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Review for Test #3 Nov 17
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  1. Review for Test #3 Nov 17 • Topics: • The Sun • Stars • The Interstellar medium • Stellar Evolution and Stellar Death • Neutron stars and pulsars • Methods • Conceptual Review and Practice Problems Chapters 9 - 13 • Review lectures (on-line) and know answers to clicker questions • Try practice quizzes on-line • Review (time Sunday, Nov 15 starting at 3pm) mainly Q&A format • Bring: • Two Number 2 pencils • Simple calculator (no electronic notes) • UNM Student ID • Reminder: There are NO make-up tests for this class

  2. Test #3 Review How to take a multiple choice test 1) Before the Test: • Study hard (~2 hours/day Friday through Monday) • Get plenty of rest the night before • Bring at least 2 pencils, UNM student ID, and a calculator 2) During the Test: • Write out and bubble your last name, space, first name and Exam color in the name space of the scantron form. Write out and bubble your Banner ID in the ID space. • Draw simple sketches to help visualize problems • Solve numerical problems in the margin • Come up with your answer first, then look for it in the choices • If you can’t find the answer, try process of elimination • If you don’t know the answer, Go on to the next problem and come back to this one later • TAKE YOUR TIME, don’t hurry • If you don’t understand something, ask me.

  3. Test #3 Useful Equations parallactic distance d = 1/p where p is parallax in arcsec and d is in parsecs Schwarschild Radius: 2 GM c2 R = Lifetimes of stars (on the main sequence): L = 1010/M2 years where M is the Mass in solar masses and L is the Lifetime Equivalence of Matter and Energy: E = mc2

  4. The Sun The Sun is a star: a shining ball of gas powered by nuclear fusion. Mass of Sun = 2 x 1033 g = 330,000 MEarth = 1MSun Radius of Sun = 7 x 105 km = 109 REarth = 1 RSun Luminosity of Sun = 4 x 1033 erg/s = 1 LSun (amount of energy put out each second in form of radiation, = 1025 40W light bulbs) The Sun in X-rays over several years

  5. Temperature at surface = 5800 K => yellow (Wien’s Law) Temperature at center = 15,000,000 K Average density = 1.4 g/cm3 Density at center = 160 g/cm3 Composition: 74% of mass is H 25% He 1% the rest Rotation period = 27 days at equator 31 days at poles

  6. The Interior Structure of the Sun (not to scale) Let's focus on the core, where the Sun's energy is generated.

  7. Core of the Sun Temperature : 15 million K (1.5 x 107 K) Density: 160 gm/cm3, 160 times that of water, 10 times the density of lead

  8. What Powers the Sun Nuclear Fusion: An event where nuclei of two atoms join together. Need high temperatures. Energy is produced. Elements can be made. nuc. 1 + nuc. 2 → nuc. 3 + energy (radiation) Mass of nuc. 3 is slightly less than mass of (nuc. 1 + nuc. 2). The lost mass is converted to energy. Why? Einstein's conservation of mass and energy, E = mc2. Sum of mass and energy always conserved in reactions. Fusion reactions power stars. Chain of nuclear reactions called "proton-proton chain" or p-p chain occurs in Sun's core, and powers the Sun.

  9. In the Sun's Core... neutrino (weird particle) proton deuteron (proton + neutron bound together) positron (identical to electron but positively charged) proton photon { 1)proton + proton→proton+neutron + neutrino + positron (deuteron) + energy (photon)

  10. 2) deuteron + proton→3He + energy He nucleus, only 1 neutron 3) 3He + 3He →4He + proton + proton + energy Net result: 4 protons →4He + 2 neutrinos + energy Mass of end products is less than mass of 4 protons by 0.7%. Mass converted to energy. 600 millions of tons per second fused. Takes billions of years to convert p's to 4He in Sun's core. Process sets lifetime of stars. Hydrostatic Equilibrium: pressure from fusion reactions balances gravity. Sun is stable.

  11. The Solar Constant If we placed a light detector (a.k.a. solar cell) above the Earth’s atmosphere and perpendicular to the sun’s rays, we can measure how much solar energy is received per square meter (Watts / m2) This is the solar constant => 1400 Watts / m2 About 50-70% of this energy reaches earth So assuming 50% of this energy reaches of this energy reaches earth • Every square meter receives 700 Watts • Solar cells - devices to convert light into electricity are about 20% efficient • So a square meter of solar cells generates 140 Watts • To power a 2,000 sq. ft. house in summer with energy to run washer/dryer etc., need about 14, 000 Watts peak or 100 sq. meter of solar cells

  12. Solar neutrino problem In 1960s Ray Davis and John Bahcall measured the neutrino flux from the Sun and found it to be lower than expected (by 30-50%) Confirmed in subsequent experiments Theory of p-p fusion well understood Solar interior well understood

  13. Answer to the Solar neutrino problem Theoriticians like Bruno Pontecorvo realized There was more than one type of neutrino Neutrinos could change from one type to another Confirmed by Super-Kamiokande experiment in Japan in 1998 50,000 gallon tank Total number of neutrinos agrees with predictions

  14. photon path "surface" or photosphere: gas density low enough so photons can escape into space. "convection zone" some electrons bound to nuclei => radiation can't get through => heats gas, hot gas rises, cool gas falls How does energy get from core to surface? core "radiative zone": photons scatter off nuclei and electrons, slowly drift outwards: "diffusion".

  15. Sunspots Roughly Earth-sized Last ~2 months Usually in pairs Follow solar rotation

  16. Sunspots They are darker because they are cooler (4500 K vs. 5800 K). Related to loops of the Sun's magnetic field. radiation from hot gas flowing along magnetic field loop at limb of Sun.

  17. The Solar Wind At top of corona, typical gas speeds are close to escape speed => Sun losing gas in a solar wind. Wind escapes from "coronal holes", seen in X-ray images. Wind speed 500 km/sec (takes a few days to reach Earth). 106 tons/s lost. But Sun has lost only 0.1% of its mass from solar wind.

  18. Active Regions Prominences: Loops of gas ejected from surface. Anchored in sunspot pairs. Last for hours to weeks. Flares: A more energetic eruption. Lasts for minutes. Less well understood. Solar Flare Video Prominences and flares occur most often at maximum of Solar Cycle.

  19. Measuring the Stars How big are stars? How far away are they? How bright are they? How hot? How old, and how long do they live? What is their chemical composition? How are they moving? Are they isolated or in clusters? By answering these questions, we not only learn about stars, but about the structure and evolution of galaxies they live in, and the universe.

  20. How Far Away are the Stars? Earth-baseline parallax - useful in Solar System Earth-orbit parallax - useful for nearest stars

  21. New distance unit: the parsec (pc). Using Earth-orbit parallax, if a star has a parallactic angle of 1", it is 1 pc away. Remember 1" (arcsecond) = 1/60 arcmin = 1/3600 degrees If the angle is 0.5", the distance is 2 pc. 1 Parallactic angle (arcsec) Distance (pc) = Closest star to Sun is Proxima Centauri. Parallactic angle is 0.7”, so distance is 1.3 pc. 1 pc = 3.3 light years = 3.1 x 10 18 cm = 206,000 AU 1 kiloparsec (kpc) = 1000 pc 1 Megaparsec (Mpc) = 10 6 pc

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

  23. Stellar Sizes - Indirect Method Almost all stars too far away to measure their radii directly. Need indirect method. For blackbodies, use Stefan's Law: Energy radiated per cm2 of area on surface every second a T 4 (T = temperature at surface) And: Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2) So: Luminosity  (temperature) 4 x (surface area) Determine luminosity from apparent brightness and distance, determine temperature from spectrum (black-body curve or spectral lines), then find surface area, then find radius (sphere surface area is 4 p R2)

  24. The Wide Range of Stellar Sizes

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

  26. Increasing Mass, Radius on Main Sequence The Hertzsprung-Russell (H-R) Diagram Red Supergiants Red Giants Sun Main Sequence White Dwarfs

  27. How Long do Stars Live (as Main Sequence Stars)? A star on Main Sequence has fusion of H to He in its core. How fast depends on mass of H available and rate of fusion. Mass of H in core depends on mass of star. Fusion rate is related to luminosity (fusion reactions make the radiation energy). So, mass of star luminosity mass of core fusion rate lifetime   Because luminosity  (mass) 3, mass (mass) 3 1 (mass) 2 or lifetime  So if the Sun's lifetime is 10 billion years, a 30 MSun star's lifetime is only 10 million years. Such massive stars live only "briefly".

  28. Star Clusters Two kinds: 1) Open Clusters -Example: The Pleiades -10's to 100's of stars -Few pc across -Loose grouping of stars -Tend to be young (10's to 100's of millions of years, not billions, but there are exceptions)

  29. 2) Globular Clusters - few x 10 5 or 10 6 stars - size about 50 pc - very tightly packed, roughly spherical shape - billions of years old Clusters are crucial for stellar evolution studies because: 1) All stars in a cluster formed at about same time (so all have same age) 2) All stars are at about the same distance 3) All stars have same chemical composition

  30. The Interstellar Medium (ISM) of the Milky Way Galaxy Or: The Stuff (gas and dust) Between the Stars Why study it? Stars form out of it. Stars end their lives by returning gas to it. The ISM has: a wide range of structures a wide range of densities (10-3 - 107 atoms / cm3) a wide range of temperatures (10 K - 107 K)

  31. Compare density of ISM with Sun or planets: Sun and Planets: 1-5 g / cm3 ISM average: 1 atom / cm3 Mass of one H atom is 10-24 g! So ISM is about 1024 times as tenuous as a star or planet!

  32. ISM consists of gas (mostly H, He) and dust. 98% of mass is in gas, but dust, only 2%, is also observable. Effects of dust on light: 1) "Extinction" Blocks out light 2) "Reddening" Blocks out short wavelength light better than long wavelength light => makes objects appear redder. Grain sizes typically 10-5 cm. Composition uncertain, but probably silicates, graphite and iron.

  33. Gas Structures in the ISM Emission Nebulae or H II Regions Regions of gas and dust near stars just formed. The Hydrogen is essentially fully ionized. Temperatures near 10,000 K Sizes about 1-20 pc. Hot tenuous gas => emission lines (Kirchhoff's Laws)

  34. Rosette Nebula Lagoon Nebula Tarantula Nebula Red color comes from one emission line of H atoms (tiny fraction of H is atoms, not ionized).

  35. Why is the gas ionized? Remember, takes energetic UV photons to ionize H. Hot, massive stars produce huge amounts of these. Such short-lived stars spend all their lives in the stellar nursery of their birth, so emission nebulae mark sites of ongoing star formation. Many stars of lower mass are forming too, but make few UV photons. Why "H II Region? H I: Hydrogen atom H II: Ionized Hydrogen . . . O III: Oxygen missing two electrons etc.

  36. HI in IC 342 from VLA Galaxy IC 342 in visible light H I Gas and 21-cm radiation Gas in which H is atomic. Fills much (most?) of interstellar space. Density ~1 atom / cm3. Too cold (~100 K) to give optical emission lines. Primarily observed through radiation of H at wavelength of 21 cm. H I accounts for almost half the mass in the ISM: ~2 x 109 MSun !

  37. Origin of 21-cm photon: The proton and electron each have “spin”. A result from quantum mechanics: if both spinning the same way, atom's energy is slightly higher. Eventually will make transition to state of opposite spins. Energy difference is small -> radio photon emitted, wavelength 21-cm.

  38. Molecular Gas It's in the form of cold (~10 K) dense (~103 - 107 molecules / cm3) clouds. Molecular cloud masses: 103 - 106 MSun ! Sizes: a few to 100 pc. 1000 or so molecular clouds in ISM. Total mass about equal to H I mass. Optically, seen as dark dust clouds. => Molecular Clouds important because stars form out of them! They tend to be associated with Emission Nebulae.

  39. We can observe emission from molecules. Most abundant is H2 (don't confuse with H II), but its emission is extremely weak, so other "trace" molecules observed: CO (carbon monoxide) H2O (water vapor) HCN (hydrogen cyanide) NH3 (ammonia) etc. . . These emit photons with wavelengths near 1 mm when they make a rotational energy level transition. Observed with radio telescopes.

  40. Gravity makes cloud want to collapse. Outward gas pressure resists collapse, like air in a bike pump. Star Formation Stars form out of molecular gas clouds. Clouds must collapse to form stars (remember, stars are ~1020 x denser than a molecular cloud). Probably new molecular clouds form continually out of less dense gas. Some collapse under their own gravity. Others may be more stable. Magnetic fields and rotation also have some influence.

  41. When a cloud starts to collapse, it should fragment. Fragments then collapse on their own, fragmenting further. End product is 100’s or 1000’s of dense clumps each destined to form star, binary star, etc. Hence a cloud gives birth to a cluster of stars.

  42. As a clump collapses, it heats up. Becomes very luminous. Now a protostar. May form proto-planetary disk. Protostar and proto-planetary disk in Orion 1700 AU Eventually hot and dense enough => spectrum approximately black-body. Can place on HR diagram. Protostar follows “Hayashi tracks”

  43. Finally, fusion starts, stopping collapse: a star! Star reaches Main Sequence at end of Hayashi Track One cloud (103 - 106 MSun) forms many stars, mainly in clusters, in different parts at different times. Massive stars (50-100 MSun) take about 106 years to form, least massive (0.1 MSun) about 109 years. Lower mass stars more likely to form. In Milky Way, a few stars form every year.

  44. Brown Dwarfs Some protostars not massive (< 0.08 MSun) enough to begin fusion. These are Brown Dwarfs or failed stars. Very difficult to detect because so faint. First seen in 1994 with Hubble. How many are there?

  45. 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.

  46. 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 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

  47. Red Giant Star on H-R Diagram

  48. 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 - 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.

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

  50. Helium Runs out in Core • All He -> C. Not hot enough • for C fusion. - Core shrinks and heats up. - 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