Extremely Light Dark Matter Particles: ΨDM

Extremely Light Dark Matter Particles:

ΨDM

Tzihong Chiueh, NTU

In collaboration with

Hsi-Yu Schive, Tom Broadhurst, Tak-Pong Woo, James Chan,

Shing-Kwang Wong, Ming-Hsuen Liao, Kuan-Wei Huang, Ue-han Chang, Su-Ron Chen

Contents

• CDM and its small scale problems

• WDM

• What is ψDM?

• Linear and nonlinear evolution of ψDM

• Soliton cores and fuzzy halos

• Determination of ψDM particle mass

• Core – halo relation

• Hints and Predictions for ψDM

• Conclusions

Cold Dark Matter (CDM)

• Thermally generated non-standard-model particles

• Heavy, e.g. 100 GeV due to WIMPS miracle

• Tiny thermal velocity because of its high mass

• Easy to implement to numerical simulations for investigations of nonlinear large-scale structures

• Fit observations, such as CMB, acoustic oscillations, Lyman-α forests, galaxy clusters, etc.

• The agreements are data of large scale and does not rule out other alternatives

• To really pin down CDM, look for singularity

• CDM is scale-free and forms halos within halos

• CDM simulation consistently shows Narravo-Frenk- White (NFW) radial profile in bound objects

ρ = a/ [r (r+ b) ²]

a & b are object-dependent

fitting parameters

Coma galaxy cluster (1 Mpc)

Fornax dwarf galaxy (1 kpc) Andromeda galaxy (30 kpc)

Three kinds of cosmic objects that have high dark matter concentration

Of the three, galaxies have too much baryon concentration at central 10 kpc

Not suitable for understanding the nature of dark matter

stacked lensing data of 4 rich galaxy clusters of 10¹⁵ solar mass

Galaxy Clusters

Observations of galaxy clusters agree with the NFW profile very well

Kleyna et al, 2003

N=10000

(7% of all stars) Ursa Minor dwarf galaxy

Dwarf Galaxies

Old & cold star clump

elliptical harmonic potential

elliptical NFW potential

1 kpc

• Another evidence against CDM is the lack of satellite galaxies near Milky Way, and this becomes more acute after the

recent Sloan Digital Sky Survey

• From CDM simulations, there should be hundreds of nearby satellite galaxies around Milky Way, but only few tens (< 10%) are detected.

• Both the galaxy core problem and the abundance problem are associated with dwarf galaxies on the scale < few kpc !!!

Dwarf galaxies

Scale symmetry of CDM is broken below few kpc ???

If so, what may be the cause?

Option 1: Warm Dark Matter

• Thermally generated WDM has residual thermal velocity that erases small scale structures due to free stream mixing

• It solves the problem of satellite galaxy deficiency

• Best observational constraint:

m > 2 keV (via Lyman-α forests)

• Major problem: for this range of mass

WDM can not produce a flat core as large as 1 kpc

CDM

2 keV 0.2 keV

Linear power spectrum

Option 2: Extremely light particles

• Non-thermally generated bosons, e.g. via axion mechanism, and cold, i.e., BEC condensate

• The universe is described by a single field obeying Klein-Gordon equation, and self-coupled via metric perturbations.

• Breaks the scale symmetry due to a finite mass, or a Compton wavelength λ_comp

λ_comp= few kpc ???

• Not really! One must take into consideration the evolution of a length scale in an expanding universe.

Linear Evolution of Compton Length

• λ_L(a) = (a/a_in) λ_comp

• a_in?

• It turns out a_in is determined by λ_comp= c/H(a_in) = Hubble radius in the radiation era

z=3000 k

primordial spectrum Harrison-Zeldovich

processed spectrum before z=3000

a₀/a = 1+z a₀: expansion factor now

(a₀/a_in)

• If λ_L(a₀) were few kpc, then m ~ 10^-20 eV

• Length scale greatly reduced during collapse of a galaxy, i.e., λ_NL = few kpc (observed dwarf galaxies size) << λ_L

Therefore, m << 10^-20 eV

• One can define λ_NL(a) = F(a) λ_L(a) and ask what F(a) is.

This nonlinear evolution must be aided by computer simulations.

Nonlinear Evolution

Nonlinear Evolution in NR regime

•

|Ψ|² : normalized number density

• Simulations carried out by solving Poisson-Schroedinger equation

• This equation is almost scale free and has an approximate scaling relation

x’ = ξ^-1 a^-1/2 x, |Ψ’|² = ξ⁴ a |Ψ|² , V’ = ξ² V, τ’ =ξ^-2 a^-1 τ In terms of bound objects, M’ = ξ a^-1/2 M

background density

AdaptiveMeshRefinement calculations:

accurate but time-consuming, Δt ~Δx ²

Nature Physics 10, 496 (2014)

|Ψ|²

ψ_r²

Fuzzy halos & Soliton cores

z = 0 dwarf galaxies for any m

obey r_c ~ ρ_c^-4 scaling relation

(Schive, et al 2014,NaturePhys)

Single halo redshift evolution

(Schive at al. 2014, PRL)

Soliton core & NFW halo

Determination of boson mass

Fornax dwarf spheroidal galaxy

Data:

• Fornax dwarf spheroidal galaxy

• good spectral and star count data

• 3 populations of stars

Analysis:

• Choose the richest population

• Solve the Jeans equation for star density, treating stars as test particles in soliton potential

• Adjusting m to yield the least χ², and similar approaches apply to opyimize Burkert and NFW and NF

• Check the result with other two populations

(Schive at al. 2014 Nature Phys)

m = 8x10^-23 eV χ² ≈ 1.2

1-σ ellipse

Core-Halo relat ^ion:

M

depends on conserved mass and energy?

M _c ~ r_c^-1

r_cσ_h ~ h/m

Non-local uncertainty principle

A dedicated numerical experiment:

soliton collision

= σ² M_c ~ σ

Thermalization of the entire halo!

Core-Halo relation: ^M

^{– M}

-z scaling

M

~ M

(1+z)

((Schive, et al.,PRL (2014))

We can predict the core for any redshift and any halo mass !

• For the earliest galaxies at z=12, M_c ~ 5 x 10⁸ solar mass (determined by λ_comp), and gravitational potential

(GM_c/r_c)_z=12 ~ (1+z) ~ 13 (GM_c/r_c)_z=0 for the same halo mass.

• The earliest quasar appeared at z=7, for which the age of universe is ~ 8 x 10⁸ yr, requiring formation of supermassive black hole of M_BH ~ 10⁹ solar mass in a short time.

• 13 times deeper potential may help BH formation

IMPLICATIONS:

M

~ M

(1+z)

, r

M

(1+z)

Nonlinear Evolution: Summary

• Nonlinearity generates a mass hierarchy of different length scales.

Erases the feature of λ_comp and replaced by a running length scale λ_Jeans ~ ρ_local^-1/4(a, x_core)

• λ_comp only important for determining the size of the earliest galaxies at z=12

• After that, galaxies of different masses gradually appear, and λ_Jeans of different ρ_local defines core sizes of the galaxies.

• At every epoch, there is a minimum halo with minimum ρ_local and maximum λ_Jeans which defines few kpc scale at present epoch.

Hints for soliton core and fuzzy halo:

(1) velocity dispersion peaks at central 150 pc

Milky Way bulge Nearby elliptical galaxies

rotation dispersion

NGC3379

M_bh=1.4 x 10⁷ solar mass

Zoccali et al., 2014

M_bh = 10⁶ solar mass

M_bh = 1.4 x 10⁸ solar mass

Shapiro et al. 2006

Krajnovi´c et al.2009

(2) Strong lens quad image flux anomaly

Possibility for detecting 7 images

7

7

5

3

Nonlinear Evolution: Summary

• Soliton is the ground state of this nonlinear Eq. and has a size of λ

~ (1+z)

m

ρ

• Fuzzy halo consists of excitations in the halo potential

• Excitations are random phased, and so granules in the fuzzy halo randomly appear and disappear

• Fuzzy halo & soliton core share the same temperature

or squared velocity dispersion ‹(|▽ln|Ψ|)

›

Conclusions

• ΨDM predicts a soliton core and a fuzzy halo in every galaxy

• ΨDM halos resemble CDM halos by the large, except for minimum halos

• ΨDM is a falsifiable model, having various predictions

different from CDM. To name a few, strong lensing,

central anomalous velocity peaks, first galaxy forming

at z=12 which affects reionization, etc.

Why is ψDM boson mass 10 ^-22 eV?

Tilted wine bottle (axion) model + one general

assumption about the dark sector naturally yields m

~ 10

eV

f

~ 4 x 10

GeV m

~ 100 eV

Φ V(Φ)

arXiv:1409-0380 f_a

Why is ψDM boson mass 10 ^-22 eV?

T = 200GeV

All particles in the same soup

Relativistic Λ dark particles + dark photon

Bright sector

Particle annihilation when non-

relativistic

Why is ψDM boson mass 10 ^-22 eV?

Present Universe Ω

=0.26

Non-relativistic axion density ~ a^-3

Non-relativistic Λ dark particles annihilate to create axion oscillation

3 species of neutrinos + Photons

Td ~ (1/3) Tb ~ a^-4

0.2 MeV > m_Λ > 0.3 eV

Matter-Radiation Equality