Exam 3 Study Guide
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Date Created: 11/16/15
EXAM III STUDY GUIDE (Chapters 7-14) Atomic Spectra: Identifying Atoms by Their Light; The Doppler Shift: 1. Atomic model. 2. Electrons and nucleus. 3. How a Spectrum is Formed a. Continuous b. Absorption 4. Excitations of Atoms a. An atom in which an electron has moved from a lower to a higher orbit. 5. Identifying Atoms by a. Their Light b. Types of Spectra c. Blackbody Radiation: Radiation emitted by a hypothetical perfect radiator; the spectrum is continuous, and the wavelength of maximum emission depends only on the body’s temperature. 6. The Doppler shift, relation to radial velocity. a. Definition: The change in the wavelength of radiation relative radial motion of source and observer. b. Relation to radial velocityThe second point to remember is that the Doppler shift is sensitive only to the part of the velocity directed away from you or toward you—the radial velocity . You cannot use the Doppler effect to detect any part of the velocity that is perpendicular to your line of sight c. Short wavelengths: Blue d. Long wavelengths: Red The Sun: 1. Size and Structure, interior (core); a. diameter 1,392,000 km 2. Chemical Composition (main elements). a. Hydrogen and helium 3. Atmosphere a. Photosphere: visible bright surface of the sun b. Chromosphere: bright gases just above the photosphere of the sun c. Corona: The faint outer atmosphere of the Sun; composed of low-density, very hot, ionized gas. 4. Energy transfer Mechanisms (radiation, convection). a. Radiation: inner energy b. Convection: Circulation in a fluid driven by heat; hot material rises, and cool material sinks. Outer energy 5. Solar Wind. a. Rapidly moving atoms and ions that escape from the solar corona and blow outward through the Solar System. b. ~400 km/s c. aurora borealis in the north and d. aurora australis in the south 6. Stability of the Sun (hydrostatic equilibrium). a. Hydrostatic Equilibrium: The balance between the weight of the material pressing downward on a layer in a star and the pressure in that layer. 7. Temperature of the Sun a. 16 million K The Sun Source of Power 1. Einstein’s Relationship between Mass and Energy a. Mass and energy is neither created nor destroyed 2. Modern theory of the Sun’s Energy Generation: a. Nuclear Fusion; Reaction that joins the nuclei of atoms to form more massive nuclei. i. Hans Bethe b. Sun’s Core; c. Matter and Anti-matter; i. Matter composed of antiparticles, which on colliding with a matching particle of normal matter annihilate and convert the mass of both particles into energy. The antiproton is the antiparticle of the proton, and the positron is the antiparticle of the electron. d. Proton’s and Electrons Version’s of Antimatter. 3. The Conversion of Hydrogen into Helium a. The fusion reaction in the Sun combines four hydrogen nuclei to make one helium nucleus 4. P-P Chain Reaction; a. A series of three nuclear reactions that build a helium atom by adding together protons; the main energy source in the Sun. 5. Mass Loss in Fusion Reactions a. Because one helium nucleus has 0.7 percent less mass than four hydrogen nuclei, it seems that some mass vanishes in the process. b. That mass difference, kg, does not actually disappear but is converted to energy according to Einstein’s famous equation (look back to Chapter 5): 6. Nuetrinos. Solar Activity. 1. Sunspots Features (magnetic field, temperature). a. Sun's surface sprinkled with small dark regions - sunspots. (cold temperature) b. Darker because they are cooler by c. 1000 to 1500 K than photosphere. d. Can last a few days or few months. i. Magnetic field: 1. Found by observation of Zeeman effect. 2. Zeeman effect: magnetic fields split spectral lines 3. studied in laboratory by atomic physicists 2. Sun Activity: a. Ejections b. Prominences, i. Bright clouds of gas forming above the sunspots. ii. Quiet – lasts days to several weeks, 40k km iii. Eruptive – lasts a few hours, 300km c. Flares, i. Eruptions more powerful than prominences. ii. Last from a few minutes to a few hours. iii. A lot of ionized material is ejected in a flare. iv. Ions have enough energy to escape the Sun's gravity. d. Coronal Mass Ejections. 3. Sun’s Rotation (different periods at different latitudes). a. differential rotation b. speed depends on latitude c. equator once/25 days d. 30º N once/26.5 days e. 60º N once/30 days 4. Solar Cycle (basic principle) Surveying the Stars. 1. Triangulation: a. Object appears to shift positions compared to the far off background b. parallax: angular shift c. baseline: the distance between the two vantage points d. Angular Shift, e. Parallax Measurements (Why is it Difficult to Measure?) 2. Limits to Parallax Measurements. 3. Arc Seconds. a. arc seconds are used as the unit of the parallax angle. b. 3,600 arc seconds per degree 4. Celestial Distances: a. Meters, b. Light Years, c. Parsecs i. more convenient unit of distance ii. abbreviated “pc”. iii. parsec = distance of a star that has a parallax of one arc second using a baseline of 1 AU. iv. 1 parsec = 206,265 AU = 3.26 LY. v. Nearest star about 1.3 parsecs from the solar system. 5. Radar Measurements. 6. Moving Stars (proper motion, radial velocity, using the Doppler shift to measure radial velocity). Light and Distance. 1. Luminosity, Brightness. a. Luminosity measures total energy emitted by a star per second – power b. Luminosity = power per square meter surface area c. same luminosity: d. single 1000 watt light bulb e. ten 100 watt light bulbs f. stars can be luminous because g. they are hot h. they are large 2. Relationship between Brightness, Luminosity and Distance (the Inverse Square Law). 3. The Magnitude System (basic idea, which magnitude corresponds to a brighter star). 4. The Difference between Absolute and Apparent Magnitudes. a. Apparent brightness of a star observed from the Earth is called the apparent magnitude. b. The apparent magnitude is a measure of the star's flux received by us. c. Examples of apparent magnitudes: d. Sun = -26.7, e. Moon = -12.6, f. Venus = -4.4, g. Sirius = -1.4, h. Vega = 0.00, i. faintest naked eye star = +6.5, j. brightest quasar = +12.8, k. faintest object = +27 to +28. l. Absolute Magnitude: i. Measure of star luminosity. ii. Luminosity is the total amount of energy radiated by the star every second iii. If you measure a star's apparent magnitude and know its absolute magnitude, you can find the star's distance iv. If you know a star's apparent magnitude and distance, you can find the star's luminosity v. A quantity that depends on the star itself, not on how far away it is vi. More important quantity than the apparent brightness vii. need the distance to determine the absolute magnitude The Temperature and Compositions of Stars. 1. Light Absorption in the Photosphere. 2. Using Absorption Lines to Determine the Chemical Composition. a. 3. Stellar Surface Temperatures. 4. Wien’s Law (color and temperature relationship). a. Cool stars will have the peak of their continuous spectrum at long (redder) wavelengths. b. As the temperature of a star increases, the peak of its continuous spectrum shifts to shorter (bluer) wavelengths. 5. Spectral Types (basic principle only). a. Spectral types: OBAFGKMLT b. O-type stars are the hottest c. T-type stars are the coolest d. Each spectral type is subdivided into 10 intervals, e.g., G2 or F5, with 0 hotter than 1, 1 hotter than 2, etc. e. Our Sun is spectral type G2 The Masses of Orbiting Stars. 1. The Importance of Star Masses. 2. Binary Stars – two stars that orbit each other, bound together by gravity. a. Visual Binaries: seen with a telescope b. Spectroscopic Binaries: unseen partner, that shows double absorption lines with appropriately changing Doppler shift. c. Eclipsing Binaries. 3. Measuring Stellar Masses with Binaries (using center of mass, Kepler’s law, Doppler shift). a. Kepler’s law: i. Need semimajor axis, D, and period, P, to measure the sum of masses ii. Use the radial velocity curve iii. Measure the period iv. Measure the velocity v. From 1 and 2 determine the circumference and hence the radius – semimajor axis vi. Get the sum of masses form Kepler’s law vii. Using the ratio of radial velocities get each of the masses separately! b. Doppler shift i. maximum dimness and maximum brightness – get the diameters of both stars if the period and the velocity is known from the Doppler shift. The Sizes of Stars 1. Using Eclipsing Binaries to Measure the Stellar Diameters (light curve). 2. The Stephan – Boltzmann Law: a. Star Luminosity = (Temperature to the fourth power) multiplied by (Surface area – equals to the square of diameter). H-R Diagram: 1. Luminosity-Temperature (orMagnitude-Spectral Class) Relationship a. 2. Main Sequence Stars. 3. Mass-Luminosity Relationship. 4. Outside Main Sequence (giants, white dwarfs) a. Giants: b. White Dwarfs: i. Sirius B – first detected white dwarf, 1862, the Pup of the Dog Star ii. 7% of stars closest to the Sun are white dwarfs iii. 40 Eridani B – 12,000 K, luminosity 1/275 L Sun radius is about the Earth radius, but the mass is 0.43 M , Su3 the density is 170,000 Sun’s density, =200 kg/cm iv. White dwarfs – dying stars Unit 59. Stellar Evolution 1. Star Formation Sequence: a. Interstellar Cloud – Protostar – Bipolar Jets (Flows) - Star Birth – Nuclear Synthesis (Main Sequence Star). 2. Low-mass and High-mass Main Sequence Stars. 3. The Stellar Evolution Cycle. Tracking the Position of the Star of the H-R Diagram (where would the star move if it temperature changes, its luminosity?) 4. Red Giants. 5. Basic Definitions a. Variable Stars b. Stellar Wind c. Supernova: i. explosion of rare high-mass stars (5 - 50 times the Sun's mass. d. Planetary Nebula: i. Planetary nebula get their name because some looked like round, green planets in early telescopes. ii. Now known to be entirely different iii. About one or more light years across 1. much larger than our solar system! e. White Dwarfs: i. mass less than 1.4 solar masses ii. Electrons prevent further collapse of the core -- degenerate electron gas. f. Neutron Stars: i. mass between 1.4 and 3 solar masses ii. Neutrons prevent further collapse of the core -- degenerate neutron gas. g. Black Holes: i. Greater than 3 solar masses -- star collapses to a point ii. Escape velocity around the point mass is greater than the speed of light iii. Event horizon--The distance at which the escape velocity equals the speed of light is called the event horizon Star Formation. Main Sequence Stars. Dust and Gas in Space 1. Molecular Clouds a. Density from hundreds to thousand particles per cubic centimeter. b. Called Molecular Clouds c. Very dense (compared to the rest of IM) d. Very cold - only a few degrees above absolute zero. e. Main gas: Molecular Hydrogen (difficult to detect) f. CO is 10,000 less common but is a strong source of emission at 2.6 mm g. 150 other molecules detected and studied (OH, N O, .2.) h. Cooling by infrared radiation (CO) 2. Interstellar Dust a. dark regions seemingly empty of stars b. not voids – dark clouds c. dark nebula block light from stars behind them d. composed of tiny sand grains e. dust flakes or needles of graphite and silicates f. coated with water ice g. formed in the cool outer layers of red giant stars and dispersed by stellar winds h. visible only in infrared i. IR satellites IRAS, Hubble 3. Molecular Clouds form Protostars. 4. Bipolar Jets (Flows) from Protostars. 5. Stellar Mass Limit. 6. Main Sequence Stars: a. Hydrostatic Equilibrium. 7. Zero Age Main Sequence. a. point at which star first reaches maturity as a main sequence star b. moving to left – temperature is increasing 8. Lifetime of a Star a. Stage 1: Giant Molecular Cloud – cold dust clouds in space b. Clumps (dust bunnies) accrete matter from cloud to form Protostar c. Stage 2: Protostar – energy generated by gravitational collapse d. Stage 3: Wind formation – protostar produces strong solar winds e. winds eject much of the surrounding cocoon gas and dust f. winds blow mostly along the rotation axes g. Stage 4: Main Sequence -- the new star becomes stable h. Equilibrium: hydrogen fusion into helium in the core balances gravity. i. Stage continues until most of the hydrogen in the core is used up. j. Stage 5: Red Giant k. collapse: fusion stops when the hydrogen in the core runs out l. shell burning: hydrogen shell surrounding the core ignites m. star begins to expand it becomes a subgiant and then a red giant n. Stage 6: Core Fusion o. helium fusion begins in the core p. star passes through a yellow giant phase as the He fusion begins q. equilibrates as a red giant or supergiant r. Stage 7: Stellar Nucleosynthesis – fusion of heavier elements (up to iron) s. core fuel in stage 6 runs out and collapse resumes t. fusion of heavier elements may ignite if star is sufficiently massive u. Stage 8: Planetary Nebula or Supernova -- the outer layers of the red giant are ejected and the core shrinks to its terminal state. Large amounts of mass lost. v. Planetary nebula: common low-mass stars (0.08 - 5 times the mass of the Sun) w. Outer layers are ejected as radiation from core pushes carbon and silicon grains in the cool outer layers x. Core forms a white dwarf. y. Supernova: explosion of rare high-mass stars (5 - 50 times the Sun's mass. z. Superheated gas is blasted into space carrying heavy elements aa. Expanding shock wave crashes into the interstellar medium, heating it to luminescence ab. Core forms a neutron star. ac.Stage 9: Core Remnant -- remains of the core after outer layers are ejected ad. White Dwarf ae. mass less than 1.4 solar masses af. Electrons prevent further collapse of the core -- degenerate electron gas. ag. Neutron Star ah. mass between 1.4 and 3 solar masses ai. Neutrons prevent further collapse of the core -- degenerate neutron gas. aj. Black Hole ak. Greater than 3 solar masses -- star collapses to a point al. Escape velocity around the point mass is greater than the speed of light am. Event horizon--The distance at which the escape velocity equals the speed of light is called the event horizon 9. The Rate of Fuel Consumption. (Why do Lighter Stars Live Longer then Massive Stars?) Giant Stars 1. Hydrogen Exhaustion in the Core. 2. Shell Burning (Fusion) a. shell layer outside the core hot and dense enough for fusion to start b. fusion in the layer just outside the core is called shell burning c. shell fusion is very rapid because the shell layer is still compressing and increasing in temperature d. luminosity of the star increases from its main sequence value e. Gas surrounding the core puffs outward under the action of the extra outward pressure f. The star expands and becomes a subgiant and then a red giant. g. surface has a red color because star is puffed out and cooler h. red giant is very luminous because of its huge surface area 3. Red Giant Branch. a. 4. Helium Fusion a. helium fusion starts at 100 million K 4 12 b. triple alpha process: three He C 5. Electron Degeneracy. 6. Helium Flash a. helium flash: onset of helium fusion produces a burst of energy b. reaction rate settles down c. yellow giant 7. High-mass and Low-mass Stars. a. Planetary nebula: low mass star (.08-5 x the mass of the Sun) b. Supernova: high mass stars (5-50x the Sun’s mass) Variable Stars. 1. Cepheid Variables. (Why do they vary?). a. large yellow pulsating stars b. first: Delta Cephei (John Goodricke, 1784) – magnitude changes over 5.4 day cycle c. hundreds known d. – periods from 3 to 50 days e. luminosities 1,000 to 10,000x Sun f. Polaris – North Star – is a Cepheid Variable g. variation within (10% of luminosity) h. period 4 days i. pulsation decreases over time j. stars are in a flickering phase of life k. gas burner turned down too low l. They vary because: i. pulsations: ii. changes in color and spectral class temperature varies iii. Doppler shift of spectra size varies iv. luminosity changes when temperature and area change v. normal stars: balance of pressure and gravity vi. variable stars: pressure and gravity out of synch 2. Measuring the Distances with Cepheid Variables (The Period- Luminosity Relation) a. Henrietta Levitt (1908): systematic search many Cepheid Variables b. found hundreds of variable stars in Magellanic Clouds c. Magellanic Clouds – nearby galaxies d. all roughly same distance away (like observing LA lights from here) – compare luminosities e. found: brighter Cepheids f. have longer periods g. Calibrate distance scale: nearby Cepheid Variables within parallax distance Mass Loss and Death of Low-mass Stars. 1. Main Sequence Star Late Life History (Red Giant – Yellow Giant – Stellar Wind – Envelope Ejection – Planetary Nebulae - White Dwarfs). Supernovae Type 1a 1. White Dwarf in a Binary System. 2. White Dwarf Accretion Disk. 3. Chandrasekhar Limit. 4. Explosion of the Supernovae of Type 1a. a. An isolated white dwarf is boring - it simply cools off to invisibility. b. White dwarfs in binary systems where the companion is still a main sequence or red giant star can have more interesting futures. c. If the white dwarf is close enough to its red giant or main sequence companion, gas expelled by the star can fall onto the white dwarf. d. The gas from the star's outer layers builds up on the white dwarf's surface and gets compressed and hot by the white dwarf's gravity. Death of Massive Stars (Supernova of Type II). 1. Heavy Element Formation (up to Iron) in Massive Stars. 2. Core Collapse of Massive Stars. 3. Massive Stars Supernova Explosion, a. Type II (Formation of Elements beyond Iron). Neutron Stars and Pulsars and Black Holes. 1. Emission from Neutron Stars. a. If the core mass is between 1.4 and 3 solar masses, the compression from the star's gravity will be so great the protons fuse with the electrons to form neutrons. b. The core becomes a super-dense ball of neutrons. c. Only the rare, massive stars will form these remnants in a supernova explosion. d. Neutrons can be packed much closer together than electrons so even though a neutron star is more massive than a white dwarf, it is only about the size of a city e. The neutrons are degenerate and their pressure (called neutron degeneracy pressure) prevents further collapse. f. Neutron stars are about 30 kilometers across, so their densities are much larger than even the incredible densities of white dwarfs: 2 x 10 14 times the density of water. g. Recently, the Hubble Space Telescope was able to image one of these very small objects (27 km across!) h. 2. X-ray Pulsars (basics); a. Escape Velocity. i. White dwarfs & neutron stars have very large surface escape velocities because they have roughly the mass of the Sun packed into an incredibly small volume. ii. A solar mass white dwarf has a radius of only 8,800 kilometers iii. Its surface escape velocity is about 5500 km/s. iv. A solar mass neutron star would have a radius of just 17 km, its surface escape velocity would be an incredible 125,000 km/s! v. Real neutron stars have masses above 1.4 solar masses and smaller radii, so their escape velocities are even larger! 3. Event Horizon a. A black hole probably has no surface b. Astronomers use the distance at which the escape velocity equals the speed of light for the size of the black hole. c. This distance is called the event horizon because no messages of events (via electromagnetic radiation or anything else) happening within that distance of the point mass make it to the outside. d. The region within the event horizon is black. 4. Schwarzschhild radius (critical radius to become a black hole). a. Within the event horizon space is so curved that any light emitted is bent back to the point mass. b. Karl Schwarzschild worked out the equations in General Relativity for a non-rotating black hole and found that the light rays within a certain distance of the point mass would be bent back to the point mass. c. The derived distance is the same as the event horizon. d. For this reason, the event horizon is sometimes called the Schwarzschild radius. 5. Observing Black Holes. a. Since the black holes themselves (their event horizons) are only several miles across, b. they are too small be visible from a even short distance away. c. Looking for black circles silhouetted against a background of stars would be an impossible task. d. indirect methods must be used! e. detect their effect on surrounding material and stars f. black hole in a binary system – watch its visible companion g. look for stars with an unseen companions: h. Kepler’s Laws – mass of black hole affects motion of visible companion i. X-ray and radio emissions – radiation from matter as it is sucked into black hole from companion
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