Void abundance predic.on and spherical evolu.on model.!!!!! Ixandra Achitouv! Universitäts- Sternwarte München!

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1 Void abundance predic.on and spherical evolu.on model!!!!! Ixandra Achitouv! Universitäts- Sternwarte München!

$on δ<δ v V(R) R Excursion set theory [Bond et al. 91]: voids V(R)= region where linear density filed is bellow some threshold (e.g. δ v ) Number voids size R = frac.$

2 Voids hierarchy - Sheth & Van de Weijgaert (04) Voids Hierarchies: Number of voids dn/dr at given redshia is sensi.ve to the cosmological evolu.on δ<δ v V(R) R Excursion set theory [Bond et al. 91]: voids V(R)= region where linear density filed is bellow some threshold (e.g. δ v ) Number voids size R = frac.on of volume leading to void 16/09/13

3 Limita.ons to the SVdW approach IA, M. Neyrinck & A. Paranjape (arxiv ) Volume of the void and smoothing procedure: Spherical voidà top hat filter in real space Extension of the spherical threshold : a) EST averages trajectories at random posi.ons à introduce a scater (e.g. IA, Y. Rasera, R. K. Sheth, P.S. Corasani. PRL 2013) b) Voids could be aspherical à addi.onal dria/scater 16/09/13

4 Mul.plicity func.on for DDB & top hat filter IA, M. Neyrinck & A. Paranjape (arxiv ) Void- in- cloud effect for a DDB: Consequences of the top- hat filter: 16/09/13

5 Zobov voids Vs. Spherical evolu.on of voids IA, M. Neyrinck & A. Paranjape (arxiv ) Assump.ons DEUSS N-body simulations (obspm-luth) ZOBOV void finder (Neyrinck 08) Voids post- processing: core density- threshold/sub- voids Reconstruc.ng the ini.al threshold distribu.on for Δ v =- 0.8: Spherical evolu.on implies R E =1.7 R L 16/09/13

6 Effects of sampling and bias Post- processing remove lots of voids Survey will uses biased object to define voids: a) Effects of sampling Less objectà larger voids a) Effects of biasing Negligible compared to sampling 16/09/13 ZOBOV result requiring only void density contrast <10

7 Discussion- Conclusion Can the abundance of voids probes non- standard cosmology? How can we take into account the effect of sampling, (DM field Vs. halos/galaxies) in the void defini.on (e.g. nv=0.2nh,,?) 16/09/13 a) Requires post- processing/developing new voids finders? b) Can theory be adapted to the void catalogue once the voids finder has a physical criteria (e.g. density contrast )? c) How this criteria will reduces the sta.s.cs of the data?

8 16/09/13 BACK UP SLIDES

Hierarchical scenario: Cosmic Structures: - Initial density perturbation = seed for LSS - Virialized structure=dm halos - Building block of the cosmic structure Dark Matter Halos mass function: -

9 Hierarchical scenario: Cosmic Structures: - Initial density perturbation = seed for LSS - Virialized structure=dm halos - Building block of the cosmic structure Dark Matter Halos mass function: - Statistics of primordial fluctuation - Non-linear gravitational processes - Evolution in time sensitive to underline cosmology Voids Abundance of a given size: - Voids Abundance evolution at different cosmic times? Measurement of the halo mass function from ROSAT (Vikhlinin et al. 2007

10 Variance Smoothing Radius & Mass 10

11 Voids hierarchy - Sheth & Van de Weygaert (04) Idea: - voids V(R)= region where linear density filed is bellow some threshold (e.g. δ v ) Defini8on: - The Probability density of finding a value δ on scale R(S) = Π(δ,R(S)) δ<δ v R V(R) - The frac.on of volume leading to voids: f (σ 2 ) = 2σ 2 df(σ 2 ) dσ 2 11

12 Excursion Set Theory Bond et al (90 s) Additional constrain: the scale which verified the threshold = the larger one (absorbing boundary) Gaussian ini8al sta8s8cs + sk filter: - No memory of previous steps: Exact analytical solution for spherical threshold and linear barrier 12

13 The Volume defini.on problem Volume contained in the smooth field: Sharp- k filter: - Undefined volume unless you regularize it (e.g. Lacey & Cole) - Incoherent with some observational and N-body simulations volume definition AND spherical evolution of the voids. 13

14 Non- Markovian Random Walks Sharp- x filter: V=V sphere but Correlation between steps à no analytical solution 14

15 Perturba.ve Approach Maggiore & RioTo (MR1 2009) In the mass range of interest we can approximate the 2-point correlator of the sx filter by the sk filter For a ΛCDM model : 15

16 Path Integral Formalism (MR1) Procedure: discre.ze S i =i ε trajectory = {δ 1. δ n } Expand around the Markovian solution: Is it enough to match the N-body voids (/halos) abundance? 16

17 A DriAing Diffusive Barrier? Spherical shell assumptions: - A single top hat perturbation in EdS universe: NO INTERNAL OR EXTERNAL SHEAR Analysis from simulations: HALOS: Critical overdensity is sensitive to the initial displacement of a given mass element from the perturbation center, thus changing how the collapse barriers depend on auxiliary properties of the tidal field. (Ludlow &Porciani 2011) VOIDS:? Take a simple Gaussian distribution to model the barrier 17

18 Implementa.on of the Barrier in the Excursion Set framework (arxiv / ) Exact Markovian solu8on: Non- Markovian correc8ons: 18

19 Comparison with N- body simula.ons Agreement within 5% N- body simula.on uncertain.es of Tinker et al with only 2 free physical parameters! Only 3 physical parameters: - β =0.057 deviation rate from spherical collapse - D B =0.3 scatter amplitude of the collapse D B and β can be predicted from ini.al condi.ons: arxiv

20 Per.nence of the void- in- cloud? Boundary condi8ons (SVdW 04) void- in- void void- in- cloud cloud- in- void Can be computed analy.cally for certain types of barrier and SK filter Shortcoming: - Spherical threshold? - Inconsistent with spherical volume (sk filter) 16/09/13

21 Per.nence of the void- in- cloud? - Void- in- Cloud small scale effect neglibible for SX walks - Peaks and Excursion Set predic.ons with DDB can be very similar!! 21

22 Comparison with N- body simula.ons Spherical voids Vs Zobov: - find density minima using watershed transform Post- processing: - Remove subvoid (void- in- void) using a sta.s.cal criteria Neyrinck 08 - Density minima threshold of the core void DEUSS N-body simulations (obspm-luth) ZOBOV void finder (Neyrinck 08) 22

23 Consistency of the spherical evolu.on Cri8cal underdensity leading to voids: - Scale dependent - ScaTer around the mean simple Bv=- 2.7 is not enough! Assump8ons: - Spherical shape for voids - R L =R E /1.7 (spherical evolu.on) 23

24 Conclusion & Percpec.ves Excursion set Theory = accurate predic8ons for abundance of voids/halos: Correct Volume defini8on DriVing Diffusive Barrier For Voids: Post- Processing is important! Voids finder algorithm? What happen for biased tracer?

The Dark Matter halo mass function:

The Dark Matter halo mass function: Path Integral, non-spherical collapse and non-gaussianity Ixandra Achitouv LUTh Observatoire de Paris in collaboration with P.S. Corasaniti Cosmo11 Porto Motivation Halos are building blocks of cosmic