that it is indeed possible for such objects to exist. There's even an idea that by carefully examining the gas distribution, missing galaxies could be found like looking for a ship by finding its wake (perhaps explaining some of those rotation curve wiggles).

But not so fast ! Even if most of these dark halos remain dark, the simulations predict that some of them are just so darn big there's no way they can avoid forming stars (the so-called "too big to fail" problem, a name I dislike). And that's worrying. Although quite popular a few years ago, practically no-one believes in giant dark galaxies any more. The latest generation of hydrogen surveys are good enough that they really should have detected them. Except for a few weird, interesting candidates, which are far too few in number to explain anything, they haven't.

To add to the confusion, more sensitive observations have discovered more, fainter galaxies... but simulations have predicted even greater numbers of missing satellites. And there are some hints that our data analysis may be missing some surprisingly bright nearby galaxies.

Nobody knows if MOND can help with this or not, because there aren't any appropriate simulations as yet. So the jury's not merely still out on this one - they've sold all their possessions and gone on a cruise around the Bahamas with some attractive celebrities, and I don't think they're coming back.

6) Orientation of satellite galaxies

Dwarf galaxies are the bad boys of the Universe. They don't let no-one tell 'em what to do. Not only are their numbers all wrong, but their orbits are just plain stupid. We saw previously that it's remarkably easy to avoid the missing satellite problem... but that simulation formed the satellites orbiting in-line with the disc, and wasn't the most orthodox approach. Regular simulations produce satellites buzzing around the larger galaxy like a swarm of bees.

From the Via Lactea project.

And the real ones ? They're orbiting at right-angles to the disc, which I suppose is the cosmological equivalent of giving us the finger.

Is it a bird ? Is it a plane ? No, it's a Vast Polar Structure !... of satellite galaxies of the Milky Way, rendered by me. The Milky Way image is an artist's concept by Nick Risinger. The satellite galaxies are shown as spheres of arbitrary size to make them easier to see.

MOND itself doesn't offer an obvious explanation to this. However one alternative explanation is that maybe hardly any of the satellites are old, primordial (left over from the formation of the Galaxy) objects, and instead they're mostly tidal dwarf galaxies. When galaxies interact with each other, they can sometimes draw out gas (sometimes a great deal of gas) into long tails. Tidal dwarf galaxies are galaxies that form in this stripped material. That would naturally explain why the Milky Way satellites are distributed in a plane and not in a cloud.

Trouble is, it's much more difficult to pull material into a polar orbit than one in the same plane as the disc. Since it's spinning in the plane already, you only need to give it a bit of a boost to move the gas further out. But, perpendicular to the plane, the gas is barely moving at all, so you need to give it a lot more energy to remove it. So the question is : can you pull enough gas into a polar orbit without completely disrupting the disc of the Milky Way ?

Other explanations of the planes of satellites, using entirely conventional dark matter explanations, are beginning to emerge. Some say that it's all about how you select the satellites in the simulations, and actually they predicted planes all along. Others say that it's the large-scale structure that's responsible. It's too early to tell, but having read these in depth (as well as hearing the counter-arguments against them), in my opinion it's now very unfair to say that the planes of satellites definitely contradict standard models.

And if the planar structure of the satellites really can be explained in ordinary dark matter models, perhaps that would also help with the missing satellite problem... after all, we've been assuming that  the whole sky should be full of galaxies. If they're only present in certain directions...

7) Existence of the Bullet Cluster

The Bullet Cluster is the poster child for how successful dark matter is. Two galaxy clusters collided, and since they're mostly empty space, they continued on their merry way, none the worse for wear. Gas in the clusters (pink) however, also collided, and since it isn't mostly empty space it got a bit stuck. Now it's found mainly between the two clusters. But the dark matter - or so the legend goes - kept going, and consequently its effects can still be seen by gravitational lensing (blue), still surrounding the galaxies in the original clusters.

It's true that this result can be very neatly explained using conventional models. But, as usual, there's more to it than that.

Sometimes you hear people say that the Bullet Cluster disproves MOND. It doesn't. It isn't clear what MOND predicts, because there isn't a well-established version that agrees with relativity* yet - so what is says about gravitational lensing is anyone's guess. But remember, MOND isn't as simple as making gravity weaker or stronger - the distribution of mass matters.

* In MOND the speed of gravity is assumed to be infinite; relativity says this is not so.

The other less-reported aspect of the cluster is that two massive galaxy clusters colliding at these speeds are predicted to be extremely rare in standard cosmology. Maybe so rare we shouldn't expect to ever detect any.  But a more recent paper has found that a single Bullet Cluster is just about compatible with standard cosmology (though finding even a single other cluster like this would be a serious challenge to conventional models). Another claims (for reasons I don't understand) that's it's not a problem at all.

Conclusion

Source.

Never mind, "science it works bitches". That's true enough when you have really well-established results, but not for real, honest-to-God front line research. The process of getting to those well-established results is messier than the Greek financial crisis and sometimes less fun than a romantic evening with Donald Trump*. People get themselves into an awful tizz about who's right and who's wrong, but sometimes you need strong opinions to drive research forward. Or backward. But always twirling, twirling toward freedom ! Or something...

* Urrrgh.

To my mind, dark matter has the edge over modifying gravity. We know that gravity works extremely well on other scales, and we know that almost-dark particles exist. We also know that the physics of gas and star formation is frickin' complicated (and no amount of modifying gravity is going to change that), so I'm prepared to bet on "gas physics" to explain most of the current anomalies. 

I also have a hard time seeing any of the problems as being really serious - difficult, sure, suspicious even... but there's no single problem that makes me think, "OH, CRAP". Some people seem to see every problem as being insurmountable and that we should throw out a theory that gets even a single thing wrong. Personally I think some considerable leeway is acceptable, and we're not nearly at the point yet we should abandon anything. For me, as usual, the consensus view is the one to go with*.

* Quite honestly I'm somewhat disappointed. I was genuinely hoping that in the course of researching this I'd find some much more compelling reason to doubt dark matter or favour MOND. Actually I've ended up reinforcing my own 75:25 bias in favour of dark matter, maybe even increasing it to 80:20. Maybe next time I'll pick something more controversial to discuss.

But, "having the edge" does not mean, "wipe the floor with", which is what the media seems to love. If I try and be as objective as possible I can't give you a decisive result either way. But being totally objective is not always the best way to advance science - it helps to have a goal, something to prove, an axe to grind. The trick is not to lose perspective and become so invested in that goal that you refuse to accept it when the answer isn't what you want.

So I'm not going to tell you what you should believe - rather the opposite. By all means, form an opinion. Just don't be certain of it just yet. The way I see it things are progressing slowly in favour of dark matter, but it would be foolish to abandon all other possibilities right now. The day may come when the predictions of MOND fail, when we forsake modified gravity and break all bonds of... well, whatever, but it is not this day.

The Universe Is A Great Big Bloody Mess And You Won't Convince Me Otherwise

Last week, Moti "Modified Newtonian Dynamics" (MOND) Milgrom visited Prague and gave a lecture. I was fortunate to have a few minutes afterwards to talk with him, which has prompted this and the previous post. Last time I explained one small line of reasoning why I think dark matter is a more likely explanation for certain observations, but I also mentioned some arguments against it. Today I wanted to go into more details on those. But I'm not going to, because I realised it's worth a short post about the the philosophical differences (or indeed, lack thereof) between those who believe in dark matter and those who favour modifying gravity.

The Crab Nebula, the remains of a massive star that exploded about a thousand years ago. Similar explosions created the heavy elements found in life on Earth.

Let's get one thing straight. The Universe is not elegant. Beautiful, sure, but creating the elements needed for life by blowing up entire stars has all the elegance of a constipated walrus in heat. Human scientists may like to think there's some kind of underlying order, but the Universe is under no obligation to behave how we think it should.

You could say to the universe this is not fair. And the universe would say: Oh, isn’t it? Sorry. - Terry Pratchett, Interesting Times.

However beautiful, obvious, simple, or mathematical harmonious a theory is tells you precisely nothing about whether it is really true. It's useful to start with the simplest theory you can come up with to explain observations (just because simpler theories tend to be easier to test), but there's no good reason to expect the Universe to follow a rule because it's simple. Or not to follow a rule because you don't understand it.

Take gravity, for instance. We started out believing that heavy objects fall faster than light ones -  a simple and obvious idea that's utter garbage. Thousands of years later we came up with the idea that there's a force acting by different amounts to keep objects of different masses accelerating at exactly the same rate toward the ground. That's a totally inelegant, contrived solution (though the equation predicting the acceleration is very very simple), but it works much better.

Centuries later and we realised that that too is wide of the mark, because actually objects are falling on the shortest paths through curved spacetime and obviously that's a much more elegant solution.

Of course the bear is only thinking that calling this idea "elegant" is ridiculous. He's not making any comment on the validity of the theory, you understand.

But Einstein's gravity works ! It works far better than Newton's model in many situations, however ridiculous making the speed of light constant for all observers (no matter their speed) may seem, or however much overkill allowing time travel might be just to sort out why things fall at the speed they do. Few people regard Einstein's theory as the last word on gravity though, because, amongst other things, it predicts the existence of singularities - points of infinite density and gravity. And apparently infinities are just silly, inelegant things... and we wouldn't want any of them, right ?*

* String theory postulates that there are eleven dimensions as a way of avoiding these singularities. I don't know about you, but I find that prospect at least as incomprehensible as the idea that gravity is infinite.
Now don't get me wrong. I don't like singularities any more than anyone else does, and I'd prefer a theory I can understand intuitively as much as the next man. But the Universe doesn't owe me anything. It has no obligation to be any more comprehensible to a short blonde Welsh astronomer as it does to a chimpanzee or even to a daffodil.

So when it comes to galaxy rotations, we've got an uncomfortable choice. Galaxies are spinning much faster than standard gravity models predict. If we want to save the theory, we've got to suppose that there must be a heck of a lot of extra mass that we can't see - about ten times more than the luminous matter. Or, we can say that there's a really fundamental problem with the theory.

It's interesting to ask what would have happened if we'd measured the rotation speed of galaxies back in 1915, before relativity passed a series of tests with astonishing precision. Maybe significant doubts would have been raised... but we didn't, so they weren't. Since relativity works so well, postulating a large amount of invisible matter doesn't seem so unlikely. We already know with certainty that neutrinos exist (particles which barely interact with other matter at all), so the idea that there might be a particle which interacts with normal matter even less is, perhaps, not so far-fetched.

Gravitational lensing, as predicted by general relativity.

Because we know how successful Einstein's theory is in most situations (singularities aside), the existence of dark matter is (in a sense) a prediction, not a fudge to save it. If we took that view, we could end up altering every theory whenever we found a flaw, and therefore end up making no predictions at all. It's true it's not a direct prediction of relativity, because relativity is a mathematical model which (by itself) says nothing about the real Universe. Like any mathematical tool, you have to couple it with observations to understand what's going on.

Those who doubt the existence of dark matter sometimes point to the fact that no such particle was ever predicted by the standard model. Which is to say that they trust the standard model of particle physics, but not the model of gravity. For those who believe in dark matter it's the other way around. Basically everyone is arguing about which bit of physics they think is wrong - hence the uncomfortable choice.

Honestly people, y'all sounding a bit silly. A classic case, methinks, of "the competition is so fierce because the stakes are so low". 

Another point people harp on about incessantly is falsifiability. If it's possible to prove that a theory doesn't work*, then that counts in is favour (it's much rarer to be able to directly determine if something is actually true). If you can't, then you might never know if the idea is good or not, and you could keep toying with it until the end of time.

* I mean in principle. If you actually disprove it, obviously your theory is just wrong and therefore no good.

Proponents of modified gravity sometimes say that their ideas are falsifiable, whereas dark matter isn't. In fact one of their theories, TeVeS, has already been falsified, as Milgrom admitted last week. The trouble is that now they're looking for other ways to modify gravity to explain away dark matter... which reminds me of the time Ireland voted the wrong way on an E.U. treaty - they were asked to vote again.

Yes, you can falsify individual theories of gravity. It's far less clear if you can falsify all theories of gravity that could explain dark matter. You could very well keep saying, "well then let's try another one", ad infinitum.

Dark matter doesn't do any better than this. Although there are direct detection experiments underway, if they don't find anything one could always say "well then the particle must be even more difficult to detect". Much worse, though, is that some people would like to define dark matter as the anomalous gravitational effects themselves, rather than any specific particle :

Even if all of this was explained by a modification of gravity rather than an unknown type of matter, it would still have to be possible to formulate this modification of gravity in a way that makes it look pretty much like a new type of matter. And we’d still call it dark matter.

Umm, no. No we wouldn't, because that is plainly ridiculous. We decided to call it "matter" for a reason. And that reason is that we didn't want to modify gravity !!!

EDIT : There is one possible way out of this - the notion that dark matter could be a spacetime superfluid, in which spacetime itself curves exactly as though deformed by mass but without any matter present. This would be dark mass rather than dark matter, but it's the nearest thing to unifying the dark matter and modified gravity camps I've come across. Gravity would be modified, but mass would also be present. That would have some huge philosophical advantages, but potentially some equally huge hurdles such as having to deal with mass without matter.

Then again I hear an equally interesting mix of noises from the MOND group. One person is prone to saying, "and thereby dark matter is falsified", almost as a reflex action.... "Merging galaxies ? Falsify CDM cosmology. Tidal dwarf galaxies ? HAH ! They disprove CDM completely. See that dog over there ? He falsifies CDM cosmology too. This piece of cheese... ? How about my enormous hat ?" (I've thought about making a drinking game out of this). Another person insists that dark matter can't be falsified. You see my dilemma.

Just to make things even more complicated, most simulations of galaxy formation with dark matter only use dark matter, because modelling the gas and stars is much more complicated (that is beginning to change, but slowly). So DM supporters cry out, "we need baryonic [normal matter] physics !" whenever a discrepancy, however major, is found between theory and observation. In contrast MONDers don't really have much in the way of simulations yet, so we don't really know how well the theory works at all. That, however, will soon change.

The reality is that front-line research doesn't always conform to the idealised standards of the scientific method. It can't. We are, after all, talking about explaining the nature of the Universe here - we are not at the point where we even know all the predictions of the theories to test them. We have no choice but to grope in the dark, but if we don't try at all we shall most certainly fail.

Philosophy, then, hasn't been of much help. The Universe doesn't give a monkey's if your theory is more elegant or not. Arguing about whether you think particle physics or gravity is more likely to be wrong isn't likely to get you anywhere. And neither the notions of dark matter nor of modified gravity are clearly falsifiable. 

But... we do know that Einstein's theory is well-tested in controlled conditions, and we know that some particles similar to dark matter do exist. Which to my mind cautiously swings it in favour of dark matter, but not by anywhere near enough to say, "let's give up modifying gravity, that was a silly idea." Since neither idea appears to have any intrinsic advantage over the other, the only way to choose between them is to look in detail at the arguments for and against both ideas. Which is what we'll do next time.

Of course, you can always just say, "I honestly don't know", but where's the fun in that ?

What Has Dark Matter Ever Done For Us ?

Well I suppose even Albert Einstein must have had an off-day, because if you ask me, a Universe full of giraffes and supernovae doesn't score highly on list of "things I definitely understand". In fact I wouldn't put it on the list at all.

I mean, Albert, what the hell were you thinking/drinking/smoking ? In what possible way is a Universe containing armadillos and exploding stars and porridge and black holes the slightest bit comprehensible ? Even very senior astronomers still insist on the old cliché that a frog is far more complicated than, say, a star or a galaxy. Which is a little bit weird considering just how little we understand about galaxies, and makes me wonder if biologists are all in the wrong profession.

ALL GLORY TO THE HYPNO-TOAD... but is he really more complicated than a galaxy ? I think not.

Nothing in astronomy seems to anger People On The Internet quite so much as the apparently simple notion of dark matter. Popular articles are universally greeted with a chorus of "scientists don't understand everything !" and "they're only looking for dark matter to keep themselves employed !" The sociology of this anti-science movement, even though dark matter is about as detached from any political or ethical concerns as it's possible to be, is almost as interesting as the physics itself. But today, let's stick to the science as much as possible.

(To digress from that just for a moment, I get kind of cheesed off when I read things like, "physicists who don't believe in dark matter are wrong." Such a level of certainty is not warranted. I do believe dark matter is the most likely explanation, but to claim that all other explanations have been falsified seems a bit strange.)


I've written about dark matter many times before, but to sum up : galaxies appear to be spinning too fast. Without some extra mass to hold them together, they should just fly apart.

Explanatory blog post.

My third-year undergraduate project has earned me a small degree of internet fame in some circles, while my fourth year project has never, until now, got a look in*. Today, in an effort to demonstrate how science is really done (and hopefully convince you that dark matter isn't such a crazy notion after all), I shall try and redress the balance.

* Unfortunately at the time I had yet to learn Python, which was a shame because it would naturally have lent itself to some pretty animations.

This was a project to try and simulate the formation of a disc galaxy without dark matter. Back then I was far less convinced about dark matter : probably, I would say, only at the 50:50 level. These days I'm more at the 75:25 level in favour - good enough to work with, but not nearly enough to bet my life on.

In my report, I described several arguments against the existence of dark matter. There are plenty more, of course, but these will do for now :


1) Halo conspiracy
Why are rotation curves* of galaxies flat as opposed to some other shape ? These days I'm a lot less convinced that this is really a problem - curves are seldom truly flat. They vary considerably, sometimes always rising, sometimes weakly declining (though not as much as if there was no dark matter). The only sense in that there's a "conspiracy" is that the curves don't agree with predictions from Newtonian dynamics. That's a lot less interesting than if they really did all have very similar shapes. Actually the details of this turn out to be very interesting, but I'll save that for a future post.

* A rotation curve just measures the speed at which a galaxy  is rotating at different distances from its center (usually by measuring its gas). That the speed doesn't drop with distance was the key piece of evidence in the discovery of dark matter.

If you're wondering about the name, dark matter clouds are usually known as halos, hence the "halo conspiracy" term - the idea being that the halo is somehow conspiring with the normal matter to always produce rotation curves of roughly the same shape.

Source - rotation curves of a sample of spiral galaxies. Irregular galaxies tend to show curves which never flatten off but just keep rising.

2) Surface brightness conspiracy
Surface brightness just means how bright galaxies are per unit area  - or to put it another way, some galaxies of a given size have more stars than others. Strangely, this doesn't seem to make much difference - it's only the total brightness that determines how fast the galaxy is rotating. But it's quite easy to show that surface brightness should make a difference. It's as though the dark matter and luminous matter are connected, and it isn't at all obvious why that should be.

The low surface brightness VCC 975 (left) compared with the normal VCC 1555 (right).

Similarly, dark matter "halos" (i.e. clouds) always seem to contain the same fraction of luminous matter, no matter their size. Galaxy formation theory says that ordinary matter falls into dark matter halos, so there's no obvious reason why the fraction of ordinary matter should be constant.


3) Dark matter inside galaxies is inferred from a single measurement - rotation curves.
If there were several observations that dark matter existed this would be a lot more convincing, but as far as we can tell dark matter does one thing, and one thing only : it keeps galaxies rotating more quickly. Even on scales just a bit smaller than the galaxy it doesn't appear to have much of an effect. And it seems a bit strange that 90% of the galaxy should do nothing very much except keep it spinning round a bit faster than it otherwise would.

Of course there are other observations in other situations where dark matter is also very important, like galaxy clusters and the large-scale structure of the Universe. But on scales smaller than galaxies, this is apparently not the case. Yes, even though galaxies come in many different sizes - dark matter only appears to be important over the whole galaxy. You may have heard recent reports to the contrary, but in my opinion that press release was actually pretty awful.

Shamelessly plugging my own work again.

It was that third point that motivated my undergraduate project - what would happen if we tried to simulate the formation of a spiral galaxy but without the dark matter ? Does the dark matter really do nothing at all except change the rotation curve ? If so, that would be a bit suspicious. You'd think that 90% of the mass of a galaxy ought to play some role beyond gathering the gas together and making it spin faster.

Yes, I know there are a whole bunch of other reasons to believe dark matter exists. But trying to test the entire dark matter paradigm at once is a monumental undertaking - so daunting a prospect that there's a risk no-one* will check it at all, thus establishing a false consensus. A much better approach is to break it down into smaller, manageable chunks. If we can say, "dark matter doesn't do anything expect make things spin faster", then we might want to start questioning other aspects of the paradigm. If, on the other hand, we can show that dark matter has some other essential role, then that strengthens the case for its existence.

* Especially a fourth-year undergraduate.

Neither scenario makes for a revolutionary breakthrough, but as I've tried to stress again and again and again : that's not how science usually works. What we'll get from the investigation is only one piece of the puzzle - nothing more, nothing less. Take enough baby steps and eventually you'll get to Outer Mongolia, write a novel, learn to play the piano, bring dinosaurs back to life, or whatever the heck else it is you want out of life.

Of course, some of us have more cerebral goals than others.

With that in mind, the simulations we ran were anyway somewhat unorthodox. Mainstream cosmology says that galaxies form by the merging of smaller galaxies. The model we used was much simpler : the collapse of a big cloud of gas straight into a rotating disc. It's called a monolithic collapse, though actually the process is a lot more complicated than a big hunk of gas suddenly turning into a galaxy.

More here. Dark matter is purple, gas yellow, and stars are red. The particles are initially in a 3D grid (filling a spherical volume), with small random motions. That's why at the start it looks like there are lots of discrete purple and yellow clouds - actually they are long columns.

I'm not sure why this approach doesn't get more attention. While dark matter is usually taken for granted, the idea of hierarchical merging is very much more openly controversial. In fact, pretty much every conference I've ever been to has left me with the distinct impression that it's only really a few prestigious diehards who actually believe it.

To me, the collapse of a single giant cloud into a galaxy - which quantitatively resembles actual spiral galaxies - seems like a much simpler idea than trying to build up a disc by lots of small galaxies that all collide in just the right way as to form a neat disc. It also has the advantage of not producing a "missing satellite" problem - unlike most other simulations, this one produces a spiral galaxy with about the same number of orbiting satellite dwarf galaxies as we observe in reality*. Unfortunately their orbits are all wrong, but meh. You can't have everything.

* That is no small achievement, but for some reason - God knows why - the paper has only 15 citations in 14 years.

The satellite galaxies of the Milky Way orbit at right-angles to
the disc, whereas the simulation predicts they should orbit in
the same plane. Ah, well, whatever, never mind.

Anyway, what you can't see too well in the gif is that on the large scale, the dark matter tends to fragment before it completely collapses. Any part of the halo which happens to become slightly denser than the rest (just through the small random motions of the particles) will have more gravity and tend to collapse faster. Remember that the gif is showing several billion years of simulation time - there's plenty of time for parts of the halo to fragment before the whole thing collapses.

Fragmentation of the collapsing dark matter (left) and gas (right). Both images are about 85 kpc across (280,000 light years).

Since the dark matter is collisionless - it doesn't interact with itself - these condensations tend to be pretty diffuse, but they're still quite massive. This means the dark matter fragments draw in some of the surrounding gas, which makes the whole collapse process very messy. Instead of a uniform sphere that just shrinks, you get a load of different clouds all heading only roughly toward the center of the cloud.

In the gif you can see a giant purple shockwave - after the dark matter collapses, most of it re-expands. That means the gravity near the center is reduced, and what you get is a bunch of gas fragments all sort of milling about, which eventually turn into a nice happy galaxy.

But... take the dark matter away and that early fragmentation doesn't happen. Instead, the gas just collapses uniformly until it reaches a very small size indeed, at which point it does, eventually, fragment*. But the final result looks nothing like a galaxy - what we found was a ring about 10% the diameter of the galaxy that formed in the case of dark matter, with the gas density being very much higher.

* The gas is much hotter than the dark matter. Temperature is basically velocity dispersion, i.e. random motions. For fragmentation to occur, gravity has to be strong enough to overcome these random motions. For the hotter gas, this means it only happens when the density is very high.

With dark matter, a galaxy around 50 kpc (163,000 light years) across is formed. Without it, what we got was this itty-bitty ring about 3 kpc (9,700 light years) across.

This lack of pre-collapse fragmentation was certainly important, but there was also another problem. The simulation lost angular momentum (which breaks physics - simulations do that all the time but usually just by a negligible amount), so everything was spinning more slowly than it should. The resulting ring was therefore smaller than it should have been. However, fourth-year undergraduate me neglected to write down exactly how much angular momentum was lost, so I can't tell you how much bigger the ring may have been if the code wasn't bugged. Well, we live and learn.

(all I did write was that while normally it's conserved to within 1% or less, in this run it was losing 8% per timestep - which is nothing short of catastrophic)

Of course we didn't just do one simulation - more like a couple of dozen, each taking a few days to run. We varied a whole bunch of parameters, which I won't go into here. Nothing worked. The one time we managed to create something that did resemble a galaxy, it was spinning much too fast - more than twice as fast as anything ever observed, and for once that's well above any measurement errors.


So, another triumph for the dark matter model then ? Heck no ! That's how the popular press would spin it... but I'm trying really hard to convince you that just because a result doesn't have Earth-shattering implications doesn't mean it's not interesting. The obsession in the media for decisive results is pretty damaging for science communication, but that's another story...

What we showed was that in this unconventional model, dark matter was necessary to forming the galaxy - it's not a case of it doing nothing much except making the gas spin faster. It doesn't merely help galaxies form more rapidly - it's essential for them to form at all. I don't know of anyone who's tried to do a more conventional galaxy formation simulation but with the dark matter simply turned off, but it would make for a fascinating comparison.

So we found one small piece of evidence in favour of dark matter. It's through a series of these small, incremental findings that I've become convinced that dark matter is the most likely explanation for what we observe. But that in no way means that there aren't still other problems, or other ways to form a galaxy without dark matter. I'll take a look at why I'm still not a True Believer in dark matter next time.