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"+D=' ?= @B +) 0  f(  x  c $p  x  c $(p`   .  0pwX ,$ 0  A simplified global solution for an advection-dominated accretion flow Yuan,Feng; Ma,Renyi; Narayan,Ramesh ApJ in press 2bQ H  0޽h ? 33___PPT10.u +V;Do' ?= @B D*' = @BA?%,( < +O%,( < +Da' =%(%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(+8+0+0 +4  0L0 3+0(    0%  "Why we do? How we do? What we get?H#0 2 G$33 G$ G$  0x+  =Outline 2C$H  0޽h ? 33___PPT10i.=`_+D=' ?= @B +  0L0   P(  ~  s *<pjn   ~  s *e   X  0A?c``  0  `A ? ? t(  H  0޽h ? 33___PPT10i.DZ+D=' ?= @B +  0L0  (  ~  s *(pjn   ~  s *te   X  0A?c``  0  `A ? ? t(  X  0AB? Z&   0  `AC ? ?h   ~   BAD ? ?& 3 F  S AFS0 RB  s *Dop0H  0޽h ? 33___PPT10i.DZ+D=' ?= @B +{  0L0 zr0 (  ~  s *$pjn   ~  s *e   X  0A?c``  0  `A ? ? p$  X  0A?` RB  s *Do H  0޽h ? 33___PPT10i.DZ+D=' ?= @B +  0L0 @(  ~  s *+B#style.visibility<* %(+   0L0 P Z(  :  3 A  ~  s *pjn   ~  s *P`     0P   fTwo Boundary Conditions: . 2~  BA ? ?uP   0X0P  \Outer: Inner: Transonic& 2 ~   BA ? ?  P ~   BA ? ?     HAE ?1~o ?% 8 $D 0H  0޽h ? 33___PPT10.DZ+:4_Db' ?= @B D' = @BA?%,( < +O%,( < +DT' =%(%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(+  0L0 `  (   :  3 A  ~  s *,7pjn   ~  s *8`     0\@P   fTwo Boundary Conditions: . 2~   BA ? ?uP   0|C0P  \Outer: Inner: Transonic& 2 ~   BA ? ?  P ~   BA ? ?    0 # lA ?1~o ?"<   <:   H  0޽h ? 33___PPT10i.DZ+D=' ?= @B +  0L0 P =(  ~  s *,apjn   ~  s *ae   X  0A?   0c`0z x>No transonic point Irrelevant to the outer boundary conditions? 2?GX  0A?Z 0  `A ? ?q   8 @   @ r  <)C"?@    6tiV [Breaks down in the inner region 2 GH  0޽h ? 33___PPT10i.DZ+D=' ?= @B +$  0L0   (i (  (X ( 0A? ~ ( s *pjn   ~ ( s *e    ( 0A ? pP,$D 0\ ( 0  P ,$ 0 Theoretically, we can get a simplified solution that are the SAME as the global one if the angular velocity equals to that of the global solution. 2L  "  (#  ( 0C"?   (2  `A  ? ?"   Wz 0 P  (  ,$D 0  ( 0C"?0 P  ( 0 V OTwo adjustable parameters 2  ( BA  ? ? R   L   (#  ( 0C"?  (2  `A *? ?Q * r8   (  ( 6C"?  ( HA9 /? ?Q /  ( 0 ` ,$D  0 ( 00 0 ,$D  0 ( 0 @ ,$D  0H ( 0޽h ? 33___PPT10.e6+gD ' = @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D+' =%(D' =%(D{' =4@BBB B%()))D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =-6B+checkerboard(across)*<3<* (Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(+8+0+(0 +b   0L0 a Y , (  ,~ , s *@ p    ,0  `A? ? ?   , 0` O  e Low High> 2333333 ,0  `A  ? ?#0  ~ , BA  ? ?) zQ   ~ , BA ? ?=py  ~  , BA ? ?K 3   , <A ??C"?m    , <A ??C"?f   ~  , BA ? ?  RB  , s *Do`RB , s *Do ` RB , s *Do   RB , s *DoRB , s *D)  ~ , BA ? ?[p  ~ , BA ? ?K9 ~ , BA ? ? 9  RB , s *Do  H , 0޽h ? 33___PPT10i.;y+D=' ?= @B +Y  0L0 XP0(  0H 0 3 A"`PB! 00  `A ? ?P   00  `A ? ?  |  H 0 0޽h ? 33___PPT10i. `7+D=' ?= @B +Y  0L0 XP4(  4 40  `A ? ?  s  H 4 3 A"`O[  40  `A ? ?  H 4 0޽h ? 33___PPT10i. `7+D=' ?= @B +Y  0L0 XP8(  8 80  `A ? ?P   80  `A! ? ?P s  H 8 3 A""`O^!H 8 0޽h ? 33___PPT10i. `7+D=' ?= @B +Y  0L0 XP<(  < <0  `A# ? ?P   <0  `A$ ? ?PP { s  H < 3 A%"`Og!H < 0޽h ? 33___PPT10i. `7+D=' ?= @B +Y  0L0 XP@(  @ @0  `A& ? ?P   @0  `A' ? ?P f  H @ 3 A("`O` H @ 0޽h ? 33___PPT10i. `7+D=' ?= @B +w  0L0 vnD(  D D0  `A)  ? ?P   D0  `A* !? ?PP  ! f D 0A+?"`O H D 0޽h ? 33___PPT10i. `7+D=' ?= @B +w  0L0 vnH(  H H0  `A, "? ?P "  H0  `A- #? ?  j # f H 0A.?"`O H H 0޽h ? 33___PPT10i. `7+D=' ?= @B +w  0L0 vnL(  L L0  `A/ $? ?P $  L0  `A0 %? ?P  O % f L 0A1?"`O)!H L 0޽h ? 33___PPT10i. `7+D=' ?= @B +w  0L0 vn P(  P P0  `A2 &? ?P &  P0  `A3 '? ?P  l ' f P 0A4?"`O!H P 0޽h ? 33___PPT10i. `7+D=' ?= @B +w  0L0 vn0T(  Tf T 0A5?"`O  T0  `A6 (? ? (  T0  `A7 )? ?  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K2 `A-A simplified global solution for an advection.-@"Verdana-.  2 `-.-@"Verdana-. +2 e@dominated accretion flow.-@Arial-.  2 er.-@"Verdana-. 2 l@Yuan,A.-@"Verdana-.  2 lLFeng.-@"Verdana-. 2 lV; Ma,A.-@"Verdana-. 2 laRenyiA.-@"Verdana-.  2 ll; .-@"Verdana-. 2 loNarayans.-@"Verdana-.  2 l,.-@"Verdana-. 2 lRamesh.-@"Verdana-.  2 t@ApJ .-@"Verdana-. 2 tIin press.-՜.+,D՜.+,() 5 ()  * +-.2 0 12 34 5 b$,[9v,+ X2$b$2>g@VEktX2b$a9DblMer)ht2$y y#Q=&x2$^JNKDU rS2$ظ`sGk&K2$`x8B2$ PO+2$wb,EfXc2$̨?qjsUb$5}m ,ushu(b$ dv 0@7ݪ2$k_B},t 32$ATEUv5986b$V`$Őu2W2$F[d#/y2$l]a1Etdf2$8~ tqvA2$pw mf2#H-2$8W\KN[2$DN0Ffn*P|2$@PiT>Aһu<H2$r޵Q:*2$}Z UޙNr2$ophR|P_Tyb${reX`C qm&2$&Pu\0qJ:~ 2$v`'͟k%R~2$fVL۾ d_|6b$`LPh@?j4_$2$t{?Kp:y82$&%c2zuR:b$-S;b:(ص&=2$5mLߜjJ{NKn> c2$&$p}֒4NHeb$hpFKZ2$s<[xL Nxb$O8iy}]Ɛb$0cv\s̛N#2$Vvv( 0ti<h2$wyl+ba穁T0k$2$kxD3.Em2$Gay=8+go2$uy&<(S"q&,0t2$l]IdL~'V,x2$(Rth8Y`j0{2$>b\ y"h~2$}r\u߇znh:2$2QI-p<2$C[вX7NeQj҅b$r=Or=&a)ȿ<2$89xsi ,2$M!e>0ؔ=O)2$/ ۬,&Р<b$ƸDӛ f2$W4NfOQ$2$ ,M H8]]7k 0AA@1~@1~1~8?@3ʚ;ʚ;g4BdBd  0(ppp@  <4dddd4x 0h80___PPT10 ?  % ,$A Simplified Global Solution of ADAFRenyi Ma (lNa)$-  Y Why we do? G"33Basic Eqs. of ADAF S Why we do? G"33Basic Eqs. of ADAF Z Why we do? G"33Basic Eqs. of ADAF [ Why we do? G"33Basic Eqs. of ADAF . Why we do? G"33Basic Eqs. of ADAF e Why we do? E33#Global Solution---- time-consuming 0$0 Why we do? E33#Global Solution---- time-consuming 0$/ Why we do? G"33%Self-similar Sol. ---- unsatisfactory&&2 How we do? G"New Set of Eqs. 3 What we get? G" 4 5  6  7  8  9  : ; < = M Disscussion A To include the outflow  A BThanks!C,E How we do? 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