PROBES OF LARGE SCALE STRUCTURE

Under construction.

Within a few years the 3D distribution of galaxies in our local universe will be mapped, and that structure can be matched to the early-time snapshot provided by the CMBR. Since any model of structure formation must explain both the tiny ripples in the Cosmic Microwave Background temperature across the sky, and the large-scale structures we see in the universe today, the combination of these two probes is especially powerful. Together they enable us to probe the spectrum of fluctuations over about 4 decades in length scale and its evolution over almost the entire age of the universe. This information, plus information from smaller, high-redshift/very early time, surveys of galaxies and neutral gas will enable us to piece together the mechanism for the formation and mode of evolution of all of the structure we see around us in the universe. (Follow this link for probes of dark energy.)



SDSS Current and Future Galaxy Surveys
(Shown is the geometry of the
SDSS:
a cone of pi steradians in the north and
three slices in the south)

Perhaps the most obvious means for surveying the large-scale structure in the universe is to measure the position of the nearest galaxies (either in 3D -- redshift surveys -- or in the 2D projected on the sky -- angular surveys).

Galaxy surveys with well defined selection criteria enable us to extract information about the clustering pattern. (Surveys during the early 1980s showed that galaxies are not distributed randomly throughout the Universe. They are found to lie in clusters, filaments, bubbles and sheet like structures.) In the early 1980s there were less than 5,000 galaxy redshifts known. We now have over 1,000,000. Recent very large scale galaxy surveys have now reached far enough out into our local volume to begin to see the end of greatness. That is they sample a large enough volume of space that the largest structures in the survey (about 100Mpc in size) are no longer of the same size of the survey itself. We are thus beginning to see a "fair" sample of the Universe which we can compare to our models in quantitative detail.

SDSS-SLICE
A slice through a large simulation of a CDM universe, showing what the SDSS expected to see. The angle across the wedge is position on the sky, the radial distance is redshift. The actual data look remarkably similar to this prediction.

To characterize the distribution of galaxies a number of statistical tools have been developed. The most widely used approach to quantifying the degree of clustering observed is to measure the correlation functions. For example the two-point correlation function is the probability, in excess of random, of finding a galaxy at a fixed distance from a random neighbor. Its Fourier transform is the power spectrum (which is now more widely used). Beyond this one investigates higher order correlation functions, for example the distribution of counts-in-cells: the distribution of the number of galaxies found in cells of a given size which one lays down atop the survey.

As the new era of surveys catalogues the 3D positions of millions of galaxies the biggest uncertainty will become the mapping from the clustering of different galaxy types to the clustering of the underlying matter which the theories most straightforwardly predict. There is no reason to expect (and observational evidence to the contrary!) that the galaxies will trace the matter exactly. The fact that the `light' does not trace the `mass' is usually called called galaxy bias (one of several technical uses of the term bias in large-scale structure) and poses a fundamental problem on which much work remains to be done.

A (partial) list of past and future galaxy surveys can be found here:


Lya Lyman Alpha Systems
Distribution of the gas density
at redshift 3 from a hydrodynamical
simulation of the Ly-a forest
performed
at NCSA.

In the spectra of distant quasars one sees a huge number of absorption lines, redward of the quasar's Lyman alpha emission (Hydrogen, 2-1 transition, 121.6nm). The absorption lines have varying strengths (or optical depths) and are seen superposed upon a background continuum emission from the quasar. These lines are thought to be due to absorption of the quasar continuum by clouds along the line of sight which contain (sometimes trace amounts of) neutral hydrogen. (For further information follow this link.)

This forest of Lyman-alpha lines was discovered over 25 years ago. Originally studied to learn about the intergalacitc medium and interpreted as small (10kpc) pressure confined clouds of pristine hydrogen gas left over from the epoch of recombination, they are now interpreted within a broader cosmological framework and thought to provide important clues about the formation of large-scale structure, the nature of dark matter and the shape of the matter power spectrum (which has important implications for inflation).


Cluster Clusters of Galaxies
A
ROSAT image of the Coma cluster of
galaxies, one of the two nearest clusters
to the Milky Way. Coma is about 80Mpc
from us, and has a size of about 3Mpc.

Clusters of galaxies are the largest gravitationally bound systems in the universe, with sizes of a few Mpc (a Mpc is about 3 million light-years). A typical cluster contains hundreds or thousands of galaxies, but most of the mass is in the form of a hot intracluster gas. This gas is heated to high temperatures (106-108K or several keV) in the potential well of the cluster. Clusters are rare objects: fewer than 1 in 10 galaxies in the universe resides in clusters, the rest are said to be ``field galaxies''.

The two most obvious means of studying clusters of galaxies are by observing the light emitted from the constituent galaxies or the X-ray emission from the hot intracluster gas. Recently it has proved possible to observe clusters of galaxies in two other ways which (in combination with the traditional methods) should prove exceptionally powerful. The first, known as the Sunyaev-Zel'dovich effect after the people who first proposed it, is to observe the cluster as a ``hole'' in the microwave sky. Due to the free electrons in the hot intracluster gas, photons from the microwave background are ``upscattered'' in energy. This leaves a decrement or deficit in the number of photons at low-frequency or a hole in the microwave sky (for some examples, see the Viper SZ survey or the APEX SZ experiment). One can also study the mass of clusters by their gravitational bending of light. One can study both the strong lensing by the cluster core and the weak lensing from the cluster as a whole (see this paper which mapped a cluster at z=0.83). These 4 methods, plus a new generation of X-ray satellites (Chandra and XMM) should allow us to learn a great deal about clusters of galaxies in the next few years.

Clusters can teach us a great deal about cosmology (see e.g. this talk by Marc Postman). Obviously clusters trace out the large-scale structure of the universe just as do galaxies. However there are several cluster properties that are interesting in and of themselves. If clusters provide a ``fair sample'' of the universe, then the fraction of their mass in baryons should equal the universal baryon fraction, known as OmegaB. The present number density of clusters is a measure of the amplitude of fluctuations in the universe on scales of around 8Mpc (see also this paper). The evolution of this number density (vs mass or temperature) with redshift can determine the mass density parameter Omega and possibly determine the equation of state (and nature) of the dark energy believed to be causing the expansion of the universe to accelerate. Recently it has been argued that the number of giant arcs, caused by strong gravitational lensing of background galaxies by the cores of clusters, can be used to determine Omega also. For a recent (short) review of high redshift clusters, follow this link.

We have performed a number of cosmological hydrodynamic simulations from which we can extract a catalogue of galaxy clusters. The following Quicktime movie illustrates the complex formation process of clusters in modern theories of structure formation. Some movies and pictures from the Los Alamos group can be found here, including an MPEG movie of the formation of a cluster. There are several movies from Ben Moore's group and even more simulations of cluster formation can be accessed via Tereasa Brainerd's home page.


Weak Lensing

Weak gravitational lensing denotes that regime where the gravitational deflection of light is so small that one does not see multiple images. Instead the images of background objects (galaxies) are sheared and magnified. The amount of this shear and magnification depend on the integral of the gravitational potential along the line of sight, times a function which depends on the redshift of the source and peaks midway between the source and the observer. By studying the shear of many galaxies one can statistically infer the amount of dark matter as a function of position and time to constrain its properties, spatial distribution and evoltion. Numerous large surveys devoted to the study of weak gravitational lensing are underway around the world, of which the ongoing CFHT Legacy Survey and Pan-STARRS and the planned DES and LSST are of note.


Quasar Clustering

Just as one can study the clustering of galaxies, one can also study the clustering of other objects. Many such objects have been studied, but Quasars hold a special appeal because they have been observed to very high redshifts (early time). Both the SDSS and the 2dF have measured the positions and redshifts of hundreds of thousands of quasars, allowing one to probe large-scale structure out to COBE scales, test the nature of the initial conditions that formed structure and measure the evolution of clustering and constrain the dark energy.

The 2dF QSO Redshift Survey web site contains information on their survey and the science that can be done with surveys of quasars.

See here for more information on high-z quasars and follow this link for an in depth theoretical discussion of how to measure the cosmological parameters using quasar clustering.


Peculiar Velocity Measurements

Because of their inherent difficulty, surveys of peculiar velocities have been few and far between and plagued with systematic errors. For more information follow this link to a review by Avishai Dekel.


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