Cosmic Structure as the Quantum Interference of a Coherent Dark Wave

1. Cosmic Structure as the Quantum Interference of a Coherent Dark Wave Hsi-Yu Schive (薛熙于), TzihongChiueh(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 • Enclosed mass within 300 pc vs. luminosity •  Surprisingly uniform around 107 M⊙ Strigari et al. 2008

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

8. Cusp Core Problem • Enclosed mass vs. radius • Cuspy profile  ρ(r) α r-1  M(r) αr2 • Cored profile  ρ(r) αr0  M(r) αr3 Walker & Peňrrubia 2011

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 Density Wave function Ultra-high resolution is required

13. GAMERGPU-accelerated Adaptive MEshRefinement Code for Astrophysics

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

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

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

17. ѱDM Simulations

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

19. ψDM on Small Scale

20. Cored instead of cuspy profiles Core profiles satisfy the solitonic solution Lower limit in M300  consistent with Milky Way dwarf spheroidal galaxies (dSph) Halo Density Profile

21. Solitonic Solution in ψDM • Only two free parameters: • λ & mB

22. mB Determination I:Stellar Phase-space Distribution Jeans Eq.: Assuming constant and isotropic velocity dispersion Find the best-fit mB & rc mB ~ 8.1*10-23eV rc ~ 0.92 kpc

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

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

25. M300 Distribution Roughly consistent with the Milky Way dSphs, where M300~ 106 – 5*107 M☉ M300 cut ~ 106 M⊙ • Desperatefor 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 • Schiveet al. 2010, ApJS, 186, 457 • Schiveet al. 2012, IJHPCA, 26, 367 • ψDM Simulations • Solitonic cores within each halo  solution to the cusp-core problem !? • Objects with M300 < 106 M☉ are highly suppressed  solution to the missing satellites problem !? • By fitting to the Fornax dwarf spheroidal galaxies  mB ~ 8.1*10-23eV