6 P PC-Phys, 9//6 OF T W TITI Y YI I T O T. Fujisawa, Okawa, Yamamoto, Yamada, AstoPhys.. 7, 559. Okawa, Fujisawa, Yamamoto, iai, Yasutake, agakua, Yamada, axiv/cs:9.95 3. Okawa, Fujisawa, Yasutake, Yamamoto, Ogata, Yamada in pep.
> 5 9 ; 6 #? C A O G: " & ' * = +, -. F:73/ I: G K L M P Q R = S T U V W X Y ^]\[OAC?Z SACRA _ ` a & b G: 6 K L M P c d e f g V W X Y Z h i j k [ \ ] ^ l m n o p q? C s b& : t u v w x e f g P y T z { W ˆ * * ƒ ~}o b Š Ž Œ :
ƒ 3? AC > AC = AC " ' & /5/.-#: 7 A u t + u u t x +C x +ft,x = u t = u c x F G 6 A. u t = u κ x. ψ = πgρ 3. 3 ; C, + * # " > = : # " 9
7 > = O A L 5 M C amiltonian and Momentum constaints ψ ψ R ψ5 K + ψ 7 à ij à ij = κ ψ5 ρ, W i + 3 i j W j + R ij W j = 3 ψ6 i K +κψ j i. Appaent oizon Finde : h,θθ + cosθ sinθ h,θ + sin θ h,φφ = Sh. Pat of Shödinge equation with potential d Ψ d + ω V Ψ =. Pulsa equation [ R Ω F RΨ ] R RΨ+ zψ RΩ F R Ψ+6π I P di P dψ =.
5 G? A K O 7 L
? G > ' M = 7 t s ν ν ν ν ν ν ν ν ν A 9 C ; L " # & I 3 ' * +, -. / 5, 6 m M : & F K O P Q R + 3+3+ S \[ZYXWVUT +
C G 7 + ' F ; > 5 -GR-oltzmann ν-eating f ν,θ,φ,ǫ ν,θ ν,φ ν ;t oltzmann eq.: c f ν t + n f ν = c 9 9+ = δfν δt coll 9ν Radius [km] 3 Liebendöfe et al. ewton+ov/c Relativistic...3..5 Time Afte ounce [s]
G ; 7 > ' > 5 T S # a adius km 6 LS FS LS FS agakua et al. b L 5 eg/s 6 L LS ν e LS ν- e LS ν x FS ν e FS ν- e FS ν x m MeV 5 5 5 3 time afte bounce ms
6 : M m Y O A = ; L 3 T S
6 : M m Y O A = \ [ Z > ; L? 3 T S
Yamasaki&Yamada 5 5 > G? Gat S 7 Ṁ? C 9 Lν PS
? G > PS 7 Gat S 9 C? Ṁ Lν uows&goshy 93 3 6 F : Yamasaki&Yamada 5
A Continuity t ρ = ρ u, t t u om t u = ρ P + Φ+ πρ, negy t ε P ρ tρ = q, Induction equation with M condition =, = u, =.
A u θ u + u θ u ϕ u + u θ ρu + sinθ u u + u θ u θ θ + u u θ u ϕ θ + u ϕu θ sinθρu θ =, u θ u θ + u ϕ u ϕ cotθ + u θu ϕ cotθ = ρ = = ρ πρ p GM πρ [ p θ + πρ [ ϕ + θ [ θ θ + ϕ θ θ ϕ ϕ + θ + ] ϕ, ϕ θ + ϕ θ ϕ cotθ ϕ θ + θ ϕ cotθ ], ], ε u p ρ ρ + u θ ε θ p ρ ρ θ = q, + sinθ θ sinθ θ =, u θ θ + u θ θ u θ θ + u θ θ + u θ cotθ u θ cotθ =, u θ u θ u θ + u θ + u θ θ u =, u ϕ u ϕ + u ϕ u ϕ + u ϕ θ θ u θ ϕ θ + u θ ϕ θ u ϕ θ θ + u ϕ ϕ u =, p = π k q =. 3 c 3 3T + ρkt, ε = π m 6 ν k T c 3 3 ρ + 3 kt m, L ν e πν Tν. T 6 egs s g.
: ; 7 C? I: q ν,θ θ, s θ ν Q = s ν Q q, Q θ = Q θ q d s s ν dθ Q q. AQ Q q +Q Q θ +CQ =, Q [ρ u u θ u ϕ T θ ϕ ] T, F j,k A + + C Qj,k Q j,k Q j,k q j q j Q j Q j,k Q j,k =.,k+ Q j,k θ PS q = q =
K fx := actanx+sinx = 3x = x+ x fx+ x fx+ xf +O x. fx.5 tan - x+sinx-.5 -.5 - -.5 - -.5-3 -3.5 - -5 5 x fx+ x = x = fx/f. x+ x x n+ = x n f/f
O 7 KI L56# 5 F x,y := x +y =, F x,y := x y =. x n+ = x n τ Fx n, : ẋ = F. = [ F x F x F y F y Kewton-Raphson ] y 3 - - -3 - -5 F x,y= F x,y= -5 - -3 - - 3 5 x
> 9 O 7 KI L56# 5 F x,y := x +y =, F x,y := x y =. x n+ = x n τ Fx n, : ẋ = F. = [ F x F x Kewton-Raphson F y F y ] y ini 3 - - -3 - -5-5 - -3 - - 3 5 #;Initial Guess Initial Guess x ini CM?
I ; F 3? Initial Guess O79K? KII O 7 5? 3 K, Okawa et al. W xn+ = xn + τxpn, pn+ = τpn τyfxn. yini - ẍ+ẋ ẊX ẋ+xyf =. - -3 ewton- A Y = X Raphson - = 6 M K -5-5 - -3 - - 3 5 x ini WUL = UL Y = U C M # ;
> 6 F Steamline eutino sphee Shock suface u ϕ [km s - ] 5e+3 e+3 3e+3 e+3 e+3 Steamline eutino sphee Shock suface [G] e+ 5e+3 e+3 5e+ e+ z [km] z [km] x [km] x [km] 6
6 3 6 Lν [5 eg s - ] = = = 6 f=. f=. f=..5.5.5.5.5.5 Ṁ [M Ȯ s - ] Ṁ [M Ȯ s - ] > F Lν [5 eg s - ] C 9
M OA Metic Ansatz : ds = f,θdt +f,θ d + dθ +f,θ sin θdϕ ω,θdt Velocity field of Pefect fluid : u t = f,θ v, uϕ = Ω, θ f,θ v, whee v = Ω ωsinθf f. egees of feedom : f,θ, f,θ, f,θ, ω,θ, ρ,θ and P,θ quations : µν G µν κ G T µν instein eqs. tt,, θθ, tϕ, Consevation of T µν µ T µ, µ T µ θ and OS.
O A Peliminay G = a + a 7 + a + a 7 f +a ω f θ +a 3 ω +a θ +a 9 ω θ +a 3 f θ f θ +a f +a f θ +a 9 f +a f ω ω θ +a f +a 5 f θ +a 5 f f +a 6 f ω +a +a 6 T = ρf f +ρω sin θω ω +f f sin θ Ω P +Ωωρ ω ρ.5 f f +f sin θω ω Lagange paticle ω f θ g tt ω θ f θ..5 z.3.....3..5.95.9.5. -....3..5.6.7..9...3..5.6.7..9.75 s z.7 s x
C > 7 I M =? ; F 9 " # & ' # K * +, -. / 3 5 6 : A G L W K O P Q R, 5 S T. W VUUL W? ; X Y Z [O3 \ ] - ^ Q T _ ` G a 3 O b c d TL,I e f g - _ h i a 3 O j Q k l m n o p q s t u v w x y z { u }