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
2η1
vvtv
0,)v(ρtρ
2
2
Schrödinger eq. can be rewritten into conservation laws
Sηv
,mfρ
,feψ
1
2
iS/
Pρ1
vvtv
:Hydro
22
ijji
2
ij fδ41
ffm
P~
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 Profile
Cored 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 wavenumber
a: cosmological scale factor
mB: 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