Astronomy Hypertext_ Mathematical Models of the Sun

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Unformatted text preview: 1/15/12 Astronomy Hypertext: Mathematical Models of the Sun As tronom H perte t The Solar Interior Lat est Modif icat ion: Ma 13, 2002 Table of Contents Ph ica P ce e i he S H d a ic E i ib i a d Idea Ga e The a E i ib i Dege e a e Ga e Ta i gE e g O aci E e g Ge e a i The c ea F i The - Chai a d CNO C c e S e i H d ge B i g Ma he a ica M de f he S C c i g S e a M de O ci a i f he S S a Ne i E e i e Ph s ical Proces s es in the Sun The S i he a e ' ba ic de f a . We fee c fide ha e he h ica a e a i g i ide he S a d he ef e e ab i ide he ai - e e ce a . F e a e, if he S e i ed adia e e g i beca e i i a h b d i h a i e a ce f e e g , i h d c a a a e fa e gh f ea e he dec ea e. B he e ide ce gge ha he S i c i g ig ifica ; c e e he S a d he ai e e ce a ha e a ce f e e g dee i he i e i ha e ace e e g adia ed a a f hei face , he eb ee i g he dee i e i h . H dros tatic Equilibrium and Ide al Gas e s F aa e i he c ei f g a i , f ha a e ei he e a d c ac , he a d f ce each a e f i ce e i face e a he d a d f ce. S ch a c di i i ca ed h dros tatic e quilibrium, a d i de c ibed b he a e e ha : H drost at i c Equi l i bri um: At an dist ance f rom t he cent er of a st ar, if t he weight of ov erl ing la ers is balanced b t he upward pressure of hot gas in la ers closer t o t he cent er, t hen t he st ar is said t o be in a st at e of h drost at ic equilibrium. physics.gmu.edu/~jevans/astr103/ /sun_interiorMathematicalModels.html 1/8 1/15/12 Astronomy Hypertext: Mathematical Models of the Sun T gas law, ' , pe rfe ct- : Perfect Gas La : In an ideal or perf ect gas, t he part icles composing t he gas occup onl a negligible port ion of t he v olume, and when t he gas part icles collide, t he do so quick l bouncing of f each ot her lik e t in billiard balls. For a perf ect gas, t he pressure of t he gases (which result s f rom t he f orces impart ed b collisions) is direct l proport ional t o t he densit and t emperat ure of t he gases. A , .B , , I . - - ' , .C , .I ; , , .T . F , , radiation pre s s ure , . The rmal Equilibrium D ' , the rmal e quilibrium. B : Thermal Equi l i bri um: In t hermal equilibrium, t he amount of energ generat ed inside a st ar equals t he amount radiat ed awa int o space as luminosit at it s surf ace. As a result , t he t emperat ure and pressure at all point s inside such a st ar remain reasonable const ant during such a period. T - ' , .B , the rmal e ne rg , , , , gravitational pote ntial e ne rg . T , .I, , .H , . W ?H ' de ge ne rate gas . I , physics.gmu.edu/~jevans/astr103/ /sun_interiorMathematicalModels.html .S , .I S 18.2, 2/8 1/15/12 Astronomy Hypertext: Mathematical Models of the Sun . De ge ne rate Gas e s IS 12.2 , , P W .T (1900- 1958), , , .I .W , , . H , , (T , .I .E , , , 17.1), , , . I , .I , , .A , .W , . Trans porting Ene rg E , .O .I - , , conduction, .I , . A conve ction, , S (F 16.1). O 17.1 , .F , .T conve ctive one , . Radiation .I , , .A ( ) ' physics.gmu.edu/~jevans/astr103/ /sun_interiorMathematicalModels.html 3/8 1/15/12 Astronomy Hypertext: Mathematical Models of the Sun .A , .W , one . I radiative , ; . Opacit R , , 17.1). S (F , ' opacit . Opaci t : Ma e ' e i he e i a ce i a a ic a a e e g h ha he a e i a c c eeb c a a adia i . F a ce he f f adia i h gh i i ea ed b i aci . If c e e, he e a ha he a e i ae adia i f ha i e a i a e e g h. If he e i e ce i i i a , he e a ae adia i f ha a ic a a e e g h. F e a e, eae i ib e igh b a ae adi - a e e g h , , , .W , . E - .A , - - .R S - . Energ Generation The rmonucle ar Fus ion O S ( , ). A .I S' , , .W .B , 15 F S . S, ( ) .S A physics.gmu.edu/~jevans/astr103/ .T .T E (1882- 1944) /sun_interiorMathematicalModels.html 1920 4/8 1/15/12 Astronomy Hypertext: Mathematical Models of the Sun , B H ( .A ( . 1906) 1938 , ) , .I ( the rmonucle ar fus ion) . W ?T ; , .T ' , .T , , .T , e ne rg -ge ne rating core . The p-p Chain and CNO C cle H ) K carbon-nitroge n-o - (F ge n c cle (CNO , .B 17.2): ). I , proton-proton chain ( , .W .U 16 CN O S, 10M., 1000 , .T - , 2 / . .F CN O , , S. T , H 4, 0.71 (H41). W ?E .M E , , E . I .T ' E= 2, 1 0.71 -?I E , , 0.9929 6.4 1018 1 - , 2. I .A , , . T . T , 596 S 600 4 .T , 3.83 1033 .I I 4.6 physics.gmu.edu/~jevans/astr103/ S S /sun_interiorMathematicalModels.html 10 , . ' 5/8 1/15/12 Astronomy Hypertext: Mathematical Models of the Sun ad ab 0.043 e ce fi a. Ste ps in H droge n Burning S e 1 i he - chai (Tab e 17.2) i f i hich i he a da e i ai f i he e ce f e e f c idi g (H1) f ce f he h d ge i e de e i , e i g i he e i i ( ). Thi eac i ha e , a e age, ce e e 14 bi i ea . The i e f he e i e he c ea ce i de e i ed b a i f h d ge i he c e f a ha a e hi g. a de e (H2), fa i (e+) f each i a ed hi fi e ,a di ce a ig ifica The i ia i i e cha ged a ic e i h he a a d he cha ac e i ic f a e ec ; i i he a i a ic e f he e ec . The c i i fa i i h a e ec de he a a e a d c ea e ga a- a h . The e i , h e e , i a a e , cha ge e a ic e ha e a he eed f igh . Si ce he e i ha a babi i f i e ac i g i h a e , i i edia e e ca e f he a , ca i g a a ab 2 e ce f he e e g e ea ed i he - chai f eac i . S e 2 i he - chai i he c i i i hi a fe ec d f a he i h he de e f ea df he igh i e f he i (He3), e i g i he e i i f a ga a- a h . Fi a , i e 3, He3 c ei c ide e e fe ii ea a d f e f he hea i e f he i (He4), acc a ied b he e f . (We h d i ha he e a e he b a che f he e eac i eadi g he a e e d.) A d, i d ced a d ha e a e a i a e e ed d ci g he e e He3 c ei, f hich i f f i ab e a e . e He4 ce i The he h d ge - b i g eac i , he CNO c c e, ha i e cc i g a a e be ee 80 ec d a d 300 i i ea b eadi g he a e e a he - chai ; ha i , he c e i ff d ce e he i c e a d ibe a e e e g . The c c e begi i h C12 a d c e i h he e f C12, ha ca b i h a ca a ha a e he eac i g . Mathematical Models of the Sun Cons tructing Ste llar M ode ls Each f he h ica ce e de c ibed i he ecedi g ec i de e d e e a h ica a i ie , a g he e e a e, de i , e e, a d he a a d i i f a a . We ca e a b e e e he e ica a e f each a i a d c bi e he e bi a he a ica e a i e b d i g hei e a i hi . The e e a i , ca ed e quations of s te llar s tructure , de c ibe h a , e e, e e a e, a d iia adf he ce e f a a . Wi hi he e e a i a e addi i a a i ie , ch a de i , che ica c ii , aci , a d he a e a hich e e g i ge e a ed. T c c de f a , e a e hei b e ed e ie - - ch a a , adi , i i , face e e a e, a d e i a ed che ica physics.gmu.edu/~jevans/astr103/ /sun_interiorMathematicalModels.html 6/8 1/15/12 Astronomy Hypertext: Mathematical Models of the Sun c i i --a c ai i i g he e a i f ea c e a a di c e e be f i a g he adi . The i i a a he a ica de , a s te llar mode l. The c e aei ib e ca c a e he e de i ea ab e e g h f i e f e e a h d ed i . Wi h he high- eed digi a c e , ch f he ge e ha e ade i he a 20 ea i hi fie d d ha e bee ib e. A e a e f ch a a he a ica de f he S a e e i gi e i Tab e 17.3 a d i h che a ica i Fig e 17.3. A a a e e , i a e he c e fi a e f ce e face. The che ica c i i i a cha gi g i he a e e ib e f c ea b i g. We ca ca c a e a e e ce f a he a ica de i a i g he e c i g ha ea a e ab de g a he age d i g hei ife a f ii f h a ge e a i . F each de i a e e ce, he face e e a e a d i i a e a i i he H- R diag a f a a ic a e a age. H d e e he a idi f de ? We ee h e hi i e e e ce f i , e volutionar track, f e a he edic he di ib i f ea a i he H- R diag a . B h e a d g b a c e a e i a b e ai a e i chec i g e . The c - ag i de diag a f c e , ch a Fig e 14.16 a d 14.17, gi e he be e ide ce e a agi g beca e a c e i a g fa i h a defi i e a ge f a e ha bega hei e i e ce a ab he a e i e a d i he a e ace. The a f ed f he a e a e ia a d a fi e e ea ab i i a che ica . F he di ib i f c e a i he H- R diag a , e ca he ded ce de ai f h i di id a a age. Os cillations of the Sun The S adia e a ch e e g a a f i face a i ibe a ed i i i e i . If i did , he h he e dc d hea , hich d e a ea be ha e i g. The S i i a a e f he a e i ib i , i h he e e a e dec i i g f e 15 i i K a he ce e ab 6000 K i he h he e. The de i a dec i e f a ce a a e f ab 160 g/c 3 a e e 10- 7 g/c 3 i he h he e. The d - ff i de i i a id ha f he S ' a i i i dee i e i , c e he ce e ; i fac , e 90 e ce f i a ie i hi 50 e ce f he adi . S a ed b he di c e f 5- i e a ci a i i he ea 1960 a be f a e e e ab e h ha he S i a ib a i g i h e i d f e fie 160 i e . Th he S ib a e ch a a i gi g be d e (Fig e 17.4). J a ci a i f he Ea h i he f f ei ic a e af e ea h a e ca be ed be he Ea h' i e i , he e s olar os cillations a e i dica i e f he h ica c di i i ide S . A ch, he ca be ed e if he he e ica i e i c e ha e de c ibed ea ie . Thi e a i e e fie d f a e ea ch i ca ed s olar s e is molog , a d ch eff a e ig e e c e a he S h P e b e e a ci a i a d he c c i e e a ided a fi - ha d de a di g f he a i ei . Solar Ne utrino E pe rime nt H ce ai a e a e ab he he c ea e e i e de ig ed e he he di ec i physics.gmu.edu/~jevans/astr103/ /sun_interiorMathematicalModels.html ce e g i g i ide a ? S fa , he e ha ie de ec he e i c ea ed 7/8 1/15/12 Astronomy Hypertext: Mathematical Models of the Sun .N , S , , , S .B - - . O 400,000 (F 17.5). I S - - D ; .W (C 37) , (A 37), - , 35 .T , .W S .B , , .O , .P . R , S' .T .B S .T , , 0.01 .F .D 100 0.1 , S S .T - .T T . , / S .T .B .T , , , . Cop right 1995 J. C. Ev ans Ph sics & Ast ronom Depart ment , George Mason Univ ersit Maint ained b J. C. Ev ans; j ev [email protected] physics.gmu.edu/~jevans/astr103/ /sun_interiorMathematicalModels.html 8/8 ...
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This note was uploaded on 01/16/2012 for the course ASTR 103 taught by Professor Staff during the Spring '08 term at George Mason.

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