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4.2 Stellar Evolution After the Giant Branch

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4.2 Stellar Evolution After the Giant Branch I*M*P*R*S on ASTROPHYSICS at LMU Munich Astrophysics Introductory Course Lecture given by: Ralf Bender and Roberto Saglia in collaboration with: Chris Botzler, Andre Crusius-Wätzel, Niv Drory, Georg Feulner, Armin Gabasch, Ulrich Hopp, Claudia Maraston, Michael Matthias, Jan Snigula, Daniel Thomas Powerpoint version with the help of Hanna Kotarba Fall 2007 IMPRS Astrophysics Introductory Course Fall 2007 1 Chapter 4 Stellar Evolution IMPRS Astrophysics Introductory Course Fall 2007 2 4.1 Stellar evolution from the main sequence to the giant branch Immediately after the contraction phase during stellar formation (before nuclear burning sets in) stars have a homogeneous chemical composition. The location of the stars in the HRD where they for the first time start with nuclear fusion in hydrostatic equilibrium is called Zero Age Main Sequence (ZAMS) For the period of central hydrogen burning the stars remain on the main sequence near the ZAMS. As the chemical composition changes slowly, the main sequence is not a line but a strip. Massive metal rich stars (M > 20MΘ) in addition loose a significant fraction of their mass due to stellar winds, which moves them a large distance away from the ZAMS even during the hydrogen burning phase. (Lower mass stars also develop winds but only in the later phases of their evolution.) How does a star move ’inside’ the main sequence? As shown above we have: IMPRS Astrophysics Introductory Course Fall 2007 3 Evolutionary paths in the HRD up to the point where He burning sets in (from Iben 1967, ARAA 5). The shade of the line segments indicates the time spent in the corresponding phases. MS (1-3) life-times: 1.0·MΘ: 9.0E9 yrs 2.2·MΘ: 5.0E8 yrs 15·MΘ: 1E7 yrs GB (5-6) life-times: 1.0·MΘ: 1.0E9 yrs 2.2·MΘ: 3.8E7 yrs 15·MΘ: 1.5E6 yrs (6-10) IMPRS Astrophysics Introductory Course Fall 2007 4 Hydrogen fusion leads to: Therefore, following our simple model, the luminosity and the temperatures during hydrogen burning should rise for both pp–chain and CNO–cycle. In reality temperature rises for the pp-chain while it decreases for the CNO-chain (where the core is convective and not radiative as assumed in the model). Once almost all of the core hydrogen is used up, hydrogen shell burning in a thick shell around the (He-) core starts. The star moves to cooler temperatures to the sub–giant branch with approximately constant luminosity. For M > 1.4MΘ the core is convective and XH so small that contraction has to set in before hydrogen shell burning can start. The hydrogen burning shell moves outward with time, whereas the helium core slowly contracts and increases its binding energy. The released gravitational energy heats the hydrogen burning shell from below, which increases the fusion (ε ~ T5..17) and forces the star out of equilibrium: The situation is analogous to the scale height of a planetary atmosphere H = kT/µmpg which is dependent on the temperature. The star expands and its temperature decreases as the energy transport is too inefficient to keep Teff constant. IMPRS Astrophysics Introductory Course Fall 2007 5 IMPRS Astrophysics Introductory Course Fall 2007 6 IMPRS Astrophysics Introductory Course Fall 2007 7 At the Hayashi–limit the star gets fully convective and the smallest possible temperature is reached. On the way from the main sequence to the Hayashi–limit the luminosity of the 4 2 −1/2 star changes only slightly: L ~ const. ~ Teff · R → Teff ~ R , i.e. R ↑ → Teff ↓. The transition from the main sequence to the Hayashi–limit is determined by the Kelvin– Helmholtz time scale (≈ 107 years — short!). The most massive stars now remain at the Hayashi–limit with constant luminosity. With the onset of helium burning they increase the temperature and move again to the left in the HRD. Less massive stars keep increasing their radius at approximate constant temperature thus increasing their luminosity ~ R2, they move upwards along the Hayashi line (→ giant branch stars!). The sun for example will expand up to the radius of the earth: Teff ≈ 3500 K, L ≈ 300 LΘ. IMPRS Astrophysics Introductory Course Fall 2007 8 Evolutionary paths in the HRD up to the point where He burning sets in (from Iben 1967, ARAA 5). The shade of the line segments indicates the time spent in the corresponding phases. MS (1-3) life-times: 1.0·MΘ: 9.0E9 yrs 2.2·MΘ: 5.0E8 yrs 15·MΘ: 1E7 yrs GB (5-6) life-times: 1.0·MΘ: 1.0E9 yrs 2.2·MΘ: 3.8E7 yrs 15·MΘ: 1.5E6 yrs (6-10) IMPRS Astrophysics Introductory Course Fall 2007 9 4.2 Stellar evolution after the giant branch The post giant branch evolution is dependent on the mass: M ≤ 0.5MΘ The pressure of the degenerated electron gas stops the contraction of the helium core 8 before Tc ≈ 10 K is reached. → no helium burning. H shell burning slowly stops, the star cools out. 0.5MΘ ≤ M ≤ 2.5MΘ The H shell burning puts more and more He onto the core, which keeps contracting. The core is supported by the pressure of the degenerate electron gas, while the pressure from the He nuclei is negligible. When the temperature has reached ~ 108 K, He–burning 30 suddenly starts (because of ε3α ~ Tc ). Because the pressure from the He nuclei is still negligible relative to the pressure of the degenerate electrons, the nuclear burning can 30 not be moderated via expansion. Again, because of ε3α ~ Tc , the energy production increases dramatically and a large fraction of the He is burned into C and O. → thermonuclear runaway! Only once the temperature of the nuclei is high enough to contribute significantly to the pressure, the core expands and the reaction is slowed down. The star expands on a hydrostatic time scale and reaches its highest luminosity at the tip of the giant branch: IMPRS Astrophysics Introductory Course Fall 2007 10 Helium flash Note: As helium burning sets in at the same core mass, all mass poor stars have the same luminosity at the tip of the giant branch. IMPRS Astrophysics Introductory Course Fall 2007 11 After the helium flash, the star is on the horizontal branch. The position on the horizontal branch depends on mass and metallicity. On the horizontal branch we have He → C burning in the core and H → He burning in a shell. In addition we have the following reactions: 12C + 4He → 16O + γ + 7.161 MeV 16O + 4He → 20Ne + γ + 4.730 MeV The result is a mixture of C and O (≈ 50 : 50) in the stars center. C/O sinks down to the core and replaces He which is driven out of the core. If the He is driven out of the core, helium burning shifts to shell burning. → same procedure as with hydrogen burning. The star expands again to the Hayashi line and then moves to higher luminosities along the asymptotic giant branch (AGB). IMPRS Astrophysics Introductory Course Fall 2007 12 Evolution of low mass stars with 0.7 and 0.8 solar masses. Times up to the giant branch are in billion years. From Iben 1971, in Boehm-Vitense: Stellar Astrophsics. IMPRS Astrophysics Introductory Course Fall 2007 13 Massive stars with M > 2.5MΘ Mostly the same evolution as for less massive stars. But, before ignition of helium burning the electron gas is not degenerated, thus we have a continous transition to helium burning. The star performs loops in the HRD at nearly constant luminosity. Evolution of a 5 solar mass star (Kippenhahn/Weigert). IMPRS Astrophysics Introductory Course Fall 2007 14 IMPRS Astrophysics Introductory Course Fall 2007 15 An important test for the theory of stellar structure and evolution is the analysis of HRD’s and color–luminosity–diagrams of open star clusters and globular clusters. These represent groups of stars of similar age and chemical composition but different mass and, therefore, the number of stars in the different parts of the HRD can directly be compared with the predictions of the theory. (diagram from Maeder et al., stars from galactic clusters) IMPRS Astrophysics Introductory Course Fall 2007 16 MS = main sequence TO = turn-off RGB = red giant branch HB = horizontal branch AGB = asymptotic giant b. P-AGB = post-AGB BS = blue stragglers IMPRS Astrophysics Introductory Course Fall 2007 17 IMPRS Astrophysics Introductory Course Fall 2007 18 4.3 Special effects 4.3.1 The Eddington luminosity The Eddington luminosity is the maximum luminosity a object of given mass can emit. At higher luminosities, radiation pressure wins over gravitational acceleration. The Eddington luminosity is an upper limit to the luminosity of stars (but also other objects, like accretion disks or active galactic nuclei, see below). Close to the Eddington luminosity, stars will start loosing their outer layers. For simplicity we work in spherical approximation. We assume we have an object of mass Mc which emits a luminosity L through a spherical surface with Radius R. The flux then is: resulting in the radiation pressure: (explanation: a single photon has a momentum of hν/c, summing over all photons and deviding by the area gives the pressure exerted by the photons if absorbed). If the gas is strongly ionized, the interaction between matter and photons can be approximated by the IMPRS Astrophysics Introductory Course Fall 2007 19 Thomson cross-section of e− and p: Therefore, the radiation pressure only works on the e− (but the protons get also accelerated because of electromagnetic coupling). A star will start disintegrating, if the accelerating force of the radiation is bigger than the force of gravitation: This defines the Eddington-Luminosity: or: IMPRS Astrophysics Introductory Course Fall 2007 20 4.3.2 Special Effects I: Winds and Thermal Pulses During the post main sequence phase stars loose a major part of their mass via winds and thermal pulses: main sequence 1 MΘ → tip of AGB 0.6 MΘ main sequence 8 MΘ → tip of AGB 0.8 MΘ The expelled gas is given back to the interstellar medium.
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