1. Cosmic Structure as the Quantum Interference of a Coherent Dark Wave Hsi-Yu Schive ( 薛熙于 ), Tzihong Chiueh ( 闕志鴻 ), Tom Broadhurst PASCOS (Nov. 24, 2013)

2. Outline Introduction  Cold dark matter (CDM) vs. wave dark matter (ѱDM) Numerical Methods ( GAMER)  Adaptive Mesh Refinement (AMR)  Graphic Processing Unit (GPU) ѱDM Simulations  Halo density profile  Halo mass function  Boson mass determination Summary

3. Introduction

4. Cold Dark Matter CDM (Cold Dark Matter):  Collisionless particles with self-gravity  Work very well on large scales  Controversial on small scales (dwarf galaxies) Main issues on small scales:  Missing satellites problem   Over abundance of dwarf galaxies ?  Cusp-core problem   Mass is too concentrated at the center ?

5. Missing Satellites Problem Weinberg et al. 2013

6. Missing Satellites Problem Strigari et al. 2008 Enclosed mass within 300 pc vs. luminosity  Surprisingly uniform around 10 7 M ⊙

7. Cusp-Core Problem Rocha et al. 2013 Density profile in CDM  cuspy  Navarro–Frenk–White profile (NFW): ρ NFW (r) α x -1 (1+x) -2, where x = r/r s

8. Cusp Core Problem Walker & Pe ň rrubia 2011 Enclosed mass vs. radius  Cuspy profile  ρ(r) α r -1  M(r) α r 2  Cored profile  ρ(r) α r 0  M(r) α r 3

9. Wave Dark Matter ( ѱDM) Governing eq.: Schrödinger-Poisson eq. in the comoving frame η ≡ m/ ћ : particle mass, ψ: wave function φ: gravitational potential, a: scale factor Background density has been normalized to unity

10. Quantum Fluid Schrödinger eq. can be rewritten into conservation laws quantum stress Jeans wave number in ѱDM

11. Numerical Methods

12. Numerical Challenge DensityWave function  Ultra-high resolution is required

13. GAMER GPU-accelerated Adaptive MEsh Refinement Code for Astrophysics

14. Adaptive Mesh Refinement (AMR) Layer 1 Layer 2 Example: interaction of active galactic nucleus (AGN) jets Energy density

15. Graphic-Processing-Unit (GPU) GeForce GTX 680 Animations, video games, data visualization …

16. Graphic-Processing-Unit (GPU) GeForce GTX 680Astrophysics !?

17. ѱ DM Simulations

18. ψDM vs. CDM (Large Scale) ψDM (GAMER) CDM (GADGET)

19. ψDM on Small Scale

20. Halo Density Profile Cored instead of cuspy profiles Core profiles satisfy the solitonic solution Lower limit in M 300  consistent with Milky Way dwarf spheroidal galaxies (dSph) Lower limit in M 300  consistent with Milky Way dwarf spheroidal galaxies (dSph)

21. Solitonic Solution in ψDM Only two free parameters: λ & m B Only two free parameters: λ & m B

22. m B Determination I: Stellar Phase-space Distribution Find the best-fit m B & r c  m B ~ 8.1*10 -23 eV r c ~ 0.92 kpc Find the best-fit m B & r c  m B ~ 8.1*10 -23 eV r c ~ 0.92 kpc

23. m B Determination II: Dark Matter Mass Profile Fornax: 3 stellar populations  get M(r i ), i=1,2,3 Consistent with the best-fit m B and r c from stellar phase- space distribution NFW in CDM fails again

24. Linear Power Spectrum  Solution to the missing satellites problem !? KJKJ

25. M 300 Distribution M 300 cut ~ 10 6 M ⊙ Roughly consistent with the Milky Way dSphs, where M 300 ~ 10 6 – 5*10 7 M ☉ Desperate for better statistics (more samples)!! Require  (1) bigger computers and/or (2) ingenious numerical schemes Desperate for better statistics (more samples)!! Require  (1) bigger computers and/or (2) ingenious numerical schemes

26. Summary Wave Dark Matter ( ψDM):  An alternative dark matter candidate  Governing eq.: Schrödinger-Poisson eq.  Quantum pressure  suppress structures below the Jeans scale Numerical Method:  Adaptive mesh refinement (AMR)  use computational resource efiiciently  Graphic processing unit (GPU)  outperform CPU by an order of magnitude  GAMER : GPU-accelerated Adaptive-MEsh-Refinement Code for Astrophysics  Schive et al. 2010, ApJS, 186, 457  Schive et al. 2012, IJHPCA, 26, 367 ψDM Simulations  Solitonic cores within each halo  solution to the cusp-core problem !?  Objects with M 300 < 10 6 M ☉ are highly suppressed  solution to the missing satellites problem !?  By fitting to the Fornax dwarf spheroidal galaxies  m B ~ 8.1*10 -23 eV