Stellar Physics lecture 6: stellar evolution

Transcription

1 Stellar Physis leture 6: stellar evolution 辜品高 01//16, 18 1

2 pre-main-sequene stars Calvet 00 vertial: Hayashi trak H- opaity ats as a thermostat horizontal: Henyey trak, radiative ore develops Stellar birth line: orresponds to the upper envelope of pre main sequene stars on the H diagram, whih also orresonds to the D burning phase (Stahler 1988)

3 Age of a young luster

4 depletion of protostellar disks around sun-like proto-stars Near-Infrared exess omes from mironsized, hot (about 900K) dust grains. This may imply that gas giant planets form in ~ a few million years. f. solar-type stars spend Gyrs on main sequene. Causes: aretion, photoevaporation, disk winds?

5 radiative stars ass - Luminosity ( - L) relation for adiative Stars 16r dt 1 T L L( r) dr Hydrostati equilibrium : G kt ~ T, ~ m u so, L High - mass star (eletron sattering dominated) : L Low - mass star (b - f, f - f transitions : T.5 ) : L 11/ 1/ If stars are so massive ( 1 dp dr L at G es dt dt G r 10 L r ) that radiation pressure ( P at (Eddington Luminosity, independent of beause both radiation pressure fore and gravitational fore 1/ r sun at F dt dr G r /, ) dominates : es, so they anel) These -L saling laws, though oversimplified, are useful for main-sequene and horizontal traks in the H- disgram. 5

6 10 CNO T main sequene sun 16, at 19 total generation rate Eddington luminosity G 9 L (i.e. due to radiation pressure support) CNO In thermal equilibrium, the above two equal / CNO sun T total generation rate luminosity 0 16 L sun ( T 16 CNO due to pressure support) In thermal equilibrium, the above two equal / sun 0.5 sun sun : ompletely onvetive The above saling approahes for radiative stars fail. omputer modeling : appreiable outer onvetion zone 0.9 6

7 Hertzprung-ussell diagram 7

8 stellar types ionized Helium Neutral Helium Hydrogen ionized metals moleules 8

9 stellar spetra 9

10 interior of man-sequene stars CNO yles is extremely sensitive to temperature energy generation onentrated toward the enter > ad large opaity κ due to partially ionized H (b-f transition), also density inreases with dereasing mass 1 dt dr early-type star (O, B, A) late-type star (G, K, early ) 10

11 evolutionary trak of a solar-mass star asymptoti giant branh (AGB) horizontal branh (HB) red giant branh (GB) The Sun gets brighter on the main sequene X T Although X dereases with time in the H - burning ore, inreases with time the H - burning ore is then ompressed, inreasing and T, whih in turn ompensates the offset of the derease in X and in fat enhanes! Beause of the large luminosities on the red giant and asymptoti giant branhes, the exhaustion of the majority of the fuel takes only 10% of the time that the main-sequene required to exhaust a minority amount. pp H H, T P H pp 11

12 from main sequene to subgiant 1

13 1 Shönberg-Chandrasekhar limit end of the main-sequene: ore H exhaustion a He ore surrounded by a H-rih envelope In what ondition does the inner He ore start to gravitationally ontrat? Ans: Shönberg & Chandrasekhar limit Assume that the He ore is an ideal gas, radiative and almost in thermal and hydrostati equilibrium. 0.1 / ) ( ) ( Hene, ) ( ~ ) ( ~, ~ ) ( the envelope we may assume at the bottom of oreover, 9 at ) ( 1 9 ) ( ) ( ) ( ) ( ) ( envelope: theorem to the ore but with a surfae pressure from its Applying the virial ore isothermal in the ore 0 0) ( & 0 max max 0 0 env s env env env g i q q P P T P T T P T G T G G P G T P E E G T P r Gmdm dr r P P r Gm dr dp at r L m T L m L m L q>q s q=q s q<q s P stable solution unstalbe solution P env given

14 Core ontration & H burning shell When an isothermal He ore is built up to the Shönberg & Chandrasekhar limit (i.e. q > q s 0.1 ), the ore annot maintain quasi-hydrostati equilibrium but starts to ontrat. the star leaves the main-sequene The He ore ontrats on the KH timesale. The weight of the envelope inreases the pressure at the base of the envelope to maintain the quasihydrostati equilibrium. The inrease of the pressure and temperature to ignite H burning in the shell at the base of the envelope. H burning shell drops He ash into ore, whih adds to its gravity and tendeny to ontrat even more. Weight and therfore pressure of H burning shell beomes greater whih makes H fusion ours faster. The gain in heat by the envelope is larger than what is lost from the photosphere. The envelope expands (i.e. due to pdv work) even as the ore ontrats. The star evolves to a subgiant. If this expansion ours while the envelope is mostly radiative, then the star must follow a more-or-less horizontal trak in the H- diagram. It finally evolves to the Hayashi line. As stars asend their Hayashi traks to the red giant branh, their envelopes beomes inreasing onvetive. 1

15 evolutionary traks on H- diagam oughly speaking, evolutionary traks of stars in the H- diagram either go horizontal (if the envelopes are radiative) or they do vertial (if the envelopes are onvetive). Evolutionary traks in the H- diagram therefore never go, for example, at a diagonal (in either branh of an X). 15

16 Asent to red giant subgiant phase (horizontal traks): luminosity roughly onst. inrease radius derease effet temperature, He ore mass exeeds q s, ontrats on the KH timesale finally enounter the Hayashi line (vertial traks): effet temperature almost onst., luminosity inreases and the red giant expands 16

17 Age of a stellar luster turn-off point from the main sequene luster age 17

18 age of globular lusters Vandenberg et al. 00 need distane andles distane modulus : ( m ) V 5log d(p) 5 A V B V E( B V ) ( B V ) B AV. E( B V ) V observed ( B V ) intrinsi isohrones best fit: age ~ 1.5 Gyrs almost as old as the universe 18

19 GB & He flash at the tip ontrating radiative ore beomes inreasingly dense, eventually making eletrons in it more degenerate. (He white dwarf inside a star) the H burning shell deposits He ash into the ore. surfae gravity of the ore (G / 5/ ) inreases with, and therefore raises T and ρ of the H burning shell enhane nulear-energy generation in the shell, raise T of the shell and ore larger luminosity enters the base of the onvetive envelope star expands tremendously and approahes the tip of the GB, some mass is lost from the stellar onvetive envelope ore beomes hot enough (~10 8 K) to ignite He fusion into C in a flash (triple alpha reations) He flash: the extra energy release raises the loal temperature, but a slight inrease in temperature adds little to the pressures that are already present in the form of the eletron degenerate pressure. However, the rate of He burning near T ~10 8 K sales as T 0. Thus, even a modest inrease in T reates a vastly enhaned rate of nulear burning. ore nulear burning means higher temperatures, whih means more nulear burning. The He flash ours on time sales that are still appreiably longer than the sound-rossing time sale in the inner regions of the star; thus, the helium flash produes only relatively slow expansional motions. The expansion lifts the degeneray of the ore. In the H- diagram, the star now desends to the 19 horizontal branh.

20 with For a pure wheret at when the post Eletron degeneray of the ore a gas of free eletrons begins to beome notieably degenerate when n e, The dividing line between non - degenerate and degenerate onditions : n T e de Broglie rit h mek 9.10 e F / rit where He plama, g m main -sequene of the Sun will not be very different from the entral density at present ~100 g/m. The ore is not far even initially from being partially eletron - degenerate onditions. Asending to the giant branh is in a more - or - less ontinuous fashion. In ontrast, the entral densities of eletron degeneray, whih means that the relatively rapid phase of ore ontration oupies a larger span of effetive temperature. m e 7 x F / for an N.. gas - de Broglie / n e.810. m Te h mekt u 7 So the ontrating He ore beomes degenerate when K 15 /, and m 1/. also obtained from kt - n h K -/. 0 F f ( )p 8 dp h K is the estimated temperature that H burning in the shell might be expeted to hold the ore - main sequene ore begins its gravitational ontration. The ore density at the end of F high - mass post - main sequene stars are farther from the ritial value for 0 F 8 p dp h m x F. the 0

21 He ore flash: He ignites under the onditions of partial eletron degeneray for solar-mass stars, but not for stars 7-15 solar masses 1

22 HB and AGB HB: He burning in the ore, H burning in the shell around the ore AGB: H and He burning shells above the inert C/O ore. mass loss during AGB probably due to stellar pulsation and radiation pressure on ondensed dust grains

23 He shell flashes

24 m thermal instability of a shell burning shell Besides, r P The above two equations give D P P T We also have, where P T P T Eliminating, we get P r / D T Now, study the1st law of For an ideal monatomi gas ( 1, if D / r ~ r shell P D q u Pv shell is small enough, Positive feedbak : p with dm G r shll 0 & r dm P r T P T, thermodynamis of r shell where D ~ onst. D Gm P r dm r P r shell ln ln P the burning shell: the gravothermal speifi heat ad /5), and ln lnt is positive and the shell burning is unstable. T. 1 q T q... (reall q for reations is an extremely sensitive funtion of T ) r D r r P p ad r / D

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26 planetary nebulae and viewing angle planetary nebula: C/O ore ontrats as the fusion has eased. The stellar winds and radiation from the ore sweep up the remnant ejeta ionizing it and leading to the formation of a planetary nebula 6

27 evolution of high-mass stars >8 Ÿ will not produe white dwarfs after mass loss photospheres expand, nulear ore soures turn off and shell soures swith on photospheres ontrat, new nulear ore soures turn on and previous shell soures weaken 7

28 a pre-supernova of high mass star the inert iron ore that approahes the Chandrasekhar limit as nulear ash ontinues to drop in from the burning layers above. 8

29 sorry, I ouldn t finish the entire subjet pulsating stars asteroseismology stellar atmospheres stellar rotation evolution of lose binary systems and many many others! 9