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

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.

The Lick galaxy counts

North Galactic Cap – Seldner et al.

The “stick man” - Slice from the CfA2 redshift survey – a bubbly universe

angular position and radial velocity are plotted for each galaxy

the “wall”CfA2 six slices superposed –

angular position and radial velocity are plotted for each galaxy

How do we get this -

CfA North and South slices

...........From this?

• COBE results after subtracting galaxy and dipole

Actually.......... from this?

Microwave sky image from WMAP

Comparison of redshift surveys

The Las Campanas Redshift Survey

What are the scales of the largest real filamentary features in the LCRS?

• Collaborators

–Somnath Bharadwaj (IIT Kharagpur)

–Jatush V. Sheth (IUCAA)

LCRS: -3o slice

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.

Coarse Graining

● Coarse grained structure is generated.

● As coarse graining proceeds the filling factor, FF, for the slices increases.

“friends of friends” (Turner & Gott 1977) define clusters

● Clusters (different colors) defined by fof are shown at several values of filling factor, FF

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).

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.

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.

-3o slice, Poissson distribution, and Shuffled slices

Shuffling: an experiment with a Poisson distribution of points

Creating a “Glass pattern”

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.

The -3o slice Shuffled at L = 70 and 80 Mpc

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.

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.

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