Transcript Observations of Large Scale Structure: Measures of Galaxy

Observations of Large Scale
Structure: Measures of Galaxy
Clustering
Kaz Sliwa
Ruben Pinto
Marc Cassagnol
The Distance Ladder
- 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.
Zone of Avoidance
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.
 (r12 )
Measures of Galaxy Clustering
• 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 r12 between 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 dV1 and 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
1.8.
 5h 1Mpc 
 (r )  

r


• 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.
• The Fourier transform of ξ(r) is the power spectrum P(k):



sin(kr) 2

( ik r ) 3
P(k )    (r )e d r  4   (r )
r dr
kr
0
• 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.
Kaz4
“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:
obs
Vr
1 z 
 1
e
c
 Doppler relation and Hubble Law gives
recession speed:
1
Vr  cz  H0d kms
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!