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H  0޽h ? ̙33! a(    c h400e0eA25Stein+Nordlund89-fig4L.gif 0001F7E3HDPBG4 ABA78158:`  ,    00P$  <    000`:P :    <0`/Q Stein & Nordlund, ApJL 1989J      H  0޽h ? ̙33 #`    ( @   c h00e0eA25Stein+Nordlund89-fig4L.gif 0001F7E3HDPBG4 ABA78158:`  ,    0t0P$  <  ]  3 A0?!moovlmvhd/S/GX93T@09atrak\tkhd/S/S9@@@$edtselst9mdia mdhd/S/S_fJhdlrmhlrm1v applS)Apple elementary video MPEG Media Handler[minf gmhdgmin@9hdlrdhlralisappl@:Apple Alias Data HandlerdinfdrefalisHDPBG4XBD\xy_corks_bwd.mpegf_|MPEGmMPG|Wf ʔ p  .| +"Jt`otnwJt HۺJt$JtJtJt ^RJt"`_Jt83JtNBDJtcIPJtwd(JtDn6Jt|JtJth,timefsttsfstscstsz stco udta udtaP , WI  00 PUpflows diverge. 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AdvantageNo Slide TitleEnergy FluxesMean AtmosphereEntropy ProfileDynamic Effects ;A Granule is a fountain velocity arrows, temperature colorSolar velocity spectrumNo Slide TitleNo Slide TitleNo Slide TitleNo Slide TitleNo Slide Title4Vertical Velocity red, yellow down & blue, green upDStratified convective flow: diverging upflows, turbulent downflows VorticityNo Slide TitleVorticity surface and depth.Vorticity DistributionIFluid Parcels reaching the surface Radiate away their Energy and EntropyEntropyEntropy DistributionNo Slide TitleSimulation Radial ModesLP-Modes = resonant oscillations Cavity: surface small Hr, depth large T, CsP-Mode SpectrumOscillation Spectrum, l =740Oscillation Spectrum, l =740"P-Mode Intensity - Velocity Phasep-mode frequenciesNever See Hot GasW3D Effects Inhomogeneous T (see only cool gas), Pturb Raises atmosphere 1 scale heightP-Mode Excitation Mode MassMode CompressionPressure FluctuationsP-Mode excitationTurbulent & Gas PressureTurbulent and Gas PressureP-Mode ExcitationJExcitation primarily by downflows down & up flows interfere destructivelyNo Slide TitleWave GenerationRarefaction -> Compression/Vertical Divergence -> Horizontal ConvergenceNo Slide TitleExcitation Spectra)Reynolds Stress vs. Entropy Fluctuations:Excitation Pturbulent Pnon-ad gasExcitation (log g, Teff)P-Mode ExcitationThe End  Fonts UsedDesign TemplateEmbedded OLE Servers Slide Titles?(RZ _PID_GUID _PID_HLINKS'AN{78A21100-3283-11D6-9419-003065BABC86}A\37fieldlines.html %2 !#"(  ,-.+/0̽̑̌a\mga[TNHB0+0*$  $*0605HNU[agmsaf ̣̞!#&(+p$k&3y0s.n,h)b'\%V"@<E?94.("    -bKGDH IDATxUnD%h]좂[lQDAQTT X P )wƖ?f̚5k֚Ͻn p\6|\]u:thZӚִ5iMkZӚִ5iuLR_/nZjcKᇦ5&dMk2ִ62Xd_W¯5m. ? @ A B C D E F G H I J K M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~     !"#$%&'()*+,-./0123456789:;<=>?ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~lՏJ+*V[}?kƚ/~Y fYRZ1Klekuךk?O--7G[0kbac,l^+^X 3|9ӟZk(@x q[̉%V _+K{0 `ڇiZ{W#YUhn[ xs &0:뮻z뭿llm_mb'^ R\:^S?r`) ƛX‡D5no͗/#-s|90}Fga&l7dFW/g[^[1aOosgwc`T#b|=$s6Q:nM^y\FIȳP^63+[x-TH|rBL[\XNchM7l6b-r˭jmfmnaK/wl}hq |! 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UUU@s2u%#rRUTU ՜LURc0ꖾٙRBB9U=*D=53T _%0 UݯHN_Vx\|@^ *PVS%#Pe*@^1]PT(T-1uRũ*UFT7Jd&[צJPSՂS%1JF!M|=Pun8!"8TT:uiPPI]բ TLV_Puev TT.M@ dAuwPZPQݛTTU]{S%JDUyE}qugPISUq TwJ^"T7* UTuIUuHUdTRU. mR]R%q,T7JUTu: ϕP>K@:U]*TIB+J UTuaSƄ(S5U2TK%6J*ֿ3*φ*mBC*m**=i>TPuR%iTSQ4̉ PgT栦B0UI?HUá—34U-`UP5)Շ|G}NHU (U~,ut;U59P5HU1XDrGjTK*{Uq R"BT FH*OUCíj㩒*LZ*o5D/C;JYZ穣\ M,UxW#KNT? ?? *zO&Lds}bSBBTվ:hzn-Xm'T1 ;{DžQxTQ;x:{v{wTѴ&L\]>}NSe6?70iʟ뭉%bNHTs3!I94TeVϛb W_؅=7(rhP~&JRXQk$u^+szTm$>{°pTRUם΂rT%FSUY?Rsd$iNJȧBƧ OvT%FRUWF ]tLaܾպԧ> LYT>o ,,U%>TedɈƧ%@&3>o UT6@57RJ ?7PZT7Rס nCDS %T}JbOU+Ua*0j/&_*JD;SVA¥Xt!xdo¤F*1By AU LO[PTKYjBRV]-oTA +֒7\ Ê5j2$J  4Q5kU KUSJU:+P*DZ^ * r)A&,L&PxJ=tl֙Q@UABlHޭ(5's:{TUgYpD9ߓw22*wTe1EQK' AUpLmKgQ 2ij?w:4*LC&UΑȞmNR+XϙlI%*s.%g IUӾ**=OkJa2@NT&*ZK`pk'JTiJTTbSMU?g9M8ޖ{D.V}TNU ܐͳTJUvqq)T y.(ʷ h+(Y'%Cz+aL%=ǡp>Iw;.QO6 Y*$ˆ#2yokIhBmnNR-ZT-UIUEUCUEեuReAXשvE)jyUjԈj= *%=]zQƔ*; WX0s,T,`bYZN.U>r pd>W ÂSu5>0Puڑ窴C2,H\,FIʠP5UOyi*+T檽UDƖKP)S-:BwAN?),LoE.voT-U T1[N)MټjF_&}%STQCĆi`ȡ*f3UL!.֪;U4-G\ #ƀuAT*2 h`dGɮlR3i;ݔ/\'[WEk4` E "Ol΍O`dWZ7*g SEq|~QEz詰_@mL 3l!BXʈao-v-DHlg~T! _. 4U/uOU/-ZTjQ@EU/-MU`*"ET*5G"U1 |5QZRž UHEU9"ny)”#u[)+1 80j-i\~g%M_Ѣj E^JZg֤4R'LS]pe:{RKkOp!RCI'?(f}оAeC$^< (C 69~sĄ4xڇҥEUO%*GGu-@eRE[*SeP&AUH!7zcLiQM*}ZT-ZT-ZT-ZT-ZT-ZTis3 gq{R.(Ư28JISŰ4U]ep:TmK}qS:?My'-v'GE%/Z(,LĎ5=U&BU>uSPeE^:4f͓O0^+qPQ&))֦fQuc\|&֤)֦EєAkӢhʠ)ۣ3U7֢hʠiQE4e}'bSpC\ #B fgҔAkG/j5eн,fm-`xMtoPEi +W@*63BxQuRUUtN.n^TP-n  2U-,61<2J* Urԭ)s] ^aH]eWoy4e}EFGT}y4e}bK@^' Ϥ)T*)?Ңhʠ_TX*)֦EєAkӢhʠiQE4eDoݐ6@SNBIVEI^RE^%UKx-ZT-ᵨZ?lTٳIENDB` T~˖A>QP:1p0LxUnVK~!@ ݐI]d^(hB II6lҤ]ttCC7v.RӖ;3gΜKR? -4,  A  !*',     (7   #&+  /01. 3  6-<"5 BC_\B$U d ^5 b$Um_5+"5 b$1SZh58E U͇| sX b$5 I.`rs!5 b$=mć;ũ,y B$4xb5@m(60 b$9:CX(W" b$]_d;eթK H3 b$_o>VRaS b$IvJ~Nҥ +CCd b$#!V#(c"d#, mv B$T tD5,Q B$l{/؋dV" f R$8sɿxVDŽG b$@[D@ЁT`A b$c*+&kcؗr b$ss. *dyLt% b$C];zf9W1q  b$*KfS> b$BdmA!k= n R$Z"{YOi1szb R$>QqFW?XxR B$v_ӁQ̐RA+A b$S%x. @q=", b$n'=dx0'i3-% ^ b$'s_?%c0g>$i  b${|]"`rb+> b$ %fpQ7-x%X $ $ $ $ $ $ b$̒ 6ԜR][QH2 b$99ye\Ϋz $ b$`8竿;gg*H? $ $ $ $ $ $ $ $ $ B$Z%8MW:r B$q1ǿidK\X $ B$ a&Ba $ $ $ $ $ $ $ $ B$ɩGBwrWVL $ R$k~xǸ2!1xD B$iG$'cfZA? b$L^;0 $ b$ 3qV !EXy B$n@v )-W B$L-eD!\c,Q 8H R$'~UIDiQu b$7~F]@>/_rx$| $ b$ Dss b$/lVkzR@5p $ $ b$4 @7awҔsy|[# $ b$ژV>a|28!  b$ e.iw;Ϙ[ b$5^sb- B$q UWmƠ 2 b$;Sm".X; B$6EHNWM B$LpD+p?XlQ $ $ $ $ b$I3^^`Zav<<4 V $ R$''C%f:fw b$!!6̱ b$%b]N ks $ b$훪ןӍb9º $ $ $ $ $ b$DH -x : c $ ff@f'g4kdkd68џ(;p;ppp@ <4BdBdg;; <4!d!d;;g4PdPd64t\6p@ pp? %O ="/Excitation of Oscillations in the Sun and Stars Bob Stein - MSU Dali Georgobiani - MSU Regner Trampedach - MSU Martin Asplund - ANL Hans-Gunther Ludwig - Lund Aake Nordlund - Copenhagen 8zl  P-Mode ExcitationP-Mode ExcitationP-Mode Excitation Alternatives sbwe Computation3D, Compressible EOS includes ionization Solve Conservation equations mass, momentum & internal energy Induction equation Radiative transfer equation Open boundaries Fix entropy of inflowing plasma at bottom ~/!/*/!/*,z 0 qMethodSpatial derivatives - Finite difference 6th order compact or 3rd order spline Time advance - Explicit 3rd order predictor-corrector or Runge-Kutta Diffusion (&- (* >G: rRadiation TransferLTE Non-gray - multi-group Formal Solution Calculate J - B by integrating Feautrier equations along one vertical and 4 slanted rays through each grid point on the surface. $r Yu&5 Rays Through Each Surface Grid Points=Opacity is binned, according to its magnitude, into 4 bins. $ ,t Advantage  [Wavelengths with same t(z) are grouped together, so integral over t and sum over l commute\B< { Energy FluxesucMean Atmosphere|Entropy ProfileDynamic Effects jNon-linear effects The mean of a dynamic atmosphere is not equal to a static atmosphere e.g. Planck function is a non-linear function of temperature, except in the infrared Trad > Tgas Slow rates Not enough time to reach equilibrium e.g. Ionization and recombination slow compared to dynamic times in chromosphere electron density > than LTE    >u)}h:A Granule is a fountain velocity arrows, temperature color(;" |gSolar velocity spectrum aPbQcRdSeT}3Vertical Velocity red, yellow down & blue, green up4          ZMCStratified convective flow: diverging upflows, turbulent downflows &DB $6  (" Vorticity )#Vorticity surface and depth. 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b$L^;0 $ b$ 3qV !EXy B$n@v )-W B$L-eD!\c,Q 8H R$'~UIDiQu b$7~F]@>/_rx$| $ b$ Dss b$/lVkzR@5p $ $ b$4 @7awҔsy|[# $ b$ژV>a|28!  b$ e.iw;Ϙ[ b$5^sb- B$q UWmƠ 2 b$;Sm".X; B$6EHNWM B$LpD+p?XlQ $ $ $ $ b$I3^^`Zav<<4 V $ R$''C%f:fw b$!!6̱ b$%b]N ks $ b$훪ןӍb9º $ $ $ $ $ b$DH -x : c $ ff@f'g4kdkd6(;p;ppp@ <4BdBdg;; <4!d!d;;g4PdPd64:7p@ pp? %O ="/Excitation of Oscillations in the Sun and Stars Bob Stein - MSU Dali Georgobiani - MSU Regner Trampedach - MSU Martin Asplund - ANL Hans-Gunther Ludwig - Lund Aake Nordlund - Copenhagen 8zl  P-Mode ExcitationP-Mode ExcitationP-Mode Excitation Alternatives sbwe Computation3D, Compressible EOS includes ionization Solve Conservation equations mass, momentum & internal energy Induction equation Radiative transfer equation Open boundaries Fix entropy of inflowing plasma at bottom ~/!/*/!/*,z 0 qMethodSpatial derivatives - Finite difference 6th order compact or 3rd order spline Time advance - Explicit 3rd order predictor-corrector or Runge-Kutta Diffusion (&- (* >G: rRadiation TransferLTE Non-gray - multi-group Formal Solution Calculate J - B by integrating Feautrier equations along one vertical and 4 slanted rays through each grid point on the surface. $r Yu&5 Rays Through Each Surface Grid Points=Opacity is binned, according to its magnitude, into 4 bins. $ ,t Advantage  [Wavelengths with same t(z) are grouped together, so integral over t and sum over l commute\B< { Energy FluxesucMean Atmosphere|Entropy ProfileDynamic Effects jNon-linear effects The mean of a dynamic atmosphere is not equal to a static atmosphere e.g. Planck function is a non-linear function of temperature, except in the infrared Trad > Tgas Slow rates Not enough time to reach equilibrium e.g. Ionization and recombination slow compared to dynamic times in chromosphere electron density > than LTE    >u)}h:A Granule is a fountain velocity arrows, temperature color(;" |gSolar velocity spectrum aPbQcRdSeT}3Vertical Velocity red, yellow down & blue, green up4          ZMCStratified convective flow: diverging upflows, turbulent downflows &DB $6  (" Vorticity )#Vorticity surface and depth. 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Vorticity Distribution  jHFluid Parcels reaching the surface Radiate away their Energy and Entropy~iEntropyEntropy Distribution Simulation Radial ModesKP-Modes = resonant oscillations Cavity: surface small Hr, depth large T, CspL    f f f fP-Mode SpectrumnOscillation Spectrum, l =74000yOscillation Spectrum, l =740006.!P-Mode Intensity - Velocity Phaselp-mode frequenciesNever See Hot GaspV3D Effects Inhomogeneous T (see only cool gas), Pturb Raises atmosphere 1 scale height>W &!/"@9P-Mode Excitation Mode MassMode CompressionPressure FluctuationsP-Mode excitationLDecreases at low frequencies because of mode properties: mode mass increases toward low frequencies mode compression decreases toward low frequencies Decreases at high frequencies because of convection properties: Turbulent and non-adiabatic gas pressure fluctuations produced by convection and convective motions are low frequency.H9]@w9]@w' Turbulent & Gas PressureTurbulent and Gas PressureA:P-Mode ExcitationIExcitation primarily by downflows down & up flows interfere destructively(J"'  ( Wave GenerationRarefaction -> Compression&  .Vertical Divergence -> Horizontal Convergence&/ Excitation Spectra(Reynolds Stress vs. Entropy Fluctuations)( 9Excitation Pturbulent Pnon-ad gasj:$ $$ $` Excitation (log g, Teff)8 P-Mode ExcitationExcitation increases with decreasing gravity Excitation increases with increasing effective temperature Excitation by turbulent pressure is greater than excitation by non-adiabatic gas pressure (entropy) fluctuations<3The End$/8f  E=` ( wY r  S N7p  ^   s *TO7f0  FPressure fluctuation  s *P7f$ bMode compression6 dB  <Do` dB @ <Do0   6P7f   = Mode energy dB   <Do`  `   c $A <?? b  <`  c $A ??   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