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A short course in Stellar Evolution

A short course in Stellar Evolution. Dr. Maura McLaughlin West Virginia University Maura.McLaughlin@mail.wvu.edu July 8 2008 Pulsar Search Collaboratory. Outline. What is a star? (5 minutes) Stellar properties (20 minutes) The HR diagram (20 minutes)

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A short course in Stellar Evolution

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  1. A short course in Stellar Evolution Dr. Maura McLaughlin West Virginia University Maura.McLaughlin@mail.wvu.edu July 8 2008 Pulsar Search Collaboratory

  2. Outline • What is a star? (5 minutes) • Stellar properties (20 minutes) • The HR diagram (20 minutes) • The life cycle of a star (20 minutes) • Supernovae (10 minutes) • Compact objects (20 minutes)

  3. The Amazing Power of Starlight By analyzing the light received from a star, what can we learn? • Brightness • Distance • Temperature • Composition • Size • Masses

  4. 0 Brightness Apparent magnitude scale m1 - m2 = -2.5log10(I1/I2) Betelgeuse Magnitude = 0.41 mag Rigel Magnitude = 0.14 mag For a magnitude difference of 0.41 – 0.14 = 0.27, we find an intensity ratio of (2.5)0.27 = 1.28

  5. 0 Distance 1 parsec (3.23 light years) is an angle of 1 arcsecond Distance in parsecs = 1 / (Angle in arcseconds) Absolute magnitude an object would have at 10 pc Betelgeuse Magnitude = 0.45 mag M = m - 5(log10D - 1) Rigel Magnitude = 0.18 mag

  6. 0 Distance Back to our example of Betelgeuse and Rigel: Betelgeuse Rigel Difference in absolute magnitudes: 6.8 – 5.5 = 1.3 => Luminosity ratio = (2.512)1.3 = 3.3

  7. Question An astronomer measures a stellar parallax to be 0.25 milli-arcseconds. The distance to the star is therefore… (a) 4 parsecs (b) 4 kilo-parsecs (c) 4 Mega-parsecs (d) 4 Giga-parsecs

  8. 0 Luminosities Luminosity is the amount of energy a body radiates per unit time.For two objects of the same apparent brightness, Betelgeuse Magnitude = 0.45 mag L1/L2=(D1/D2)2 Rigel Inverse square law Magnitude = 0.18 mag

  9. Question The Sun has an apparent magnitude of -26.7 as measured from Earth. What would the apparent magnitude be as measured from Saturn (10 AU) (a) -26.7 (b) -31.7 (c) -21.7 (d) -16.7

  10. 0 Temperatures The light from a star is usually concentrated in a rather narrow range of wavelengths. The spectrum of a star’s light is approximately a thermal spectrum called a blackbody spectrum. A perfect blackbody emitter would not reflect any radiation. Thus the name ‘blackbody’. Betelgeuse Magnitude = 0.45 mag Rigel Magnitude = 0.18 mag

  11. 0 Temperatures The hotter an object is, the more luminous it is. Intensity is proportional to T4. Betelgeuse Magnitude = 0.45 mag 2. The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases. Wien’s displacement law: lmax≈ 3,000,000 nm / TK (where TK is the temperature in Kelvin). Rigel Magnitude = 0.18 mag

  12. 0 Temperatures B band The color of a star is measured by comparing its brightness in two different wavelength bands. The bluer a star appears, the smaller the color index B – V. The hotter a star is, the smaller its color index B – V. V band

  13. 0 Question Orion Which star has a smaller color index?? Betelgeuse Rigel

  14. Compositions Spectral lines are the absorption of photons at discrete energy levels. Temperatures too high produce higher energy photons which ionize all hydrogen. Temperatures too low do not produce enough excitation into higher energy states.

  15. Compositions

  16. 0 Spectral Classes

  17. 0 Spectral Classes Sun is a G2 star!!

  18. 0 Mnemonics to remember the spectral sequence:

  19. 0 Sizes We already know that hotter stars are brighter. But brightness also increases with size! Star B will be brighter than star A, even if they have the same temperature. A B Quantitatively: L = 4 p R2s T4 Surface flux due to a blackbody spectrum Surface area of the star

  20. 0 Question Polaris has just about the same spectral type (and thus surface temperature) as our sun, but it is 10,000 times brighter than our sun. How much larger is it than our Sun?

  21. 0 Masses Recall Kepler’s 3rd Law: Py2 = aAU3 Valid for the solar system: star with 1 solar mass in the center. We find almost the same law for binary stars with masses MA and MB different from 1 solar mass: aAU3 ____ MA + MB = Py2 (MA and MB in units of solar masses)

  22. 0 Examples: a) Binary system with period of P = 32 years and separation of a = 16 AU: 163 ____ MA + MB = = 4 solar masses. 322 b) Any binary system with a combination of period P and separation a that obeys Kepler’s 3rd Law must have a total mass of 1 solar mass. c) Since we also know MA/MB = rA/rB, we can solve for masses.

  23. What can we learn about the Sun? 0 • Average star • Spectral type G2 • Only appears so bright because it is so close. • Absolute visual magnitude = 4.83 (magnitude if it were at a distance of 32.6 light years) • 109 times Earth’s diameter • 333,000 times Earth’s mass • Consists entirely of gas (av. density = 1.4 g/cm3) • Central temperature = 15 million K • Surface temperature = 5800 K

  24. 0 Organizing the Family of Stars: The Hertzsprung-Russell Diagram Example: useful way to understand populations

  25. 0 Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of Luminosity versus Temperature (or spectral type) Absolute mag. Hertzsprung-Russell Diagram or Luminosity Temperature Spectral type: O B A F G K M

  26. The Hertzsprung Russell Diagram 0 Most stars are found along the mainsequence

  27. The Hertzsprung Russell Diagram 0 Same temperature, but much brighter than MS stars Must be much larger Stars spend most of their active life time on the Main Sequence. Giant Stars Same temp., but fainter → Dwarfs

  28. 0 Radii of Stars in the HR Diagram 1,000 times the Sun’s radius 100 times the Sun’s radius As large as the Sun 100 times smaller than the Sun

  29. Masses of Stars in the Hertzsprung-Russell Diagram 0 The higher a star’s mass, the more luminous (brighter) it is: L ~ M3.5 High-mass stars have much shorter lives than low-mass stars: tlife ~ M-2.5 Sun: ~ 10 billion yr. 10 Msun: ~ 30 million yr. 0.1 Msun: ~ 3 trillion yr.

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  32. 0 A Census of the Stars Faint, red dwarfs (low mass) are the most common stars. Bright, hot, blue main-sequence stars (high-mass) are very rare. Giants and supergiants are extremely rare.

  33. 0 Life Cycle of a Star ?

  34. 0 The Contraction of a Protostar

  35. 0 Evidence of Star Formation Nebula around S Monocerotis (Foxfur) Contains many massive, very young stars, including T Tauri stars: strongly variable; bright in the infrared.

  36. 0 Energy generation in the Sun:Nuclear Fusion Need large proton speed to overcome Coulomb barrier (electromagnetic repulsion between protons). Basic reaction: 4 1H 4He + energy 4 protons have more mass than 4He. T ≥ 107 K = 10 million K • Energy gain = Dm*c2 What reaction rate does Sun need to resist its own gravity?

  37. 0 Hydrostatic Equilibrium Outward pressure force must exactly balance the weight of all layers above everywhere in the star. This condition uniquely determines the interior structure of the star. This is why we find stable stars on such a narrow strip (main sequence) in the HR diagram.

  38. Question a) electrons must be moving quickly to change orbitals b) the high temperature is necessary to fully cook the new atom c) protons need high speeds to overcome repulsive force d) protons need high speeds to overcome gravity Why are high temperatures needed for nuclear fusion?

  39. Masses of Main-Sequence Stars 0 Stars with masses greater than 100 solar masses are unstable. Stars with masses less than 0.08 solar masses cannot fuse hydrogen in their cores - brown dwarfs.

  40. The Life of Main-Sequence Stars 0 Stars gradually exhaust their hydrogen fuel. In this process of aging, they are gradually becoming brighter, evolving off the zero-age main sequence. Death line

  41. 0 The Lifetimes of Stars on the Main Sequence

  42. 0 Expansion onto the Giant Branch Once Hydrogen in the core is completely converted into He, H burning continues in shell. Lots of energy produced -> star expands to form Red Giant. Giants and supergiants are 10-1000 times larger than the Sun and 10 - 106 times less dense. Expansion cools the star and makes it more luminous. Sun will expand beyond Earth’s orbit!

  43. Question After Hydrogen burning in the core of the Sun ends, its SURFACE temperature will ________ and its size will __________. • increase; decrease • decrease; increase • increase; increase • decrease; decrease

  44. 0 Red Giant Evolution H-burning shell keeps dumping He onto the core. He core gets denser and hotter until the next stage of nuclear burning can begin in the core: He fusion through the “triple-alpha process”: 4He + 4He 8Be + g 8Be + 4He 12C + g The onset of this process is termed the helium flash

  45. Hyades Star Cluster 0 Open cluster in constellation Taurus. About 100 stars.

  46. HR Diagram of Hyades 0 High-mass stars evolved onto the giant branch Turn-off point Low-mass stars still on the main sequence

  47. 0 Estimating the Age of a Cluster The lower on the MS the turn-off point, the older the cluster.

  48. 0 Endpoints of stellar evolution… Depends almost completely on its mass. Let’s start with the least massive stars and go to the most!

  49. 0 Red Dwarfs (0.08 - 0.4 solar masses) Stars with less than ~ 0.4 solar masses are completely convective. Hydrogen and helium remain well mixed throughout the entire star. No phase of shell “burning” with expansion to giant. Star not hot enough to ignite He burning. Could live for 100 billion yrs or more! Universe only 14 billion years old so can’t test this though…

  50. 0 Sunlike Stars Sunlike stars (~ 0.4 – 8 solar masses) develop a helium core. Expansion to red giant during H burning shell phase Ignition of He burning in the He core  Formation of a degenerate C,O core

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