Angular Momentum Transfer in Dark Matter Halos: Erasing the Cusp
(Tonini et al. 2006,ApJ,649,591)
「Dark Matter Halo のカスプ問題」とは ?
CDM Cosmology →
cuspy halo を予言
観測 → core structure in some galaxies
解決策
１）観測がおかしい：quality and applicability of rotation curves
２）理論の修正
2.1. cosmological に解決
* CDM is wrong : Warm dark matter (Bode+, 2001,ApJ,556,93) / collisional dark
matter(Spergel & Steinhardt, 2000,Phys.Rev,Lett.,84,3760)
* CDM is OK, but cosmological N-body simulations are not accurate
2.2. galaxy level での解決
CDM and simulation results are both OK, but
* bar stirring (Weinberg & Katz, 2002,ApJ,580,627)
* galactic wind (Navarro,Eke,Frenk 1996, MN, 283,L72: Gelato & Sommer-Larsen
1999, MN,303,321; Reed & Gilmore, 2005, MN,356,107;van den Bosch+,2000
本論文 「銀河のバリオン成分（clump）の力学的効果(dynamical friction)によってカスプ
を破壊できる。
」
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１）観測の問題点
銀河の rotation curve V(r) →
mass 分布 M(r) （軸対称を仮定）
* 要件１ minimize the effect of baryons
LSB (μ0,B>23 mag/arcsec-2) galaxies are preferable
(HSB galaxies: poorly determined M/L makes disk subtraction ambiguous:
i.e.,“disk-halo degeneracy”)
* 要件２
avoid non-circular motions (barred galaxies)
→ unbarred LSB galaxies
HI 21cm line →
“beam smearing”
.
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*解決法１ constructs mass model and simulate observation to get best fit
van den Bosch+,2000,AJ,119,1579
*解決法２ use Hα rotation curve
[misalignment between slit and kinematical axis (de Blok+, 2003,MN,340,657)]
Example of recent attempts using Hα
Gentile+,2004,MN,351,903
HI+Hα rotation curve of five late-type bulgeless spirals (HSB, 1.5 mag fainter
than L* , Vmax∼ 100-150 km/s)
with I-band photometry
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Decomposition into disk+gas+halo
Halo mass models usually used in fitting rotation curves
ρ(r) ∝ r-γ as r → 0
Burkert(1995,ApJ,447,L25)
γ=0
Navarro,Frenk,White(1997,ApJ,490,493) γ=1
Moore+(1999,MN,310,1147) γ=1.5
Conclusions
Burkert halos: well fitted to observation with reasonable I-band M/L of 0.5-1.8
Core radius ∼optical radius(=3.2 rd)
NFW: poor fit (large χ2), with unrealistically low M/L (∼0.2)
Moore : worst
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Other works
* Obs. in favor of cores:
Zackrisson+, 2006, AA,452,857 6 LSBs (mostly V_max<60km/s) ,optical rotation
curves
* Cusp not rejected
Spekkens+, 2005,AJ,129,2119 165 low-mass galaxies (70km/s < V_max < 130km/s),
optical rotation curves
* Variety in slope
Simon+, 2005,ApJ,621,757 5 galaxies with V_max ∼100km/s, Hα+CO 2D velocity
field
0< γ <1.2
This paper
similar papers
*El-Zant+, 2004,ApJ,675,L75
“Gas clump feel dynamical friction against dark matter “
*Mashchenko+, 2006, Nature,442,539
“stellar feedback and gas clumps in dwarf galaxies erase cusps”
→ ad hoc initial condition
1) Construct distribution function f(E,L) having NFW density profile
2) distribute gas clumps (point mass)
3) calculate dynamical friction acting on each clump
4) calculate
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initial conditions
uniform distribution within Rvir
Maxwellian velocity with dispersion (σr2+σt2)/2
Mass spectrum ∝Mc-δ (10-5 Mvir < Mc < 10-2Mvir)
Total mass 0.16 Mvir
Run for 2Gyr
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Cosmological N-body simulations の信頼性
結果は人によって様々….
* Steep cusp: Fukushige & Makino 1997, ApJ,477,L9; Moore+ 1998, ApJ,499,L5,;
Ghigna+ 2000,ApJ,544,616)
* Shallow profile: Kravtsov+ 1998, ApJ,502,48
* Mass-dependent: Ricotti 2003, MN, 344, 1237
Numerical convergence of V(r)
Power+, 2003,MN,338,14
1) Δt (time-step) → orbital period: P(r)/P(r200) > 15(Δt/t0)5/6
2) ε(softening) → acceleration Vc2(r)/r < 0.5 V2002/ε
3) N(particle number) trelax(r)/ P(r200) > 1
“Recent” simulation (Navarro+, 2004,MN,349,1039 ;Fukushige+,2004,ApJ,606,625
Reed+, 2005,MN,357,82)
→ inner slope continuously changing (no asymptotic value)
Not Confirmed by
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Diemand+, 2005,MN,364,665
109 body-simulation
cluster sized halo inner slope converge to 1.2
Use of Fitting formulae [both for observed and simulated V(r)] often involves
* extrapolation to inner radii
* degeneracy
Hayashi+( 2004,MN,355,794)
V(r)=V0 [1+(rt/r)γ]-1/γ
Observation not reject CDM
Triaxial halo → noncircular motions
Hayashi+, 2007,MN,on line
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