Archive for large-scale structure of the Universe

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The Zel’dovich Universe – Day 2 Summary

Posted in History, The Universe and Stuff with tags , , , on June 25, 2014 by telescoper

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Day Two of this enjoyable meeting involved more talks about the cosmic web of large-scale structure of the Universe. I’m not going to attempt to summarize the whole day, but will just mention a couple of things that made me reflect a bit. Unfortunately that means I won’t be able to do more than merely mention some of the other fascinating things that came up, as phase-space flip-flops and one-dimensional Origami.

One was a very nice review by John Peacock in which he showed that a version of Moore’s law applies to galaxy redshift surveys; since the first measurement of the redshift of an extragalactic object by Slipher in 1912, the number of redshifts has doubled every 2-3 years ago. This exponential growth has been driven by improvements in technology, from photographic plates to electronic detectors and from single-object spectroscopy to multiplex technology and so on. At this rate by 2050 or so we should have redshifts for most galaxies in the observable Universe. Progress in cosmography has been remarkable indeed.

The term “Cosmic Web” may be a bit of a misnomer in fact, as a consensus may be emerging that in some sense it is more like a honeycomb. Thanks to a miracle of 3D printing, here is an example of what the large-scale structure of the Universe seems to look like:

IMG-20140624-00350

One of the issues that emerged from the mix of theoretical and observational talks concerned the scale of cosmic homogeneity. Our standard cosmological model is based on the Cosmological Principle, which asserts that the Universe is, in a broad-brush sense, homogeneous (is the same in every place) and isotropic (looks the same in all directions). But the question that has troubled cosmologists for many years is what is meant by large scales? How broad does the broad brush have to be? A couple of presentations discussed the possibly worrying evidence for the presence of a local void, a large underdensity on scale of about 200 MPc which may influence our interpretation of cosmological results.

I blogged some time ago about that the idea that the Universe might have structure on all scales, as would be the case if it were described in terms of a fractal set characterized by a fractal dimension D. In a fractal set, the mean number of neighbours of a given galaxy within a spherical volume of radius R is proportional to R^D. If galaxies are distributed uniformly (homogeneously) then D = 3, as the number of neighbours simply depends on the volume of the sphere, i.e. as R^3, and the average number-density of galaxies. A value of D < 3 indicates that the galaxies do not fill space in a homogeneous fashion: D = 1, for example, would indicate that galaxies were distributed in roughly linear structures (filaments); the mass of material distributed along a filament enclosed within a sphere grows linear with the radius of the sphere, i.e. as R^1, not as its volume; galaxies distributed in sheets would have D=2, and so on.

We know that D \simeq 1.2 on small scales (in cosmological terms, still several Megaparsecs), but the evidence for a turnover to D=3 has not been so strong, at least not until recently. It’s just just that measuring D from a survey is actually rather tricky, but also that when we cosmologists adopt the Cosmological Principle we apply it not to the distribution of galaxies in space, but to space itself. We assume that space is homogeneous so that its geometry can be described by the Friedmann-Lemaitre-Robertson-Walker metric.

According to Einstein’s theory of general relativity, clumps in the matter distribution would cause distortions in the metric which are roughly related to fluctuations in the Newtonian gravitational potential \delta\Phi by \delta\Phi/c^2 \sim \left(\lambda/ct \right)^{2} \left(\delta \rho/\rho\right), give or take a factor of a few, so that a large fluctuation in the density of matter wouldn’t necessarily cause a large fluctuation of the metric unless it were on a scale \lambda reasonably large relative to the cosmological horizon \sim ct. Galaxies correspond to a large \delta \rho/\rho \sim 10^6 but don’t violate the Cosmological Principle because they are too small in scale \lambda to perturb the background metric significantly.

The discussion of a fractal universe is one I’m overdue to return to. In my previous post I left the story as it stood about 15 years ago, and there have been numerous developments since then, not all of them consistent with each other. I will do a full “Part 2” to that post eventually, but in the mean time I’ll just comment that current large surveys, such as those derived from the Sloan Digital Sky Survey, do seem to be consistent with a Universe that possesses the property of large-scale homogeneity. If that conclusion survives the next generation of even larger galaxy redshift surveys then it will come as an immense relief to cosmologists.

The reason for that is that the equations of general relativity are very hard to solve in cases where there isn’t a lot of symmetry; there are just too many equations to solve for a general solution to be obtained. If the cosmological principle applies, however, the equations simplify enormously (both in number and form) and we can get results we can work with on the back of an envelope. Small fluctuations about the smooth background solution can be handled (approximately but robustly) using a technique called perturbation theory. If the fluctuations are large, however, these methods don’t work. What we need to do instead is construct exact inhomogeneous model, and that is very very hard. It’s of course a different question as to why the Universe is so smooth on large scales, but as a working cosmologist the real importance of it being that way is that it makes our job so much easier than it would otherwise be.

PS. If anyone reading this either at the conference or elsewhere has any questions or issues they would like me to raise during the summary talk on Saturday please don’t hesitate to leave a comment below or via Twitter using the hashtag #IAU308.

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Fly through of the GAMA Galaxy Catalogue

Posted in The Universe and Stuff with tags , , , , , , , , on March 13, 2014 by telescoper

When I’m struggling to find time to do a proper blog post I’m always grateful that I work in cosmology because nearly every day there’s something interest to post. I’m indebted to Andy Lawrence for bring the following wonderful video to my attention. It comes from the Galaxy And Mass Assembly Survey (or GAMA Survey for short), a spectroscopic survey of around 300,000 galaxies in a region of the sky comprising about 300 square degrees;  the measured redshifts of the galaxies enable their three-dimensional positions to be plotted. The video shows the shape of the survey volume before showing what the distribution of galaxies in space looks like as you fly through. Note that the galaxy distances are to scale, but the image of each galaxy is magnified to make it easier to see; the real Universe is quite a lot emptier than this in that the separation between galaxies is larger relative to their size.

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A Three-dimensional Map of the Early Universe

Posted in The Universe and Stuff with tags , , , , on August 14, 2013 by telescoper

I found this video via a web page describing the FastSound project, which is surveying galaxies in the Universe which are at such a huge distance that we are seeing them as they were over nine billion years ago. Using the Subaru Telescope‘s impressive new Fiber Multi-Object Spectrograph (FMOS). This project is “work in progress”. The survey so far contains only 1,100 galaxies, but while that is small by the standards of a modern redshift survey, and will in fact still only comprise about 5000 galaxies when complete, what is amazing about it is that the galaxies are at such enormous distances. Even using a telescope with an 8.2 metre primary mirror, this survey will take another year or so to be completed.

A survey of a representative region of the Universe at such high redshift allows astrophysicists to test theories of the growth of the large-scale structure of the Universe. In the standard cosmology, these form by a process of gravitational instability: small irregularities in the distribution of matter get amplified by the action of gravity to become large structures such as galaxies and galaxy clusters. Comparing the level of clustering at early times with that observed around us today allows us to check whether this growth matches theoretical predictions. There should be much less clumpiness earlier on if the theoretical picture is right.

I began my PhD DPhil at the University of Sussex in 1985, working on the large-scale structure of the Universe. Coincidentally, the largest redshift survey available at that time, the CfA1 Survey, also contained 1,100 galaxies – as displayed in the famous “stick man map”:

cfa2.n30

The galaxies mapped out in that survey, however, are all (relatively speaking) in our back yard: none is further than a few hundred million light years away…

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An Integral Appendix

Posted in Biographical, Cute Problems, The Universe and Stuff with tags , , , , , , on August 7, 2013 by telescoper

After the conference dinner at the Ripples in the Cosmos meeting in Durham I attended recently, a group of us adjourned to the Castle bar for a drink or several. I ended up chatting to one of the locals, Richard Bower, mainly on the subject of beards. I suppose you could call it a chinwag. Only later on did  we get onto the subject of a paper we had both worked on a while ago. It was with some alarm that I later realized that the paper concerned was actually published twenty years ago. Sigh. Where did all that time go?

Anyway, Richard and I both remembered having a great time working on that paper which turned out to be a nice one, although it didn’t exactly set the world on fire in terms of citations. This paper was written before the standard “concordance” (LCDM) cosmology was firmly established and theorists were groping around for ways of reconciling observations of the CMB from the COBE satellite with large-scale structure in the galaxy distribution as well as the properties of individual galaxies. The (then) standard model (CDM with no Lambda) struggled to satisfy the observational constraints, so in typical theorists fashion we tried to think of a way to rescue it. The idea we came up with was “cooperative galaxy formation”, as explained in the abstract:

We consider a model in which galaxy formation occurs at high peaks of the mass density field, as in the standard picture for biased galaxy formation, but is further enhanced by the presence of nearby galaxies. This modification is accomplished by assuming the threshold for galaxy formation to be modulated by large-scale density fluctuations rather than to be spatially invariant. We show that even a weak modulation can produce significant large-scale clustering. In a universe dominated by cold dark matter, a 2 percent – 3 percent modulation on a scale exceeding 10/h Mpc produces enough additional clustering to fit the angular correlation function of the APM galaxy survey. We discuss several astrophysical mechanisms for which there are observational indications that cooperative effects could occur on the scale required.

I have to say that Richard did most of the actual work on this paper, though all four authors did spend a lot of time discussing whether the idea was viable in principle and, if so, how we should implement it mathematically. In the end, my contribution was pretty much limited to the Appendix, which you can click to make it larger if you’re interested.

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As is often the case in work of this kind, everything boiled down to evaluating numerically a rather nasty integral. Coincidentally, I’d come across a similar problem in a totally different context a few years previously when I was working on my thesis and therefore just happened to know the neat trick described in the paper.

Two things struck me looking back on this after being reminded of it over that beer. One is that a typical modern laptop is powerful enough to evaluate the original integral without undue difficulty, so if this paper had been written nowadays we wouldn’t have bothered trying anything clever; my Appendix would probably not have been written. The other thing is that I sometimes hear colleagues bemoaning physics students’ lack of mathematical “problem-solving” ability, claiming that if students haven’t seen the problem before they don’t know what to do. The problem with that complaint is that it ignores the fact that many problems are the same as things you’ve solved before, if only you look at them in the right way. Problem solving is never going to be entirely about “pattern-matching” – some imagination and/or initiative is going to required sometimes- but you’d be surprised how many apparently intractable problems can be teased into a form to which standard methods can be applied. Don’t take this advice too far, though. There’s an old saying that goes “To a man who’s only got a hammer, everything looks like a nail”. But the first rule for solving “unseen” problems has to be to check whether you might in fact already have seen them…

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A Sense of Proportion – Postscript

Posted in The Universe and Stuff with tags , , on October 30, 2012 by telescoper

It took all day to do so, evidently because I’m old and slow, but this morning’s post eventually got round to reminding me of this cartoon, the context of which is described here. Was that really in 1992? That was twenty years ago!

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Merseyside Astronomy Day

Posted in Books, Talks and Reviews, The Universe and Stuff with tags , , , , on May 11, 2012 by telescoper

I’m just about to head by train off up to Merseyside (which, for those of you unfamiliar with the facts of British geography, is in the Midlands). The reason for this trip is that I’m due to give a talk tomorrow morning (Saturday 12th May) at Merseyside Astronomy Day, the 7th such event. It promises to be a MAD occasion.

My lecture, entitled The Cosmic Web, is an updated version of a talk I’ve given a number of times now; it will focus on the large scale structure of the Universe and the ideas that physicists are weaving together to explain how it came to be the way it is. Over the last few decades astronomers have revealed that our cosmos is not only vast in scale – at least 14 billion light years in radius – but also exceedingly complex, with galaxies and clusters of galaxies linked together in immense chains and sheets, surrounding giant voids of empty space. Cosmologists have developed theoretical explanations for its origin that involve such exotic concepts as ‘dark matter’ and ‘cosmic inflation’, producing a cosmic web of ideas that is in some ways as rich and fascinating as the Universe itself.

Anyway, I’m travelling to Liverpool this afternoon so I can meet the organizers for dinner this evening and stay overnight because there won’t be time to get there by train from Cardiff tomorrow morning. It’s not all that far from Cardiff to Liverpool as the crow flies, but unfortunately I’m not going by crow by train. I am nevertheless looking forward to seeing the venue, Spaceport, which I’ve never seen before.

If perchance any readers of this blog are planning to attend MAD VII please feel free to say hello. No doubt you will also tell me off for referring to Liverpool as the Midlands…

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The World as a Beach

Posted in Biographical, The Universe and Stuff with tags , , , , , , on April 10, 2012 by telescoper

Well, as some of you will have noticed, I’ve been offline over the long weekend. There’s no internet connection – not one that I could get to work, anyway – at the residence I’m staying in and I couldn’t be bothered to traipse all the way up the hill to the department in the pouring rain to connect from my office. Hence the first gap in my postings this year. I don’t suppose anyone minds that much. Anyway, here are a few pictures and random thoughts from the weekend.

Here’s a picture of the residence, by the way. It’s called Kopano, although when I previously stayed it was called Driekoppen. The old name was a relic of the days of slavery – three slaves were tortured and executedin public  after rebelling against the terrible conditions they were held in. Their heads were displayed on pikes nearby, hence the name which means “Three Heads”. This was in 1724. I’m not surprised that the end of apartheid brought a change in the name, although keeping it as it was would have served as a reminder of South Africa’s terrible past. One shouldn’t  become obsessed by events that took place such a long time ago, but neither should one forget them.

Good Friday was a very Good Friday indeed, starting with a lovely breakfast and a walk on the beach in Muizenberg. Apparently this is something of a surfer’s paradise but, as I said, I didn’t have an internet connection so couldn’t join in. Also, they have sharks here. I mean big ones. Great White ones, as  a matter of fact. None showed up while I was there, though, and in any case I was only paddling along the shoreline. It may not be obvious from the picture, but it was pretty hot. Almost 30 degrees.

 I was watching a chap surfing while we walked along and it reminded me of the post I did a while ago about teaching analogies. Standing on a beach looking out towards the horizon is a bit like doing cosmology. Off in the far distance everything looks smooth; the waves on the surface are much lower in amplitude than the depth of the sea out there, so everything evolves linearly and is quite easy to understand. That’s like looking back in time at the early Universe imprinted on the cosmic microwave background. Nearer to the shore, however, the waves become non-linear because their height is comparable to, or larger than, the depth of the water. These waves evolve in a non-linear way producing, breaking on the beach to produce foam and spray, just as the primordial waves collapse to form galaxies and the foam of large-scale structure when their self-gravity becomes sufficiently strong.

That’s enough of that, I think.

Unfortunately, the weather changed for the worse over the rest of the Easter weekend and torrential rain kept me from doing much on Saturday or Sunday. The finishing section of the  Two Oceans Marathon, which ended on the UCT campus on Saturday, was like a quagmire. As you can see from the picture, I reached the line well in front of the pack. About two days in front, actually. I took this as they were building the stands and hospitality tents a few days before the race.

Anyway, the good side of the bad weather was that I got quite a lot of work done, catching up on things I have let slip for far too long. I also exhausted the reading material I brough with me, so will have to find a good bookshop in the next day or two. Well, that’s about enough for now. I hope to continue regular dispatches from now on until I return to Blighty  next week.

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What’s the Matter?

Posted in The Universe and Stuff with tags , , , , , on September 19, 2011 by telescoper

I couldn’t resist a quick comment today on a news article to which my attention was drawn at the weekend. The piece concerns the nature of the dark matter that is thought to pervade the Universe. Most cosmologists believe that this is cold, which means that it is made of slow-moving particles (the temperature of  a gas being related to the speed of its constituent particles).  They also believe that it is not the sort of stuff that atoms are made of, i.e. protons, neutrons and electrons. In particular, it isn’t charged and therefore can’t interact with electromagnetic radiation, thus it is not only dark in the sense that it doesn’t shine but also transparent.

Cold Dark Matter (CDM) particles could be very massive, which would make them much more sluggish than lighter ones such as neutrinos (which would be hot dark matter), but there are other, more complicated, ways in which some exotic particles can end up in a slow-motion state without being massive.

So why do so many of us think the dark matter is cold? The answer to that is threefold. First, this is by far the simplest hypothesis to work on. In other words, good old Occam’s Razor. It’s simple because if the dark matter is cold there is no relevant physical scale associated with the speed of the particles. Everything is just dominated by the gravity, which means there are fewer equations to solve. Not that it’s exactly easy even in this case: huge supercomputers are needed to crunch the numbers.

The second reason is that particle physics has suggested a number of plausible candidates for non-baryonic candidates which could be cold dark matter particles. A favourite theoretical idea is supersymmetry, which predicts that standard model particles have counterparts that could be interesting from a cosmological point of view, such as the fermionic counterparts of standard model bosons. Some of these candidates could even be produced experimentally by the Large Hadron Collider.

The final reason is that CDM seems to work, at least on large scales. The pattern of galaxy clustering on large scales as measured by galaxy redshift surveys seems to fit very well with predictions of the theory, as do the observed properties of the cosmic microwave background.

However, one place where CDM is known to have a problem is on small scales. By small of course I mean in cosmological terms; we’re still talking about many thousands of light-years! There’s been a niggling worry for some time that the internal structure of galaxies, especially in their central regions,  isn’t quite what we expect on the basis of the CDM theory. Neither do the properties of the small satellite galaxies (“dwarfs”) seen orbiting the Milky Way seem to match what what we’d expect theoretically.

The above picture is taken from the BBC website. I’ve included it partly for a bit of decoration, but also to point out that the pictures are both computer simulations, not actual astronomical observations.

Anyway, the mismatch between the properties of dwarf galaxies and the predictions of CDM theory, while not being exactly new, is certainly a potential Achilles’ Heel for the otherwise successful model. Calculating the matter distribution on small scales however is a fearsome computational challenge requiring enormously high resolution. The disagreement may therefore be simply because the simulations are not good enough; “sub-grid” physics may be confusing us.

On the other hand, one should certainly not dismiss the possibility that CDM might actually be wrong. If the dark matter were not cold, but warm (or perhaps merely tepid), then it would produce less small-scale structure whilst not messing up the good fit to large-scale structure that we get with CDM.

So is the Dark Matter Cold or Warm or something else altogether? The correct answer is that we don’t know for sure, and as a matter of fact I think CDM is still favourite. But if the LHC rules out supersymmetric CDM candidates and the astronomical measurements continue to defy the theoretical predictions then the case for cold dark matter would be very much weakened. That might annoy some of its advocates in the cosmological community, such as Carlos Frenk (who is extensively quoted in the article), but it would at least mean that the hunt for the true nature of dark matter would be getting warmer.

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The Bull’s-Eye Effect

Posted in The Universe and Stuff with tags , , , , on February 10, 2011 by telescoper

What a day.

For a start we had another manic UCAS admissions event. Applications to study physics here have rocketed, by more than 50% compared to last year, so it’s all hands on deck on days like this. Next weekend we have our first Saturday event of the year, and that promises to be even more popular. Still, it’s good to be busy. Without the students, we’d all be on Her Majesty’s Dole. At least some of our advertising is hitting the target.

After that it was back to the business of handing out 1st Semester examination results to my tutees – the Exam Board met yesterday but I skived off because I wasn’t involved in any exams last semester. Then a couple of undergraduate project meetings and a few matters related to postgraduate admissions that needed sorting out.

Finally, being a member of our esteemed Course Committee, I spent a little bit of time trying to assemble some new syllabuses. All our Physics (and Astrophysics) courses are changing next year, so this is a good chance to update the content and generally freshen up some of the material we teach.

In the course of thinking about this, I dug about among some of my old course notes from here there and everywhere, some of which I’ve kept on an old laptop. I chanced upon this cute little graphic, which I don’t think I’ve ever used in a lecture, but I thought I’d put it up here because it’s pretty. Sort of.

What it shows is a simulation of the large-scale structure of the Universe as might be mapped out using a galaxy redshift survey. The observer is in the centre of the picture (which a two-dimensional section through the Universe); the position of each galaxy is plotted by assuming that the apparent recession velocity (which is what a redshift survey measures) is related to the distance from the observer by Hubble’s Law:

V\simeq cz =H_0 R

where V  is the recession velocity, z  is the redshift, H_0 is Hubble’s constant  and R is the radial distance of the galaxy. However, this only applies exactly in a completely homogeneous Universe. In reality the various inhomogeneities (galaxies, clusters and superclusters) introduce distortions into the Hubble Law by generating peculiar velocities

V=H_0 R+ V_p

These distort the pattern seen in redshift space compared to real space. In real space the pattern is statistically isotropic, but in redshift space things look different along the line of sight from the observer compared to the directions at right angles as described quite nicely by this slide from a nice web page on redshift-space distortions.

There are two effects. One is that galaxies in tightly bound clusters have high-speed disordered motions. This means that each cluster is smeared out along the line of sight in redshift space, producing artefacts sometimes called “Fingers of God” – elongated structures that always point ominously at the observer. The other effect caused by large-scale coherent motions as matter flows into structures that are just forming, which squashes large-scale features in the redshift direction more-or-less opposite to the first.

These distortions don’t simply screw up our attempts to map the Universe. In fact they help us figure out how much matter might pulling the galaxies about. The number in the upper left of the first (animated) figure is the density parameter, \Omega. The higher this number is, the more matter there is to generate peculiar motions so the more pronounced the alteration; in a low density universe, real and redshift space look rather similar.

Notice that in the high-density universe the wall-like structures look thicker (owing to the large peculiar velocities within them) but that they are also larger than in the low-density universe. In a paper a while ago, together with Adrian Melott and others, we investigated  the dynamical origin of this phenomenon, which we called the Bull’s-Eye Effect because it forms prominent rings around the central point. It turns out to be Quite Interesting, because the merging of structures in redshift-space to create larger ones is entirely analogous the growth of structure by hierarchical merging in real space, and can be described by the same techniques. In effect, looking in redshift space gives you a sneak preview of how the stucture will subsequently evolve in real space…


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Astronomy Look-alikes, No. 40

Posted in Astronomy Lookalikes, The Universe and Stuff with tags , , , on September 10, 2010 by telescoper

Obviously someone else has already noticed the remarkable similarity between the structure of the human brain and that revealed by computer simulations of the large-scale structure of the Universe.

Does this mean that dark matter is really just all in the mind?


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