Aa1d HH $ @d HHHHff@  d Footnote TableFootnote**.\t.\t/ - :;,.!?+  `1 `1TOCHeading1Heading2  EquationVariables6 6 s5 V5 h5 j5 l6J y6 6 6 6 6  ) I > )<$lastpagenum> *<$monthname> <$daynum>, <$year>Nb +"<$monthnum>/<$daynum>/<$shortyear> ,;<$monthname> <$daynum>, <$year> <$hour>:<$minute00> <$ampm>5Y> -"<$monthnum>/<$daynum>/<$shortyear> .<$monthname> <$daynum>, <$year> /"<$monthnum>/<$daynum>/<$shortyear> 0 <$fullfilename> 1 <$filename> 2 <$paratext[Title]> 3 <$paratext[Heading1]> 4 <$curpagenum> 5 <$marker1> 6 <$marker2> 7 (Continued) 8+ (Sheet <$tblsheetnum> of <$tblsheetcount>)t 9Heading & Page <$paratext> on page<$pagenum> :Pagepage<$pagenum>O ;See Heading & Page%See <$paratext> on page<$pagenum>. < Table All7Table<$paranumonly>, <$paratext>, on page<$pagenum>q =Table Number & Page'Table<$paranumonly> on page<$pagenum> h FFAJy HHA JJ LL NN PP RA$  n5y  soe>5|  s > 5  ui> 5 t>"5 ! u/um5 " ta5 # wn$d5 $ x se5 % v so>/5 & y s$ea5 ' } vfi5 ( v v 5 ) v } 5 *  vele5 +  vte5 , } v]5 - v vg5 .  va5 / } va5 0  vod)5 1  v+t 5 2 } vu<$5 3  }nt5 4 v vnge5 5 v vx p5 6 y vu5 7 v veen5 8 z vHe5 9 v ve<5 : { v e5 ; ~ v5 < ~ ve5 = vl$p5 > v vo<5 ? v vTa5 @ v v&'5 A y vay>5 B vp>5 C v vh5 D vF5 E vJ5 F z v5 G v v5 H z vJ5 I { v5 J { v5 K y v6 L v v6 M z v6 N z vR6 O v v$ 6 P vs6 Q v vs6 R v vu6 S v6 T vu6 U vt6 V v vw6 W v vx6 X z vv6 Y v vy6 Z v}6 [ x vv6 \ v vv6 ] y v6 ^ v6 _ v v}6 ` v vv6( a v6) b x v}6* c v v6+ d { v6, e ~ v}6f f v6i g x vv6j h } vv6k i vy6l j v vv6m k } vz6n l vv6o m v v{6p n } v~6q o y v~6v p v6w q v vv6x r v vv6y s  vv6z t v vy6 u v v6 v vv6 w x v6 x v v6 y vz6 z v6 { z6 | {6 } {6 ~ y6  v6 z6 z6 v vv6 v v6 vv6 | vv6 v6 v 6 6 vv6 | vv56 dq5}PF6dq6LH6dq7x}8C6+Hm3R q897 Hm3R H RH R FootnoteHr@ q98:7 m }Hr@ HzHz  Single LineH'q:9<7v ;;Footnote v  5_;:y     HD q<:=7 6HD HH  Double LineH q=<@76>?v Double Line 5c>?=v5e?>=66 H q@=B7 AA Single Line}5hA@HZqB@C7q TableFootnoteEGxR qCB7 9EGxR EPwEPw  TableFootnoteod5pDRRHH5xE5 HH vFe   HH5zFN5 HHlEE DHH5{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  ` # The Milky Way Galaxy ;` $ Structure and Evolution X` %  u` ) '+  General features and Populations ` * Shape and objects ` ( ˪ U` ' +  Galactic Rotation ` + Evidence for dark matter ` - K #` , +  Spiral Arms @` . UVAre they there? ]` 0 Where do they come from? z` 4 ! ` / +  The Galactic Center ` 1 A giant black hole? ` 5  ` 2 "+  The Evolution of the Galaxy  ` 3  A first look HH5RDUUHHlUQQ Hd5SUUHH5TS HH V VVU  ` 6 laGalactic Rotation ;` 7 d  lX 8 3It seems clear that stars in the disk are rotating resu@ 8  about the center of the galaxy. je` 9 ( ` : '&The rotation is difficult to measure: ` ; en% Stellar motions are hard to detect K` < ,( Our sun is one of the rotating stars! UV` = *  The Oort formulas (Zeilik Sec.15-4) #` > 4 !@ ? //Determine rotation curve of the Galaxy, i.e. ] H ? le3tangential velocity  Q  versus radius R:  HH5US3HHlRcTT UUH#5VSW`T -5WXVU-H-- 5XWYV- V-- HfgTP5YXZV t RHfgTPHH "Distance from center of Galaxy (R) 1`bMp5ZY[V  ٛpbM  Rotational speed  Q6?h5[Z\Vidi6?he: 6??6HP5\[]V6HPur n 6H^`]!-vE:RPu5]\^V uu-u- This is what you see.umZ5^]_V ?lemZ~~ This is what you mighthq5_^`V hqdZdZ have expected.d^ȝbM5`_V d^ȝbMd^ d^ i.e. V (1/ R )d5accHH5ba HHQ  YXZhlc R  ` & The Galactic Rotation Curve o;` @ ˏ` MX` B [Start with  F=ma , where  u` D RoF  is due to gravity and  h E \)a  is from circular motion. Then  ` C   h F ]0If most of the mass is in the bulge, then  `` G v E h H DIf there is a  uniform  halo with density  r , then  ` I i h, J ϛF  It looks like  r( r )  is not quite a constant, but I@ J y&falls off more slowly than the bulge. HH5cadZHHlUfbb  d5d VffHH5ed cHH[af K Are the Spiral Arms from lC @ K Galactic Rotation? Thf` L n  v` M @>Rotation velocity  v= Q  is about the same at all R. ` N Ro5  The center winds up faster than the outside. ` O ar t P 1If this makes spiral arms, the sun has orbited f@ P e /a couple of times since the Galaxy was made. ` Q he i1` R  "Check to see if this makes sense: N` S I$  Q SUN   220  km/sec lk` T 5 R SUN   8.5  kpc =2.510 19  km J` U re o` V . .  One revolution takes 250 Million years. ` W   X 9However, the Galaxy is  15  Billion years old, so  X -these spirals would long ago have wound up @ X cand disappeared. 6` Y  S` Z :  Spiral arms are  not  from galactic rotation! HH5fd?ThHHlcoee ty ݀ 5gh Pja;2݀ $up'requal[(*q"Green"q*)times[(*q"Green"q*)char[(*q"Green"q*)G],over[(*q"Green"q*)times[(*q"Green"q*)char[(*q"Green"q*)M],char[(*q"Green"q*)m]],power[(*q"Green"q*)char[(*q"Green"q*)r],num[(*q"Green"q*)2.00000000,"2"]]]],times[(*q"Green"q*)char[(*q"Green"q*)m],over[(*q"Green"q*)power[(*q"Green"q*)char[(*q"Green"q*)v],num[(*q"Green"q*)2.00000000,"2"]],char[(*q"Green"q*)r]]]]NH5hjaggb  V. 5ija. WZ?QL~}s  H 6@~s H o;$ 6Bsy;$ ? 6Ds6 ? H 6FsH 6'$ 6Hs$ d6rh 6My    T6NyTuTT06Oy0n009-6Py 9-tio9KKB9-B 6Qy6:-B hu9 6Ry6<u9  6Sy6> 9 6Ty6@9  6Uy6B y 6Vy6D  B 6Wy6F B ; 6Xy6H; 9 6Yy6r9 hH 6ZyH  6[y HH6s HH0`6O ` o nThe Evolution of the Galaxy ;` w A first look X` x  u h y ׀0Consider the free fall time. Recall that  ` v ׀/for a collapsing cloud of density  r . `  ` +Suppose the Milky Way started as a uniform 9` 3cloud with a radius  R  100  kpc. Then jPfP f`` 6UUr = 10 12  M SUN /(4p R 3 /3) = 1.610 -23   kg/m 3 ̰` and therefore ̳fP f`` 7t ff  = 710 15   sec  200  Myr 6X``  H `` +'0equal[times[over[num[1.00000000,"1"],num[2.00000000,"2"]],char[m],power[char[v],num[2.00000000,"2"]]],approx[times[char[G],char[M],char[m],id[plus[over[num[1.00000000,"1"],char[r]],minus[over[num[1.00000000,"1"],indexes[0,1,char[R],num[0.00000000,"0"]]]]]]],over[times[char[G],char[M],char[m]],char[r]]]]NO6 _6i?equal[(*q"Green"q*)indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)t],times[(*q"Green"q*)char[(*q"Green"q*)f],char[(*q"Green"q*)f]]],sqrt[(*q"Green"q*)over[(*q"Green"q*)num[(*q"Green"q*)1.00000000,"1"],times[(*q"Green"q*)num[(*q"Green"q*)6.00000000,"6"],char[(*q"Green"q*)pi],char[(*q"Green"q*)G],char[(*q"Green"q*)rho]]]]]NP6  d5Leftd6Rightd7 Reference*dDr[00dS,"dida0,nddd00"]dm00nudpnd,1d"][nd00 a ,tif a Body. f b *)[ "Bulleted\tG. *)f c CellBody. f d  CellHeading. f e a ,Footnote. 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. f | Body. f }  Body. $f ~  Body. 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