Angular Momentum Transfer in Dark Matter Halos: Erasing the Cusp

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
1)観測がおかしい:quality and applicability of rotation curves
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
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”
*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
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
Decomposition into disk+gas+halo
Halo mass models usually used in fitting rotation curves
ρ(r) ∝ r-γ as r → 0
Navarro,Frenk,White(1997,ApJ,490,493) γ=1
Moore+(1999,MN,310,1147) γ=1.5
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
Other works
* Obs. in favor of cores:
Zackrisson+, 2006, AA,452,857 6 LSBs (mostly V_max<60km/s) ,optical rotation
* 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
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
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
Cosmological N-body simulations の信頼性
* 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
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