Baryon acoustic oscillations

In cosmology, baryon acoustic oscillations (BAO) refers to an overdensity or clustering of baryonic matter at certain length scales due to acoustic (sound) waves which propagated in the early universe. Similar to supernova experiments providing a "standard candle" for astronomical observations , BAO matter clustering provides a "standard ruler" for length scale in cosmology. The length of this standard ruler (~150Mpc in today's universe) can be measured by looking at the large scale structure of matter using large astronomical surveys. BAO measurements help cosmologists understand more about the nature of dark energy (the acceleration of the universe) by constraining cosmological parameters.

The Early Universe

Figure 1: Temperature anisotropies of the CMB based on the five year WMAP data.

The early universe consisted of a hot, dense plasma of elections and baryons (protons and neutrons). Photons (light particles) traveling in this universe were essentially trapped, unable to travel for any considerable distance before interacting with the plasma via Thomson scattering.[need ref] As the universe expanded, the plasma cooled to below 3000 K -- a low enough energy such that the electrons and protons in the plasma could combine to form neutral hydrogen atoms. This "recombination" happened when the universe was around 400,000 years old, or at a redshift of z = 1100.[need ref] Photons interact with neutral matter much less than with charged matter, therefore at recombination the universe suddenly became transparent to photons, allowing them to [[1]] from the matter and free-stream through the universe.[need ref] In other-words, the mean free path of the photons became on the order of the size of the universe. The cosmic microwave background (CMB) radiation is light from recombination which is only now reaching our telescopes. Therefore when we look at Wilkinson Microwave Anisotropy Probe (WMAP) data, we are looking back in time to see an image of the universe when it was only 400,000 years old.[need ref]

WMAP paints a picture of a smooth (Figure 1), homogeneous universe with density anisotropies of one part in 10⁵.[need ref]. However, when we observe the universe today we find large amounts of structure and density fluctuations. Galaxies, for instance, are 10⁶ times more dense than the universe's mean density. The current belief is that the universe was built in a bottom-up fashion, meaning that the small anisotropies of the early universe acted as gravitational seeds for the structure we see today. Overdense regions attract more matter, while underdense regions attract less, and thus these small anisotropies we see in the CMB become the large scale structures we observe in the universe today.

Cosmic Sound

File:BAO soundwave.jpg

Figure 2: BAO soundwave propagating outward from a single overdensity over time. The baryon density is shown in the left-most column, the photon density is in the middle column, and a graph of the mass profiles are in the right-most column.

Let us imagine an overdense region of the primordial plasma. The overdensity is gravitationally attracting matter towards it, however there is also a large amount of pressure due to the heat of photon-matter interactions in the plasma. These counteracting forces of gravity and pressure create oscillations, analagous to sound waves created in air by pressure differences.

Consider a single wave originating from this overdense region in the center of the plasma. This region contains dark matter, baryons and photons. The pressure results in a spherical sound wave of both baryons and photons moving with a speed slightly over half the speed of light outwards from the overdensity (Figure 2, row 1). The dark matter only interacts gravitationally and so it stays at the center of the sound wave, the origin of the overdensity. Before decoupling, the photons and baryons move outwards together (Figure 2, rows 2-3). After decoupling (Figure 2, row 4) the photons are no longer interacting with the baryonic matter so they diffuse away (Figure 2, rows 5-6). This relieves the pressure on the system, leaving a shell of baryonic matter at a fixed radius. This radius is often referred to as the sound horizon. Without the photo-baryon pressure driving the system outwards, the only remaining force on the baryons is gravitational. Therefore, the baryons and dark matter (still at the center of the perturbation) form an equilibrium configuration which includes overdensities of matter both at the original site of the anisotropy and in a shell at the sound horizon (Figure 2, row 7-8).

What do these baryon acoustic oscillations look like in today's universe? The ripples in the density of space (shown at the bottom of Figure ) continue to attract matter and eventually galaxies formed in a similar structure, therefore we expect to see a greater number of galaxies separated by the sound horizon than by other comparable length scales. Of course there wasn't just one anisotropy which created BAO but many, and therefore the universe is not composed of one sound ripple, but many overlapping ripples. The analogy would be like dropping many pebbles into a pond and watching the resulting wave patterns in the water. We cannot see the preferred clustering of galaxies on the sound horizon by eye, but we can see this signal statistically by looking at the separations of large numbers of galaxies.

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Look at the description of this process at the following link: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html to add to this description

Standard Ruler

We understand that BAO causes galaxies to be distributed in a specific way, but why is this useful? The physics of the propagation of the baryon waves in the early universe is fairly simple so cosmologists can predict the size of the sound horizon at recombination. In addition the CMB provides a measurement of this scale to high accuracy. However in the time between present day and recombination the universe has been expanding. This expansion is well supported by observations and is one of the foundations of the Big Bang Model. In the late 90's, observations of supernova determined that not only is the universe expanding, it is expanding at an increasing rate. Better understanding the acceleration of the universe, or dark energy, has become one of the most important questions in cosmology today. In order to understand the nature of the dark energy, it is important to have a variety of ways of measuring this acceleration. BAO can learn more about this acceleration by comparing observations of the sound horizon today by observing the clustering of galaxies to the sound horizon at the time of recombination using the CMB. Thus BAO gives us a measuring stick with which to understand better the nature of the acceleration that is completely independent from the supernova technique.

BAO Signal in the Sloan Digital Sky Survey

File:Sloan BAO Slice.jpg

Figure 3: A slice through the SDSS map of the distribution of galaxies. Earth is at the center, and each point in the slice represents a galaxy, the color is the luminosity. This image shows 60,000 galaxies and is 2 billion light-years deep.

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The Sloan Digital Sky Survey (SDSS) is a 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico. The goal of this five-year survey was to take images and spectra of millions of celestial objects. Sloan data gives us a three-dimensional map of the objects in the nearby universe (Figure 3). The SDSS catalog provides a picture of the distribution of matter such that we can look for a BAO signal by looking at the separation of galaxies and seeing if there is a larger number of galaxies separated at the sound horizon.

The Sloan Team looked at a sample of 46,748 luminous red galaxies (LRGs), over 3816 square-degrees of sky (approximately five billion light years in diameter) and out to a redshift of z = 0.47. They analyzed the clustering of these galaxies by calculating a two-point correlation function on the data. The correlation function ($\xi$) is a function of comoving galaxy separation distance (s) and describes the probability that another galaxy will be found within a given distance bin. One would expect a high correlation of galaxies at small separation distances (due to the clumpy nature of galaxy formation) and a low correlation at large differences. The BAO signal would show up as a bump in the correlation function at a comoving separation equal to the sound horizon (see Figure 4). This signal was detected by SDSS team in 2005.

File:Correlation Function for BAO.jpg

Figure 4: Large-scale redshift-space correlation function, $\xi(s)$, from the SDSS LRG sample (black data points). The colored lines represent theoretical models using different cosmologies. The inset shows an expanded view with a linear vertical axis.