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Lec 7

Lec 7. II-8c. Late Stages of Evolution and Death (Main Ref.: Lecture notes; Parts of FK Ch. 19 and 20). (i) Introduction

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Lec 7

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  1. Lec 7 II-8c. Late Stages of Evolution and Death (Main Ref.: Lecture notes; Parts of FK Ch. 19 and 20)

  2. (i) Introduction When ~ 10 – 30 % of mass in the central core becomes He, H-burning cannot catch up with energy lost by radiation, because temperature outside the He core is too low for H-burning (see Fig. II-41). Then, the only other energy source is gravitational energy through contraction, and so the star starts to contract again  End of the long, relatively stable middle-age era as a main sequence (MS) star. What happens, afterward, depends on mass. Life after MS (= post main sequence) is drastically different for massive stars ( M ≥ ~8 M☉) and less massive stars (M ≤ ~ 4 M☉). We will follow the fate of low mass stars first, then high mass stars. Then discuss the fate of intermediate mass stars ( ~ 4 M☉ ≤ M ≤ ~ 8 M☉).

  3. (ii) Low Mass Stars( M ≤ 4 M☉)(Main Ref.: Class notes; FK Sec.19-1 to 4, 20-1 to 3; CD photos shown in class) When the contraction proceeds, both density c and temperature Tc of the central core increases while the core radius Rc decreases. Since thermal pressure P is proportional to ~ kT, increased central Tc means increased core Pc, which pushes up the surrounding envelope  larger size (i.e. larger stellar radius R) and lower surface temperature Ts. Note: This process, of contracting core resulting in increased Tc and decreased Rc, while decreased Ts and increased R, takes place repeatedly during subsequent evolutionary stages. Note also, that in the reverse situation, where the central core expands, decreased Tc and increaded Rc,will result in increased Ts and decreased R. That also takes place repeatedly during the evolution.

  4. As the contraction of the core proceeds further and the core heats up, and when the central Tc reaches ~108 K, it is sufficiently high to trigger He burning, where He changes to carbon C and oxygen O (see FK p. 541). This He burning is called `triple  process’, because He nuclei are called  particles, and in this process 3 He nuclei combine to become one C, etc. By the time He burning starts, the star gets so large that it is called a `red giant’. Since the He burning can supply new nuclear energy source to balance the energy lost by radiation, contraction stops, and the star (as a red giant (RG) and horizontal branch (HB) star) can exist as a stable star, with an increasing core of C and O. When the C/O core grows and its mass gets ~ 20%, however, the temperature of the core boundary gets less than the critical T required for He burning. So, again due to lack of sufficient nuclear energy source, contraction resumes, as AGB (asymptotic giant branch) star. However, about this time, something very important happens in a low mass star like the sun – called Electron Degeneracy.

  5. Electron Degeneracy: Degeneracy takes place when density effect gets larger than temperature effect. When density gets high enough, QM (quantum mechanics) becomes important – electrons are `quantized’, i.e., they can take only discrete energy levels. Then, the Pauli Exclusion Principle forbids more than two electrons to occupy one energy level. This causes a tremendous pressure – called `Degeneracy Pressure’. (See class notes for the details.) In a low mass star, since it is relatively denser and cooler than more massive hot stars, the density increase due to contraction is relatively larger than temperature increase  the result is that the degeneracy pressure of electrons overtakes thermal pressure of gas. Once that stage is reached, the electron degeneracy pressure can support the gravity and so contraction stops. Then, no more contraction means no more core temperature increase. Without further increase of core temperature, no more higher-level nuclear reactions to `cook’ heavier elements. What happens then?

  6. The story is rather complicated, due to `Helium flash’, etc. The red giant, after the intermediate stages such as `Horizontal Branch (HB) Star, Asymptotic Giant Branch (AGB) Star, Planetary Nebula, finally ends up as White Dwarf. See Fig. II-62 for the structure of an AGB star. Note: From the red giant to the planetary nebula stage, a lot of mass is lost. This is due to instability, pulsation, etc., during the HB and AGB stages. A planetary nebula is clouds of gas ejected from the central star which are illuminated by the central hot UV star and shine (like an emission nebula). Enjoy beautiful photos of planetary nebulae in Fig. II-66 and CD photos shown in class. (Study class notes and FK 20 -1 through 3, for the details.)

  7. Fusion of helium into carbon and oxygen begins atthe center of a red giant Fig. II-61: Stages in Stellar Evolution • When the central temperature of a red giant reaches about 100 million K, helium fusion begins in the core • This process, also called the triple alpha process, converts helium to carbon and oxygen

  8. Fig.II-62: Structure of AGB star. Evolutionary Track on the HR-Diagram: Although the evolutionary track of a low mass star on the HR diagram is rather complicated, most parts again can be explained by the Stefan Boltzman Law, as done for pre-main sequence stars earlier. L = 4  R2 T4. Eqn(16) (See Fig. II-63, and class notes for the details.) See Fig. II-31 (= FK Fig. 21-6, Fig. II-32 (= FK Fig. 22-1), FK Sec. 22-1 to 4, and class notes for the details.

  9. Fig.II-63: Post MS evolution of low mass low stars. Lifetime: Lifetime of a red giant tRG is less than that of main sequence stars. a MS star: Reason: He burning releases less energy, and so it takes less time. Example: Sun tRG ~ 2 x109 years < ~1010 years for MS. EX 37: Shell of a ~ circular-shaped planetary nebula (PN) is observed to expand at velocity of 20 km/sec. The diameter of the shell is 1 ly. How old is this PN? Ans: 8333 years. Hint: Useful equation is t = R/V Eqn(28) (See class notes for the details.)

  10. As stars age and become giant stars, they expand tremendously and they eject matter into space EX 38b EX 38b Fig. II-64: Red Giant in M50 Fig. II-65: A Mass Loss Star HD 65750

  11. EX 39 Fig. II-66: Various Planetary Nebulae

  12. Fig. II-67: Formation Mechanism of some planetary nebulae (iii) High Mass Stars (M ≥ ~8M☉)(Main Ref.: Lecture notes; FK Sec 20-5,6,7,9,10; CD photos shown in class) When ~ 30% of central mass becomes He, the temperature at the boundary of the core gets less than ~107 K required for H burning, and due to lack of nuclear energy source, the star starts contracting, and as in low mass stars, the core temperature and density increases while the envelope expands

  13. and radius increases. When the central temperature Tc reaches ~108 K that is high enough for He burning (triple  process), which supplies nuclear energy source and so the contraction stops. The star can exist as a stable (non-contracting) star for a while while He burning continues and C/O core increases with time, as it happens in low mass stars. One difference from the low mass case, however, is that luminosity at this point (start of He burning) is so high that the star is a red supergiant, not red giant. Another is that He burning is stable and He flash does not take place. Since the energy available from He burning is less than H burning, the energy source is exhausted quickly. What happens next is very different from the low mass case.

  14. Degeneracy never happens in high mass stars! Why?. Reason: High mass stars are hotter and less dense than low mass stars. Remember that degeneracy takes place when density effect overtakes temperature effect. (see class notes for the details.) What happens next? In the absence of degeneracy pressure which prevents further contraction of the core, the core contraction resumes, releasing further gravitational energy, and the central temperature Tc increases again. When Tc reaches 6 x 108 K, C (carbon)-burning starts, which transforms C to Ne (neon). Eventually the Ne core grows in size, and the boundary temperature gets too low for C-burning. Then contraction again resumes.

  15. . This cycle of nuclear fusion involving heavier and heavier elements involving higher and higher temperatures and gravitational contraction in between each nuclear fusion with higher levels continues – after C-burning, Ne and O burning follow, and finally Si burning produces heavy elements all the way up to Iron (Fe). During this process various elements from C to Fe are produced. (See class notes and FK for further details.) At this point, the central core is made predominantly of Fe, surrounded by layers of elements, from lighter to heavier, as you go from surface to center – looking like an onion (see Fig. II-68). This core, looking like an onion, is only the size of the earth. However, by this time the envelope expanded to such a huge degree that the radius of the entire star is as large as Jupiter’s orbit! The core gets denser, core temperature gets higher, and timescale of each nuclear fusion gets shorter as it gets to more advanced stages involving heavier elements. See Table II-6. Note: substantial mass loss takes place during the supergiant stages.

  16. Fig. II-68: Structure of pre-supernova high mass star • Table II-6: Post main sequence evolution of massive star

  17. EX 40 Fig. II-69: Mass Loss from a Supergiant Star

  18. Fig. II-70: Turbulence in a Supernova EX 41 Fig. II-71: Cas A Supernova Renmant

  19. In 1987 a nearby supernova gave us a close-up look at the death of a massive star Fig. II-72: SN 1987A EX 42

  20. Supernova Explosion: When the nuclear fusion proceeds all the way to `cooking’ of Fe, and the onion-like structure with an Fe core is reached, something drastic happens – a supernova explosion! How does it happen? Photodisintegration: By this time the central temperature is so high that heavy nuclei hit by high energy photons (gamama rays) disintegrate to He nuclei ( particles)- so, photodisintegration. Core Collapse: Fusion of light elements up to Fe releases nuclear energy. However, the reverse, from Fe to He, requires energy input. The only source of such energy input is gravitational energy. So, catastrophic core collapse – implosion! Also, in the central core efficient production of neutrinos takes place. The escaping neutrinos carry energy – need more energy input  accelerates collapse further! Birth of a Neutron Star: When the collapsing core reaches nuclear density (N = 4 x 1017 kg/m3), the core is predominantly made of neutrons. These neutrons are degenerate and the degenerate pressure of neutrons can support the core, and so it gets suddenly very stiff, and further contraction stops  birth of a neutron star!

  21. Core Bounce: Due to the sudden stopping of collapse the core bounces back. Explosion: The sudden core bounce sends powerful wave of pressure, which ejects the outer envelopes  supernova explosion! The ejected envelopes travel fast – when the speed gets faster than the sound speed shocks form. Shocked ejected material and interstellar medium emit a lot of light (radio to gamma rays)  supernova remnants as nebulae, e.g. the Crab Nebula. See class notes and FK for further details. Enjoy CD photos shown in class and in Fig. II-71, 72. Why nuclear fusion stops at Fe? Because `cooking’ of elements heavier than Fe from Fe requires extra energy. See class notes with BE/A vs A diagram, for the reason. Then how are these elements heavier than Fe formed? This belongs to nuclear physics – beyond the level of ASTR 373. There are r(rapid)-process, n(neutron)-process, s(slow)-process, etc., through which these very heavy elements are formed.

  22. Note: 10M☉ (main sequence) star: final collapsed core is a ~ 1.4M☉ neutron star. The rest, 8.6M☉, is ejected and becomes an extended supernova remnant, as the surrounding nebula. Note: White dwarfs, made from low mass stars, are supported by degenerate pressure of electrons. Neutron stars are supported by degenerate pressure of neutrons. Neutron degenerate pressure is much larger than electron degenerate pressure, since neutron mass is ~2000 times larger than electron mass. Bith of a Black hole: When original M > ~ 25M☉, even neutron degenerate pressure cannot support the collapsed core, so the collapse continues indefinitely  Birth of a black hole! See class notes and later sections for further details. (iv) Intermediate Mass Stars ( 8M☉> M > ~ 4M☉) (Main Ref.: Lecture notes) Hard to calculate evolution of intermediate mass stars due to various complications such as instability, mass loss, etc., which become even

  23. more serious than for low mass stars. One thing sure appears to be that in most cases, due to larger mass and higher temperature involved in the central core, in these stars nuclear fusions of higher levels can proceed, before degeneracy stops further gravitational contraction before they go all the way to creation of an iron core and catastrophic explosion. So most of them probably will go through the planetary nebula stage and eventually end up as white dwarfs. However, before the degeneracy sets in finally in the core, elements heavier than C and O would be synthesized. So, their core will consist of elements heavier than C and O, e.g., Mg, Si, but not Fe. However, some calculations show that some of these stars on the heavier side, near 8M☉, may manage to become a supernova, but it will be all explosion, with no collapsed core left. I mean, all matter is ejected. So far, we covered evolution of isolated stars. The evolution of binary stars is far more complicated. Due to lack of time I will not cover that topic, but one section of FK devotes to this topic.

  24. (v) Late Stages of Stellar Evolution - Summary Fig. II-73: Pathways of Stellar Evolution Horizontal branch star

  25. Fig. II-74: Post-Main Sequence Evolution of Stars in HR Diagram

  26. II-8d. Stellar Cluster Evolution(Main Ref.: Lecture notes; FK 18-6,19-4, 20-1) Star Clusters: Stellar Association: Youngest, mostly bright, high mass, hot O and B stars – called O, B associations. Gravitationally unbound, mostly moving away from each other right after birth. Not many, extended. Open Clusters (= Galactic Cluster): Relatively young, high mass, bright O,B stars. Gravitationally only loosely bound, relatively young. Not as many and densely populated as globular clusters. More extended than globular clusters. Examples: Pleiades, NGC 2264. Globular Clusters: No bright, high mass hot stars – they have already evolved away. Brightest stars are red giants. Very old, (1 – 2) x 1010 years, ~ spherical, tightly bound and compact ~ 100 pc. Many stars ~ 106 stars. Example: M10 Enjoy pretty pictures in II-75 and CD photos shown in class!

  27. EX 43 Fig. II-75a: Young Cluster NGC 2264

  28. EX 44Fig. II-75b: Open Cluster Pleiades

  29. EX 45 Fig. II-75c: Globuler Cluster M10

  30. Fig. II-76: HR Diagram of a Globular Cluster Fig. II-77: HR Diagram of Clusters

  31. Cluster Evolution: Stars in clusters are born at the same time. So, by looking at and studying carefully the distribution of stars in clusters on the HR Diagram, you can find the evolution and approximate age of the cluster! The best way to demonstrate this is by examples. See Fig II-78 and class notes for the details. As a cluster ages, the main sequence is “eaten away” from the upper left as stars of progressively smaller mass evolve into red giants • So, the cluster’s age is equal to the age of the main-seq uence stars at the turnoff point (the upper end of the remaining main sequence)

  32. Fig II-78: the Evolution of a Theoretical Cluster supergiants supergiants

  33. Fig II-78: (conti.) EX 46: M55: Globular cluster,Very old!. Why? See Fig. II-79b and class notes.

  34. Age of Clusters: How to estimate the age of a cluster from the HR Diagram of the cluster?Best way to demonstrate is by examples – see class notes for the details! EX 47: How old is h &  Persei? Ans: ~ 107 years EX 48: How old is M41? Ans: ~ 2 x 108 years EX 49: How old is M67? Ans: ~ 8 x 109 years EX 50: Roughly how many times older is M3 cluster than h &  Persei? Ans: M3 ~ 700 times older.

  35. Fig II-79a: HR Diagram of Many Stars Fig II-79b: M55 in HR Diagram Fig. II-80: Age of Clusters

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