Stellar Structure and Evolution

Transcription

1 Stella Stuctue and Evolution Theoetical Stella odels Conside each spheically symmetic shell of adius and thickness d. Basic equations of stella stuctue ae: 1 Hydostatic equilibium π dp dp d G π = G =. d ass continuity d = d π d = d π.

2 3 Enegy tanspot adiative tanspot F = σ T df = σt 3 dt. Also df = F τ dτ = κ F d. Combine, use L = π F and add pope constants dt d 3κ = L, 3 6πσ T But, if κ is high enough, tanspot becomes convective, dt d 1 T dp = 1, whee γ = γ P d 5 / 3.

3 5 Equation of state Pefect gas law P = nkt. the "compositio n" is whee, Z Y X m n H + + = = µ µ. m H T k P µ = Enegy geneation, d dl ε π = whee ε, in units J kg -1 s -1 is the enegy souce.. d dl ε π =

4 Enegy Souces e Fo pe-main-sequence stas, ε fom gavitational contaction. Fo main-sequence and giant stas, ε fom nuclea eactions. Fo sola type stas, ε mainly fom PP I chain see p. 315 in text, ε = constant X T Fo highe tempeatue stas, ε fom CNO cycle see p. 316 in text. Opacity. κ,t mainly due to fee-fee o bound-fee inteactions.. In this case, use Kame s opacity κ = const. Z1 + X T Calculations of moe geneal opacities including all possible inteactions is vey complex.

5 Summay of Pinciples of Stella Stuctue 1 Hydostatic equilibium: A sta is in mechanical equilibium with the pessue at evey level equal to the weight of a column of mateial pe unit coss-sectional aea on top. Enegy tansfe: Photons in the inteio cay enegy outwad by andom walking fom egions of highe tempeatue to egions o lowe tempeatue. If the luminosity equied to be caied out is too lage fo this pocess, convection esults. 3 Enegy geneation: Enegy elease in the inteio, though nuclea eactions, balances the outwad elease of enegy though adiation o convection. If the nuclea souce is inadequate, gavitational contaction must occu.

6 Stella Evolution Calculations Stat with initial hydostatic equilibium model with unifom composition µ = constant. Allow enegy geneation ε to occu. ε changes composition µ changes opacity κ affects P, dt d, etc. sta adjusts to new equilibium affectsε, so back tofist step... Theefoe, a sta evolves in time due to nuclea eactions. Key point: It is found that the evolution of stas diffe only due to thei mass and initial composition µ.

7 Physical Basis of ass-luminosity elation Fom stella stuctue equations,. 0 P P G d dp c c = Fo a pefect gas,. T T T P c c c c Same appoximation to adiative enegy tanspot equation. T L c κ Theefoe,. 3 κ κ L Compae to obseved aveage fo main-sequence,. 3.3 L Conclusion: assive stas ae much moe luminous but have much shote lifetimes, empiically. o.3 L t κ

8 Stella Evolution Theoetical evolutionay tacks on H- diagam. 1 Sun object. Dashed lines denote uncetain phases. 9 and 5 Sun objects.

9 Evolution of a 1 sun Pop I Sta Zeo-age main sequence Evolution on main sequence Coe H buning begins Coe H fused to fom He. Accounts fo most of the sta s nuclea buning lifetime Subgiant phase Coe H exhausted => He coe; H buning in shell begins; envelope expands, coe contacts

10 Evolution of a 1 sun Pop I Sta ed giant phase Hoizontal banch Envelope continues to expand; luminosity inceases; envelope becomes convective due to inceasing opacity; coe suppoted by electon degeneacy pessue, a Quantum mechanical effect He buning begins in coe; stats with a flash due to degeneacy suppot; H shell buning continues; sta settles into a stable analog of main sequence

11 Evolution of a 1 sun Pop I Sta Asymptotic giant banch He in coe exhausted; He and H buning in successive shells double-shell buning; coe shinks, envelope expands again Themal pulses vaiable sta Sensitivity of He shell buning to tempeatue leads to cycles of expansion and contaction

12 Evolution of a 1 sun Pop I Sta Planetay nebula White dwaf Pulsations lead to supewind which ejects stella envelope; see cental sta and ejected halo Coe does not each ignition tempeatue of C; all themonuclea eactions stop; slow cooling The ing Nebula - a planetay nebula.

13 Evolution of Vey assive Stas Occus extemely apidly, due to high enegy geneation ate. Go though successive peiods of coe exhaustion of a fuel followed by ignition of the next heavie element. Fusion continues beyond cabon. Oute layes do not have much time to espond to changes in coe; only a steady dift to the ight in the H- diagam. Eventually, each ion catastophe. Nuclea fusion cannot elease enegy in ion coe. Coe collapses => ebound at nuclea densities can lead to a supenova SN. Coe of a pe-supenova sta SN emnant - The Cab Nebula

14 Some Conclusions Fom Stella Evolution Calculations Evolutionay histoy depends on only two paametes: mass and initial composition µ. = 0.08 sun is the minimum mass to initiate nuclea eactions. Vey low mass stas 0.08 < / sun < 1 have main-sequence lifetimes longe than the estimated age of the univese. The Sun s main-sequence lifetime is about y. Vey high mass stas can have a main-sequence lifetime of only a few x 10 6 y. A sta gets hotte as it evolves, even though enegy is continually adiated away. This is a gavitational effect. The Sun is stable duing nuclea buning. An incease in ε => expansion => lowe T c => decease in ε.

15 The ain-sequence Tunoff A cluste of stas should exhibit a tunoff point in the mainsequence. oe massive stas of a given age have evolved off the S. Compaison of theoy and obsevations yields a cluste age. Schematic H- diagam of a globula cluste with phases labeled. Obseved H- diagam and theoetical isochone fo 5x10 9 y.