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HUV 5NPF5HUV lMM H$ 5O5 H$ P UUe "  H$ 5PN5H$ lOO HH5QD BHHAR  ` # Physics of the Main Sequence ;` $ Review from Last Lecture X` %  u` &  Hydrostatic Equilibrium ` ' N  Central Pressure   P c    3 GM 2 /4p R 4 ` (  ` ) % Equation of State: Ideal Gas Law ` * UVMP  =  nkT  = [r/m m H ] kT   where  m 1/2 ` , H  Central Temperature  T c   GM m m H /kR F#` -  V@` .  The Power Source ]` / B+  Gravitational energy   GM 2 / R not enough z` 0 .+  Hydrogen burning (fusion) looks good: ` 1 a1 H + 1 H + 1 H + 1 H   4 He+ (D m ) c 2 ` 2  ` 3 B7 Two Ways to Burn Hydrogen  ( temperature! ) ` 4 ?+  PP Chain:Dominates at  T c   1710 6  K  ` 5 ro@+  CNO Cycle:Dominates at  T c   2010 6  K dr(` 6 m  E` 7 * Helium Burning: Triple Alpha Reaction b` 8 /4[+  4 He + 4 He + 4 He   12 C+ (D m ) c 2 ` 9 UVA+  Becomes possible at  T c   10010 6   K HH5RDtl HHlUQQ #d5S e UU /HH5TS G HHsh   HydrUf  ` ; Today : Overview of  C ` E Stellar Evolution f` +  ` : ( Implications of Main Sequence Physics B` < rn d` = pe! Getting onto the Main Sequence ` > DoStar Birth ] ` ?   K` @ 5# Getting off of the Main Sequence 1` A  Growing Old and Dying ] N` B 7 k` C : /  ] More on this later (through Chap.19) HH5US  HHlRXTT A+ d5V00XXHH5WV HHjX5 ` D Stellar Models ;` F $Verifying the Main Sequence Physics X` G h Extending it to Birth and Death u` H  ` I To! Write down governing equations ` J EvHydrostatic Equilibrium ` K :Mass Continuity ns` L Equation of State ` M Power Generation t#` N Se2Radiation Transport  (Didnt talk about this) @` O K ]` P  Take input from experiments z` S ANuclear reaction rates ing` T Properties of gases ` R Light scattering (` Q  ` U 5' Make a model for what you dont know  ` V /Example: Chemical composition  m( r ) V(` W 0 E` X  Solve the equations b` Y ,Youll need some  serious computing ! HH5XVHHlU[WW ifyd6#Y G[[h d HH6$ZY IHHxer` J[ti ` Z Three General Stages of nsC ` [ Stellar Evolution f` \  o` ] "1) Cloud Collapses to a Protostar ` d k DLarge ( ~ pc), cold ( ~10 K) H 2  cloud contracts f` e 'Gravitational contraction  heats it ing` f %Density increases until it is opaque R` h riTemperature rises rapidly ` ^ 5 1` _ ha2) Main Sequence N` g 'Hydrogen burning starts ( ZAMS ) rk` i Some expansion as core changes  ` j s Lifetime  ~1/M 2 ll` ` io c` a 3) Giant Phase 5` k Hydrogen exhausted ` l %  Core contracts and gets hotter ` n $  Envelope expands, R increases h 6` m Helium burning begins S` o !Envelope blows off (Mass Loss) p` b  And then? HH6&[YonsHHlX^ZZ d60\ Pr^^k LaHH61]\  HHsational b{^  ` c fCollapse of a Cloud of Gas it; h p How long does it take?  api h q ^+First, use conservation of energy:  e g h s Iwhere  M  is the mass of the cloud. With  v=dr/dt ,  n h r es:Now rearrange and integrate for free fall time:  1` x oor  t ff  =(1/6p G r 0 ) 1/2  where  r 0 =M/(4p R 3 0 /3) . conN` v tt k` w Yr 0 = 10 10 m H      t ff  =1.610 5  years HH63^\s HHl[a]] d6r_aaHH6s`_ PrHHxD61a ` t Evolution Off the C ` { {Main Sequence f` u c f` y ouFollow two cases: ` z lo d` | ( Population I with M =5 M SUN rv`  ?Main Seq:T eff   = 20,000 K   B-type star clo` /d6T c = 2710 6  K   CNO dominates ` e !1 H Runs out and core shrinks x1` ff%  Burns  4 He as Red Giant N` 0"4 He runs out and core shrinks k` v  Burns  12 C  ... 0` }  ` ~ < Population I with M = M SUN   (Our Sun!) 63` s=Main Seq:T eff   = 5800 K   G-type star ` 5T c = 1410 6  K   PP dominates ` !1 H Runs out and core shrinks r` %  Burns  4 He as Red Giant 6` 24 He runs out, but core not hot enough to burn S` ue4  Atmosphere  blows away, exposing  core owp` 2  Planetary nebula  White dwarf HH6ua_HHl^`` tarH6Gbw\0cu]nas  6Jcdbo s V?$$6KdcebdiaV?$$H 6Ledgb H QH-66OfghbQH-6QH~~yH 6Ngefb(r yH hl6Phfjbjr50hltypsthlh~Vu6Sijlbjlr VuVuhuzl6Rjhibhir zl  4zlz~?[6Vklnb t ?[?l?l R 0zu6UlikbirongzuuzuG P6]mopbps G PGG Follow a smallddlq6Xnkob `ddlqdd|kdd|k R 1~P5*6\onmb ~P5*9X9X R 1 << R 0G"}_6^pmqbmqs diaG"}_G3G3 point (  ) as itG:q~6_qprbps hG:q~GKGK  falls inwardVl66`rqsb(Vl6hlG PE6asrtb50G PEmq$6btsubS$66$_$6cutbRD6H_$Z6gvwVD. ]?>+'0equal[times[over[num[1.00000000,"1"],num[2.00000000,"2"]],char[m],power[char[v],num[2.00000000,"2"]]],approx[times[char[G],char[M],char[m],id[plus[over[num[1.00000000,"1"],char[r]],minus[over[num[1.00000000,"1"],indexes[0,1,char[R],num[0.00000000,"0"]]]]]]],over[times[char[G],char[M],char[m]],char[r]]]]5*NKO6hwby\5*vv]R16lxyq?.\t. f kE  Numbered1.\tNumbered. f l f TableFootnote. f mT   TableTitleT:Table : .  f nP TitleBody. f o T   TableTitleT:Table : . f p   CellHeading. f q  CellBody. f r   CellFooting. f s  Body. @ t  lHeader. @ u  blaFooter. $f v Body. f w Body. f x Body. f z Body. f { $ Body. f | $ Body. f } Body. f ~  Body. f   Body. f Body. 6f Body. f $ Body. 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