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)

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

Introduction

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 ?

Missing Satellites Problem

Weinberg et al. 2013

Missing Satellites Problem

Strigari et al. 2008

Enclosed mass within 300 pc vs. luminosity Surprisingly uniform around 107 M⊙

Cusp-Core Problem

Rocha et al. 2013

Density profile in CDM cuspy Navarro–Frenk–White profile (NFW): ρNFW(r) α x-1(1+x)-2, where x = r/rs

Cusp Core Problem

Walker & Peňrrubia 2011

Enclosed mass vs. radius Cuspy profile ρ(r) α r-1 M(r) α r2

Cored profile ρ(r) α r0 M(r) α r3

Wave Dark Matter (ѱDM)

1)ψ(x)4πGa(t)((x)

(x)ψ(x),ηψ(x)2η1

tψ(x)i

22

2

Governing eq.: Schrödinger-Poisson eq. in the comoving frame

η ≡ m/ћ: particle mass, ψ: wave functionφ: gravitational potential, a: scale factor

• Background density has been normalized to unity

Quantum Fluid

ff

2η1vvt

v

0,)v(ρtρ

2

2

Schrödinger eq. can be rewritten into conservation laws

Sηv,mfρ,feψ

1

2

iS/

Pρ

1vvtv:Hydro

22

ijji

2

ij fδ41ffmP ~

quantum stress

2/10

4/1 )()6( HaJk Jeans wave number in ѱDM

Numerical Methods

Numerical ChallengeDensity Wave function

Ultra-high resolution is required

GAMERGPU-accelerated Adaptive MEsh Refinement

Code for Astrophysics

Adaptive Mesh Refinement (AMR)

Layer 1

Layer 2

Layer 2

Example: interaction of active galactic nucleus (AGN) jets

Energy density

Graphic-Processing-Unit (GPU)

GeForce GTX 680 Animations, video games, data visualization …

Graphic-Processing-Unit (GPU)

GeForce GTX 680 Astrophysics !?

ѱDM Simulations

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

ψDM on Small Scale

Halo Density ProfileCored instead of cuspy profiles

Core profiles satisfy the solitonic solution

Lower limit in M300 consistent with Milky Way dwarf spheroidal galaxies (dSph)

Solitonic Solution in ψDM

Spherical symmetric and static ψ(r,t) = eiwtψ(|r|) Solve ψ(|r|) numerically

Non-dispersive wave thanks to self-gravity

Obey the scaling relation:(r, ψ, ρ, M) → (λ-1r, λ2ψ, λ4ρ, λM)

Only two free parameters:λ & mB

mB Determination I:Stellar Phase-space Distribution

Jeans Eq.:

Assuming constant and isotropic velocity dispersion

Find the best-fit mB & rc

mB ~ 8.1*10-23 eV rc ~ 0.92 kpc

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

Linear Power Spectrum

mB ~ 8.1*10-23 eV Jeans length ~ 125 h-1 kpc (at z ~ 47) Substructures are highly suppressed

KJ: Jeans wavenumbera: cosmological scale factormB: boson mass

Solution to the missing satellites problem !?

KJ

M300 Distribution

M300 cut ~ 106 M⊙

Roughly consistent with the Milky Way dSphs, where M300 ~ 106 – 5*107 M☉

Desperate for better statistics (more samples)!!Require (1) bigger computers

and/or(2) ingenious numerical schemes

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 M300 < 106 M☉ are highly suppressed solution to the missing

satellites problem !? By fitting to the Fornax dwarf spheroidal galaxies mB ~ 8.1*10-23 eV