50 Years of the Cosmic Web

Posted in The Universe and Stuff with tags , , , , , , on November 21, 2018 by telescoper

I’ve just given a lecture on cosmology during which I showed a version of this amazing image:

The picture was created in 1977 by Seldner et al. based on the galaxy counts prepared by Charles Donald Shane and Carl Alvar Wirtanen and published in 1967 (Publ. Lick. Observatory 22, Part 1). There are no stars in the picture: it shows the  distribution of galaxies in the Northern Galactic sky. The very dense knot of galaxies seen in the centre of the image is the Coma Cluster, which lies very close to the Galactic North pole.The overall impression  is of a frothy pattern, which we now know as the Cosmic Web. I don’t think it is an unreasonable claim that the Lick galaxy catalogue provided the first convincing evidence of the form of the morphology of the large-scale structure of the Universe.

The original Shane-Wirtanen Lick galaxy catalogue lists counts of galaxies in 1 by 1 deg of arc blocks, but the actual counts were made in 10 by 10 arcmin cells. The later visualization is based on a reduction of the raw counts to obtain a catalogue with the original 10 by 10 arcmin resolution. The map above based on the corrected counts  shows the angular distribution of over 800,000 galaxies brighter than a B magnitude of approximately 19.

The distribution of galaxies is shown only in projection on the sky, and we are now able to probe the distribution in the radial direction with large-scale galaxy redshift surveys in order to obtain three-dimensional maps, but counting so many galaxy images by eye on photographic plates was a Herculean task that took many years to complete. Without such heroic endeavours in the past, our field would not have progressed anything like as quickly as it has.

I’m sorry I missed the 50th anniversary of the publication of the Lick catalogue, and Messrs Shane and Wirtanen both passed away some years ago, but at last I can doff my cap in their direction and acknowledge their immense contribution to cosmological research!

UPDATE: In response to the comments below, I have updated this scan of the original rendition of the Lick counts:

Celebrating the Sloan Telescope

Posted in The Universe and Stuff with tags , , , , , , , , on May 9, 2018 by telescoper

A little bird tweeted at me this morning that today is the 20th anniversary of first light through the Sloan Telescope (funded by the Alfred P. Sloan Foundation) which has, for the past two decades, been surveying as much of the sky as it can from its location in New Mexico (about 25% altogether): the Sloan Digital Sky Survey is now on its 14th data release.

Here’s a picture of the telescope:

For those of you who want the optical details, the Sloan Telescope is a 2.5-m f/5 modified Ritchey-Chrétien altitude-azimuth telescope located at Apache Point Observatory, in south east New Mexico (Latitude 32° 46′ 49.30″ N, Longitude 105° 49′ 13.50″ W, Elevation 2788m). A 1.08 m secondary mirror and two corrector lenses result in a 3° distortion-free field of view. The telescope is described in detail in a paper by Gunn et al. (2006).

A 2.5m telescope of modest size by the standards of modern astronomical research, but the real assets of the Sloan telescope is a giant mosaic camera, highly efficient instruments and a big investment in the software required to generate and curate the huge data sets it creates. A key feature of SDSS is that its data sets are publicly available and, as such, they have been used in countless studies by a huge fraction of the astronomical community.

The Sloan Digital Sky Survey’s original legacy’ survey was basically a huge spectroscopic redshift survey, mapping the positions of galaxies and quasars in three dimensions to reveal the cosmic web’ in unprecedented detail:

As it has been updated and modernised, the Sloan Telescope has been involved in a range of other surveys aimed at uncovering different aspects of the universe around us, including several programmes still ongoing.

The Cosmic Web – my Lincoln lecture slides…

Posted in Talks and Reviews, The Universe and Stuff with tags , on February 28, 2017 by telescoper

For those of you who are interested, here are the slides I used for the 1st Annual Robert Grosseteste Lecture on Astrophysics/Cosmology, given at the University of Lincoln on Thursday 23rd February 2017.

The Zel’dovich Lens

Posted in The Universe and Stuff with tags , , , , on June 30, 2014 by telescoper

Back to the grind after an enjoyable week in Estonia I find myself with little time to blog, so here’s a cute graphic by way of  a postscript to the IAU Symposium on The Zel’dovich Universe. I’ve heard many times about this way of visualizing the Zel’dovich Approximation (published in Zeldovich, Ya.B. 1970, A&A, 5, 84) but this is by far the best graphical realization I have seen. Here’s the first page of the original paper:

In a nutshell, this daringly simple approximation considers the evolution of particles in an expanding Universe from an early near-uniform state into the non-linear regime as a sort of ballistic, or kinematic, process. Imagine the matter particles are initial placed on a uniform grid, where they are labelled by Lagrangian coordinates $\vec{q}$. Their (Eulerian) positions at some later time $t$ are taken to be

$\vec{r}(\vec(q),t) = a(t) \vec{x}(\vec{q},t) = a(t) \left[ \vec{q} + b(t) \vec{s}(\vec{q},t) \right].$

Here the $\vec{x}$ coordinates are comoving, i.e. scaled with the expansion of the Universe using the scale factor $a(t)$. The displacement $\vec{s}(\vec{q},t)$ between initial and final positions in comoving coordinates is taken to have the form

$\vec{s}(\vec{q},t)= \vec{\nabla} \Phi_0 (\vec{q})$

where $\Phi_0$ is a kind of velocity potential (which is also in linear Newtonian theory proportional to the gravitational potential).If we’ve got the theory right then the gravitational potential field defined over the initial positions is a Gaussian random field. The function $b(t)$ is the growing mode of density perturbations in the linear theory of gravitational instability.

This all means that the particles just get a small initial kick from the uniform Lagrangian grid and their subsequent motion carries on in the same direction. The approximation predicts the formation of caustics  in the final density field when particles from two or more different initial locations arrive at the same final location, a condition known as shell-crossing. The caustics are identified with the walls and filaments we find in large-scale structure.

Despite its simplicity this approximation is known to perform extremely well at reproducing the morphology of the cosmic web, although it breaks down after shell-crossing has occurred. In reality, bound structures are formed whereas the Zel’dovich approximation simply predicts that particles sail straight through the caustic which consequently evaporates.

Anyway the mapping described above can also be given an interpretation in terms of optics. Imagine a uniform illumination field (the initial particle distribution) incident upon a non-uniform surface (e.g. the surface of the water in a swimming pool). Time evolution is represented by greater depths within the pool.  The light pattern observed on the bottom of the pool (the final distribution) displays caustics with a very similar morphology to the Cosmic Web, except in two dimensions, obviously.

Here is a very short  but very nice video by Johan Hidding showing how this works:

In this context, the Zel’dovich approximation corresponds to the limit of geometrical optics. More accurate approximations can presumably be developed using analogies with physical optics, but this programme has only just begun.

The Power Spectrum and the Cosmic Web

Posted in Bad Statistics, The Universe and Stuff with tags , , , , , , on June 24, 2014 by telescoper

One of the things that makes this conference different from most cosmology meetings is that it is focussing on the large-scale structure of the Universe in itself as a topic rather a source of statistical information about, e.g. cosmological parameters. This means that we’ve been hearing about a set of statistical methods that is somewhat different from those usually used in the field (which are primarily based on second-order quantities).

One of the challenges cosmologists face is how to quantify the patterns we see in galaxy redshift surveys. In the relatively recent past the small size of the available data sets meant that only relatively crude descriptors could be used; anything sophisticated would be rendered useless by noise. For that reason, statistical analysis of galaxy clustering tended to be limited to the measurement of autocorrelation functions, usually constructed in Fourier space in the form of power spectra; you can find a nice review here.

Because it is so robust and contains a great deal of important information, the power spectrum has become ubiquitous in cosmology. But I think it’s important to realise its limitations.

Take a look at these two N-body computer simulations of large-scale structure:

The one on the left is a proper simulation of the “cosmic web” which is at least qualitatively realistic, in that in contains filaments, clusters and voids pretty much like what is observed in galaxy surveys.

To make the picture on the right I first  took the Fourier transform of the original  simulation. This approach follows the best advice I ever got from my thesis supervisor: “if you can’t think of anything else to do, try Fourier-transforming everything.”

Anyway each Fourier mode is complex and can therefore be characterized by an amplitude and a phase (the modulus and argument of the complex quantity). What I did next was to randomly reshuffle all the phases while leaving the amplitudes alone. I then performed the inverse Fourier transform to construct the image shown on the right.

What this procedure does is to produce a new image which has exactly the same power spectrum as the first. You might be surprised by how little the pattern on the right resembles that on the left, given that they share this property; the distribution on the right is much fuzzier. In fact, the sharply delineated features  are produced by mode-mode correlations and are therefore not well described by the power spectrum, which involves only the amplitude of each separate mode. In effect, the power spectrum is insensitive to the part of the Fourier description of the pattern that is responsible for delineating the cosmic web.

If you’re confused by this, consider the Fourier transforms of (a) white noise and (b) a Dirac delta-function. Both produce flat power-spectra, but they look very different in real space because in (b) all the Fourier modes are correlated in such away that they are in phase at the one location where the pattern is not zero; everywhere else they interfere destructively. In (a) the phases are distributed randomly.

The moral of this is that there is much more to the pattern of galaxy clustering than meets the power spectrum…

Illustris, Cosmology, and Simulation…

Posted in The Universe and Stuff with tags , , , , , , on May 8, 2014 by telescoper

There’s been quite a lot of news coverage over the last day or two emanating from a paper just out in the journal Nature by Vogelsberger et al. which describes a set of cosmological simulations called Illustris; see for example here and here.

The excitement revolves around the fact that Illustris represents a bit of a landmark, in that it’s the first hydrodynamical simulation with sufficient dynamical range that it is able to fully resolve the formation and evolution of  individual galaxies within the cosmic web of large-scale structure.

The simulations obviously represent a tremendous piece or work; they were run on supercomputers in France, Germany, and the USA; the largest of them was run on no less than 8,192 computer cores and took 19 million CPU hours. A single state-of-the-art desktop computer would require more than 2000 years to perform this calculation!

There’s even a video to accompany it (shame about the music):

The use of the word “simulation” always makes me smile. Being a crossword nut I spend far too much time looking in dictionaries but one often finds quite amusing things there. This is how the Oxford English Dictionary defines SIMULATION:

1.

a. The action or practice of simulating, with intent to deceive; false pretence, deceitful profession.

b. Tendency to assume a form resembling that of something else; unconscious imitation.

2. A false assumption or display, a surface resemblance or imitation, of something.

3. The technique of imitating the behaviour of some situation or process (whether economic, military, mechanical, etc.) by means of a suitably analogous situation or apparatus, esp. for the purpose of study or personnel training.

So it’s only the third entry that gives the meaning intended to be conveyed by the usage in the context of cosmological simulations. This is worth bearing in mind if you prefer old-fashioned analytical theory and want to wind up a simulationist! In football, of course, you can even get sent off for simulation…

Reproducing a reasonable likeness of something in a computer is not the same as understanding it, but that is not to say that these simulations aren’t incredibly useful and powerful, not just for making lovely pictures and videos but for helping to plan large scale survey programmes that can go and map cosmological structures on the same scale. Simulations of this scale are needed to help design observational and data analysis strategies for, e.g., the  forthcoming Euclid mission.

One Hundred Years of Zel’dovich

Posted in The Universe and Stuff with tags , , , , on March 12, 2014 by telescoper

Lovely weather today, but it’s also been an extremely busy day with meetings and teachings. I did realize yesterday however that I had forgotten to mark a very important centenary at the weekend. If I hadn’t been such a slacker that I took last Saturday off work I would probably have been reminded…

The great Russian physicist Yakov Borisovich Zel’dovich (left) was born on March 8th 1914, so had he lived he would have been 100 years old last Saturday. To us cosmologists Zel’dovich  is best known for his work on the large-scale structure of the Universe, but he only started to work on that subject relatively late in his career during the 1960s.  He in fact began his life in research as a physical chemist and arguably his greatest contribution to science was that he developed the first completely physically based theory of flame propagation (together with Frank-Kamenetskii). No doubt he also used insights gained from this work, together with his studies of detonation and shock waves, in the Soviet nuclear bomb programme in which he was a central figure, and which no doubt led to the chestful of medals he’s wearing in the photograph.

My own connection with Zel’dovich is primarily through his scientific descendants, principally his former student Sergei Shandarin, who has a faculty position at the University of Kansas. For example, I visited Kansas back in 1992 and worked on a project with Sergei and Adrian Melott which led to a paper published in 1993, the abstract of which makes it clear the debt it owed to the work of Ze’dovich.

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel’dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is ‘enhanced’ by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel’dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

The Zel’dovich Approximation referred to in this abstract is based on an extremely simple idea but which, as we showed in the above paper, turns out to be extremely accurate at reproducing the morphology of the “cosmic web” of large-scale structure.

Zel’dovich passed away in 1987. I was a graduate student at that time and had never had the opportunity to meet him. If I had done so I’m sure I would have found him fascinating and intimidating in equal measure, as I admired his work enormously as did everyone I knew in the field of cosmology.  Anyway, a couple of years after his death a review paper written by himself and Sergei Shandarin was published, along with the note:

The Russian version of this review was finished in the summer of 1987. By the tragic death of Ya. B.Zeldovich on December 2, 1987, about four-fifths of the paper had been translated into English. Professor Zeldovich would have been 75 years old on March 8, 1989 and was vivid and creative until his last day. The theory of the structure of the universe was one of his favorite subjects, to which he made many note-worthy contributions over the last 20 years.

As one does if one is vain I looked down the reference list to see if any of my papers were cited. I’d only published one paper before Zel’dovich died so my hopes weren’t high. As it happens, though, my very first paper (Coles 1986) was there in the list. That’s still the proudest moment of my life!

Anyway, this post gives me the opportunity to advertise that there is a special meeting called The Zel’dovich Universe coming up this summer in Tallinn, Estonia. It looks a really interesting conference and I really hope I can find the time to fit it into my schedule. I’ve never been to Estonia…