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Final exam

Final exam. 40% - new material Ch. 15-18, 60% - previous chapters All - multiple choice questions Bring green scantron form 1/3 numerical problems, 2/3 concepts Don’t forget to prepare formula sheets Bring your calculator Textbook and lecture notes are not allowed. Preparing to the test.

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Final exam

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  1. Final exam • 40% - new material Ch. 15-18, 60% - previous chapters • All - multiple choice questions • Bring green scantron form • 1/3 numerical problems, 2/3 concepts • Don’t forget to prepare formula sheets • Bring your calculator • Textbook and lecture notes are not allowed

  2. Preparing to the test • Pay extra attention to the following: • Your tests 1-3 • Homework problems • Formula sheets indicating the meaning and units for all formulas • Test reviews • Summary and review questions in the end of each chapter

  3. Chapters 1-3 • Scale of different objects: planets, sun, orbits of planets, interstellar distances, Milky Way galaxy, distances between galaxies, Universe • No need to memorize exact numbers, but try to remember the order of magnitude! • It will help you to check whether your answers make sense

  4. Distance scale 107 m planets 109 m Sun and stars 1011 m ~ 1 AU Solar System 1021 m ~ 10 kpc galaxy 1022 m ~ 1 Mpc Distance between galaxies 1017 m ~ 3 pc distance between stars 1025 m ~ 500 Mpc Largest structure 1026 m ~ Gpc Hubble radius Definitions and meaning of new units: AU, pc, kpc, Mpc

  5. 90o-L Celestial equator

  6. Seasons - summary • Seasons are NOT caused by varying distances from the Earth to the Sun • The primary cause of seasons is the 23.5 degree tilt of the • Earth's rotation axis with respect to the plane of the ecliptic. The Seasons in the Northern Hemisphere Note: the Earth is actually closest to the Sun in January 4! Perihelion: 147.09 × 106 km; Aphelion: 152.10 × 106 km

  7. Eclipses

  8. Moon’s orbit is tilted by 5o from the ecliptic

  9. L D  Small Angle Formula Convert from radian to arcseconds: • radian = 180 degrees 1 deg = 60 arcmin = 3600 arcsec Note units!!

  10. Relationship between magnitudes and intensities Define the magnitude scale so that two stars that differ by 5 magnitudes have an intensity ratio of 100.

  11. Chapters 4,5 • Galileo and his discoveries • Kepler’s laws, especially the third law • Newton’s accomplishments • Gravity force • Application to the orbital motion

  12. Elliptical orbits Remember parameters: perihelion, aphelion, semimajor axis a = (Rp + Ra)/2

  13. LAW 3: The squares of the periods of the planets are proportional to the cubes of their semimajor axes: For the Earth P2 = 1 yr, a2 = 1 AU Note units!!

  14. m r M Uniform circular motion III Kepler’s law:

  15. Chapters 6,7 • Telescope powers • Different types of telescopes • Electromagnetic spectrum • Black body radiation • Doppler effect • Spectral classes of stars

  16. Refracting/Reflecting Telescopes Refracting Telescope: Lens focuses light onto the focal plane Focal length Reflecting Telescope: Concave Mirror focuses light onto the focal plane Focal length Almost all modern telescopes are reflecting telescopes.

  17. Telescope parameters • Light-gathering power (ability to see faint objects) • Resolving power (ability to see fine details) • Magnification (least important)

  18. Two Laws of Black Body Radiation 1. The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases. Wien’s displacement law: lmax≈ 3x106 nm / T(K) (where T(K) is the temperature in Kelvin).

  19. L = A*s*T4 Two Laws of Black Body Radiation 2. The hotter an object is, the more luminous it is. The Stefan-Boltzmann law: Radiation Flux, or power emitted by unit area of a black-body emitter, is proportional to the fourth power of its surface temperature: s = Stefan-Boltzmann constant Luminosity, or total radiated power: whereA = surface area

  20. (Observed wavelength - Rest wavelength) Shift z = (Rest wavelength) The Doppler effect: apparent change in the wavelength of radiation caused by the motion of the source Doppler effect:

  21. The Doppler Effect (2) The Doppler effect allows us to measure the source’s radial velocity. vr

  22. The Doppler Effect (3) Take l0 of the Ha (Balmer alpha) line: l0 = 656 nm Assume, we observe a star’s spectrum with the Ha line at l = 658 nm. Then, Dl = 2 nm. We findDl/l0 = 0.003 = 3*10-3 Thus, vr/c = 0.003, or vr = 0.003*300,000 km/s = 900 km/s. The line is red shifted, so the star is receding from us with a radial velocity of 900 km/s.

  23. Spectral Classification of Stars (2) Mnemonics to remember the spectral sequence:

  24. Sun - basic facts • What is the Sun • Internal structure and composition • Source of energy • Lifetime • Sun’s activity and variability Spectral class: G2 Surface temperature: 5800 K Lifespan: 10 billion years Composition by mass: ~ 71% Hydrogen, 27% Helium

  25. Proton-proton cycle

  26. The CNO Cycle In stars slightly more massive than the sun, a more powerful energy generation mechanism than the PP chain takes over: The CNO Cycle.

  27. Net result is the same: four hydrogen nuclei fuse to form one helium nucleus; 27 MeV is released. Why p-p and CNO cycles? Why so complicated? Because simultaneous collision of 4 protons is too improbable

  28. Energy Transport Structure Inner convective, outer radiative zone Inner radiative, outer convective zone CNO cycle dominant PP chain dominant

  29. Absolute magnitude Recall that for two stars 1 and 2 Let star 1 be at a distance d pc and star 2 be the same star brought to the distance 10 pc. Then m2 = M Inverse: Note also:

  30. H-R diagram • 90% of stars are on the main sequence and obey the mass-luminosity dependence L ~ M3.5 • Most stars are lower main sequence red dwarfs • Stars on the main sequence generate energy due to nuclear fusion of hydrogen • In the end of their lives stars move to the upper right corner of the H-R diagram

  31. The mass-luminosity relation for 192 stars in double-lined spectroscopic binary systems. L ~ M3.5only for main-sequence stars!

  32. Amount of hydrogen fuel Lifetime = Rate of energy loss Lifetime T ~ M/L ~ 1/Mp-1 = 1/M2.5 ; p ~ 3.5 T ~ 3x108 years M = 4M;

  33. Estimating the Age of a Cluster Age of a cluster = lifetime of stars on the turnoff point The lower on the MS the turn-off point, the older the cluster.

  34. Measuring diameters and masses Binary Stars More than 50 % of all stars in our Milky Way are not single stars, but belong to binaries: Pairs or multiple systems of stars which orbit their common center of mass. If we can measure and understand their orbital motion, we can estimate the stellarmasses.

  35. Estimating Stellar Masses RecallKepler’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)

  36. 0 Deaths of stars

  37. Summary of Post Main-Sequence Evolution of Stars Supernova Fusion proceeds; formation of Fe core. Evolution of 4 - 8 Msun stars is still uncertain. Mass loss in stellar winds may reduce them all to < 4 Msun stars. M > 8 Msun Fusion stops at formation of C,O core. M < 4 Msun Red dwarfs: He burning never ignites M < 0.4 Msun

  38. Evolution of sun-like stars: red giant, planetary nebula, white dwarf • Evolution of massive stars: red giant or supergiant, supernova • Three types of compact objects – stellar remnants: white dwarfs, neutron stars, black holes. Limits on their masses. Pulsars as rotating neutron stars • Compact objects in binary systems. Accreting X-ray binaries

  39. Compact Objects with Disks and Jets White dwarfs, black holes and neutron stars can be part of a binary system. Matter gets pulled off from the companion star, forming an accretion disk. => Strong X-ray source! Infalling matter heats up to billions K. Accretion is a very efficient process of energy release.

  40. Continuing cycle of stellar evolution

  41. The Structure of the Milky Way (1) Disk Nuclear Bulge Sun Halo Globular Clusters

  42. Cepheid Variables: The Period-Luminosity Relation The variability period of a Cepheid variable is correlated with its luminosity. The more luminous it is, the more slowly it pulsates. => Measuring a Cepheid’s period, we can determine its absolute magnitude!

  43. Measuring the mass of the Galaxy Rotation curve

  44. Matter extends beyond the visible disk!

  45. Dark matter halo

  46. Ages of the stars Two populations of stars Walter Baade 1893-1960 Their main difference is in chemical composition Population I – metal-rich Population II – metal-poor Metals: all elements heavier than helium

  47. Stellar Populations Population I: Young stars: metal rich; located in spiral arms and disk Population II: Old stars: metal poor; located in the halo (globular clusters) and nuclear bulge

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