1. 2. 3. 4. 5. ( )
() http://www-astro.physics.ox.ac.uk/~wjs/apm_grey.gif http://antwrp.gsfc.nasa.gov/apod/ap950917.html ( ) SDSS : d 2 r i dt 2 = Gm jr ij j i rij 3
= Newton 3 0.1% 19
20 20 2 ( ) 3 3 (2 )
3 3 3 2,3 Sun L4 L5 Jupiter Figure-8 solution 10 Figure-8 Solution 3 (0.005% )
d 2 x = f(x) (1) dt2 x(0) = x 0, dx dt t=0 = v(0) = v 0 (2) 1 dx/dt = f(x) x(t +Δt) =x(t)+δtf(x(t)) 1 1987 2
e 2 8.5 45 2 Nature : Laskar and Gastineau 2009 ( 0.38mm)
1 2
= 2 1920 1930 10 1/10
ρ R d 2 R dt = 4 2 3 πgρr3 /R 2 = 4 πgρr (3) 3 d 2 r dt 2 = 4 3 πgm/r2 (4) M ρr 3 a(t) ρ(t) =ρ 0 /a 3, r = r 0 a (5) 2 a d 2 a dt 2 = 4 3 πρ 0/a 2 (6) 3 2 a 0 t
( ) )
? X X 2 Hot dark matter Cold dark matter
1
Ill-posed problem?? 2+ 3 2 +
f(x, v) :6 f(x, v)dxdv dxdv f t + v f Φ f v =0, (7) Φ 2 φ = 4πGρ. (8) G ρ ρ = m dvf, (9)
. 1996
10 10 10 4 6 +10 7 M82 X NASA Chandra X
2 2 D = 709 2 D
f t = A(f(x)) (10) ( A f 2) (1) df df f 0 (x) A(f 0 (x)) = 0 f = f 0 + df df (2) : df f 0 df : df t = B(df (x)) (11) B(αdf 1 (x)+βdf 2 (x)) = αb(df 1 (x))+βb(df 2 (x)) (12) (3) df 1 df 1 df 1, df 2 df 1 + df 2
λ λdf = B(df ) (13) df = e λt df 0 λ f 0 f 0 df df
, D =1.05 (2), D =10 λ: (3), D = 100, D = 709
, D = 1000 gravothermal instavility V. Antnov (1961) : Hachisu & Sugimoto (1978) Hachisu et al. (1978) : Cohn (1980):
3 (Nature Vol 428 No 6984 724-726, Formation of massive black holes through runaway collisions in dense young star clusters ) 1. : 2. M82 IMBH 3. : Classic View (Rees 1984) 2...
() ( ) 3 merger : ( ) M82 BH Matsumoto et al. ApJL 547, L25 BH 10M BH > 10 6 M
M82 IMBH ( ) () >> 10, << 10 6 BH M82 (K band) 700M = IMBH (intermediate-mass BH). M82 200 : BH (2) HST NICMOS/Keck NIRSPEC McCrady et al. (astro-ph/0306373) IMBH ( ) IMBH IMBH How IMBHs were formed? ()
McCrady et al. 2003 (astro-ph/0306373) Cluster #11 (MGG-11) σ r =11.4 ± 0.8km/s half-light radius 1.2 ± 0.17pc 1. 2. IMBH ( ) 3. IMBH ( ) kinetic mass 3.5 ± 0.7 10 5 M Age 10Myrs. M/L ( ) (< 10 Myrs) King model with W 0 = 7-12 Salpeter IMF (as suggested by McCrady et al) Star-by-star simulation for MGG-11 (MGG-9 is scaled) W 0 8 (MGG-11 ) MGG-9 ( )
( ) BH 100 1000 M ( ) IMBH IMBH IMBH / M82 IMBH ( ) (BH2003 talk) 2MASS Chandra M82-X1 MGG11 0.6 Radiation recoil
IMBH SMBH Merger 1. 2. SMBH Growth timescale would be too large 3. SMBH IMBH? ( ) Ebisuzaki et al. 2001 ApJ 562, 19L 1) 2).... 3) 4).... 1. 2. IMBH 3. IMBH 4. IMBH IMBH Katz and Gunn 1992 : + + 1 Cray YMP 1000 1 : 1000
Saitoh et al. 2005 animation + + 200GRAPE-5 1 (!) 1 : 1 : 1 : 4-5 : 1000 8 1-2
Saitoh et al. 2007 Star formation with SPH Large scale structure formation with AMR 15 15 animation (Baba et al 2009) 1 2 SPH Cray XT4 ASURA 10pc ( 500pc) 10K ( 10 4 K) 3000M ( 10 5 M )
2006: Xu et al, Science 311, 54 Nov 2008: Burst of results from VLBA Several data from VERA (Compiled by Dr. Asaki)
( 30km/s)
( ) ( ) + (Fujii et al. 2010) animation a1 animation a2 animation b1 Stable against radial mode (a1, a2) Spiral arms form They seem to be maintained for very long time
2 30 20 1000 10
148Gflops 952 10 1 40 Gflops 10 (GRAVITY PIPE, GRAPE) GRAPE Host Computer Time integration etc. GRAPE Interaction calculation : :
GRAPE 1988 GRAPE-4 1995 GRAPE-6 2002
GRAPE GRAPE = GRAPE: 1/100 GRAPE-6 ( ()) 1990 1μm 1500 1997 0.25μm 1 2004 90nm 3 2010 45nm 10 GRAPE-DR :
GRAPE-DR R i = j f(x i,y j ) (M) 2 y j PEID BBID A x + ALU B T 32W 256W 256 (K M ) 512 1 200-250W 400-433MHz 820-887 Gflops PCIe 20
GRAPE-DR GRAPE-DR : 128-, 128- (105Tflops peak) : Intel Core i7+x58 12-24 GB : x4 DDR LU ( 1A: CPU 2 ) 430Gflops(1 ) 670Gflops(2 ) 1 CPU 11 GDR 4 chips GDR 1 chips GRAPE-6 HD5870 Performance for small N much better than GPU (for treecode, the multiwalk method greatly improves GPU performance, though)
Little Green 500, June 2010 (nm) (GF/W) GRAPE-DR 90 4.1 GRAPE-6 250 3.24 Tesla C2050 40 2 Xeon 5680 32 0.6 45 2 #2: IBM PowerXCell, #9: NVIDIA Fermi GRAPE-DR 10 GRAPE-6 GRAPE-6 10 : 30 GRAPE-DR FPGA ASIC
2 : 100 30% 300 1100 A4 1 1000 1. 2. 3. 4. Green 500 12/24