Popular in Descriptive Astronomy
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This 14 page Study Guide was uploaded by Samantha Bynum on Saturday December 12, 2015. The Study Guide belongs to 2010 at Wayne State University taught by Boris E. Nadgorny in Summer 2015. Since its upload, it has received 42 views. For similar materials see Descriptive Astronomy in Science at Wayne State University.
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Date Created: 12/12/15
I. Big Bang Theory a. widely accepted theory for the origin and evolution of our universe b. 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimeters across c. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit II. Expanding Universe a. widely accepted theory for the origin and evolution of our universe b. 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimeters across c. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit III. Hubble Law: Redshift – Distance a. Hubble Law: velocity of expansion b. v = Hd c. far away galaxies faster speed d. faster greater redshift e. only technique for measuring distances of farthest objects IV. Expansion Resolves Olber’s Paradox a. close to us: b. later in time c. more galaxies d. less redshifted e. farther out: f. earlier g. fewer galaxies h. more redshifted V. Measuring Distances a. Measure Doppler Shift b. Calculate Velocity from Doppler Shift c. Calculate Distance From Hubble’s Law. d. d = V/H e. Example: A galaxy is found to receed at 49,000 km/s. f. Its distance d=V/H = 49000/70 = 700 Mpc. VI. Steps to the Hubble Constant a. Hubble Law/Redshift b. 7. Brightest Galaxy in a group c. 6. Type-I Supernova d. 4. Variable Stars (Cephied and RR Lyre Stars) e. 3. Spectroscopic distances -- HR diagram f. 2. Parallax g. 1. Radar -- direct distance measurement VII. Expanding Universe a. The Doppler effect tells us about the relative motion of stars with respect to us. b. The spectral lines of nearly all of the galaxies in the universe are shifted to the red end of the spectrum. c. These galaxies are moving away from our Milky Way galaxy. d. Evidence for the expansion of the universe. VIII. Acceleration? a. is the expansion slowing down? b. expect slowing in standard big bang model c. some data may indicate its speeding up d. distance survey using supernovae type Ia (white dwarf becoming neutron star) e. always have the same peak luminosity f. if you catch the peak, you can measure absolute magnitude IX. Edwin Hubble: Distance to Andromeda using Cepheid Variables Proved Andromeda outside Milky Way X. Black Hole Formation a. supernovae explosion b. if the core remnant has a mass greater than 3 solar masses, then not even the super-compressed degenerate neutrons can hold the core up against its own gravity c. gravity compresses everything to a point d. the point object is a black hole e. Only the most massive, very rare stars (greater than 10 solar masses) will form a black hole when they die f. As the core implodes it briefly makes a neutron star for just long enough to produce the supernova explosion XI. Ultra-strong gravity a. The gravity of the point mass is strong enough close to the center that nothing can escape, not even light! b. Within a certain distance of the point mass, the escape velocity is greater than the speed of light. c. Reminder: escape velocity is the speed an object needs to avoid being pulled back by the gravity of a massive body. XII. Escape Velocity a. 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. b. A solar mass white dwarf has a radius of only 8,800 kilometers c. Its surface escape velocity is about 5500 km/s. d. 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! e. Real neutron stars have masses above 1.4 solar masses and smaller radii, so their escape velocities are even larger! XIII. 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. XIV. Schwarzschild Radius 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. XV. Detecting 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. XVI. Kepler’s Laws a. black hole and visible star orbit around a center of mass b. motion of visible companion betrays black hole c. Kepler's 3rd law total mass of the system. d. estimate the mass of the visible companion from luminosity assuming its a main sequence. e. the rest of the total mass is the unseen object's mass. f. If the mass of the unseen object is too big for a neutron star or a white dwarf, then it is very likely a black hole! XVII. Galaxy is mostly invisible matter a. Observe star’s orbital period, P, stars or interstellar matter vs. distance, D, from center b. Kepler’s Third Law period c. of orbit determined by mass d. within orbit e. D3 = (Mgalaxy + Msun)P2 f. earth orbit sun’s mass g. farther from the galactic h. center, the more mass i. within orbit j. FIND: more mass than we see -- dark matter halo XVIII. The Milky Way a. Sun is ~ 30000 LY from the center of our Galaxy. b. From our location within the galaxy, we cannot see through its far rim because the space between stars is not empty – interstellar dust or gas which absorbs visible light. c. The interstellar gas is the fuel for the formation of stars. d. Possibility of dark matter. e. Star have a long life (billions of years) but not infinite – they die or collapse in spectacular ways. XIX. Pulsars a. A rapidly rotating object with a bright spot on it could produce the quick flashes if the bright spot was lined up with the Earth. b. Neutron stars are compact enough and strong enough to rotate that fast. The pulsar at the center of the Crab Nebula rotates 30 times every second. c. In the figure it is the left one of the two bright stars at the center of the HST image XX. Death of Massive Stars – Supernova (Type II) a. Enough of the huge number of neutrinos produced when the core collapses interact with the gas in outer layers, helping to heat it up. b. During the supernova outburst, elements heavier than iron are produced as free neutrons produced in the explosion rapidly combine with heavy nuclei to produce heavier and very rare nuclei like gold, platinum, uranium among others. XXI. Supernova Energy Output a. Neutrinos formed when the neutron core is created fly away from the stiff core, carrying most of the energy from the core collapse away b. Some energy goes into driving the gas envelope outward. c. The rest of the energy goes into making the supernova as 11 bright as 10 Suns as bright as an entire galaxy! XXII. XXIII. Supernovae Type I (a) 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. XXIV. Life Cycle of Stars: the Corpse a. Stage 9: Core Remnant -- remains of the core after outer layers are ejected b. White Dwarf c. mass less than 1.4 solar masses d. Electrons prevent further collapse of the core -- degenerate electron gas. e. Neutron Star f. mass between 1.4 and 3 solar masses g. Neutrons prevent further collapse of the core -- degenerate neutron gas. h. Black Hole i. Greater than 3 solar masses -- star collapses to a point j. Escape velocity around the point mass is greater than the speed of light k. Event horizon--The distance at which the escape velocity equals the speed of light is called the event horizon XXV. Life Span vs. Mass a. stars shine because of nuclear fusion in core b. massive stars – short lives c. rate of consuming their fuel is very much greater. XXVI. evolution to main sequence a. ages of forming stars in years as they grow towards main sequence b. mass determines position on main sequence c. XXVII. Stage 5, part 2: Shell Burning 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 XXVIII. red supergiant a. core radius earth-sized b. heavy element fusion in shells c. envelope 5 AU XXIX. Stellar Nucleosynthesis a. H, He, some Li, Be, B produced during the Big Bang. b. Other elements produced in stars through nuclear fusion. c. When the outer layers of a star are thrown back into space, the processed material can be incorporated into gas clouds that will later form stars and planets. d. Source for the stuff our Earth is made of. e. All of the atoms on the Earth except hydrogen and most of the helium are recycled material---they were not created on the Earth. They were created in the stars. XXX. White Dwarfs a. Form as the outer layers of a low-mass red giant star puff out to make a planetary nebula. b. Since the lower mass stars make the white dwarfs, this type of remnant is the most common endpoint for stellar evolution. c. If the remaining mass of the core is less than 1.4 solar masses, the pressure from the degenerate electrons (called electron degeneracy pressure) is enough to prevent further collapse. XXXI. Supernovae Type I a. An isolated white dwarf has a boring future: it simply cools off, dimming 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 hydrogen-rich 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. XXXII. 10 11Suns (as bright as the entire galaxy) Crab Nebula a. A famous supernova remnant is the Crab Nebula. b. Chinese astronomers recorded the explosion on July 4, 1054 c. Anasazi Indians painted a picture of it. XXXIII. 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. XXXIV. Cosmic 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 XXXV. Protostar a. gravity pulls more matter into clump b. energy from falling matter creates heat c. protostar forms as hot matter begins to glow in infrared d. protostar surrounded by "cocoon" of dust e. matter falling into a rotating star tends to pile up in a disk XXXVI. Star Parallax a. Aristarchus based on the realization that the Sun was so much bigger than the Earth speculated that the Sun must be the center of the Universe. b. Greek astronomers/philosophers were aware of the phenomenon of parallax. c. Aristotle in particular observed that stars display no parallax - their apparent position does not change through the year. d. He thus concluded the Sun could not be the center. XXXVII. Key Properties of Stars a. Sun's key properties b. mass = 333,400 x Earth mass c. surface temperature: color yellow 5860 K d. chemical composition: spectrum mostly hydrogen e. size = 110 x Earth diameter f. luminosity = 3.8 x 10 26watts (spectral type G2V) g. Magnitude – 26.7 apparent, +4.8 absolute h. Deduce: core burns – fueled by thermonuclear fusion i. hydrogen helium j. Stars: how do we infer mass, temperature, chemical composition, size from observations? k. XXXVIII. Star Brightness a. Star brightness specified with the magnitude system. b. Devised by the Greek astronomer Hipparchus around 150 B.C.E. c. brightest stars into the first magnitude class, d. next brightest stars into second magnitude class, e. and so on, until he had all of the visible stars grouped into six magnitude classes. f. dimmest stars were of sixth magnitude. g. brighter objects have smaller magnitudes than fainter objects! h. magnitude system was based on how bright a star appeared to the unaided eye XXXIX. Apparent Magnitude 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. XL. Absolute Magnitude a. Measure of star luminosity. b. Luminosity is the total amount of energy radiated by the star every second c. If you measure a star's apparent magnitude and know its absolute magnitude, you can find the star's distance d. If you know a star's apparent magnitude and distance, you can find the star's luminosity e. A quantity that depends on the star itself, not on how far away it is f. Provides information about the structure of the star – this is the real luminosity g. More important quantity than the apparent brightness h. need the distance to determine the absolute magnitude XLI. How Magnitude Works a. Luminosity changes by a factor of 100 from 1 to 6 magnitude 1/5 b. A magnitude interval of 1 corresponds to a factor of 100 = 2.512 times the amount in actual intensity c. Each magnitude reduces luminosity by 1/2.5 d. raise the number 2.512 to a power equal to the difference in magnitudes. XLII. Extra magnitude? a. Some objects go beyond Hipparchus' original bounds of magnitude 1 to 6. b. Very bright objects can have magnitudes of 0 or even negative numbers. c. Very faint objects have magnitudes greater than +6. d. Remember: brighter objects have smaller magnitudes than fainter objects! e. XLIII. Star Luminosity vs Temperature a. stars are luminous because b. they are hot c. they are large d. or both! e. Luminosity of an object = the amount of energy every square meter produces multiplied4by its surface area. f. Luminosity = s× T , g. Luminosity of a star increases very quickly with even slight increases in the temperature. XLIV. Star Luminosity vs Size a. Luminosity ~ surface area. b. 1,000 watt bulb has same luminosity as a row of ten 100 watt bulbs c. Luminosity of a bigger star larger than a smaller star at the same temperature. d. From the apparent brightness, temperature, and distance of a star, one can determine its size. XLV. Absolute vs Apparent a. Star brighter if closer b. brightness fades with distance c. inverse square law d. if stars were all the same brightness than apparent luminosity would measure distance XLVI. Color and Temperature a. Stars are dense hot balls of gas b. Their spectrum is close to that of a perfect thermal radiator c. Which produces a smooth continuous spectrum d. So called blackbody spectrum. e. Color of stars depends on their temperature: f. hotter stars are bluer g. cooler stars are redder. XLVII. B-V Color Index a. Measure of the temperature based on apparent color. b. Based on two different filters. c. A blue (B) filter that only lets a narrow range of colors or wavelengths through centered on the blue colors. d. A “visible”' (V) filter that only lets the wavelengths close to the green- yellow band through. e. A hot star has a B-V color index close to 0 or negative, while a cool star has a B-V color index close to 2.0. Other stars are somewhere in between. f. Defined as the difference in magnitude between the B and V bands. XLVIII. Wien’s Law Temperature 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. XLIX. Star Masses a. Mass is one the key parameters of stars b. Determines the behavior and life cycle of the star c. Determined for binary stars – most common case: spectroscopic binary stars L. Orbit of Binary Stars Masses a. Kepler's third law: b. speed of orbit determines mass c. orbital period P and semimajor axis D of ellipse related to masses M 1 and M 2 d. period of mutual revolution M + M 1 2 3 2 e. D = (M +M1)P 2 f. D in AU, P in years g. individual motion of each star determines individual masses h. each star orbits a common point – the center of mass i. star distances from center or mass determines the stars' individual masses. LI. Spectroscopic Binary Stars a. most known binaries are spectroscopic binaries b. distance too great to resolve the two stars individually c. binary nature is indicated in the periodic shift of their spectral lines as they orbit around each other d. can measure their speeds from the Doppler shifted lines e. speed determines the mass LII. Stellar Diameter a. The Moon crosses in front of star – eclipse b. brightness of the star decreases gradually during the eclipse c. time for decrease depends on size of star d. eclipsing binary stars LIII. Eclipsing Binary System a. stars orbiting each other in a plane parallel to the line of sight: b. orbit is seen edge-on. c. one star periodically eclipses the other: d. total brightness of the combined stars decreases during the eclipse. e. The reduction in brightness depends on the luminosity and relative size of the two stars. LIV. Mass vs. Luminosity a. each point on this plot represents the absolute magnitude (luminosity) and color (temperature) of a star LV. Distance from Spectral Types a. close star – parallax b. variable star – if you find one c. alternative: spectral class + HR diagram d. spectrum temperature e. spectral lines broad classes f. supergiants g. bright giants h. giants i. subgiants j. main sequence k. HR diagram luminosity l. luminosity distance LVI. H-R Diagram a. relationship between temperature (color) and luminosity (absolute magnitude) for 90% of the stars b. 90% of stars lie along diagonal band called the main sequence c. plot of luminosity vs. temperature is called the Hertzsprung-Russell diagram d. or just H-R diagram for short. LVII. Sun: a. +4.8 magnitude b. B-V color index 0.62 LVIII. s spectral class i n r l o ( y i o i m l temperature (Kelvin) LIX. Period – Luminosity Relationship 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 LX. Why Cepheid Variables Vary a. pulsations: b. changes in color and spectral class temperature varies c. doppler shift of spectra size varies d. luminosity changes when temperature and area change e. normal stars: balance of pressure and gravity f. variable stars: pressure and gravity out of synch LXI. Cepheid Variable Stars 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 e. 3 to 50 days f. luminosities 1,000 to g. 10,000x Sun h. Polaris – North Star – is a Cepheid Variable i. variation within 10% of 1 of magnitude (10% of luminosity) j. period 4 days k. pulsation decreases over time l. stars are in a flickering phase of life m. gas burner turned down too low LXII. What is Parallax? a. nearby star appears to move back and forth compared to more distant stars b. Barnard's star: 6.0 LY c. parallax effect depends on distance d. how can we use parallax to measure distance? LXIII. “Standard Candle” to Measure Distance a. If stars were all the same brightness then apparent luminosity would measure distance b. LXIV.
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