1. 14 December 2006 Dark Matter Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) with OLIVER HAHN, Marcella Carollo, Avishai Dekel

2. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam A bit of background (and advertisement)  ~28,000 spectra for galaxies at 0.2<z<1.2 to have I AB <22.5 at a sampling rate of 70%  ~12,000 spectra of galaxies at 1.2<z<3 with B AB <25 and chosen by different color criteria at a 70% sampling rate  Understanding how galaxies evolve in different environments is the primary goal of the collaborations PI: Nick Scoville (Caltech) PI: Simon Lilly (ETH) Multiwavelength imaging from X-ray to radio over 2 sq. deg. including HST ACS imaging of the entire field

3. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam HOW CAN WE OPTIMALLY DEFINE THE ENVIROMENT? Need a template to test several plausible and operative definitions!

4. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam The Cosmic Web Courtesy V. Springel

5. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Galaxies and DM Halos as Tracers of the Cosmic Web Courtesy V. Springel

6. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Defining the “environment” of a DM halo  Although the LSS of matter is prominently reflected in the halo distribution, no efficient automated method has been proposed to associate a given halo to the dynamical structure it belongs to.  Most of the environmental studies performed so far use the local mass density within a few Mpc as a proxy for environment.

7. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam A new (ideal) method  We present a novel and SIMPLE approach that associates DM haloes to structures with different dynamics  Voids, sheets, filaments and clusters are distinguished based on a local-stability criterion for the orbit of test particles based on the theory of dynamical systems and which is inspired by the Zel’dovich approximation

8. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Orbit stability and environment - I  Consider a test particle in the peculiar gravitational potential generated by a cosmological distribution of matter  The linear dynamics near local extrema of  is fully governed by the eigenvalues of the “tidal”-field tensor T ij (the Hessian of the gravitational potential)  The number of positive eigenvalues of T ij is equivalent to the dimension of the stable manifold at the fixed points

9. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Orbit stability and environment - II We thus define as  Voids the region of space where T ij has no positive eigenvalues (unstable orbits)  Sheets the set of points with one positive and two negative eigenvalues (1D stable manifold)  Filaments the sites with two positive and one negative eigenvalue (2D stable manifold)  Clusters the zones with three positive eigenvalues (attractive fixed points )

10. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Practical implementation  Assign particle masses on a Cartesian grid and smooth the density field with a Gaussian kernel of radius R  Solve Poisson’s equation on the grid via FFT to obtain the gravitational potential   Apply the second derivative operator to the potential  Compute the eigenspace of the tidal tensor at each desired point

11. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Testing the algorithm with simulations  Three N-body simulations with 512 3 particles in periodic boxes of size 45 h -1 Mpc, 90 h -1 Mpc, and 180 h -1 Mpc  One simulation with 1024 3 particles within a 90 h -1 Mpc box  All simulations performed using GADGET-2 (Springel 2005) on the Gonzales cluster  FOF haloes with b=0.2 (plus unbinding)  Only haloes containing more than 300 particles are considered since most halo properties show strong numerical artefacts for less well resolved haloes  Our catalog spans 5 orders of magnitude in halo mass with well resolved objects ranging from the size of dwarf galaxies (10 10 h -1 M  ) to massive clusters (10 15 h -1 M  )

12. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam

13. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Optimisation  Our classification scheme contains one free parameter, the smoothing radius R  The particular choice of R affects the eigenstructure of the tidal tensor and changes the classification of environment

14. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam What happens changing from R=2.1 to R=4.5 Mpc/h (a factor of 10 in volume)? Some of the regions where one of the eigenvalues was close to zero change classification. Basically no halo inverts the sign of more than one eigenvalue. S to V C to F F to C F to S S to F

15. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Volume fractions: 13.5% V 53.6% S 31.2% F 1.7% C Each cluster contains at least one halo with M> 10 13 h -1 M  plus a number of smaller halos orbiting around or infalling onto the central one The typical cluster diameter is a few Mpc R=2.1Mpc/h

16. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Orbit Stability vs Density  Density correlates with the dimension of stable manifold  The median overdensity in a volume-weighted sample is -0.79 for voids, -0.55 for sheets, 0.28 for filaments and 4.44 for clusters  Densities are typically a factor of 2 larger for statistics weighted by halo abundance R=2.1Mpc/h

17. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Redshift Evolution z=0.5 z=1.0 For a fixed comoving smoothing scale of 2.1 Mpc/h 84% of the haloes which are in voids at z=0 were in voids at z=1 (the remaining 16% were is sheets) Of the halos that were in voids at z=1: 61% are in voids at z=0 37% are in sheets 2% are in filaments

18. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Redshift Evolution - II z=0.5 z=1.0 z=0.0

19. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Mass function and environment M dn/dM (v c > 50 km/s & in voids) ~ 10 -3 Mpc -3 (in voids) M dn/dM (v c > 50 km/s & in voids) ~ 10 -4 Mpc -3 (everywhere)

20. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam

21. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Two-point correlation functions Voids Sheets

22. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Halo shapes and environment Sphere Needle Prolate Oblate

23. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Assembly history and environment 5 x 10 10 h -1 M  <M<5 x 10 11 h -1 M  2 x 10 10 h -1 M  <M<10 11 h -1 M 

24. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Formation time and environment

25. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Halo spin and environment 5 x 10 10 h -1 M  <M<5 x 10 11 h -1 M  M>5 x 10 12 h -1 M 

26. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Halo spin and formation time 5 x 10 10 h -1 M  <M<5 x 10 11 h -1 M  M>5 x 10 12 h -1 M 

27. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Halo spin and LSS  Do halo spin directions retain memory of the cosmic web in which the haloes formed? v J v J filaments sheets

28. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Halo spin and LSS - II M/M *

29. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Spin-spin correlation function  Are spins of haloes in the same environment preferentially aligned?  This would likely generate a spurious signal in weak lensing studies

30. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Spin-orbit correlation function  Are intrinsic spins and orbital angular momenta of haloes in the same environment preferentially aligned?

31. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Orbit Stability vs Density  Density correlates with the dimension of stable manifold  The median overdensity in a volume-weighted sample is -0.79 for voids, -0.55 for sheets, 0.28 for filaments and 4.44 for clusters  Densities are typically a factor of 2 larger for statistics weighted by halo abundance R=2.1Mpc/h

32. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Density vs environment - II

33. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Density and shear

34. QSO clustering DM Haloes in the Cosmic Web Cristiano Porciani (ETH Zurich) Cosmic Voids - Amsterdam Conclusions  We presented a classification scheme that allows to distinguish between haloes in clusters, filaments, sheets and voids  Applying this scheme to simulations we found that many halo properties retain memory of the environment in which they formed  This provides a first step towards understanding how the galaxy formation process is influenced by the LSS  We also showed that density-based definitions of environment are nearly optimal at late times (if you can infer the underlying DM density)