Voids size distribution in the 2dFGRS

Voids size

distribution in

the 2dFGRS Volker Müller, Sander von Benda-

Beckmann

AIP

• Voids finder and void sizes

• Analysis of 2dF: self-similar distribution

• Faint galaxies in 2dF voids

• Comparison with SAM of Millenium

01/10/23 Amsterdam Workshop 2

2dF voids

• smoothed density field or galaxies

• underdensity or empty volumes: spheres, ellipsoids, convex on grid

• void size distribution provides void probability F(>r) -> P₀(r)

• void sizes depend on sample -> void hierarchy

• count-in-cell study: Croton et al. -> P₀(r) as function of N₂

• void finder of Hoyle, Vogeley -> wall and void galaxies - large voids

• Patiri et al. -> abundance of large voids

• here: void finder of Kauffmann & Fairall on grid ->

fast & ‚complete‘

Void galaxies

• much interest, but difficult (low number, wide fields)

Void definition

100 Mpc/h

Void filling factor (VFF) or void size distribution, as

function of diameter:

f(<D) is fraction of survey volume not

M., Arbabi, Einasto, Tucker, 00 & 02

LCRS & CDM-mock samples M. & Maulbetsch 04

SDSS

Void search

yellow: void search

including extensions, red:

base voids

M_*

M << M_*

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percentile sizes

form samples with mean

separation , e.g. diffent random dilution or

different magnitude cuts:

0

D

p

= D + ∗ υ λ

25, _med , 75: D D D

Void

statistics

void hierarchy: broad differential size

distribution Poisson

SDSS

SDSS equatorial slices

€

x = D /λ f ∝ x

ax +1 exp −x (

²

/a

²

),

€

a ≈ 3

01/10/23 Amsterdam Workshop 6

2dF volume limited

samples

_{z B}

lim V / 10⁶

Mpc³/h³ 

Mpc/h

N_void D>20 Mpc/h 1 .

05-.1 -18.5 .8

1.3 4.4

5.4 7 18 2 .

1-.14 -19 1.1

2.4 5.8

6.3 55 51 3 .

14-.2 -20 4.7 7 9.4

10 196 246

k+e-correction

uniform completeness

threshold: c > 0.6 75%

of galaxies 5% of sky surface undersampled

2x3 volume limited samples:

6000 to 10000 galaxies each

5.5 rsp. 7.5 deg thickness

(15 - 70 Mpc/h)

sample are

a

galaxi es

2dF versus Millenium

SAM

B_lim = -20 Springel et al., Croton et al.

01/10/23 Amsterdam Workshop 8

Abundance of 2dF voids by number

yellow:

void search

including extensions ,

red: base voids

voids up to radius of 26 Mpc/h

void size

distribution without

extensions strong

dependence on samples

€

f = exp −D /λ − (D /3λ ) [

³

] 2dF size distribution

compare Hoyle &

Vogele 04

01/10/23 Amsterdam Workshop 10

Void size quartiles lie on tight linear relations:

Scaling of 2dF size distribution

 = 18 Mpc/h

 = 4 Mpc/h

0

D

p

= D + ∗ υ λ

 = 0.4, 0.8, 1.3 for 25-, med, & 75 percentile

Voids in SAMs of Millenium simulation (Croton et al.) with survey masks:

N/SGP vs. model

01/10/23 Amsterdam Workshop 12

Selection effects: sample size, real vs. redshift space, inhomogeous sampling:

voids in redshift space are 10% larger than in real space

voids in masked fields are 15% smaller than in complete box

N/SGP2 versus 500 Mpc/h box

survey real mask

Sampples with B <

-18, -19, -20, -21 60%

dilutions redshi

ft

void sizes depend on galaxy brightness, voids with max.

size 40 Mpc/h

Mock size distribution (Millenium

simulation)

01/10/23 Amsterdam Workshop 14

Voids among fainter galaxies have larger relative size

€

F(< D) = exp −D /λ − (D /bλ ) [

³

]

€

b ≈ 3L 4 Void scaling

€

P

₀

(R) = ∫ f (D)(R − D/2)

²

^/D

³

^dD

2dF/SDSS LCRS

groups

Self-similarity of voids among different objects:

galaxies, groups and clusters

D D =

0

+ × ν λ

Void size distribution for different

objects

01/10/23 Amsterdam Workshop Arbabi, M. 03 16

Evolution of radial void profiles

Size

evolution of voids in small

(left) and large halos (right)

Void size evolution

• bright galaxies define large voids

• large voids among faint galaxies have large D / 

• faint galaxies define same structures as bright ones

• void size distribution mainly parametized by galaxy separation 

• parameter b describes cut off: f(r) flat from  to b



, b = 3 - 4

• selection effects due to finite volume

• voids about 20% larger among red than blue galaxies

Void galaxies

• special conditions for galaxy formation?

Void statistics depends on galaxy

sample

01/10/23 Amsterdam Workshop 18

Void galaxies

(voids D > 8 Mpc/h by B < -20 galaxies)

Color distribution fit by sum of two Gaussian (cp. Baldry et al. 04)

similar results for void galaxies in SDSS by Royas et al. (04) and Patiri et al. (06)

here: shift of the blue maximum

Void

galaxies

^{2df millenium}

01/10/23 Amsterdam Workshop 20

Void

galaxies

Weak influence of void environment on spectral parameter 

Similar results for 2dF by Croton et al. (05) for

underdense regions on 8 Mpc/h abundance of passive galaxies reduced especially among

brighter magnitude bin

Void

galaxies

Continuous transition from field to void galaxies:

higher star formation rates

central void galaxies

environme nt

01/10/23 Amsterdam Workshop 22

2dF vs. simulation

• self-similar distribution

• median void size covering 50% of volume quite small: 5 Mpc/h + 

• maximum voids depend on survey volume: exponential cut-off at 3-5 

• void size distribution provides void probability:

F(>r) <-> P₀(r)

• size distribution in excellent agreement with mock samples

Void galaxies

• similar bimodality of blue and red galaxies as in the field

• fraction of red galaxies reduced, blue increased

• effect stronger for voids among bright galaxies

• weak effect: blue shift of the colors of blue galaxies

void filling factor