AaId HH $ @d HHHHff@  d/ Footnote TableFootnote**.\t.\t/ - :;,.!?/0 `U/, `XTOCHeading1Heading2  EquationVariables8; 5W5Y5^5`6e6g6!l6Fn6667 ) I > )<$lastpagenum> *<$monthname> <$daynum>, <$year>OA +"<$monthnum>/<$daynum>/<$shortyear> ,;<$monthname> <$daynum>, <$year> <$hour>:<$minute00> <$ampm> Aa -"<$monthnum>/<$daynum>/<$shortyear> .<$monthname> <$daynum>, <$year> /"<$monthnum>/<$daynum>/<$shortyear> 0 <$fullfilename>ff 1 <$filename> 2 <$paratext[Title]> 3 <$paratext[Heading1]> 4 <$curpagenum> 5 <$marker1> 6 <$marker2> 7 (Continued) 8+ (Sheet <$tblsheetnum> of <$tblsheetcount>)- 9Heading & Page <$paratext> on page<$pagenum> :Pagepage<$pagenum>n ;See Heading & Page%See <$paratext> on page<$pagenum>. < Table All7Table<$paranumonly>, <$paratext>, on page<$pagenum>b =Table Number & Page'Table<$paranumonly> on page<$pagenum> ` FFA!l HHA JJ LL NN PP RA$  5y  soe>5|  s > 5  u> 5 ta"5 ! u/um5 " ta5 # wn$d5 $ x se5 % v so>/5 & y s$ea5 ' sfi5 ( ~ vf 5 ) ~ v 5 * y vele5 + v vte5 , ~ v]5 - ~ vg5 . va5 / ~ }a5 0 vod)5 1 ~ v+t 5 2 ~ vu<$5 3 ~ vn- 5 4 w vnge5 5 vx p5 6 v vu5 7 { veen5 8 v vHe5 9 { ve<5 : v e5 ; s5 < ~ ve5 = v ~l$p5 > } vo<5 ? ~ vTa5 @ v&'5 A ~ vay>5 B ~ vp>5 C v`5 D vF5 E v!5 F w v5 G v v5 H  vJ5 I  v5 J v v5 K w 5 L z v5 M ~ 5 N v ~R5 O v $ 5 P v s5 Q s6 R vu6 S z vt6 T u6 U z ~t6 V w6 W w x6 X v vv6 Y v vy63 Z v6$ [ v v~6% \ v v~6& ] vy64 ^ v vv65 _ ~66 ` ~67 a 6: b v v~6; c v v6< d v v~6= e v v~6> f v~6G g v vw6H h v6O i  vv6P j  v{6Q k v vv6R l v{6S m v v6Z n ~6] o v~6^ p v vv6a q ~}6d r ~6i s 6w t v ~6x u w v~6y v v6~ w v v6 x w v6 y vw6 z w vv6 { v7 | v v6 } vv6 ~ v vw6  vz7 ~~7 vv6 w vv6 vv6 v v6 w 6 v z6 v6 vz6 v v6 ~ vw6 ~ vv6 ~ ~v6 ~ ~6 ~ ~v6 y vv6 v6 ~ vv6 v6 v6 v6 vv6 vv6 vv6 v vv6 v6 vv6 v6 v6 ~ v6 ~ vv6 v6 vv6 ~ v7 | v7 vv7 ~ v7 ~ v7 v7 vv7 ~ vw7 v7 vv7 vw83 w w7$ w vw7% 7* vv7+ v7. vv7/ ~ 72 v73 ~ v74 ~ vw75 v7: y v80 v vw8- ~ vv7@ ~ v7A v7F vv7 v~7 ~ v~7 v~7J v~7O v~7P vy7S v7T ~ v~7U ~ v7V v7a ~ v7b ~ v7c v7w ~7x ~ ~v7y ~ ~7 v v7 ~ v7 ~ ~7 ~ ~~7 ~~7 w 7 ~ ~7 ~ v~7 v|7 v7 v~7 ~ v~7 v7 v7 v v~7 v7 ~ v7 ~ v7 vw7 vw7 ~ v7 v7 ~ v7 y v7 ~ v~7 v7 v~7 ~ v~7 ~ v7 ~ vy7 vv7 ~ v7 ~ v~7 v7 v7 v8 v~8 ~ v8 v8 v8 ~ v8 ~ v8 v~8 v~8 ~ v8# ~ v~8& ~ v~8) ~ v88 ~5W7xdq5vPF7dq6~LH7dq7|8C7Hm3R q897 Hm3R H RH R FootnoteHr@ q98:7 ~Hr@ HzHz  Single LineH'q:9<7 ~;;Footnote ~  5_;:~     HD q<:=7 7HD HH  Double LineH q=<@78>? Double Line 5c>?=5e?>=8#8& ~H q@=B7xAA Single Line5hA@HZqB@C7q TableFootnoteEGxR qCB7 9EGxR EPwEPw  TableFootnoteod5pDRRHH5xE5 HH Fe   HH5zFN5 HHlEE HH5{G6 HH @>?HDoe   HH5}HJ6HHlGG HUV 5~I6 HUV AAJUU`   HUV 5JLH6HUV lII H$ 5K6 FtnH$ ELUU` tn oH$ 5LJ6H$ lKK HUV 5M5 HUV N UUe !  HUV 5NPF5HUV lMM H$ 5O5 H$ P UUe "  H$ 5PN5H$ lOO HH5QD HHAR ` # 79205 Astronomy Fall 1996 5 ` $ Course Summary X` %  u` & "Some suggestions for studying ... ` (  Make your own course outline ` *Todays lecture just hits the high points ڀ` ) Be familiar with the textbook ` ,  Review the homework problems 5` - UV# Work problems from other sources 1` .  +  Check out other web sites N` +  k` * ... and for taking the final ` / * Do the questions you  know  first ` 1  Try not to look up answers ` 0 +  Trust what you know ` 2 & Use look up for hardest questions  ` 3 " Remember: Grades will be curved HH5RDHHlUQQ d5S #UUll99HH5TS HH\uggestioW`Ug  ` ' ҥ Basic Physics ;` 4 ̀Gravitation and Motion leX` 6 e  hu` 5  Newtonian Gravity r S' S' h 7 Force:  ,l% S' h 9 hPotential Energy:  ~` 8 rk o,~` : ou Circular Motion \##[ h < ec where  te` = + ` > *  Applications ing×` ? Motion of binary systems t` @ Example: Cygnus X-1 1` A Mass at the galactic center ` B usEscape velocity 7` D ץ Schwartzschild radius T` C Newtonian cosmology erHH5US5HHlR\TT 95VW599I  S''bequal[char[F],over[times[char[G],char[M],id[char[r]],char[m]],power[char[r],num[2.00000000,"2"]]]]&;5WYSVVT6e5XY6e6ePX S'wt'Nequal[char[U],minus[over[times[char[G],char[M],id[char[r]],char[m]],char[r]]]]& 8e5YW^SXXTotn d5Z\\ >HH5[Z ?HHr4teExampleg\ 1 ` ; aBasic Physics ;` F Electromagnetic Radiation X` G ˥  cu` H s * Regions of the electromagnetic spectrum ` I  Diffraction ` J  Doppler shift ` L !Nonrelativistic and relativistic ` Q  1` K -Primary sources of electromagnetic radiation ,N` M ,c [k` N r[* Line sources: Atomic & Molecular states ` R 5Bohr atom, Balmer formula ` O + Blackbody radiation: Thermal, continuous ֳ44 h S $Stefan-Boltzmann law     eq4` T ov*Wiens Displacement Law    Color "34 h V Remember: Thermal energy  M4` P X0 Synchrotron radiation: Nonthermal, continuous j4` U Spectrum falls like  1/n HH5\ZHHlUc[[ \T5]^ss TT+_}at'%equal[char[F],times[char[m],char[a]]]Hl#V5^Y`Stm ]]TffctHVn95_`HVn9HVn9%+7#[ti'?equal[char[a],over[power[char[v],num[2.00000000,"2"]],char[r]]] of ~JVn;5`^SM,c__T ned5accr rmHH5ba tn:HHAnefan-Bollnc ` E T Telescopes Dis;` X  X` b 1 Different telescopes for different wavelengths u` d ot ` e ma Images or data ` c tr f` Y " Diffraction limit of resolution  ] 1Telescope with aperture  d  observing at a   H ] 9wavelength  l,    with  q  in radians &` [  qC` \ ch Measures of angle #`` Z 360=2p  radians }` _ 57.3=1  radian ` ` 1=60  arcmin (  ) ` a ti1=60  arcsec (  ) ar[` ^ "2 , h f ~0Example: For  q  in arcsec , write _HH5caHHl\jbb 46de44K4ol' equal[(*q"Green"q*)char[(*q"Green"q*)L],times[(*q"Green"q*)num[(*q"Green"q*)4.00000000,"4"],char[(*q"Green"q*)pi],power[(*q"Green"q*)char[(*q"Green"q*)R],num[(*q"Green"q*)2.00000000,"2"]],char[(*q"Green"q*)sigma],power[(*q"Green"q*)char[(*q"Green"q*)T],num[(*q"Green"q*)4.00000000,"4"]]]]esl 46egZhpedd[at D.6fg D.D.#V']approx[(*q"Red"q*)char[(*q"Red"q*)E],times[(*q"Red"q*)char[(*q"Red"q*)k],char[(*q"Red"q*)T]]] ǘW34F.6geZff[ ard6h6jjr[HH6ih xplHH}2csHj ` r Measuring Stars ;` W Distances and magnitudes X`  u` C Parallax:  1  parsec (pc)  = 1  a.u./sin( 1 ) "Gr` q"# Magnitude: Measure of brightness "4" f`` *)8+  Apparent (m,V,...) or absolute (M,M V ,...) q*9 S' h ch+  Inverse log scale:  ^` "G+  Color Index >^ h ,"+  Distance modulus  6[^` h+  Bolometric magnitude atx^`  ^` Binary systems D.^` t  ^` ox Not unusual! (*q^` *q' Important for determining properties *)T^` "Combine physics with observations 5^` !  Mass and radius determined X24 h 6Example:  (approximately) u2` &This is for main sequence stars only! HH6jhHHlcqii ;\*6kl\*\*/m 'yequal[(*q"Magenta"q*)char[(*q"Magenta"q*)theta],fract[(*q"Magenta"q*)char[(*q"Magenta"q*)lambda],char[(*q"Magenta"q*)d]]]">^*6 lna. okkb..q*6Dmnl (lvu(6e$x 'equal[(*q"Green"q*)char[(*q"Green"q*)theta],cross[(*q"Green"q*)cross[(*q"Green"q*)over[(*q"Green"q*)num[(*q"Green"q*)360.00000000,"360"],times[(*q"Green"q*)num[(*q"Green"q*)2.00000000,"2"],char[(*q"Green"q*)pi]]],cross[(*q"Green"q*)num[(*q"Green"q*)60.00000000,"60"],num[(*q"Green"q*)60.00000000,"60"]]],over[(*q"Green"q*)char[(*q"Green"q*)lambda],char[(*q"Green"q*)d]]],cross[(*q"Green"q*)num[(*q"Green"q*)206265.00000000,"206265"],over[(*q"Green"q*)char[(*q"Green"q*)lambda],char[(*q"Green"q*)d]]]]e NAH6Enlammbd6IoqqHH6Jpo mHH[q"nta"q*)tqq" ` s a"Stellar Properties & Evolution ]]";` g  X` i .) Spectral class and surface temperature ` j  Luminosity class and size ` k  HR Diagrams ` l q*-+  Historical, Observational, or Physical o` n er$+  Main sequence, giants, dwarfs 00` m *q Properties of Main Sequence 1` o q"-+  Mass and luminosity    Lifetime "N` q "]+  Mass and radius z` p [( Stellar structure re` [(5+  Hydrostatic Equlib.    Central pressure 6` 656+  Equation of state    Central temperature ` +  Nuclear reactions `  Evolutionary paths ` +  Study on HR diagrams 6` 0+  Solar mass stars  vs  massive stars S` +  Population II stars HH6LqoHHljtpp ` gd6era attHH6fsr HH[ D q*\t ` h oSpecial Case Stars $+ ;` u g.Small, Variable, Violent, or just plain Weird X` w e  u` +  Small (i.e. compact) stars Li` +  White dwarfs and` +  Neutron stars ru` +  Black holes `  Variable stars u` ,+  Cepheids (Type I and II) and RR Lyrae l 1` Distance indicators! l]` Ӏ Violent stars z` +  Novae ` on+  Type I Supernovae ` la+  Type II Supernovae s߀`  Weird stars ` st)+  Close binaries with compact object ` "Cygnus X-1 (black hole companion) 6` 'Centaurus X-3 (neutron star companion) aS` SS 433: Weird jets! HH6htrHHlqwss d6zus+ wwl,arHH6{vu HHxcompactw ` v itThe Interstellar Medium ;` x n  rX` Composition acu`  Dust and gas ble`  Dust scatters light ` nd&+  Dense areas (clouds) are dark ڀ` #+  General areas are reddened z` +   Modify distance modulus! + #` va Gas absorbs or emits light ype@` /+  Hot gas emits in optical (HII regions) st]` ri-+  Cold gas emits in radio (HI regions) yz` le Stirring it up ` au+  Planetary nebulae an` +  Supernova remnants s`  ` Star formation  ` $ Collapsing clouds of gas and dust (` +  Time scale for collapse E` ar+  Mass scale for collapse p`  Disks and planet formation HH6}wuHHltzvv n d6xzzasleHH6yx HHj re dark z   ` y ar Galaxies ;` z The Milky Way and Others X` |  u` so" Size and shape of the Milky Way ` t +  Bulge and disk H` !+  Halo and globular clusters iڀ` eg" Star motion and rotation curves ` +  Dark matter in the halo #` ! Characteristics of spiral arms s@` #+  Radio emission from cold gas ion]` &+  Areas of intense star formation z` +  Winding problem `  Galaxy classification ca€` ++  Spirals (like the Milky Way and M31) n ߀` %+  Ellipticals (like M32 and M87) ` (+  Irregulars (like the LMC and M82) (`  Common properties E` as"+  Core emits X-rays and radio b` %+  Dark matter in rotation curves HH6zxHHlw}yy thed6{so}}Miy HH6|{ i HHHT*+ usters i}   ` { ta The Universe ;` ~ +  X`  h Hubbles Law `  h st"+  For nearby galaxies:  e` em#  Interpret as Doppler shift ` e` *+  For distant galaxies need cosmology e` ob(+  Implies the universe is expanding ic e`   The age of the universe &e f`` 1)E+  Find H TODAY   =  H 0  75  (km/sec)/Mpc G*` .Consistent with the age of globular clusters? d*` p e*`  Large scale structure X*` +  Clusters of galaxies mat*` rvThe local group *` The Virgo cluster *` The Coma cluster *` +  Superclusters and voids /*` Isotropic on a grand scale HL*` Anisotropic on a small scale HH6}{iHHlz|| d6~bsst+ HH6~ HH>as w ` } coActive Galaxies and Quasars + ;` iv*Galaxies with very bright central regions X` u eu`  Starburst galaxies O` H Radio galaxies k` +  Ellipticals ڀ` of++  Compact (M87) or extended (Cygnus A) *` '+  Suspect supermassive black holes ` f Accretion disk    jets 1` +  The core of M87 ]` * Seyfert galaxies Coz` '+  Spirals with very bright centers ds ` +  Strong emission lines ` .Forbidden lines   low density regions ߀` Quasars ` '+  Old days: Starlike radio sources ` +  Very large redshifts 6` *+  Today: Very distant active galaxies HH6~HHl} MMd6 rit HH6 HHjrs` H xi ` + Cosmology ;`  fX` 87 The Flat Universe A)u` ;+  Relation between  dR/dt ,  R , and  M ` ` sk++  Relation between  H  and  r he ` ,  The universe is  probably  flat ڀ` ir+ Justification through General Relativity ` ` e'+  Energy gravitates: Light bending bid#`  Cosmic Microwave Background @` s +  Lots and lots of photons ays]` ou%+  Photons are low energy (today) y`  The Big Bang ` y '+  Photons ruled the early universe €` /+  Particle creation in the primordial soup ߀` M*+  The first three minutes: H, He, ...  `  Formation of the galaxies (` +  Looking back in time jE` !+  Protogalaxies with the HST b` /+  Research today: Connect the anisotropies HH6 HHl M96ten99C S''`propto[char[m],log[over[num[1.00000000,"1"],fract[char[L],power[char[d],num[2.00000000,"2"]]]]]]Re>`;6hr giid[6od [[c-of'lequal[plus[char[m],minus[char[M]]],plus[times[num[5.00000000,"5"],log[char[d]]],minus[num[5.00000000,"5"]]]]Gs^[6hay i KK46upKK4KK4&4th'ipropto[(*q"Red"q*)char[(*q"Red"q*)L],power[(*q"Red"q*)char[(*q"Red"q*)M],num[(*q"Red"q*)3.00000000,"3"]]] ^MK46hotiQ6e7 e Q6eQ6e) '3equal[char[z],times[over[char[H],char[c]],char[d]]]qS8e7{6|d5Lefttod600Right,d7nu Reference"dDdSidZ[dad dh-ofdoinr[dr00],du00,"dxd {id ~Kd  a 84f a Body. f b e Bulleted\te. [cf c CellBody. f d  CellHeading. f e r 0Footnote. f fT Heading1Body. f gT  Heading2Body. f hT   HeadingRunInBody. f i l yIndented. f j g Numbered.\t. f kE  Numbered1.\tNumbered. f l f TableFootnote. f mT   TableTitleT:Table : .  f nP TitleBody. f o T   TableTitleT:Table : . f p   CellHeading. f q  CellBody. f r   CellFooting. f s  Body. @ t  lHeader. @ u  blaFooter. f v Body. f w  Body. f x $ Body. f y   Body. $f z  Body. $f { .Body. 6f |  Body. f }  Body. $f ~ Body. f  Body. $f Body. $f  Body. Hf  Body. f $ Body. f   Body. $$f  Body. Hf  ..Body. f Body. f $ Body. Hf Body. f  Body. f $ Body. Hf ..Body. f  Body. f Body. $f  Body. Hf ..Body. $f  Body. $f Body. f Body. Qf  Body. f Body. f  Body. $f  Body. Hf  Body.  $  Emphasis  EquationVariables )   ڝ  ڝ ڝ tu  [  ڝ tu )  w $)  )   ڝ \S  ڝ ڝ ڝ $)   ڝ \S  w tu w ڝ w \S  ڝ w  ڝ tu tu w ڝ w    Thin Medium Double Thick@  Very Thin     oH p q rH p q rH p q rH p q rH p q rFormat A   oH p q rH p q rH p q rH p q rH p q rFormat B U e V UComment d BlackT!WhiteddAReddd Greendd  Blued Cyand Magentad Yellow  Times-Roman Times-Bold Times-Italic ZapfDingbats ZapfDingbatsHelvetica-BoldSymbolSymbolTimes HelveticaSymbol ZapfDingbats Regular Regular BoldRegularItalicw]`jUv)-Xx/B> mo;P? ʊ>.% \w R66&$"]v*p?.fö"en=4 zLҥj&Zhoʺ'tHPM8Oe