Astronomy Hypertext_ Mathematical Models of the Sun

Astronomy Hypertext_ Mathematical Models of the Sun -...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern