The Filament-Void Network andthe Scale of Homogeneity in the Universe

Suketu P. Bhavsar

University of Kentucky

Graduate Student Seminar, 2005

Outline

• A brief history of filamentary structureSky surveys and redshift surveysAre the filaments real?

• Analysis of the Las Campanas Redshift SurveyIs there a largest scale for physical filaments?

• Conclusions: Homogeneity - for L > 80Mpc

The Lick galaxy counts

North Galactic Cap – Seldner et al.

1st a rock group “The Filaments2nd

3rd 4th

5th structure in the Universe

“Filaments”

The Lick counts – southern galactic cap'grey scale' matters for what the eye tells the brain

South 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

● ● Note: data permuting technique = SHUFFLE

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?

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

Microwave sky image from WMAP

Famous Cosmological Problems

● The formation and description of structure remains a crucial problem in cosmology

Comparison of redshift surveys

● 1D, 2D and 3D surveys

The Las Campanas Redshift Survey

● Six slices through space

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

• Collaborators

–Somnath Bharadwaj (IIT Kh)

–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 neighboring 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.

Smoothing

● FF = filling factor

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

● Shown are 4 levels of smoothing, note how clusters grow (clockwise) with FF

● Colors represent separate clusters

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 out of L and S.

Extremes: F = 0 ...... circleF = 1 ...... a line

•Use Shapefinders to obtain average filamentarity, F2, of

the features as a function of FF.

(Bharadwaj et al. 2000).

Shuffling

–A procedure for randomising structure larger than some scale and keeping it intact below that scale.

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

● Top: original LCRS slice and a Poisson distribution● Bottom: Shuffled slices

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.

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

Future Projects

• The Sloan Digital Sky Survey

• The 2dF survey• N-body simulations