1. Spectral Classes Strange lettering scheme is a historical accident. Spectral Class Surface Temperature Examples OBAFGKMOBAFGKM 30,000 K 20,000 K 10,000 K 7000 K 6000 K 4000 K 3000 K Rigel Vega, Sirius Sun Betelgeus e Further subdivision: BO - B9, GO - G9, etc. GO hotter than G9. Sun is a G2.

2. Main Sequence White Dwarfs Red Giants Red Supergiants Increasing Mass, Radius on Main Sequence The Hertzsprung-Russell (H-R) Diagram Sun A star’s position in the H-R diagram depends on its mass and evolutionary state.

3. H-R Diagram of Well-known Stars H-R Diagram of Nearby Stars Note lines of constant radius!

4. Stellar Evolution: Evolution off the Main Sequence Main Sequence Lifetimes Most massive (O and B stars): millions of years Stars like the Sun (G stars): billions of years Low mass stars (K and M stars): a trillion years! While on Main Sequence, stellar core has H -> He fusion, by p-p chain in stars like Sun or less massive. In more massive stars, “CNO cycle” becomes more important.

5. Evolution of a Low-Mass Star (< 8 M sun, focus on 1 M sun case) - All H converted to He in core. - Core too cool for He burning. Contracts. Heats up. Red Giant - Tremendous energy produced. Star must expand. - Star now a "Red Giant". Diameter ~ 1 AU! - Phase lasts ~ 10 9 years for 1 M Sun star. - Example: Arcturus - H burns in hot, dense shell around core: "H-shell burning phase".

6. Red Giant Star on H-R Diagram

7. Eventually: Core Helium Fusion - Core shrinks and heats up to 10 8 K, helium can now burn into carbon. "Triple-alpha process" 4 He + 4 He -> 8 Be + energy 8 Be + 4 He -> 12 C + energy - Core very dense. Fusion first occurs in a runaway process: "the helium flash". Energy from fusion goes into re-expanding and cooling the core. Takes only a few seconds! This slows fusion, so star gets dimmer again. - Then stable He -> C burning. Still have H -> He shell burning surrounding it. - Now star on "Horizontal Branch" of H-R diagram. Lasts ~10 8 years for 1 M Sun star.

8. Core fusion He -> C Shell fusion H -> He Horizontal branch star structure More massive less massive

9. Helium Runs out in Core - - All He -> C. Not hot enough - for C fusion. - - Core shrinks and heats up, as - does H-burning shell. - Get new helium burning shell (inside H burning shell). Red Supergiant - High rate of burning, star expands, luminosity way up. - Called ''Red Supergiant'' (or Asymptotic Giant Branch) phase. - Only ~10 6 years for 1 M Sun star.

11. "Planetary Nebulae" - Core continues to contract. Never hot enough for C fusion. - He shell dense, fusion becomes unstable => “He shell flashes”. - Eventually, shells thrown off star altogether! 0.1 - 0.2 M Sun ejected. - Shells appear as a nebula around star, called “Planetary Nebula” (awful, historical name, nothing to do with planets). - Whole star pulsates more and more violently.

14. White Dwarfs - Dead core of low-mass star after Planetary Nebula thrown off. - Mass: few tenths of a M Sun - Radius: about R Earth - - Density: 10 6 g/cm 3 ! (a cubic cm of it would weigh a ton on Earth). - - Composition: C, O. - White dwarfs slowly cool to oblivion. No fusion.

15. Evolution of Stars > 12 M Sun Higher mass stars fuse heavier elements. Result is "onion" structure with many shells of fusion-produced elements. Heaviest element made is iron. Strong winds. Eventual state of > 12 M Sun star Low mass stars never got past this structure: They evolve more rapidly. Example: 20 M Sun star lives "only" ~10 7 years.

16. Star Clusters Comparing with theory, can easily determine cluster age from H-R diagram. Open Cluster Globular Cluster

17. Following the evolution of a cluster on the H-R diagram 100 L Sun Temperature Luminosity L Sun

18. Globular clusters formed 12-14 billion years ago. Useful info for studying the history of the Milky Way Galaxy. Globular Cluster M80 and composite H-R diagram for similar-age clusters.

19. Schematic Picture of Cluster Evolution Time 0. Cluster looks blue Time: few million years. Cluster redder Time: 10 billion years. Cluster looks red Massive, hot, bright, blue, short-lived stars Low-mass, cool, red, dim, long-lived stars

20. Fusion Reactions and Stellar Mass In stars like the Sun or less massive, H -> He most efficient through proton-proton chain. In higher mass stars, "CNO cycle" more efficient. Same net result: 4 protons -> He nucleus Carbon just a catalyst. Need T center > 16 million K for CNO cycle to be more efficient. (mass) -> Sun

22. Neutron Stars If star has mass 12-25 M Sun, remnant of supernova expected to be a tightly packed ball of neutrons. Diameter: 10 km only! Mass: 1.4 - 3(?) M Sun Density: 10 14 g / cm 3 ! A neutron star over the Sandias? Please read about observable neutron stars: pulsars. Rotation rate: few to many times per second!!! Magnetic field: 10 10 x typical bar magnet!

23. Black Holes and General Relativity The Equivalence Principle Here’s a series of thought experiments and arguments: 1) Imagine you are far from any source of gravity, in free space, weightless. If you shine a light or throw a ball, it will move in a straight line. General Relativity: Einstein's (1915) description of gravity (extension of Newton's). It begins with:

24. 2. If you are in freefall, you are also weightless. Einstein says these are equivalent. So in freefall, light and ball also travel in straight lines. 3. Now imagine two people in freefall on Earth, passing a ball back and forth. From their perspective, they pass it in a straight line. From a stationary perspective, it follows a curved path. So will a flashlight beam, but curvature of light path small because light is fast (but not infinitely so). The different perspectives are called frames of reference.

25. 4. Gravity and acceleration are equivalent. An apple falling in Earth's gravity is the same as one falling in an elevator accelerating upwards, in free space. 5. All effects you would observe by being in an accelerated frame of reference you would also observe when under the influence of gravity.

26. Examples: 1) Bending of light. If light travels in straight lines in free space, then gravity causes light to follow curved paths.

27. Observed! In 1919 eclipse.

28. Gravitational lensing. The gravity of a foreground cluster of galaxies distorts the images of background galaxies into arc shapes.

29. Saturn-mass black hole

30. 2. Gravitational Redshift Consider accelerating elevator in free space (no gravity). time zero, speed=0 later, speed > 0 light received when elevator receding at some speed. light emitted when elevator at rest. Received light has longer wavelength because of Doppler Shift ("redshift"). Gravity must have same effect! Verified in Pound-Rebka experiment. 3. Gravitational Time Dilation Direct consequence of the redshift. Observers disagree on rate of time passage, depending on strength of gravity they’re in.

31. Escape Velocity Velocity needed to escape an object’s gravitational pull. v esc = 2GM R Earth's surface: v esc = 11 km/sec. If Earth shrunk to R=1 cm, then v esc = c, the speed of light! Then nothing, including light, could escape Earth. This special radius, for a particular object, is called the Schwarzschild Radius, R S. R S  M.

32. Black Holes If core with about 3 M Sun or more collapses, not even neutron pressure can stop it (total mass of star about 25 M Sun ?). Core collapses to a point, a "singularity". Gravity is so strong that not even light can escape. R S for a 3 M Sun object is 9 km. Event horizon: imaginary sphere around object, with radius R S. Event horizon RSRS Anything crossing the event horizon, including light, is trapped

33. Like a rubber sheet, but in three dimensions, curvature dictates how all objects, including light, move when close to a mass. Black hole achieves this by severely curving space. According to General Relativity, all masses curve space. Gravity and space curvature are equivalent.

34. Curvature at event horizon is so great that space “folds in on itself”.

35. Effects around Black Holes 1) Enormous tidal forces. 2) Gravitational redshift. Example, blue light emitted just outside event horizon may appear red to distant observer. 3) Time dilation. Clock just outside event horizon appears to run slow to a distant observer. At event horizon, clock appears to stop.

36. Do Black Holes Really Exist? Good Candidate: Cygnus X-1 - Binary system: 30 M Sun star with unseen companion. - Binary orbit => companion > 7 M Sun. - X-rays => million degree gas falling into black hole.

37. 1. White Dwarf If initial star mass < 8-12 M sun. 2. Neutron Star If initial mass > 12 M Sun and < 25 ? M Sun. 3. Black Hole If initial mass > 25 ? M Sun. Final States of a Star