Dynamic void finders with respect to cosmological probes

A. Elyiv, F. Marulli, G. Pollina, M. Baldi, E. Branchini, A. Cimatti, L. Moscardini

University of Bologna, DIFA

Post-doc presentation days - Friday Feb. 6th, 2015

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Voids and findersdensity criteria, voids as regions empty of galaxies or with ρ<ρ

lim (Colberg et al. 2005; Brunino et al. 2007; Elyiv et al.

2013)

geometry criteria, voids as geometrical structures: spherical cells, polyedra, Voronoi tess., etc. (Platen et al. 2007; Neyrinck 2008, ZOBOV; Leclercq et al. 2014)

dynamical criteria, galaxies are test particles and not the tracers of mass distribution (Hahn et al. 2007; Lavaux & Wandelt 2010)

Void finder problems● Voids are low density

regions δ ~ -0.8

↓● Low statistics of tracers

↓● High shot noise

↓● Variation of void statistics

and shape

Toy model of LSS● Randomize somehow the set of

points

↓

● Uniform distributions of the information per unit of volume

● Quasi velocity field a

● Assumption of constant velocity in comoving space

● Points from the high density regions (clusters and filaments) are flowing down to the empty or low populated areas (voids).

div a>0div a<0

● We call voids the regions with div a < 0

Toy model of LSS

div a>0div a<0

1. The Uncorrelating Void Finder

● Small shift of point in random direction

● Acceptance of new configuration if CF is reduced

● Stop the iteration when CF is near 0 at all scales

2. Lagrangian Zeldovich approximation based void finder

● Finding the least action solution for straight line particle paths at evolution, PIZA (Croft & Gaztanaga, 1997)

● Putting the random set of points or glass.

● Picking data-random pairs of points and interchanging their end-points

● Acceptance the swap if the sum of the path lengths squared being smaller,

● minimization

Application to CoDECS mock catalog

coupled DM N-body sim.at z=0116129 halos803 (Mpc/h)3

M>2.4x108Mo/h

R0=1.6 Mpc/h

(Baldi 2012)

Uncorrelating VF Lagrangian Zeldovich VF

disp

lace

men

t fiel

ddi

verg

ence

fiel

d

Voids identification in divergence field

● Considering just grid cells with div a < 0

● Founding the local minima of the divergence field

● Each local minimum defines subvoid around, watershed technique (Platen et al. 2007)

●

div a >0

div a < 0

LM 1 LM2

subvoid 1 subvoid 2

dam

Formation of void list● Linking of subvoid with R

eff

smaller some Rlim

with larger

neighbor subvoid if they

have common dam.

LM 1 LM2

subvoid 1 subvoid 2 subv. 3

Uncorrelating and Lagrangian Zeldovich VF vs. ZOBOV

● Thick lines – UVF

● Thin lines – LZVF

● Filled areas – ZOBOV finder

Problem of void centerG - geometrical center of void, just on the base of shape,B - barycenter of halos which reside in void,W - weighted center over divergence field inside of void,M - position of divergence field minimum inside given void.

Uncorrelating and Lagrangian Zeldovich VF vs. ZOBOV

Voids stacking and ellipticity two groups to have similar void size samples: R

eff = 4-7 and 7-10 Mpc/h,

void stacking with centering on their minimum divergence position, second moments of the divergence Θ(q) distribution at the void position,

- the i-th Cartesian component of the grid point in Lagrangian space q with respect to the void center. The sum runs over all grid points within a distance of 0.7 · Rmax from the void centre.

Ellipticities:

- eigenvalues of the matrix

for ZOBOV voids ellipticities was calculated using observed coordinates of galaxies:

Conclusions

Overdensity profiles are more self-similar for voids selected on the base of divergence field

The significance of the divergence signal in the central part of voids obtained from both our finders is 60% higher than for overdensity profiles in the ZOBOV case

Average ellipticities and their variances are almost the same for ZOBOV and our finders

The ellipticity of the stacked void measured in the divergence field is closer to unity, as expected, than what is found when using halo positions and ZOBOV VF

Elyiv A., Marulli F., Pollina G., et al. 2014, arXiv:1410.4559, accepted in MNRAS

Future plans: Alcock Paczynski test, bias factor from voids in Euclid-like surveys