MAIN SEQUENCE STARS, Red Giants and White Dwarfs

1. MAIN SEQUENCE STARS, Red Giants and White Dwarfs Stars are powered by fusion reactions. When a fuel is exhausted the star’s structure changes dramatically, producing Post-Main Sequence Evolution

2. ENERGY GENERATION • Key to all MS stars’ power: • conversion of 4 protons (1H nuclei) into 1 alpha particle (4He nucleus) • with the emission of energy in the form of • gamma-ray photons, • neutrinos, • positrons (or electrons) • and fast moving baryons (protons).

3. Stellar Mass and Fusion • The mass of a main sequence star determines its core pressure and temperature • Stars of higher mass have higher core temperature and more rapid fusion, making those stars both more luminous and shorter-lived • Stars of lower mass have cooler cores and slower fusion rates, giving them smaller luminosities and longer lifetimes

4. Fusion on MS: p-p chain

5. The Proton Proton Chains • The ppI chain is dominant in lower mass stars (like the Sun) • Eq 1) p + p  d + e+ +  • Eq 2) d + p 3He +  • Eq 3) 3He + 3He 4He + p + p • We saw all of these when talking about the Sun --so this is a review. • But at higher temperatures or at later times, particularly for stars which have less metals (mainly CNO) than the sun, and when there is: • more 4He around and • less 1H (or p) left, other reactions are important:

6. ppII chain instead of Eq (3): (4) 3He + 4He 7Be +  (5) 7Be + e-7Li +  (6) 7Li + p 4He + 4He Net effect: 4 p4He This dominates if T>1.6x107K ppIII chain Eqs (1) (2) and (4), but then, in lieu of (5): (7) 7Be + p 8B +  (8) 8B 8Be + e+ +  (this was the first solar neutrino detected) (9) 8Be 4He + 4He Net effect: 4 p 4He This dominates if T>2.5x107K Other pp-chains: Eqns (1) & (2) always there

7. Balancing Nuclear Reactions • Balance baryons (protons+neutrons) • Balance charge (protons and positrons vs electrons) • Balance lepton number (electrons and neutrinos vs positrons and anti-neutrinos) • Balance energy and momentum (with photons if only one particle on the right hand side)

8. Alternative Nuclear Reactions:The CNO Bi-Cycle • This is a complicated network of reactions involving isotopes of Carbon, Nitrogen and Oxygen (and Fluorine) that eventually adds 4 protons to a C or O nucleus which finally also gives off an alpha particle. • BUT IT STILL YIELDS THE SAME NET REACTION: • 4 protons  1 4He nucleus, plus energy • Here 12C or 16O acts like a catalyst in chemical reactions • The CNO bi-cycle dominates energy production in: -Pop I stars (i.e., those with compositions similar to the Sun's -- roughly 2% "metals") -which are also more massive than about 1.5 M -i.e., O, B, A, F0-F5 spectral classes.

9. CNO Cycle vs p-p Chain

10. Hydrostatic Equilibrium on MS

11. Sources of Pressure • Hydrostatic equilibrium holds on the MS: • that is to say, pressure balances gravity, essentially perfectly, at every point inside the star. • Most stars, those up to 10 M, are mainly supported by THERMAL or GAS PRESSURE: • Pgas T, with  the density and T the temperature. • RADIATION PRESSURE is very important in the most massive, hottest stars • (above about 10 M): • Prad T4

12. Energy Transport • The internal structures of stars depend upon their masses and the temperatures go up for higher mass stars. • This means different energy transport mechanisms dominate in different parts of different stars. • For stars < 0.5 M(M stars) the entire star is convective. • For stars like the sun (between 0.5 and 2 M) the interior is radiative and the outer layer is convective. • For stars between 2 and 5 Mthere is a complex structure: convective core, radiative middle zone, convective envelope. • Stars more massive than 5 Mare convective at the centers and radiative in their envelopes.

13. X-rays and Mass Loss on MS • Stellar chromospheres and coronae are produced in low mass stars by the convective outer layers; these can yield X-rays. • Hot stars can also produce X-rays from powerful winds, driven by very strong radiation pressure in their outer layers. • Stars of above 20 M lose appreciable fractions of their masses during their short life times. • The winds of these massive stars are driven by radiation pressure; • winds of lower mass stars are driven by energy from their convective outer layers.

14. On the MS Things Change SLOWLY • Fusion depletes H and increases He, mainly in the core • Only slight adjustments in temperature, density and pressure are required to retain hydrostatic equilibrium for millions, billions or trillions of years

15. Hydrostatic Equilibrium at Different Times: Pressure & Gravity Adjust

16. STELLAR LIFETIMES • The amount of fuel is proportional to the star's mass, so you might think more massive stars live longer. • BUT the rate at which it is burned is proportional to the star's luminosity. • AND more massive stars are hotter in the core, meaning their nuclear reactions go much faster and they are more luminous. • This explains the MASS-LUMINOSITY relation for MS stars. Specifically we have, as you will • RECALL: L  M3.5 --- on the MS (only). • So the lifetime, t  (amount of fuel / burn rate) • Main Sequence Lifetime Applet

17. Lifetimes in Math That’s  the proportionality. As an equation  Example: you know the Sun lives 1.0x1010yr, so how long does a 5 M star live? So a 5M star lives less than 200 million years!

18. POST-MAIN SEQUENCE EVOLUTION • THE END OF THE MAIN SEQUENCE • A star leaves the MS when it exhausts H at the core. During the MS, there is an excellent balance between P and gravity: HYDROSTATIC EQUILIBRIUM • When H is gone, the core is essentially all He and (at between 6 and 40 million K), far too cool to start nuclear fusion of He. • The structure must readjust since the H fusion, which had provided the energy and pressure, at the center.

19. SUBGIANT PHASE • All H gone in core: He "ash" is too cold to "burn" • Pressure provided by energy from fusion in the core disappears. • The He core contracts -- gravity wins over pressure again. • Contraction heats the core. • Most of this heat is trapped, so core T rises. • Rising density and T imply core P rises pretty fast, so there is a contraction, NOT a collapse.

20. Hydrogen Burning Shell (Subgiant)

21. Thought Question What happens when a star can no longer fuse hydrogen to helium in its core? A. Core cools off B. Core shrinks and heats up C. Core expands and heats up D. Helium fusion immediately begins

22. Thought Question What happens when a star can no longer fuse hydrogen to helium in its core? A. Core cools off B. Core shrinks and heats up C. Core expands and heats up D. Helium fusion immediately begins

23. Subgiant, 2 • Increased core T diffuses into the H BURNING SHELL -- the layer of H hot enough to fuse outside the inert He core. • This higher T causes a dramatic increase in L from that shell (both pp chains and CNO cycle fusion rates are VERY SENSITIVE to T) • Higher L in shell causes the inert H envelope to expand. • Work is done in producing this expansion, so the star's surface T declines (an expanding cloud of gas cools just as an opaque contracting one heats). • This corresponds to the star moving to the right and up on the H-R diagram and it enters the SUBGIANT phase.

24. Life Track after Main Sequence • Observations of star clusters show that a star becomes larger, redder, and more luminous after its time on the main sequence is over

25. RED-GIANT PHASE • As the core continues to contract and heat up, T = 108 K is finally reached; • Then higher electric repulsion of Helium nuclei can be overcome • AND He CAN FUSE INTO CARBON: 3 4He 12C +  (the TRIPLE-ALPHA REACTION). • Really, 4He + 4He 8Be but Be-8 is unstable, so 3 He-4's are needed to come together nearly simultaneously. • This generates more energy, and both L and T in core increases.

26. Helium Flash • For M < 2 M this occurs while the He core is degenerate; (more about this later when we discuss White Dwarfs) • As P doesn't rise with T for degenerate matter, the “thermostat” is broken • So he core temperature rises fast when He fusion begins: and the Luminosity from He goes up even faster: HELIUM FLASH • until thermal pressure is large again and expands core again, again dropping the core temperature • This causes a very fast expansion of the star's envelope, and a further cooling of its surface,yielding a RED GIANT (with size 100's of that of Sun on MS but lower Ts ).

27. Life Track after Helium Flash • Models show that a red giant should shrink and become less luminous after helium fusion begins in the core

28. Pop Quiz • Print your name (1) • 1) Complete, and explain the balancing of, the following nuclear reaction (5): • 15N + 1H  12C + ___ • 2) Sketch, on a labeled H-R diagram, the path of a 1 M star from the time of accretion as a protostar to the red giant phase. (5)

29. THE HORIZONTAL BRANCH • He Flash ends quickly, once core pressure has grown, causing the core radius to rise, thus, yielding a decline in Tc to just about 108 K. • Now He burns smoothly in the core -- producing the He BURNING MAIN SEQUENCE -- which is visible on an H-R diagram as the HORIZONTAL BRANCH (lower L but higher Ts than during the He flash). • Stars are again in HYDROSTATIC EQUILIBRIUM throughout: the thermostat works again • These are still RGs, and on HB the higher masses are to the left part of the HB. • Most stars spend most of their POST-MS life on the HB, but this is typically < 10 % of their MS life.

30. Back up to the Red-Giant Branch on the H-R Diagram (Asymptotic Giant Branch)

31. Thought Question What happens when the star’s core runs out of helium? A. The star explodes B. Carbon fusion begins C. The core cools off D. Helium fuses in a shell around the core

32. Thought Question What happens when the star’s core runs out of helium? A. The star explodes B. Carbon fusion begins C. The core cools off D. Helium fuses in a shell around the core

33. AGB for Lower Mass Stars • Increased core T diffuses into the He BURNING SHELL -- the layer of He hot enough to fuse outside the inert C core. • This higher T causes a dramatic increase in L from that shell. • Higher L in shell causes the inert He envelope, as well as the H burning shell and inert H envelope to expand. • Work is done by the gas in producing this expansion, so the star's surface T declines by a bit. • Star is hotter inside and more luminous than before

34. Helium Burning Shell

35. Double Shell Burning • After core helium fusion stops, He fuses into carbon in a shell around the carbon core, and H fuses to He in a shell around the helium layer • This double-shell burning stage never reaches equilibrium—fusion rate periodically spikes upward in a series of thermal pulses • With each spike, convection dredges carbon up from core and transports it to surface

36. ON TO WHITE DWARFS • For stars with MS masses less than about 7 to 8 M : AGBs or Supergiants lose a good bit of mass, and some of these pulsations become so powerful that massive shells (of 0.1 to 0.2 M) are ejected.

37. End of Fusion • Fusion progresses no further in a low-mass star because the core temperature never grows hot enough for fusion of heavier elements (some He fuses to C to make oxygen) • Degeneracy pressure supports the white dwarf against gravity

38. Planetary Nebulae • Double-shell burning ends with a pulse (or pulses) that eject most of the H and He into space as a planetary nebula • The core left behind becomes a white dwarf

39. Ejected Shells = Planetary Nebulae

40. CENTRAL STARS OF PN The cores of the RGs/SGs are very hot and excite the PN gas. These Central Stars of PN have C or C+O cores, and He envelopes (All the H was expelled as winds or PN).

41. Dead Core Evolution • They are not massive enough to compress the C core to T > 7 x 108 K at which it could fuse, so these CSPN's just cool off and fade in power, slowly shrinking in size • BUT, when density of the core reaches 106 g/cm3 (or one ton / teaspoon!) the PAULI EXCLUSION PRINCIPLE takes over: • no 2 electrons can be in the same energy state; • this Quantum Mechanical effect provides a HUGE DEGENERACY PRESSURE that stops the continued contraction at a radius of about 1/100th of R (nearly the same as R ).

42. White Dwarfs • Once it is held up by degeneracy pressure: • we call it a WHITE DWARF. • The MAXIMUM MASS electron degeneracy pressure can support is about 1.4 M-- the CHANDRASEKHAR LIMIT. • So 7-8 M stars on the MS leave WDs close to the Chandrasekhar limit • But the more common 0.8-2 M stars leave WDs around 0.6-0.7 M (the typical mass of a WD).

43. Observed White Dwarfs • Sirius B is a bound companion to the nearby very bright star Sirius (A): M=1.1 M R=5100 km • M4 the nearest globular cluster, about 16 pc across at 2100 pc distance • Nearly 100 WDs are seen in a small region

44. Size of a White Dwarf • White dwarfs with same mass as Sun are about same size as Earth • Higher mass white dwarfs are smaller!

45. Earth’s Fate Errors on Scale: 100 10 1 • Sun’s radius will grow to near current radius of Earth’s orbit

46. Earth’s Fate • Sun’s luminosity will rise to 1,000 times its current level—too hot for life on Earth • Life and Death of the Sun Applet

47. Summary for Low Mass Stars • What are the life stages of a low-mass star? • H fusion in core (main sequence) • H fusion in shell around contracting core (red giant) • He fusion in core (horizontal branch) • Double-shell burning (red giant) • How does a low-mass star die? • Ejection of H and He in a planetary nebula leaves behind an inert white dwarf

48. Asymptotic Giant Branch (for Massive Stars) Supergiants • Once the He in the core is all burned up, we reach the end of the He BURNING MAIN SEQUENCE. • As at the end of the MS: Pressure provided by energy from fusion in the core disappears. • The Carbon core contracts -- gravity wins over pressure again. • Contraction heats the core; Most of this heat is trapped, so core T rises. • Rising density and T imply core P rises, so again there is a contraction, not a collapse.

49. Supergiants for Higher Mass Stars • For more massive stars the same thing happens, but the star starts way up on the H-R diagram, and it enters the SUPERGIANT phase. • The ESCAPE VELOCITY from such big stars gets low: Vesc = (2 G M / R)1/2 as R increases while M stays the same. • They lose a lot of mass via winds. • Also, RGs and SGs are subject to opacity driven instabilities which cause the outer layers to expand and cool and contract and heat up. • This produces VARIABLE STARS if the atmosphere lies in the INSTABILITY STRIP. • Important classes of variable stars are the RR LYRAE (horizontal branch) and two types of CEPHEID VARIABLES (supergiants), since they are wonderful DISTANCE INDICATORS

50. Massive Star Post-MS Evolution • Stars starting the MS with more than ~8M are unlikely to leave behind WDs(though up to about 10M may leave behind Carbon-Neon WDs);they leave cores w/ M > 1.4M : the Chandrasekhar limit. • Evolutionary History • MS • H is exhausted in core • H shell burning starts, with modest increase in L and fast decrease in TS (fast move to right on H-R diagram) • He fusion starts (non-degenerately, so no flash) • Modest increase in L and core He burning -- a SUPERGIANT • He is exhausted in core