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by: Katherine Quigley


Katherine Quigley
GPA 3.78


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Class Notes
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This 61 page Class Notes was uploaded by Katherine Quigley on Monday October 19, 2015. The Class Notes belongs to ASTR 2050 at Rensselaer Polytechnic Institute taught by Staff in Fall. Since its upload, it has received 31 views. For similar materials see /class/224870/astr-2050-rensselaer-polytechnic-institute in Astronomy at Rensselaer Polytechnic Institute.




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Date Created: 10/19/15
ASTRZOSO Spring 2005 Lecture I I am 8 February 2005 In this class we will 0 Review what we ve learned about stars What we can measure about stars I Temperature More properly Effective Surface Temperature The old way Spectral Classi cation ie OBAFGKM with numerical subclasses The modern way Color Index Uses color lter bands UBVRl V Visual Index based on difference of ltered magnitudes eg mB mV ZMg MV ZB V 2 2 ghtness The appropriate physical quantity is Luminosity Relative brightness mgnitude m1 m2 2510g1of2f1 Standard brightnesszAbsolute magnitude m M 2510g10d10 pc2 Convert to luminosity Bolometric magnitude MBoz MBoz 2510g10 lLL l These are related to stellar radius by L 4TER2OT4 NoteWe cannot measure stellar mass or radius directly 3 Imw uwcsm W53 AIWV 05m 35 mcnmmnrpzwm ZZZ mmacmznm N u S L L v w s n m M u L MD nun n nun mnnn MZ 1565 In x Binary Star Systems Two stars in orbit about their common center of mass See Studio Labomiory this Friday 5 Example Sirius Alpha Canis Majoris The brightest star in the sky is actually two stars The Orbit Sirius AAl Main Sequence star SiriusB White dwarf ea gm I glass o IS39IE 915 I558 x t N 53 gmiiol z i918 SIRIUS A and B o In 2 3 u 5 5 1 The APPARENT OFlBIT m2 SCALE Visual Xr ay Lots of Xrays from Sirius B Luminosity in solar luminosity Mass Luminos mg Example Masses of stars I i DehciedecipmsisiemsM o oaecipmmms m Resolvedspemmbinaries A Visualbmarles gggo 3 5 8 L olt M A 53 ff A A a I I l in Mass in solar ma ity Relation mo sses 7 Massive stars are much much brighter than lighter stars An important goal of our study of stellar structure will be to understand how this relation comes about A model for studying stars E laking mm mm H 20050202 1653 UT Basic Internal Structure of the Sun Eamnal Sirgamm Premiums Doppler Broadening of Spectral Lines MaxwellBoltzmann distribution of molecular velocities Heat energy realized as random motion 1 3 mltv2gt kT 2 2 This broadens spectral lines by Doppler Shift A 7 v2 vrm C C 0 200 400 600 300 1000 1200 Speed msec w 90N 30N E O 308 05 04 03 Sunspots Cooler Regions and Magnetic Fields SUN SPOT AREA IN EQUAL AREA LATITUDE STRIPS o OF STRIP AREA Igt 00 Igt 01 Igt 10 l i H L L i K i I 39 I in i Ih i l l Ii i I i1 xquot M 39i i i I l i39fi i quotquot quotquot 1Fquoti i i i ii quotwimp w i I i 4 i i i i i 1 u 1 39 i i x Hi 139quot 1 iii i i i ii iiiii i ii quotiiiiii i411 iiiii39i39 i quotiiiquot iiiiii iiii r i i l ili I Hi i u Hi Hi i i HM i i ri i quoti H quot il 1 iii 39 W477 H i1 l lquot1 i r a h u i i 39 H v quot I i i i 3 I 11111111 1 JUN 1quot 39 01513111111 u l iiiruil l lq iill m iiwuiiliyiw L 411111111 119311111511 iii uHJIVM II i IWH il i HM l I H I Y H i i quotI u x ml H W H il l l i I ll i 1 1 H i i I I 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1990 2000 AVERAGE DAILY SUN SPOT AREA o OF VISIBLE HEMISPHERE 1 u I I 1920 1930 1950 1960 1970 1980 I 1880 1890 1900 1910 1940 1990 2000 E Solar Rotation Differential Flntation Period The sun rola es a faster at the aqua I than at higher Iatitudea 213mm IE Elba y Uquot u iif m r g ULU new L Hg l2 ASTRZOSO Spring 2005 Lecture II am I2 April 2005 In this class we will cover Normal Galaxies 0 Types of galaxies 0 Spiral arms and star formation 0 Rotation curves and dark matter Types of Galaxies V i it Anglo AuStraliar Observatdry Properties of spirals and ellipticals See Kutner Table 7 Gas Yes Some Dust Yes Some Young stars Yes None Shape Flat Round Stellar motions Circular rotation Random Color Blue Red Mass range 107 t0 1011M 106 to 1012 MG 3 Luminosity functions Galaxy brightness falls off from the center according to empirical laws for the luminosity per unit area Elliptical galaxies LO Log Vro14 de Vancouleur s Law TYPlcall LO Q 2 X 105LQp62 with large spread in r0 Spiral galaxies disk LO LowD Typically D m 5 kpC Views and Classes of Spiral Galaxies Edge0n View Barred Spiral 3 Malin iAQRGQ quot quot 39 iii Anglo Australian Observatbry The Hubble Tuning Fork Normal spirals 5b 5 m z 11 F b 391 quotr if 39 N quot x I g 4 t h 3139 p 7 s v39 v inl 39 e I f gt u A39 y r a hi 39it Ii ap39 Ellipticals Despite the suggestion this is not an evolutionary path See Kutner Fig I 7 Barred spirals Other types of galaxies AngloiAustraian Obsewatory Star Formation in Spiral Arms M8 in Visible Light From UV to IR Blue Stars are hot therefore massive therefore oun stars 9 Spiral arms are not from windup We know the speed z220 kmsec of stars in the disk So Start 50 Million Years 00 Million Years 500 Million Years But today l5000 Million Years later we see Present Understanding Density Waves Cars can move quickly on a highway but they will slow up if the encounter a region of high density before moving on Smoochf DC The same thing can happen to galactic gas dust and stars incoming clouds H and Stars density wave u onlyf the long lived Star s make it out stapa arm d noity wave enhanced gravity O I bi i i speed kmfsi 1 Rotation Curves and Dark Matter 350 SUD 250 2W 1 0 1 J MD 50 See also Kutner Fig I 72 NGC 4378 NGC 3145 NGC 1510 NSC 75611 Just as with the MilkyWay galaxies in general show fat rotation curves This is evidence for dark matter I l i I 5 10 15 2D 25 Distance from center of galaxy Milt 1s l2 ltgt 0 O W 0 g 92 lt9 29 we 8 9 9 0 co 1 4000 4500 5000 5500 6000 6500 7000 7500 Truncaked Ju an Date ASTRZOSO Spring 2005 Lecture I lam I 8 january 2005 In this class we will cover The brightness of stars Electromagnetic radiation 0 The color of stars Blackbody radiation The Planck Radiation Formula Brightness and Magnitude The ancients looked at the stars and saw that some of them appeared brighter than othersThey divided them into about ve different socalled magnitudes First magnitude meant the brightest star observed Sixth magnitude meant the faintest star observed Today we know better how to measure brightness but we are stuck with the ancients convention This leaves us with two minor complications 0 Smaller magnitude means larger brightness 0 Converting magnitude to brightness uses logarithms For now we consider only ratios of brightness which correspond to differences in magnitude 5 100m2 m15 10m2 m125 192 b m2 m1 Am 2510g10b 1 2 Examples How much brighter is a third magnitude star than a fourth magnitude star 191192 2 1004 3V5 10002 251 A certain telescope allows you to see a million times more light than your naked eye What is the faintest magnitude star that you can see now Am 2 2510g10106 25 X 6 15 m26 l Am21 Electromagnetic Radiation normal violet IZIEar39If hitE r39 h IjE 11t1IIr39I Elf tht rHIZI rag g hi ii iii 3 H ii ggf i t can visible light gamma rays ultr ui u lgt light 013 1994 EncuclcFaeiia Er itannia Inc Depending on circumstances it may be more or less convenient to express the type of radiation in terms of either its frequency or its wavelength Frequency V Ck Wavelength For astronomers a very important issue is to what extent various types of electromagnetic radiation can penetrate the Earth s atmosphere w w ui nf See also Figure 23 in your textbook Why do stars have colors This is Figure 24 in your textbook Color Temperature Think about a light bulb As the current through the lament increases the color turns from red to bluewhite d l l B l 1l l This is called Black Body Radiation Eiack Body Radiaminn Specmim Trend mniy MDT ta intact scale gt3TDOH 3 m h 1 ET 1 a p E E 41 51 Ell T J39J Wavelengthfpm Cheated in Team CEETET I Thinkl neat ivtl Am 2 290 X 106 nmoKT Energy per unit area 2 0T4 Planck s Radiation Law Photons Zlzczk5 c This is the radiated energy intensity per unit area and per unit wavlength or frequency interval It is now understood that this formula was the rst early evidence that electromagnetic radiation came in bundles Eh39v ody radiators So we connect brightness to the total energy radiated by a star iii IIIII i m gl 4EII nuglllgi lil39hill L 4nR2 0T4 Luminosity Immummmn Emum ASTRZOSO Spring 2005 Lecture I I am I March 2005 In this class we will talk about stars in their dying throes 0 Planetary nebulae Low mass stars 0 Supernovae High mass stars Recall from last class Low mass stars M lt 5M9 Relatively long lived Hydrogen burns in shell until degenerate helium ignites gt Red Giant High mass stars M gt lOMQ Relatively short lived Kutner 03 Please note quot errata Ef g Continuous burning to Mum heavier elements as core mg shrinks and gets hotter and hotter gt Supergiant Planetary Nebulae The death song of low mass stars The outer shells of the red giant are held to the core only very loosely F GmMR2 The shells are pushed out by some mechanism maybe radiation pressure Evolution of a One l 12 Asympiptiti WINDquotH Planetary nebulaquot 11 glam i Eggsjawed 39 a blamh A g g 100 H fang W 5 3 RHOrlzonlal a V E I labldllcllma a lEH E E l a xquot 5 all M x H 3 a a quot 1E a 13 a E a 3 White dwarf x x mm m 11 Fl 5 l i km l 30000 l 39 EDGE 3000 Surface temperature K H 3 3 39 Solar Mass star As the core burns out of heliumthe envelope expands and the star brightens some more Thenthe planetary nebula is formed and the hot core of the star is exposed moving horizontally to the left The carbon core burns no moreThe star dies elix NGC 7293 HSTACS CTIO Mosaic NASA ESA and LR o39Den Vanderbilt Universiw srsmacauzn Features of the Helix Nebula Northeast 1quot K object r Nor east Northeast arc h shock Northwest outer 39 featu re West outer feature I Sogsrgeefst Butermost rlng p feature 39400 arcsec Egg Nebula Hourglass Nebula 7 5 quot 39 n a 39 wtquot NGC 702 7 The Ring Nebula in true color and using lters A 5007 See also Kutner Figure I 09 7 Supernovae The death song of high mass stars Binding energy per nucleon MeV Recall Nuclear binding energy Fusion can no longer proceed for Agt56 iron Frusitm Fissinn a 51 IDD 150 Atomic Mass A 9 I EDD Just before the endwe have Red supergiant star nonburning hydrogen hydrogen fusion heiium fusion carbon fusion magnesium fusion silicon fusion inert iron core and then there is no more burning to create pressure so nature nds a way to get rid of the electrons A burst of neutrinos and a neutron star is born IO Supernova SN 987A Core hellum exhaustion r u 3 45000 30 Jupiter39s orbit Homo sapiens Carbon ignition 10000 B Agriculiure Vs 4 1 1 Presupernova o starhquot c Nitrogen burning u LA Core hydrogen exhaustion quot o ono B c ceiphf39m Helium burning u sa Ions 3V 39 quotmmquot ems re supergianl 650000 30 Fire and tool making 2 E c E E E i o v s m 1 m m o 5 a E a E E 4 SkGS39 202 born 11 million EL In 3 r 1571 Neon Ignition 1983 Ox en l nilion 1537 Silicon Ignition 13 Eeb 1987 Supernova 23 Feb I mun 7 u 5000 Surface temperature K The neutrino burst was observed in underground detectors Supernova remnants Crab nebu54 Tycho l572 SN987A in I994 o ASTRZOSO Spring 2005 Lecture I I am 22 March 2005 In this class we will cover Clusters of Stars Types of clusters Distances to clusters Cluster dynamicszTheVirial Theorem 0 HR diagramszAges and populations Types of Clusters AssumptionAII stars in a cluster are about the same age 0 Galactic or Open clusters 0 In the Galactic disk 0 S 000 stars and S l 0pc across 0 Sometimes associated with gasdust clouds 0 Globular clusters 0 Appear grouped about the Galactic center I Find center of the Galaxy at IOkpc 39 04 to ID6 stars and 20 to ICC pc across 0 No gasdust clouds 2 Examples of Open Clusters M6 Butterfly Cluster Age5 iin years V Ae 300 Million year See liminer Figure l 3 3 M5 Age l3 Billion years Age l5 Billion years See Kutner Figure 32 4 Distances to Clusters 0 Main Sequence matching 0 Recall l8 Feb studio class PIeiades 0 OK for all clusters but later this class 0 Cepheids and RR Lyrae stars 0 Useful if you can nd them 0 Globular clusters have many RR Lyrae 0 Star motion in moving clusters 0 Accurate method but 0 Clusters must be nearby 5 Distances to Moving Clusters Kutner Fig 33 Observer 2 2 2 v v VT tanszTvr The Doppler shift is used to measure the radial velocity vr Distance d is determined from proper angular motion M which arises from tangential speed VT VTkm sec d km or for dpc and uarcsecyear d VT474t vr tanA474t Mindsec So how can we measure A 6 A cluster of stars will appear to move towards a convergent point This makes it possible to determine the angle A Convergent Point ExampleThe Hyades Identi l the convergent point using a large number of moving stars m 7 u 1 ICRS mm 25 Cluster Dynamics and TheVirial Theorem Consider the motion of a mass in a circular orbit 1 2 1 mvz 1 GMm 1GMm 1 Kz mv R R U 2 2 R 2 R2 2 R 2 Sothe total energy is E K l U U2 lt O For a collection of objects like a cluster of stars that are moving in equilibriumthis relationship still holds 00 ltUgt2 and E 00 ltUgt ltUgt2 This powerful result is known as the virial theorem See Kutner section I 33 for the derivation 8 Example2Why don t clusters fly apart See Kutner Section 332 Assume the cluster is a sphere 3 GM2 I5 F b 0 of mass M and radius RThen 6 am If the cluster has N stars each of mass m then N gm 12 11 11 so that M 2KM UM 3 5GMR WV i E Also Homework problem on Virial Mass We ll use this later HR DiagramszAges and Populations An old cluster Globular clusters are different G Stellar Populations Globular clusters are nearly pure H and He no metals and stellar evolution details are sensitive to composition Galactic clusters are more typical of stars in the galactic disk including metals We call these Population I stars Low metallicity stars like those found in globular clusters are called Population II stars We think of Population stars as young and made up of recycled materials Population II stars are old and might be made from primordial materials from the birth of the universe


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