Selected Questions from Minute Papers

1. Selected Questions from Minute Papers • Black Holes: • Will all the material in the Milky Way eventually be sucked into the BH at the center? • Does the star that “gives up” mass to a BH eventually get pulled in to the BH? • Star properties: • If Betelgeuse is so much more luminous than the sun, why isn’t it hotter than the sun? • Is it more difficult to measure the distances that are farther away (because the parallax is very small)? • Binary Stars: • How do you know there are 2 stars (since you can’t see 2 stars)? • Why are binary stars so very common? • Can binary stars have planets around them?

2. Outline - March 2, 2010 • Stellar properties recap • “Spectral Type” for stars (pgs. 525-527) • Hertzsprung-Russel Diagram (pgs. 530-533) • How does the sun shine? (pgs. 495-497, 499-503) • Lifetimes of stars: gas guzzlers vs. econoboxes (pgs. 533-534) • Where are the oldest known stars? (pgs. 536-538)

3. Stellar Properties Recap Luminosity (from L = 4 b d2) factor of about 10 billion: 10-4 Lsun to 106 Lsun Temperature (from T = 0.29 / max) factor of about 10: 3,000 K to 30,000 K Radius (from R = {L / 4 T4}1/2) factor of about 50,000: 0.01 Rsun (white dwarf) to 500 Rsun (supergiant) Mass (from “spectroscopic” binary stars) factor of about 1,800: 0.08 Msun (smaller = can’t run nuclear fusion) to 150 Msun (larger = pressure overwhelms gravity)

4. Stellar Properties Just because a star has a radius that is bigger than the sun doesn’t necessarily mean that it is more massive than the sun! Just because a star is more luminous than the sun doesn’t necessarily mean that it is more massive than the sun! Just because a star is hotter than the sun, doesn’t necessarily mean that it is more massive than the sun! It turns out that this is due to the fact that the radius, temperature and luminosity of stars evolve over time…

5. Patterns to the StarsStellar Spectra Depending upon the surface temperature of the star, you see different absorption lines. The hottest stars show strong Helium lines, stars with T = 10,000 K show the strongest Hydrogen lines, and the very coolest stars show strong lines due to molecules (like titanium oxide). This is really is a temperature effect, it is not reflective of different chemical composition for the different stars!

6. Spectral Type(Astronomers like to classify things / put them in bins) The letters O, B, A, F, G, K, M are called the “spectral type” of the star and describe the appearance of the spectrum (i.e., strong helium lines but weak hydrogen lines, strong hydrogen lines but no helium lines). The spectral type classifications are historical and come from a time when we didn’t know that the different spectra were due to different stellar temperatures. The notation persists today, though! Time-honored mnemonic: “Oh Be A Fine Girl/Guy, Kiss Me”

7. Hertzprung-Russel (H-R) Diagram for Stars Take a huge random sample of stars and plot up their luminosity (vertical) and their surfacetemperature / spectral type (horizontal, with T increasing to the LEFT). Remarkably, you don’t get a random plot at all! Roughly 90% of all stars fall on “the Main Sequence”. These are stars that produce energy by fusion of hydrogen (E = mc2). Any star that is not on the Main Sequence is getting close to the end of its life.

8. How do stars shine?Sun as a typical example Ideas that don’t work: Flame (like coal or wood) - can’t account for sun’s observed luminosity and can’t produce energy for very long Gravitational contraction (“shrinking sun”) - could only last for 25 million years, plus violates observations of the sun Sun has been generating about 3.84x1026 W of power (more or less) every day for about 4.5 billion years!!

9. slower faster slower Sun cannot be solid Rotation time is 30 days at the poles and 25 days at the equator (“differential rotation”)

10. Solar Properties Radius = 696,000 km (about 109 times radius of Earth) Mass = 2x1030 kg (about 300,000 times mass of Earth) Luminosity = 3.8x1026 W Composition (by mass) = 70% hydrogen, 28% helium, 2% heavier elements Surface temperature = 5,800 K Core temperature = 15x106 K Core average density = 36 g / cm3 (about 3 times density of lead) Core pressure = about 200 billion “atmospheres” (pressure at sea level is 1 atmosphere; pressure deep in the ocean is hundreds of atmospheres)

11. All “Main Sequence” Stars are Stable (not expanding or contracting by large amounts) Pressure pushing out exactly balancing gravity pulling in: “gravitational equilibrium” Energy generation takes place in the core only for main sequence stars (e.g., the sun) Only in the core is it sufficiently hot and dense for nuclear fusion (“nuclear burning”) to occur!! In the sun, the core is about 25% of the diameter and contains about 40% of the total mass.

12. E = mc2There is a tremendous amount of energy associated with mass! For about the first 90% of a star’s lifetime, it lives on the Main Sequence of the H-R diagram, “burning” hydrogen. Properly, the star converts hydrogen into helium through nuclear fusion (but astronomers are notoriously casual about the language). In the core, it is too hot and too dense for “atoms” to exist. Instead, you have “bare nuclei swimming in a sea of electrons”

13. Pause to reflect… What are the nuclei of atoms made of? What actually holds them together? Gravity is MUCH too weak to overcome mutual repulsion of protons!!

14. The Strong Force The “strong force” is truly the strongest force in nature, but it is extremely short-range. Strong force is only effective over lengths comparable to the size of atomic nuclei (10-15 m or so); actually limits how big nuclei of atoms can be! If you can get 2 protons within about 10-15 m of each other, the strong force can “bind” them together (“nuclear fusion”). Key: high temperature (protons moving FAST) and high density (many, many protons all in the same place).

15. Proton-Proton Chain(all stars with M < 8 Msun) Net result: 4 protons are fused, producing 1 helium nucleus

16. So where does the energy come from???? The mass of 4 protons is greater than the mass of 1 helium nucleus. The mass that is lost is converted into energy (in the form of light). The sun (and all stars that are not white dwarfs or “neutron stars”) are very slowly losing mass in order to power themselves. Note: only a tiny amount of mass is actually lost. By the end of its lifetime the sun will have lost about about 10% of its total mass to energy generation.

17. In principle, how long could the sun last by “burning” hydrogen at its present rate? Mass of 4 protons = 6.690x10-27 kg Mass of 1 helium nucleus = 6.643x10-27 kg Mass lost (mlost) = 0.047x10-27 kg Energy gained = mlost c2 = (0.047x10-27)(3.0x108)2 = 4.23x10-12 J Energy produced by the sun every second = 3.8x1026 J Sun must run this fusion reaction 8.9x1037 times every second or it would collapse under gravity!!!! In other words, the sun must fuse 6.0x1011 kg of hydrogen every single second. That’s a lot of hydrogen, but the sun has a lot of mass…

18. In principle, how long could the sun last by “burning” hydrogen at its present rate? The sun must fuse 6.0x1011 kg of hydrogen every single second. The sun’s mass is 1.99x1030 kg, and at a current age of 4.5x109 years, we know that 70% of that mass is in hydrogen, or 1.39x1030 kg of hydrogen remains. If the sun converted ALL of it remaining hydrogen into helium (at today’s rate of “nuclear burning”), how much longer could the sun live? Remaining lifetime in seconds = remaining H mass / rate of H fusion Remaining lifetime in seconds = 1.39x1030 / 6.0x1011 = 2.32x1018 seconds Remaining lifetime in years = 73.4 billion years!!

19. In principle, how long could the sun last by “burning” hydrogen at its present rate? So, if the sun could turn ALL of its hydrogen into helium at its present rate, you would think the sun would live a total of (4.5 + 73.4) = 77.9 billion years. But, sadly, the sun’s lifetime is limited to only about 10 billion years because it can’t actually convert all of its hydrogen into helium. HUGE structural changes will happen to the star long before it can “burn up” all of its hydrogen.

20. What determines a star’s Main Sequence lifetime? It’s all about MASS. The more massive is a star, the hotter and denser is the star in its core. The hotter and denser it is in a star’s core, the FASTER the conversion of hydrogen to helium happens. High-mass (> 8 Msun) stars are “gas guzzlers” Low-mass (< 2 Msun) are “economy cars”

21. Main Sequence is a MASS Sequence The highest mass stars live only a few million years. They have a lot of fuel and they’re burning it really fast. The lowest mass stars live for 100’s of billions of years. They have very little fuel, but they’re burning it extremely efficiently.

22. Estimating the Age of the Universe(What are stars “good for”?) It stands to reason that you are younger than your mother. It therefore stands to reason that the objects within the universe cannot be older that the universe itself. The ages of the oldest stars puts a limit on the minimum age of the universe!!

23. The Oldest Stars in the Milky WayGlobular Star Clusters Spherical groupings of 10,000 to 1 million stars (about 158 known in our Galaxy). All of the stars formed at roughly the same time. Globular clusters have lots of RED stars, but no BLUE stars (because they died long ago and were not “replenished”).

24. Globular Cluster H-R Diagram Globular Cluster M55 Globular clusters have short, stubby main sequences that “turn off” to the red giant region. The “turn off” point tells you the approximate age.

25. Oldest Stars in the Milky Way Globular cluster M4 is one of the oldest known star clusters (about 13 billion years old), and contains many white dwarfs (the dead cores of low-mass stars that used up all their fuel).