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Double Line 5c>?=5e?>=66 H q@=B7AA Single Linew5hA@HZqB@C7q TableFootnoteEGxR qCB7 9EGxR EPwEPw  TableFootnoteod5pDRRHH5xE5 HH XFe   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 HHMAR  ` # Stars and Our Galaxy ;` $  X % # Until now, information is mainly 5u@ % Fobservational.  & % Want to look at physics of stellar @ & structure and evolution.  ' # Need to establish terminology of @ ' the local environment. ` (  # ) +  Today:  What do we know about the @ ) 'collection of stars weve been looking ]@ ) &at, i.e. the galaxy in which we live? z` .   Shape, layout, and size ` /   Extra pieces ` 0   Gravitation and rotation ` * UU "` + Note:  We call our galaxy  ` 1 the  Galaxy   or (` 2 the  Milky Way . QE` ,  HH5RDHHlUQQ ur d5S %UUti iHH5TS ol.HHxics of sU ` - d Does our Galaxy have C ` E o Spiral Arms? nf` 3  ` 4 al*Probably, but evidence is not conclusive. ` 5   6 w0Premise: Hydrogen (and therefore stars) collect on@ 6 enin the spiral arms. ` 7 t g` 8 liTwo ways to look at hydrogen: 1` 9 s N` : * HII Regions:  Ionized (hot) hydrogen k` ; n Directions and distances of *` F young star clusters c` < +  OB Associations Ga` = +  Example: M16  ` >  ` ? * HI Regions:  Neutral (cold) hydrogen ` @ "Radio emission at  l=21  cm 6` A  S` B  p` C *Well return to this later in the course! HH5USHHlRXTT d5VXX nHH5WV rabHH6fPt ` 5 X ` D n Globular Clusters ;` G  X` U pi"Examples: M2, M3, M4, M5, M9, ... u` M li w` N hy About 200 are known. s` O :( Located away from the galactic plane. rofPfP` H ;K Spherically shaped clusters of  ~10 5  to  10 6  stars cP` J # Brighest stars are yellow to red 7P` K am  These are old clusters! cfP` L ? Distance measured with tfP` Q n Main sequence fitting  and fP` R Magnitudes of variable stars fP` I  fP P We+  They determine the geometry of our HfP@ P galactic environment: fP` S  Diameter is ~100 kpc RX.fP` T - We are  8.51.0  kpc from the center HH5XV5HHlU[WW d5Y[[sts HH5ZY iExHHj,  li w[ N ` V n.Stellar Populations :;` W ro hX` Y ro,Based on metal content: Stars are made of stu` Z 50 Hydrogen (Z  = 1 );mass fraction  X ` \ . Helium (Z  = 2 );mass fraction  Y ` ^ te0 Metals (Z   3);mass fraction  Z t` X n  a` [ g CPopulation I:  Large metal abundance ( Z     0.01) ` ]  # _ ey2Mainly found in galactic disk, especially in star @@ _ ir0forming regions (clusters and OB associations). pc]` a T z` c ϱ1BPopulation II:  Low metal abundance ( Z     0.01) ` b 9Also extreme Population II ( Z     0.001) ` e   d /Found mainly in globular clusters and galactic 5@ d ihalo, i.e. old stars.  ` g  (` h 6Population III:  No metals ( Z   = 0 ) E` f W ob` ` Y'Theorized, but none identified so far. maHH5[Y HHlX^ZZ d6&\^^  HH6']\ Xn HHg _e metal __^Z  ` i Galactic Rotation ;` j ey aX k ct3It seems clear that stars in the disk are rotating minu@ k s about the center of the galaxy. ` l  ` m on&The rotation is difficult to measure: ` o % Stellar motions are hard to detect i` n  ( Our sun is one of the rotating stars! ` q Fo*  The Oort formulas (Zeilik Sec.15-4) #` r d i@ s ta/Determine rotation curve of the Galaxy, i.e. 6Po] H s No3tangential velocity  Q  versus radius R:  oHH6)^\dtiHHl[k]]  H#6`_\`l]-6c`a_^-H-- 6da`b_g - _-- HfgTP6ebac_ t RHfgTPHH "Distance from center of Galaxy (R) 1`bMp6fcbd_  ٛpbM  Rotational speed  Q6?h6gdce_idi6?he: 6??6HP6iedf_6HPur n 6H^`]!-vE:RPu6jfeg_ uu-u- This is what you see.umZ6kgfh_ sNomZ~~ This is what you mighthq6lhgl_ ihqdZdZ have expected.d6nikkHH6oji HH}v- pvk6d` p Newtons Theory of Gravity --` t ̙ J u - The force between two masses is inversely ig H u o8proportional to the square of their separation.   h x  9 Circular (and elliptical) orbits are possible.   P h y ;  Escape velocity decreases with distance.   HH6qkiHHl^jj d^ȝbM6lh_ d^ȝbMd^ d^ i.e. V (1/ R )vl6q6ms ovl6qvlFkvlFk M 1d6nl4j^.>6op4 j^.>4j^.>0^'1list[equal[char[F],times[char[G],over[times[indexes[0,1,char[M],num[1.00000000,"1"]],indexes[0,1,char[M],num[2.00000000,"2"]]],power[char[R],num[2.00000000,"2"]]]]],equal[char[U],minus[times[char[G],over[times[indexes[0,1,char[M],num[1.00000000,"1"]],indexes[0,1,char[M],num[2.00000000,"2"]]],char[R]]]]]]oNZ6priaonooj x q$j96qrsblTjV9q$j9)ca'list[equal[char[F],times[indexes[0,1,char[M],num[1.00000000,"1"]],char[a]],times[indexes[0,1,char[M],num[1.00000000,"1"]],over[power[char[v],num[2.00000000,"2"]],char[R]]]],therefore[id[equal[(*q"Red"q*)times[(*q"Red"q*)char[(*q"Red"q*)G],indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)M],num[(*q"Red"q*)2.00000000,"2"]]],times[(*q"Red"q*)indexes[1,0,char[(*q"Red"q*)v],num[(*q"Red"q*)2.00000000,"2"]],char[(*q"Red"q*)R]]]]]]N.U6rpsi6qqj jH6srvi[etmj,or[-??6tws",i-??TΟAw6uv200jh-{y/kTΟAwYha'atop[equal[plus[times[over[num[1.00000000,"1"],num[2.00000000,"2"]],indexes[0,1,char[M],num[1.00000000,"1"]],power[indexes[0,1,char[v],times[char[e],char[s],char[c]]],num[2.00000000,"2"]]],minus[times[char[G],over[times[indexes[0,1,char[M],num[1.00000000,"1"]],indexes[0,1,char[M],num[2.00000000,"2"]]],char[R]]]]],num[0.00000000,"0"]],therefore[id[equal[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)v],times[(*q"Red"q*)char[(*q"Red"q*)e],char[(*q"Red"q*)s],char[(*q"Red"q*)c]]],sqrt[(*q"Red"q*)fract[(*q"Red"q*)id[(*q"Red"q*)times[(*q"Red"q*)num[(*q"Red"q*)2.00000000,"2"],char[(*q"Red"q*)G],indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)M],num[(*q"Red"q*)2.00000000,"2"]]]],char[(*q"Red"q*)R]]]]]]]N06vsiuuj ZH 6wtxsZH lH-6xwzslH-,ilHH)lH6yz{s 0h-)lH)lXdZ)lXdZ M 2H 6zxys,"]H c[6{y|s ",pc[clcl M 1@=6|{}s m[c@=QQ  v=v escvZ%76}|~s 0"2vZ%7vjdZvjdZ v=0ref|8 6~}s 0,c|8 gg #E=M 1 v esc 2 /2 + Ucha}O ) $6~ms "d"}O ) $}O9X}O9X E=0"Red6es[d")MHH6 qedHHq u ` v 'Gravitation inside a Mass Distribution Z-` w  J` z z9We usually talk about gravity from a  point  mass. lg` { 6  | h-;If an object moves inside a  spherical distribution   | 1of mass, consider all the mass inside the radial  H | ,p position of the object:    ~ :For example, if the mass distribution is  uniform ,  H ~ 5then the mass about which the object orbits is  HH6|8HHlk gHH6n /+ HH[d"}OO } Are the Spiral Arms from C @ } Galactic Rotation? d"f`   ` >Rotation velocity  v= Q  is about the same at all R. ` 5  The center winds up faster than the outside. t`   1If this makes spiral arms, the sun has orbited @ l/a couple of times since the Galaxy was made. an ` e  1` bu"Check to see if this makes sense: N` l $  Q SUN   220  km/sec k` o5 R SUN   8.5  kpc =2.510 19  km l` tr t`  .  One revolution takes 250 Million years. ` rb  9However, the Galaxy is  15  Billion years old, so  -these spirals would long ago have wound up @ + and disappeared. 6`  S` :  Spiral arms are  not  from galactic rotation! HH6n?d"HHl ty H6 ~ e ntH6Hu6 msubit ull$6w mll$~6 s~sen: ~~6 $$  )fg6 )fg)-)- Mass distrubtiones)5fgx6 )5fgx)E)E  Total mass MZ6thu6ZZ)MfgX6 )MfgX)])] Radius R)fgE6oti)fgED|6 D|DD  Object orbitsD_6 D_DD  at radius r66kC wxG>1'equal[indexes[0,1,char[M],num[2.00000000,"2"]],times[over[num[4.00000000,"4"],num[3.00000000,"3"]],char[pi],power[char[r],num[3.00000000,"3"]],char[rho]],times[char[M],indexes[1,0,id[over[char[r],char[R]]],num[3.00000000,"3"]]]]NVc6fg l66Mal6ЛM6 ЛM Use thisss蛦/6 蛦/ mass?-66?Zl?-6Z d5Leftd6Right|d7 ReferencedDctdSdVdYad6d\didneqded00 a 4[of a Body. f b  Bulleted\t. 6f c CellBody. f d  CellHeading. f e V 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. 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