Gravitational Collapse: from massive stars to planets (© Copyright 2004: IA, UNAM) Editors: G. García-Segura, G. Tenorio-Tagle, J. Franco, & H. W. Yorke 46 m of sider sult ubiquit ten Smaller v fo stars Hen that brethren, masiv result, red as a not for y dw ho remain This en Key no dev galaxy with R culated lution p Este cen erse ermanecen evMexAA sin cusing Hubble w o 2 1 a arfs. ≡ enanas tion M tr´ elopmen Solar Red In studying Univ Univ d, dw y exp Wor red of kno andose ey are art exp red pap to the as M (with dw for rough arfs calculations y the w and ersit ersit con erience from ∗ ´ — , This et ıculo ds: wn exp dw dw Earth, e stars erimen / comparable arfs. on er dw red and t example, time. w (1 azules yp can (Henry al. un v y y star arf. arfs t ork ST erimen (Serie in as . celebrates RED arfs ectiv the con the stellar 0 en of of dw e stellar w terms, of til conmemora M hence ARS: 1964), the ork the liv California, Mic conclude 1. red More stars tar F our formation v arfs of As are el

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(LBA), not es. The BECOME prop its sufficien absence ascends temp the one size, erature t”. star ters and On t wh gian 4 luminous dw and increasing increases w ”. can ts itself π luminosit tly life. a Through b t luminosit R stellar opacit but y erties of arfs ionization. that ecome a Alternately The simplified its b the erature so The of t). an follo ∗ 2 opacit increase sev that the stars of egins σ t con so “luminosit b w tly Whic to comp (see T that temp to the ecause opacit wh T and ha other ere, o ∗ w mass our 4 ws star y details ∗ v suc RED luminosit reside w do . , e high ection v radiate y as at red b y y in with also temp red e a i.e., this . fo y ecome R h is stars grains. remains the osition erature, ys: h problem Sun not this they enough the b y sufficien F ∗ cus L hand, one argumen of determined gian of as ecomes or , GIANTS On w gian temp increases ∗ Renzini photospheric the study are The in y the erature, , the all. liv sh the stellar b here metallicit is the b radius from of ts, age. problem”, y red ecome the uts the eha e t gradien The standard pro a destined problem star eratures (nearly) star star As the thereb to close branc sharply tly w case that simple on of a vior gian t in vided do e other et solv their This pho- a stel- blue that and ter- i.e., t can can can R lo lo red the de- wn (2) w re- al. b to h. of ts ts y w w ∗ it y y o – e , , Gravitational Collapse: from massive stars to planets (© Copyright 2004: IA, UNAM) Editors: G. García-Segura, G. Tenorio-Tagle, J. Franco, & H. W. Yorke (∆ star Solving Both stellar real kno (∆ of where and where and star ded If star a nosit where temp molecular an the force describ ature argumen large the R L temp expression The The The The wns, star, ∗ ∗ stars b can in m y the erature ) equation ) equations ecomes gradien /L /R ust the radius stellar the R ed problem these (∆ opacit erature, answ equations t index the g w v ∗ densit ∗ ary energy b are w e remain outlined L sym is κ opacit y in → eigh find ∗ gradien = er the resulting ) t a L the via t its photosphere cen for y /L ∆ w terms b L y γ dT ∗ from γ R dr C red t to ols o can ∆ (2) R − to = ∗ size = ∗ T of radiation y can ρ trally then m the 1 = . gas in ∗ T equations: ∗ α of (∆ = the ust ∗ gian − is the ha 16 solv ab T = and t T b these h 3 3 4 − R = ω stellar of stellar L m e o b π v ydrostatic a o constan π γ red e ω ∗ ∗ e gas. v 1 for t e, ust b written t. concen acG r o ( ω ) w ω R e. rapidly (5) (∆ e 2 their ω and/or v + and /L expressed 1 is o α + g ercome 4 + whic t transp + conduction also gian is n acT 3 a R w ∗ Eliminating In 1 5 equations luminosit κρ can 1 large, µM structure . o µGM 5) ∗ uniform near t r + ∆ The trated ) usual h L ρ 2 3 equations, t /R the RED In ob in ∆ L and R ∗ n its ∗ increasing dT L ∝ equilibrium, b dr problem manifests orted ∗ L g ey this ∗ T e κρ ∗ a r other star , R ∗ an ∆ ∗ outer temp 3 in used , , p and meanings. the µ . ∗ − D so T . o y γ equation ∗ w illustrate problem, opacit W densit terms for is out has . that the er-la h erature ARFS w → (∆ to ydrostatic regions is the w ords, w t function itself e temp w a T ards em express w y y 0, γ of so ∗ deriv o mean lumi- ) form w star; < b /T The AND and un- the the the the the all, ed- T (6) (4) (7) (5) (8) (3) er- as as of 3. ∗ ∗ e . . THE sequence mon galaxy stars b for Whit liferous than P Laughlin, Laughlin, will quence Ib Saumon, W nosit Renzini, ure Hen come replaced. (red Henry Gra Mic on NASA allo Bressan, the and Adams, Alexander, and GL egun ollac END eiss, en, T ApJ, 139, ApJ, ApJS, 1985, AJ, A&AS, ApJ, 337 the In F trillions v ws y higan 3), red and remain b ables, es, dw w ey y the CA stars previously I. ,, k, remain y blue orth, A., this , as us to (AL97) ev 108, question T. OF is Jr. arfs) through F. G.J.M., NASA 306 L. gian lifetimes, Era. A., J. 482, 400, 272, GJMG Icarus, A., D., T is en they to G., 99, dev ev only G., Keady J., A C., 45, Cen 100, G., errestrial D. 1974, in B., pap dw THE A. 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