コールドダークマターハローのコア-カスプ問題の解決と その観測的経験則の起源

扇谷 豪 (筑波大学)

目次 ・導入 ・ダークマターハローの観測的経験則の起源 ・コア-カスプ問題の周期的振動外場による解決 ・まとめ

Mass-Density Profile of DM Halo

Observation Theory (ΛCDM)

log(ρ

) [1

0-3

M☉

pc

-3]

-1 0 1

log(r) [kpc]

van Eymeren et al. (2009)

Core

log(r) [kpc]

log(ρ

) [ 10

10M☉

kpc

-3]

Cusp

Navarro et al.(1997)

Burkert (1995) NFW profile

Inoue & Saitoh (2011) Pontzen & Governato (2012) GO & Mori (2011, 2012) etc.

2

• Strigari relation

– Mass within 300pc, M(<300pc)~ 107𝑀

– Strigari et al. (2008)

Cf. Walker et al. (2009);

Hayashi & Chiba (2012)

Observational Laws of DM Halos

• 𝜇0D relation – Central surface density,

𝜇0D≡𝜌0𝑟0 ~ 140 𝑀

pc−2

– Kormendy & Freeman (2004)

Cf. Donato et al. (2009);

Salucci et al. (2012)

Dwarf galaxies

Dwarf + Spiral galaxies Dwarf + Spiral galaxies

3

Motivation

log(r)

Cusp

log(ρ

)

Core

Cusp-to-Core Transformation

Link??

Link??

Lin

k??

4

Assumption & Procedure

5

Using the following equations, we can determine 𝜌s and 𝑟s

for given 𝑀200 and z

Concentration parameter:

Virial mass: (halo mass)

Scale density:

NFW profile

c(𝑀200, z) c

𝑀200 [ℎ−1𝑀

]

Prada+ (2012)

Assumption & Procedure

log(r)

Cusp

Core

Cusp-to-Core Transformation

6

log(ρ

)

1. Halos form following an NFW profile

with the c(𝑀200, z) for given 𝑀200 and z

→ 𝜌s, 𝑟s

2. NFW halos are transformed into

Burkert halos (Preservation of virial mass and outer density)

→ 𝜌0, 𝑟0

NFW profile

Burkert profile

Generation of the 𝜇0D Relation 𝜇0𝐷 relation

7

3σ density peak

𝑡cool ≤ 𝑡ff

and

The Cusp-to-Core transformation naturally reproduces the 𝝁𝟎𝐃 relation!

GO, Mori, Ishiyama & Burkert

Relation between Observational Laws

• Assume Burkert profile and Strigari or 𝜇0D relation

• Consistent for DM halos of dSphs

– Consistency breaks for larger halos

• The 𝜇0D relation holds good in the broader range

– Strigari relation may be an indirect evidence of the 𝜇0D relation

dSph

dSph

8

Strigari relation

Assume Strigari relation

𝜇0D relation

Assume 𝜇0D relation

How to Flatten Central Cusps

Taken from A. Pontzen’s slide

Effects of Gas Mass-Loss • The central cusp becomes flatter when mass-loss occur

in short timescale.

• But the central cusp still remains.

Initial condition

GO & Mori (2011)

10

Galactic Fountain • Moderate feedback

→Repetition of gas inflow and outflow (Oscillation)

11

Recurring Change in Potential

1) Gas heating by supernovae

3) Energy loss by radiative cooling 4) Contraction towards the center 5) Ignition of star formation again

Repetition of these processes

Gas Oscillation

Change of potential ⇒DM halo is affected gravitationally

⇒Cusp-to-Core transformation?

2) Gas expansion

DM halo Gas

12

• Equilibrium system (0) by external force (ex) ⇒ induced values (ind)

• Focus on the particle group with 𝜌0 = 𝑐𝑜𝑛𝑠𝑡. , 𝑣0 = 𝑐𝑜𝑛𝑠𝑡.

• External force :

(A: strength, k: wavenumber, Ω: frequency)

Linearized continuity eq. and Euler eq.

Resonance condition:

Linear Analysis: Resonance Model

13

Numerical Model

Baryon (external potential): Hernquist potential (Hernquist 1990)

DM halo (N-body system): NFW model (Navarro et al. 1997)

Number of particles N 16M, 128M

Softening parameter ε 0.004kpc

Virial mass of a DM halo 𝑀vir 109𝑀☉

Virial radius of a DM halo 𝑅vir 10kpc

Scale radius of a DM halo 𝑅DM 2kpc

Total baryon mass 𝑀b,tot 1.7×108𝑀☉

Property of DM halo

Oscillation period of the external force, T

T = 1,3,5,10 τ τ ≡ 10Myr ~𝑡d(0.2kpc)

14

N-body simulations using Tree-code developed for GPU clusters

Density Profile

The cusp-core transition and the resultant core scale

depends on the oscillation period of the external potential, T.

T =1τ=10Myr

T =10τ

T =3τ (HR)

Initial condition

Prediction of Core Scale ・Virial mass 𝑀vir ・Concentration c

・Oscillation period T

T =5τ

after 10 cycles

15

GO & Mori

Number of Cycles

• Energy transfer rate

• Analytical model

– Core scale will glow double between 10 and 50 cycles of oscillation

• Simulation

– T=3τ, till 50cycles

– Core scale doubles!

W/(dK/dt)

16

10

# of cycles=50

30

50

30

10

Initial

Summary

• The Cusp-to-Core transformation naturally forms the 𝜇0D relation.

• Strigari relation may be an indirect evidence of the 𝜇0D relation.

• Resonances between DM particles and density waves of gas play crucial roles to flatten cusps.

• Predictions of our model well match to results of simulations.