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

1. 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)

2. Contents • Introduction • The Core-Cusp problem (GO & Mori; arXiv1206.5412) • Change of galactic potential • Analytical model • Results of simulations • Summary& Discussion

3. Ishiyama et al. (2012)

4. 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)

5. 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

6. 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

7. Idealized Model DM halo Gas 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?

8. 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:

9. 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

10. 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)

11. 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 ・Virialmass ・Concentration c ・Oscillation period T T =5 T =10

12. 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 Resonance & Core creation Fourier spectrum of radial velocity Peaks appear when ω=2π/T . Each position of the peaks matches the core scale. r [kpc]

13. Result3 -Overtones- ω=nΩ→ Spectrum with peak (Resonance) ω=2π/ ω=2π/ ω=2π/ ω=2π/ ω=2π/ n=1 for T=1 1 n=1 for T=1 1 3 5 5 2 10 ω=2π/ ω=2π/ ω=2π/ ω=2π/ ω=2π/ 1 r [kpc]

14. 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

15. 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 ~0.5kpc (Oh et al. 2011) Regarding as an oscillatory SFH, T ~ 100Myr