A method to determine the largest true structures in the Universe
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A method to determine the largest true structures in the Universe
Suketu P. Bhavsar
Dept. of Physics & Astronomy&
Honors ProgramUniversity of Kentucky
Cal Poly Pomona - April 27, 2006
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OutlineA brief history of filamentary structure.
Are the filaments real?
The Las Campanas Redshift Survey.A largest scale for physical filaments?
Method and Results
No “real” structure beyond 80Mpc.
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The Lick galaxy counts
North Galactic Cap – Seldner et al.
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The “stick man” - Slice from the CfA2 redshift survey – a bubbly universe
angular position and radial velocity are plotted for each galaxy
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the “wall”CfA2 six slices superposed –
angular position and radial velocity are plotted for each galaxy
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How do we get this -
CfA North and South slices
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...........From this?
• COBE results after subtracting galaxy and dipole
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Actually.......... from this?
Microwave sky image from WMAP
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Comparison of redshift surveys
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The Las Campanas Redshift Survey
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What are the scales of the largest real filamentary features in the LCRS?
• Collaborators
–Somnath Bharadwaj (IIT Kharagpur)
–Jatush V. Sheth (IUCAA)
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LCRS: -3o slice
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Method Identifying Filamentary Structure
• Embed a 1 h-1 Mpc x 1 h-1 Mpc rectangular grid on each slice.
• Generate “coarse grained” map by filling neighbouring
cells of occupied cells. This creates larger structure, as the filling factor, FF, increases for a slice.
• Use “friends of friends” to define features for at each
value of the FF.
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Coarse Graining
● Coarse grained structure is generated.
● As coarse graining proceeds the filling factor, FF, for the slices increases.
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“friends of friends” (Turner & Gott 1977) define clusters
● Clusters (different colors) defined by fof are shown at several values of filling factor, FF
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Filamentarity
In 2D, the shape of an object can be characterised by: perimeter (L) and area (S).
A dimensionless Shapefinder statistic, filamentarity, F (0 ≤ F ≤ 1), can be constructed from L and S to describe the shape of a cluster.
Extremes: F = 0 ...... circleF = 1 ...... a line
(Bharadwaj et al. 2000).
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The Average Filamentarity F2
• Large clusters contribute most to the overall morphology of structure
• F2 is a measure of filamentarity weighed by the area of the cluster
• We obtain the average filamentarity, F
2 , of a slice as a function of FF.
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Shuffling
● Shuffling is a statistical method to create a fake slice. It maintains clumping on scales below a fixed length while breaking apart structures beyond that length.
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-3o slice, Poissson distribution, and Shuffled slices
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Shuffling: an experiment with a Poisson distribution of points
Creating a “Glass pattern”
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Consequences of Shuffling
Large scale structures that are real, break, and do not re-form when Shuffled
Large scale structures that are visual, i.e. due to chance, are formed again and again due to statistical chance.
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The -3o slice Shuffled at L = 70 and 80 Mpc
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Determining the number of real filaments at various values of L
Plot F2 versus FF for the original data and the
Shuffled slices for L from 10 Mpc to 100 Mpc The excess of F2 in the LCRS above its values for Shuffled slices gives the REAL filamentarity through the range of FF for each slice.
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The -3o slice Shuffled at L = 70 and 80 Mpc
● The shuffled slices at L=70 and 80 Mpc look statistically similar to the original LCRS slice.
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Conclusions
The scale of the largest real structures in the LCRS are ~80 h-1 Mpc
The filament void network is statistically repeated on scales > 80-1 Mpc.
This is the scale on which the universe is statistically homogeneous