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Observations of Large Scale Structure: Measures of Galaxy Clustering

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### Observations of Large Scale Structure: Measures of Galaxy Clustering

Kaz Sliwa

Ruben Pinto

Marc Cassagnol

- There is clearly a hierarchy of structure in the universe:
- Stars > Star Clusters > Galaxies > Galaxy Clusters > Superclusters
- Is there any larger structures than this?
- Before 1980: Nothing larger.

1980’s:

Redshift data revealed more interesting

structures. Very non-spherical structures such as …….

Voids

- Vast empty spaces between filaments, anywhere from 10 – 150 Mpc in diameter
- Few or no galaxies are contained in these regions
- Strangely large voids (500+ Mpc) are called supervoids
- About 27 known supervoids.

Filaments

- Sponge-like, or thread-like structures, which are 70-150 Mpc long
- Form boundary between voids
- Composed of galaxies, particularly dense regions of a filament are called superclusters.

Surface Brightness Fluctuation (SBF) Method

- This technique is used to find distances to galaxies, and can be used where individual stars cannot be resolved.
- The brightness of each pixel will fluctuate a certain amount, depending on the distance to the galaxy.
- Further away galaxies produce smaller fluctuations.
- N = number of stars per pixel of detector.

- If galaxies were distributed uniformly throughout space with average spatial density n per cubic megaparsec, then the probability dP of finding a galaxy in a volume dV1 would be the same everywhere, dP = ndV1.
- If galaxies tend to cluster together then the probability of having a galaxy in another random volume dV2 is greater if the separation r12between the two regions is small.
- However, the galaxies are not scattered randomly throughout space and thus the joint probability of finding a galaxy within both volumes dV1and dV2 is written as:
- Where is the two-point correlation function.

The two-point correlation function describes whether the galaxies are more concentrated or separated than average.

- If ξ(r) > 0 at small r, then the galaxies are clustered, and if ξ(r) < 0 then the galaxies are more dispersed.
- Generally the correlation function ξ(r) is computed by estimating the galaxy distance from their redshifts, correcting for distortion introduced by the peculiar velocities.
- For small separations of r≤ 50h-1 Mpc, the correlation function takes the form:
- where r0 is the correlation length, and γ >0.

In the range 2h-1 ≤ r ≤ 16h-1 Mpc where ξ(r) is well measured the correlation length ro ≈ 6h-1 Mpc and γ ≈ 1.5.

- An average over many surveys results in ro ~ 5h-1 Mpc and γ ~ 1.8.
- Around r ≥ 30h-1Mpc, ξ(r) starts to oscillate around zero.
- While galaxies are not clustered randomly, at larger scales it approaches a random distribution.

Kaz4

- The Fourier transform of ξ(r) is the power spectrum P(k):
- The power spectrum indicates the amount of clustering on a given length scale.
- An important fact is that the power P(k) ∝ V, that is, it scales with volume and is thus not dimensionless.

“Lumpiness” of Galaxy Distribution

- < δ2R> is a dimensionless quantity that measures the lumpiness of the galaxy distribution on this scale.
- < δ2R> can be related to k3P(k), the dimensionless quantity that defines the fluctuation in density within a volume:

where k ≈ R-1

- Often the clustering is parameterized by σ8 which is defined as the fluctuation on a scale of R = 8h-1 Mpc.

Wedge Diagrams

- Resemble two pizza slices joined at the apex and provide 3-d view.
- Formed because of system of observation used: Cone.
- Counter-clockwise 90 degrees for actual view.
- Sides “empty” due to gas and dust obscuring optical view on Milky Way’s plane.
- 21cm Line reveals galaxies do exist in the plane.

Redshift Measurements

- Recession Speed, or redshift is a measure of fractional change in wavelength
- Gives us an approximate distance to galaxies that exhibit radial velocities
- Doppler formula for speeds well below speed of light:
- Doppler relation and Hubble Law gives recession speed:

The Great Wall

- Largest known super-structure in the universe.
- Very thin, 500 x 300 x 15 light years in size.
- It is a filament of galaxies about 200 million light years away from us.
- Could be thicker, the plane of the Milky Way obscures our view of the great wall.

The Great Wall (cont’d)

- Popular theories do not account for regular “sheet” patterns, or the enormous size.
- Covers more than a quarter of northern hemisphere (redshift survey figure).
- Overall Picture: Layers of filaments approx 15 Lyrs thick of high density galaxy distribution – between sheets there is empty space.
- Recent studies show, that the initial “facts” of the biggest structures in our universe might be a little exaggerated…

Overestimates

- Great Wall has great mass – density is larger than surrounding volumes.
- Result: pulls in surrounding galaxies.
- Note that the cores of walls have not collapsed yet, hence this is the first time galaxies are “falling” and hence these measurements can be made.
- Galaxies in front of wall have higher Vr; behind wall lower Vr.
- According to recession speeds, the walls are denser than they really are.
- Consequently surrounding regions are not that empty
- Truth: walls are only a few times denser than the cosmic mean.

Bias

- Not every galaxy can be seen; the types of galaxies observed do depend on the system of observation chosen.
- Recession speeds need the galaxies to be of a certain lower limit of luminosity; at cz > 40,000kms-1, only the most luminous systems can be plotted (hence thinning out in diagram).
- 21cm line: Optical brightness does not matter – E.g. gas rich dwarf galaxies will dominate over luminous Ellipticals that lack HI gas.
- No easy task to map the luminosity-varying Universe!

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