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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)

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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

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Introduction

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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 ?

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Missing Satellites Problem Weinberg et al. 2013

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

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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

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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

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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

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

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Numerical Methods

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Numerical Challenge DensityWave function Ultra-high resolution is required

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GAMER GPU-accelerated Adaptive MEsh Refinement Code for Astrophysics

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

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

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

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ѱ DM Simulations

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

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ψDM on Small Scale

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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)

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

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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

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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

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

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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

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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

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