1. Xiaohu Yang (SJTU/SHAO) With: H. Wang, H.J. Mo, Y.P. Jing, F.C van den Bosch, W.P. Lin, D. Tweed… 2014.11.04, KIAS Exploring the Local Universe with re- Constructed Initial Density fields （ ELUCID ）

2. Motivation Shortcomings in comparing theory (simulations) with data in a statistical way: (1) cosmic variance (environmental effects); (2) only part of information is used. If we can accurately reconstruct the initial condition of the local Universe, we can compare data and theory ‘directly’.

3. The ELUCID Project Constrained simulation (formation history of local universe) group catalogue (“real space”) Galaxy redshift survey group catalogue (redshift space) Wang et al. 2012 Correct redshift distortion Reconstructed mass density field of local universe Wang et al. 2009;2013 Domain cross correlation Yang et al. 2005;2007 Reconstructed initial conditions Group finder Simulation code Future works HMC+PM (Wang et al. 2013;2014)

4. Finding galaxy groups in SDSS DR7 Sky coverage: 7748 deg^2 Galaxies with redshifts: 639359 Groups are found and assigned with halo masses

5. Reconstruct the current density field using halos above a certain mass

6. Method: (1) Each point in space is assigned to its nearest halo according to distance scaled by halo virial radius; (2) The density at the point is given by the cross-correlation between halos and mass given by the chosen cosmological model.

7. Test with mock catalogs simulation + halo occupation + SDSS selection function + redshift space + group finder

8. The SDSS MTV

9. First, the linear density field δ(k) should obey the following distribution: Second, the density field, ρ mod, evolved from δ(k), should match a given final density field ρ f. We seek the appropriate δ(k) to minimize a ‘cost parameter’: Assuming that the likelihood of ρ mod given ρ f is exp(-χ 2 ), the posterior probability distribution for δ(k) given ρ f can be written as: We seek the solutions for δ(k) that maximize this posterior probability distribution function or sample the distribution. Hamiltonian Markov Chain Monte Carlo Method (prior) (likelihood)

10. Phase correlation K 95 : the k that have C p =0.95

11. ZA: k 95 ~0.3 h/Mpc (Nusser & Dekel 1992; many previous works) MZA: k 95 =0.33 h/Mpc (Wang et al. 2013) 2LPT: k 95 =0.37 h/Mpc (Jasche & Wandelt 2013; Kitaura 2013) ALPT: k 95 =0.45 h/Mpc (Heβ et al. 2013) Particle-Mesh dynamics

14. Checking the properties of the halos 2-way halo matching: halos in catalog A and B:  halos are associated by tracing particles ids only, NOT halo positions  when comparing A to B, several halos in A can be associated to a single halo in B  when comparing B to A, several halos in B can be associated to a single halo in A  We consider halos in A and B to be a "match", if only the association is consistent when I compare A to B and B to A.  We consider halos in one catalog to be a "double", if the association only goes one way.

15. Test with SDSS Mock Catalogs re-simulation originalreconstructed

16. Application to SDSS The Great Wall Region z=3 z=2z=1z=0

17. z=3z=0z=1z=2 Formation of Coma Cluster

18. Velocity field

19. In a void region

20. Coherent motion No tracers here

21. Model: Galaxy properties: galaxy redshift survey; ISM properties: 21cm emission, millimeter/submillimeter emissions; IGM properties: quasar absorption line systems; X-ray observations; Sunyaev- Zel’dovich effect. N-body+ hydrodynamics simulation of local Universe (including radiative cooling, star formation and feedback) Semi-analytical model of galaxy formation Observation: