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ランダウ共鳴が 与えるダークマターハロー密度 構造への影響. ○扇谷 豪  森 正夫 ( 筑波大 ). Contents. Introduction The Core-Cusp problem ( GO & Mori; arXiv1206.5412) Change of galactic potential Analytical model Results of simulations Summary & Discussion. Ishiyama et al. (2012). What is the Core - Cusp Problem ?.

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○扇谷 豪  森 正夫


  • Introduction
  • The Core-Cusp problem (GO & Mori; arXiv1206.5412)
    • Change of galactic potential
    • Analytical model
    • Results of simulations
  • Summary& Discussion
what is the core cusp problem
What is the Core-Cusp Problem?

Mass-density profile of DM halo

Observation vs Theory (CDM)

Constant : Core

log(ρ) [10-3M☉pc-3]

log(ρ) [ 1010M☉kpc-3]

Divergent : Cusp

-1 0 1

log(r) [kpc]

van Eymerenet al. (2009)

See also Burkert (1995)

log(r) [kpc]

Navarro et al.(1997)

effects of mass loss
Effects of Mass-Loss
  • The central cusp becomes flatter when mass-loss occur in short timescale.
  • But the central cusp still remains.

GO & Mori (2011)

Initial condition

realistic simulation
Realistic Simulation
  • Mashchenkoet al. (2008)
    • CosmoligicalN-body+SPH simulation
      • Supernova feedback etc.
      • Blue: gas, Yellow: star
    • Gas
      • Blown out (expansion)
      • Fall back towards center (contraction)
      • Repeat many times
      • Gas Oscillation
    • Cusp-Core transition
      • Physical mechanism???

Motivation: understand the mechanism for cusp flattening

idealized model
Idealized Model

DM halo


1) Gas heating by supernovae

2) Gas expansion

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 transition?

linear analysis resonance model
Linear analysis: Resonance model
  • Equilibrium system (0) by external force (ex) ⇒ induced values (ind)
  • Focus on the particle group with
  • External force :

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

Linearized continuity eq. and Euler eq.

Resonance condition:

resonance condition for cdm halo
Resonance condition for CDM halo
  • Resonance between particles and density waves
  • Some arithmetic calculations (n = 1)
  • CDM mass-density:

Resonance occurs when the condition is satisfied

⇒efficient energy transfer

⇒system expands

⇒Cusp-Core transition

Gauss’s hyper-geometric function

numerical model
Numerical Model

DMhalo (N-body system):

NFWmodel(Navarro et al. 1997)

Baryon (external potential):

Hernquistpotential (Hernquist1990)

Property of DM halo

Oscillation period of the external force, T

T = 1,3,5,10 (0.2kpc)

results1 density profile
Results1 -Density Profile-

The cusp-core transition and the resultant core scale depends on the oscillation period of the external potential, T.

Initial condition

T =1=10Myr

after 10cycles

T =3(HR)

Prediction of Core Scale


・Concentration c

・Oscillation period T

T =5

T =10

result2 fourier spectrum of v elocity
Result2 -Fourier Spectrum of Velocity-

Initial condition

T =1=10Myr

Density profiles of DM halos

after several oscillation periods

T =3

T =5

T =10



Core creation

Fourier spectrum of radial velocity

Peaks appear when ω=2π/T .

Each position of the peaks matches the core scale.

r [kpc]

result3 overtones
Result3 -Overtones-

ω=nΩ→ Spectrum with peak (Resonance)






n=1 for T=1


n=1 for T=1













r [kpc]

summary core cusp problem
Summary -Core-Cusp problem-
  • Study the dynamical response of a DM halo
    • The Core-Cusp problem
    • Oscillatory change of gravitational potential
  • Analytical Model
    • Resonance between particles and density waves
    • Resonant condition:

dynamical time oscillation period

  • N-body simulations
    • Resonance plays a significant role to flatten central cusp
      • Resonance →Efficient energy transfer
      • →Cusp to Core transition
    • Core scale is well matched to our predictions
discussion link to observations
Discussion -Link to Observations-
  • If DM halos resonate with their host galaxies, resonant condition may be satisfied in observed galaxies.
  • SFHs of galaxies and density profiles of DM halos
    • ex. Holmberg II

McQuinn et al. (2010)

~ 50Myr

at core scale


(Oh et al. 2011)

Regarding as an oscillatory SFH,

T ~ 100Myr