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(1)EVOLUTION DES DISQUES D’ACCRETION PROTOPLANETAIRES Sebastien Fromang. To cite this version: Sebastien Fromang. EVOLUTION DES DISQUES D’ACCRETION PROTOPLANETAIRES. Astrophysique [astro-ph]. Université Paris-Diderot - Paris VII, 2004. Français. �tel-00011405�. HAL Id: tel-00011405 https://tel.archives-ouvertes.fr/tel-00011405 Submitted on 18 Jan 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(93) # /A%6"S *+3,.-0/ " & 572(]  NBw"(](D )D( ` @G ) MN57GO3Q71G!$#.(4'6578)]# h& MV4 18 M$F3#& EX 'I8'6(4'#&% 5&!$(4FG5&!$#&@8'#&%  @r^ #&1G(D!$  )]#ih&[  M 18 MWF8#&EX '8'6(4'#&%|Xw57%657'I@8#&%|# h& MY571 )4#&3) 1  G"( =z #&x 8) M$F8#&01GYM"#& ) %_^ 'I8)D(4#.y3'%I'6( V9 j )D\@ "h& %65&X8Xw  MN!45 6 ( b"(%6 @3')401GK@G"hH'6 2(](41G!$y318%6 2(   #&'6 ( g)D 18%s%6 3'6h& #&1 @G )$#.(41G!$#dt -.

(94) p ; a j eA[ x . j eL[  = pRe j . *. . . . ?- .- + ;+ * * - -0* *M- * * * , *+ * ,.- * * ), M-N, * * * , * ./ , * * + , + 9- * + * * -0,%+ * * , %* , , *+ * .* + ,%- *H+ - * * ', + * + + ,.- * * 9+ ,  + , ),.( G-0/  5, , ,%+ ,%, + *9/ , , -0* * * , , * * + + )* -N/ -N, M-* * + * .- )-N, * + * >- * * * * - * H/ - ",. - * * -0, * - -0,%+ #*H- - * * - * .* * .* * ,%-0* * * / + , + * + * 9, %* , ),../. . R

(95)  -   *=  N97

(96)  +; F P+(

(97)  ?P-   D Q

(98)     7  V +(-=  T+ -)$ Z :S >$7-=P3      !.F0  -= %& !C-  5 ?-= $7(   $

(99) $0-U6$ *  P+(

(100)  ?P-

(101)   5$ A   -;O -   ( !)    -= $ (#  !U ;  )F$ ;?- $ &A -(OI- $ *  )- (-U  E 2T QC-  )7A   -=  5 S  +;-=  *+ -)$ F0  0  ) 

(102)  D-=C 5?-  =(-U C J    L    +( 0

(103)  + 0$P  (.7A   3 0$&

(104) + 

(105) 7 . -= 

(106) -U $7CC-= C :RO   /

(107)  ! ;$    B L- V4WUXGXWZ .  . .

(108) . . . . (4'657  M$F8#&GGQ&p Y@r^ 18G`)$'E]13%#.(4'657 #q %u^ #&1G(D!4k"( # h& MY %18'R%6`(4#&1  @8`(D!$#&8)DXw5&!4( @G`E57E 2( M"' "(4'01G A(4#&1   )D( (D!$#&@3'6(4'6578G %I%6 E 2(kE )41G! >X3#.!%AX3#.!$#&EV"q (D!$ 018'3 )D (s %L!$#.X8Xw5&!4( @GT%#VMN57ETX 57)$#&o(D @81 (D 8)D 1G!*@8 )*MN57o(D!W#&'o(D )+"(+@GT%#\X3!4 )4)4'657 jn% # "(  '2(D!45H@818'6( Xw571G! %#YX8!4 ET'_"q !4  57') X3#.! { F8 # 8H1G!$# { 18oS7 #."h "  U7J.Z & "(T1G(4'%I')   @G"X 18') @8#&8) @G\G57E  t y8!4 1  E5H@rq %6 )s)D ET' 2 #&3#&%6S2(4'I021G ) @G:@8'I)40218 )  =zb#&/ 8) MN )sE5H@wq %6 ) 2)457K  HX8!4 )4)$'657 )D(!4 %' " @GKEK#&8' "q !4TX3F  857E  G57%65&Q7'01G #<q %#VhH')4MN57)4'(  #`)4(D!$18MN(41G!4K5&y8(D 218KXw571G!*%6K@3')401G )D(  8)413'6(DLMN57EX3#.! " z#&1 5&y3)D"!4h.#.(4'6578d

(109) ) / oMN:018'8)D5713%'6Q7GR%_^ 'ETX 5&Z!$(4#&8MNL@GA%#,@ "  (D"!WET'8#.(4'657 @G .@31]E57'I8)   5&!W@G!4@8sQ&!W#&8@G 1G!  )g)4'E 18%#.(4'578) %5M"#&%6 ) = 57o( E572(D! L01G V )D( MN57E t X8!$'I)R o(D!$   "(z0218 %0218 )L@8' G' q E )A)4 %657%#T(D5&X 57%5&Q7'6+@81<M$F84 #&EX 3/  ):Q&!$#&8 @G )Ahd#&% 1G!$) )D572(AG5&(4#&ETET o(A#.(D(D 'Io(D ):%65&!$)401r^ 18\M$F3#&EX`h&"!4(4'M"#&% # h& M]18 1 \G"4 (R )D(LX8!  )4 o(L(4#&3@8') 01G%6 )z)4'E 18%#.(4'6578):MN57ETE , M"6 #&2(+#ih& M18 M$F8#&EX 5&!$(4FG5&!$#&@8'#&%b)4#&8) 1 G"(,@G578G 2(,%6 ) (4#&1 K@GA(D!$#&8)DXw5&!4( @8:E57E 2(M"'I " (4'0218:%6 ) X3%18)  #&'6y3% )  q { %_^ FG 1G!$A#&MN(41G %%6 %#*MN57GO3Q7 1G!$#dt (4'657 @81KMWF8#& EX\r^f )D( X #&)MN572(D!$#&'2(D:X #.!%6 )5&y3)D"!4h.#.(4'6578) '313K4 M$F3#&EX 'I8'6(4'#&%H )D(X8!  )D 2( #<q Q&!$#&8@G  MWFG %%6\ @8#&8) p %6 MN52 1G! @G 8)4  '%  )D(+X8!$5&y3#.y3%6K01r^ 18 1  G"( G57 218% (D !$# h&"!W)D %6K@3')401GT@r^ #&M"MN! "(4'657 "Xw 8@3#&o(+%I#V!45&(4#.(4'657 @8'CB "!4 o(4' %%6K#(D 8 @8#&8MN #q X8!W'6h'I% "Q7'6"!*18 M$F3#&EX 5&!4(4FG5&!$#&@8 'I#&2% bMNV018'!4 8@ MN"(D(D`0218 )D(4:/'657 #&)4)D  4V'8MN"!$(4#&'G j %  #&13@G!$#<X8!45&y3 %6 ET o( #.(D(D 8@G!$ %_^ #.!$!$'6h " @G %_^ '2(D"!  "!$57E\"q (D!4 !$#&@8'65 9 Xw571G!># h&57'6!,188]E '%I%6 1G!4+'I@ " @G %# (D 5&Xw57%65&Q7'6T@81 MWF8#&EX  x GO3)  XwZ 571G!,MN578M"%1G!$ MN"(D(D @8')4M"13)4)4'657Y)41G!*%6 )zX3!45&X8!$' " (   )*ET'I)D )z  "h U&'I@GU  8MN X3#.!,%6 )z)4'E 18 %#.(4'6573) = %65HM"#&%6 ) r[E 2(4'6578G578)>%6 )z)4'E 18%#.(4'578):@8 ;>

(110) # /A%"S *H+,.-N/ " * &s018'8572(E572(D! ,0218:%_^ '3)D(4#.y3'%'( A9 j Xw57)4)" q @8>'2(D!$'3)Nq 021G ET o(s18TNBw"(s@8S8#&ET5  %%6,X #.!4h' o(+#Tq #&EX %'6O8"!|X318'I)+#q ET#&'2(D 8'6!L18`MWF8#&EX'I8'6(4'#&%w#&%   #.(D57'6!4  X8! q )TMN"(D(DVX8!$ ET' "q !4 \Q    " !$#.(4'657 @8\M"#&%IM"18%) Z = %65M"#&1 -g%_^ #&E   %'65&!W#.(4'657  @G ) E5iS& 3) @G,M"#&%M"18%I)s# Xw"!$EK')%I#+!  #&%'I)4#.(4'657V@G,)4'E 18%#.(4'578) Q7%5&y3#&%6 )R@G,@8')$021G )sET#.Q7 "(4')  ) " !$ET'Ct (4#.Q&   U&U&P 1 ;>

(111) #  /A%6"S        G.1 { (D 'I8#&9M 8&"!  ag#.X3#&%657' 4"5731    7 &  x %%6. ?)- 57o(|(D571G(|@r^ #.yw5&!$@ MN57GO8!WE s%6 ) !  )418%6(4#.(4)g@G ) )4'E 18%#.(4'6573) %65HM"#&%6 ) ag#.!b   ET X3%6   %I#LO8Q71G!${  E57o(D!$%6s8'6h& #&1 @G>)4#.(41G!$#.(4'657 @Gz%#*(418!4y318%6 3MNLXw571G!@G )s)4'E 18%#.(4'578) !  #&%') " )|X #.! (D 'I8#&9M 8&"! ab#.X #&%657'Ct * . . . . .

(112) iJ. . + + * * , H* + * .- , 9+ , + + , * *H+ * * -0,%+ + * - , + * N- , + )- * * 5/ %+ * * ), + - * - , ), + *H+5*H+ * * * , + *+ , + * 9-N, * ,%+ ,%*/ + F, + * >* - - * R" (A#&%  ./.  * 

(113) -.$ -=  9 -=  Q?- C:9 ;$&$

(114)  5

(115)

(116)  D-  - 4-= :9 -= E-   ! V  . -= 

(117)  5?-   

(118) 2 * Z -U E9 ;$  5  -=P3-  $    /       $P-  E9 ;   5@:9 -= H  9 -= $7-=E)    :9 -  1-  ( L

(119) ?- 4  * Q?P- :R O  (  F : D & V4WUX;X(YZ. 4"571"   7 &"(RMN57ETE ,M"6 #&2(R# h& Mz18 M$F8#&EXVET#.Q7 " (4'I021G,)4#&3) 4 1 KG"(" +;-= *  *+ ,-)$)* &  "( %#`h.#&%6 1G! MN5&!4!4 )DXw578@8#&2(D @8 5&y8(D 1G" +(-= * *(N + * &  => X3%18)

(120)  MN ) )$'E]13%#.(4'6578) Q7%65&y3#&% )A572(:Xw"!$EK')LXw571G!>%#TX8!$ ET' "q !4  57')>@G @  MN!$'6!4 @G )>E5@rq % )>@8]@8')$021G ):@  MN5718%#&2( )D 18% E o(,@GX3 !$'8M"'6Xw  )AX3FoSH)4'01G )z@G y3#&)D )$#&8),#n 5718(*@G X3#.!$#&EV"q (D!4 )]#&@ 2FG5HM 571 @r^ 18G @G )4MN!W'6X8(4'657 X3F  G57E  G57%65&Q7'I021G @G %# (41G!4y318% 8MN MN57ETET @3#&8) %YM"#&)\@G. )\E5H@wq %6 )\@G @8')$021G ) >  H E X3 % 7 Z @r ^ 18x 8K(D %%6 )D(D!$18MN(418!4K )D(E572(D! V)41G! %#O3Q71G!4 * g  H(D!$#&'6(D\@G =>  z '%%'6"!W)>*+,.-0/ " & %%6 !4"X8!  )D 2(D  13GMN571GXwT@GT%#V-@G 8)$'6( T@8#&8),18 @8'I)40218 018' "h&57%1G#&1G(D571G!z@r^ 18(D!4571YG57'6!z@8#&8)A13G]E "(D!$'I021G !4 %#.(4'h')4(D <X  18(LS`h&57'6!z%#KEK#.(4' "q !4 . @81V@8'I)40218:X3%57GQ& #&o(R)418!L%# )4'GQ718%I#.!$'6( , MN o(D!$#&%*)D57 18)R%_^ #&MN(4'657@G,%# (41G!4y318% 8MNz9<;>=  /  @8')$021G, )4(Ayw5&!$@ + @G] X3#.!4(L"(>@r^ #&1G(D!4 @G+ )D57X3%#&   0x 18#.(D5&!$'I#&% X3#.!>18G, 2h& %65&X8Xw]MN5&!$578 #&%6  5&!4(D E 2( ET#.Q7 "(4'I) "V"(+5 1 q %#@G 3)4'6( K )D(  #&'6y3%6 GO3) 13 D"(])D E]y3%6 " (D!4  HX318%I)  %6 %657GQ @8%_^ # H@G)DSHE " (D!$'6<@81 )DSH)D(Nq E<X #.!K%6 )X3#.!$(4Z '6 )T'2(D"!$G )T@31 @8')401G  jn%  #&18(KG5.t (D"!z021G  E  E @8+G57 ,) D571G!$

(121) ) G(D571G(D )zMN )A)4'E 18%#.(4'578) = )D572(A  H(D

(122) !  E E 2(zMN)5 1G (D 18 )D ):  (D EX3)@GAM"#&%M"13%8"(   MN )4)$'6(D o(|%_^ 1G(4'I%')4#.(4'657@8AET#&M$F3'G ) X3#.!W #&%% q %6 )k(D! q )X318'I)4)4#&2(D ) '8)42' . E   EK)$'  %%6 ),@G573G o(,X3!45&y3#.y3%6 ET o(,18GT#&)$)D  4Tyw578G'@ "T@GT%u^ "h&57%I1G(4'657 @8 )*@8')401G )  %#X FoSH)4'01G*018'rS\  )D(:@   MN!W'6(D]#&'3)4' 01G+%#!   )457%1G(4'657<218E " !W'0218+1G(4'%'I) " *)D57o(: 8MN5&!4 @G )  #&MN(D 1G!$)A%I'ET'6(4#&2(4) >GK@   MN 83'6K@GKM"#&%IM"18%)*#&8#&%S2(4'01G ),"( @GK)4'IE]18%I#.(4'6578), / 18E " !$'01G )* #`@8[578MTE5H@8'6O   @G!$#&EK#.(4'0218 E o(*85&(D!4TXw"!$ MN"X8(4'657 @8 )*@8')401G ),@r^ #&M"MN! "(4'57 ^ '8)D(4#.y3'I%'6( T9 jz#.X3X3#.!$# 6( #&1 D571G!$@r^ F18'|MN57ETE<18 E  M"#&8')4ET  573@8#&E 2(4#&%|X 5718!TMN57EX8!4 8@8!4V%6 1G!T@GSH8#&ET '01G "(  @G G57E]y8!4 13)D ) "(418@G )`)D572(V(D571 D571G!$)\  MN5718!$)\Xw571G !V  # KG"!`G5&(D!$ MN57EX8!  FG 8)$'657 9<#&')13 KX8!$5&y3% q E:'IEXw 5&!4(4#&o(s@G E 1G!$A(D571G(D  57')sXw57) >@8#&3) %6zM"#&)s /X3#.!4(4'M"18%I'6"! @G )s@8')401G ) @r^ #&M"MN! "(4'657 X3 !45&(D5&X3%#& "(4#&'6!$ ) w'%)L)457o(>(D!"q )  !457'I@8)L"(>(D!"q )z@G 8)D )   (4#&1 @r^ '6573')4#.(4'657VS  )D(kX #.! MN578)  01G o((D!"q )  #&'6y3%s"(%6LMN571GX3%#.Q&A o(D!4:%6LM$F8#&ETX ET#.Q7 "(4'01GL"(s%6 ) X3#.!$(4'M"18%6 ) iJ .

(123) p ; a j eA[ x . j eL[  = pRe j . P. . .  J , * * 9+ ** + F, + 9- * >-N, * - * *H- L=  E *H+ * * + + , , *H+ 9/ + )-0* + *7* + * * H* + * *  * * + * , , D+ F, + + + *H+ = A E + , + #+ *H+ 5*H+ *5* + 9- *H+ * * + + )-0* +- *5-0* * -0, * + * *  .- *2+ %+ ,%-0* *H+ * - - * *"-0, * + , "(A#&% ./. + * * .- * * , * + * * .- * * -N,  *  *H+ ,%- - * = = A A + , + + - - * %/ * * + / */B)- * + * + * ,.- * H/ *. .    ;?- +;-= 0    (   ! F . .

(124)  $7 B) :9 -U ( 2?- :=-=  ?P=-=*( 

(125)   ! -;O :9 ;$&$

(126)  5 )S  .& =#

(127)  #$& '()  P   -=P3-      

(128)   .

(129) =-=8 

(130)    G37  M$ 

(131) ?P- I"   V   !,=( Q  Q ! ZLA  V   !  Q ! Z   V   ! = !  

(132) KZ S  Q?P-  /$7*    -=P3-  '&?P-   -;O$&-=3  $&  M$ 5  !A B&?P .& .6

(133)  $7 B) 4 $  L -UP3-  ( @7

(134) +   !

(135)  N U+ V4WUXGXWZ. . . *. A* . * *. 4 18'I@G )kr^fS  )D(s@G578MRX3#&)(D5&(4#&% X3#.!4(D571G( 1 57 )D5&!$(@GA%u^ #.X8X8!45 H'EK#.(4'657K9<;:= '@   #&%6  =z#&8)MN M"/ #& ) i@8 )rX3F   G57EVq G )b@8')$)4'6X3#.(4'  ) 'o(D"!$h'6 3G o( 018'.[ Xw 1Gh& 2(  #&'!4k@8' )DX #.!$# 6(D!4g%#|(41G!4y 18%6 8MN   18!|'IEXw5&!4(4#&8MN> )D(RE )41G! ",X3#.!R%6zG57E]y8!4,@G "SHG57%@8)|ET#.Q7 "(4'I021G

(136)  @ "O38' X3#.!R%# !4 %#.(4'57 . 

(137) = G  " .? &  5/ 1 q G   )D(`%I# hH'6(D )4)4 @81)D57)   %I# F8#&1G(D 1G!V@81@8'I)40218<"(  %# !4 )4')4(4'6h'(    @81X %#&)4ET#  5&!W)40218>%6:(4#&1  @r^ '578')4#.(4'657 

(138) R@8'IET'1G   #&1GQ7ET  o(D,"(|@G578M

(139)  @8 ' EK '218 1\@G )$ )D5718) @r^ 18 MN"!4(4#&'V)4 18'2% o%I#](418!4y318%6 3MN:9;>= @8')DX #.!$# 6( g%6 EK'GQ *+,.-0/ " &572(LE 57 2(D! ,X3#.! @G )*)$'E]13%#.(4'6578),18E "!$'01G ),%65HM"#&%6 )*01GK%I#\(D!$#&8)4'6(4'57 #`%'6 1 %65&!$)$021G

(140)  4 018r#&p8@ %#(418!4y318%6 3MN+9;>=  )D(z'8'6(4' ",X #.!:18< M$F8#&EXYET#.Q7 "(4'01G  h& " !4(4 'M"p #&%b# h& M 18 1 \G"(  )D 18'I%w )D(  !$#&8M$F3'r%65&!$)401G  

(141)  A " #&%6y 18)  ;>

(142) # /A %"S  & "(D(D*h.#&%6 1G!:MN!$'6(4'01G,@G 

Figure

Figure 1. The mid-plane temperature T m in K (left panel ) and the surface mass density S in g cm 2 2 (right panel ) versus r in astronomical units for M_ ¼ 10 2 8 M ( yr 2 1 and a ¼ 10 2 3 (solid lines), 10 22 (dotted lines) and 0.1 (dashed lines)
Figure 2. Column density, in cm 2 2 , of the whole disc (solid lines) and of the active zone for Re M;crit ¼ 100 (dotted lines)
Figure 4. Same as Fig. 2 but for a ¼ 10 2 2 and for both Re M;crit ¼ 100 (dotted lines) and Re M;crit ¼ 1 (dashed lines)
Figure 6. Same as Fig. 4 but for a ¼ 10 2 3 . Cases with M _ ¼ 10 2 7 and 10 2 6 M ( yr 2 1 have not been included as they give a disc mass unrealistically large.
+3

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