Spectral Classes

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

2. Increasing Mass, Radius on Main Sequence The Hertzsprung-Russell (H-R) Diagram Red Supergiants Red Giants Sun Main Sequence White Dwarfs 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 Msun , focus on 1 Msun case) - All H converted to He in core. - Core too cool for He burning. Contracts. Heats up. - H burns in hot, dense shell around core: "H-shell burning phase". - Tremendous energy produced. Star must expand. - Star now a "Red Giant". Diameter ~ 1 AU! - Phase lasts ~ 109 years for 1 MSun star. - Example: Arcturus Red Giant

6. Red Giant Star on H-R Diagram

7. Eventually: Core Helium Fusion - Core shrinks and heats up to 108 K, helium can now burn into carbon. "Triple-alpha process" 4He + 4He -> 8Be + energy 8Be + 4He -> 12C + 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 ~108 years for 1 MSun star.

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

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). - High rate of burning, star expands, luminosity way up. - Called ''Red Supergiant'' (or Asymptotic Giant Branch) phase. - Only ~106 years for 1 MSun star. Red Supergiant

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

14. White Dwarfs - Dead core of low-mass star after Planetary Nebula thrown off. - Mass: few tenths of a MSun - Radius: about REarth • - Density: 106 g/cm3! (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 MSun Low mass stars never got past this structure: Eventual state of > 12 MSun star Higher mass stars fuse heavier elements. Result is "onion" structure with many shells of fusion-produced elements. Heaviest element made is iron. Strong winds. They evolve more rapidly. Example: 20 MSun star lives "only" ~107 years.

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

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

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

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

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 Tcenter > 16 million K for CNO cycle to be more efficient. Sun (mass) ->

22. Neutron Stars If star has mass 12-25 MSun , remnant of supernova expected to be a tightly packed ball of neutrons. Diameter: 10 km only! Mass: 1.4 - 3(?) MSun Density: 1014 g / cm3 ! Rotation rate: few to many times per second!!! Magnetic field: 1010 x typical bar magnet! A neutron star over the Sandias? Please read about observable neutron stars: pulsars.

23. Black Holes and General Relativity General Relativity: Einstein's (1915) description of gravity (extension of Newton's). It begins with: 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.

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 light received when elevator receding at some speed. later, speed > 0 Consider accelerating elevator in free space (no gravity). Received light has longer wavelength because of Doppler Shift ("redshift"). Gravity must have same effect! Verified in Pound-Rebka experiment. time zero, speed=0 light emitted when elevator at rest. 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. 2GM R vesc = Earth's surface: vesc = 11 km/sec. If Earth shrunk to R=1 cm, then vesc = c, the speed of light! Then nothing, including light, could escape Earth. This special radius, for a particular object, is called the Schwarzschild Radius, RS. RSM.

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

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

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 MSun star with unseen companion. - Binary orbit => companion > 7 MSun. - X-rays => million degree gas falling into black hole.

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