1. Tracing the Halo – Cosmic Web Connection Marius Cautun Kapteyn Astronomical Institute Rien van de Weygaert, Wojciech Hellwing, Carlos Frenk, Bernard J. T. Jones September 6 th 2012 CosmoComp 2012, Trieste

2. Sloan Digital Sky Survey galaxies Introduction

3. Outline I - The NEXUS+ algorithm

4. Outline II – Halos and the Cosmic Web I - The NEXUS+ algorithm

5. I – The NEXUS+ Algorithm Challenges: Multiscale distribution No clear defined boundaries Orders of magnitude variation in the density field

6. The NEXUS+ algorithm 1.Apply a filter to the input field. filter I – The NEXUS+ Algorithm

7. The NEXUS+ algorithm 1.Apply a filter to the input field. I – The NEXUS+ Algorithm

8. 1.Apply a filter to the input field. f 2.Compute the Hessian of the filtered field f. The NEXUS+ algorithm I – The NEXUS+ Algorithm

9. The NEXUS+ algorithm 1.Apply a filter to the input field. f 2.Compute the Hessian of the filtered field f. 3.Use the Hessian eigenvalues to assign an environment signature to each point. I – The NEXUS+ Algorithm

10. The NEXUS+ algorithm 1.Apply a filter to the input field. f 2.Compute the Hessian of the filtered field f. 3.Use the Hessian eigenvalues to assign an environment signature to each point. I – The NEXUS+ Algorithm

11. The NEXUS+ algorithm 1.Apply a filter to the input field. f 2.Compute the Hessian of the filtered field f. 3.Use the Hessian eigenvalues to assign an environment signature to each point. 4.Repeat steps 1-3 for a range of filter scales. increasing filter size I – The NEXUS+ Algorithm

12. The NEXUS+ algorithm 1.Apply a filter to the input field. f 2.Compute the Hessian of the filtered field f. 3.Use the Hessian eigenvalues to assign an environment signature to each point. 4.Repeat steps 1-3 for a range of filter scales. 5.Combine the environmental signatures of each scale to get a scale independent result. I – The NEXUS+ Algorithm

13. The NEXUS+ algorithm 1.Apply a filter to the input field. f 2.Compute the Hessian of the filtered field f. 3.Use the Hessian eigenvalues to assign an environment signature to each point. 4.Repeat steps 1-3 for a range of filter scales. 5.Combine the environmental signatures of each scale to get a scale independent result. 6.Use physical criteria to identify the valid clusters, filaments and walls. I – The NEXUS+ Algorithm

14. NEXUS+ results I – The NEXUS+ Algorithm

15. Cosmic Web evolution I – The NEXUS+ Algorithm volume rendering. Using the data from CosmoGrid simulation ( Ishiyama+ 2011 ).

16. Halos and environments II – Halos and the Cosmic Web Halo mass functionHalo fraction

17. Halos and environments II – Halos and the Cosmic Web Angular momentum directionMajor axis of halo shape Aragon-Calvo+ (2007), Hahn+ (2007), Codis+ (2012), Trowland+ (2012)

18. Environment characteristics II – Halos and the Cosmic Web

19. Environment characteristics Filament diameter II – Halos and the Cosmic Web

20. Environment characteristics Filament diameter II – Halos and the Cosmic Web Filament linear density

21. II – Halos and the Cosmic Web Dependence on filamentary density Halo angular momentum vs. environment

22. II – Halos and the Cosmic Web Closer to home: Milky Way Wang, Frenk, Navarro, Gao and Sawala (2012): 3 MW satellites with maximum velocity > 30 km/s

23. II – Halos and the Cosmic Web Closer to home: Milky Way Wang, Frenk, Navarro, Gao and Sawala (2012): 3 Milky Way (MW) satellites with maximum velocity > 30 km/s

24. II – Halos and the Cosmic Web Substructure and environment MW resides in a wall-like environment (Tully+ 2008) For MW-like halos in the Millennium 2 simulation: 90% in filaments 10% in walls

25. II – Halos and the Cosmic Web Substructure and environment 7% of halos in filaments 14% of halos in walls Number of subhalos with maximum velocity larger than 30km/s for a MW-like halo with 200km/s.

26. Conclusions The NEXUS+ algorithm: a tool for multiscale and automatic Cosmic Web environment detection. Very successful in following the evolution of the cosmic environments. Ideal tool for measuring the influence of the Cosmic Web on dark matter halos and galaxies. Understanding how the Cosmic Web influences the formation and evolution of halos and galaxies. II – Halos and the Cosmic Web