AaHd HH $ @d HHHHff@  d Footnote TableFootnote**.\t.\t/ - :;,.!? `.9 `.TOCHeading1Heading2  EquationVariables665Z5\5^6/c ) I > )<$lastpagenum> *<$monthname> <$daynum>, <$year> +"<$monthnum>/<$daynum>/<$shortyear> ,;<$monthname> <$daynum>, <$year> <$hour>:<$minute00> <$ampm> -"<$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 <$tblsheetcount>) 9Heading & Page <$paratext> on page<$pagenum> :Pagepage<$pagenum>.\ ;See Heading & Page%See <$paratext> on page<$pagenum>. < Table All7Table<$paranumonly>, <$paratext>, on page<$pagenum> =Table Number & Page'Table<$paranumonly> on page<$pagenum> on FFA HHA\ JJ LL NN PP RaA$  m _B5y  soe>5|  s > 5  ui> 5 t"5 ! u/um5 " ta5 # n$d5 $ s5 % v so>/5 & v$ea5 ' vfi5 ( v 5 ) v 5 * vele5 + vte5 , v]5 - vg5 . va5 / x va5 0 vod)5 1 v+t 5 2 x vu<$5 3 vn5 4 w snge5 5 x p5 6 z u5 7 een5 8 w He5 9 { e<5 :  e5 ; 5 < e5 = y l$p5 > y yo<5 ?  Ta5 @ ~ &'5 A ay>5 B p>5 C on6 D F5 E 5 F 5 G \6 H J5 I 5 J 5 K 6 L w 5 M 5 N R5 O $ _6 P | }s6 Q }s6 R }u6* S t6 T u6 U t6 V 6+ W ~ 6! X v60 Y 61 Z 62 [ 63 \ 64 ] 65 ^ 5ed/5dq5aPF5dq6xuLH5dq7zu8Cen5Hm3R q897  Hm3R H RH R FootnoteeHr@ q98:7 Hr@ HzHz  Single Liney>H'q:9<7 ;;Footnote  5_;:J     HD q<:=7 5HD HH  Double LineH q=<@76>?t Double LineT 5c>?=s5e?>=6263 H q@=B7AA Single Linea5hA@HZqB@C7q TableFootnoteEGxR qCB7 9EGxR EPwEPw  TableFootnoteod5pDRRHH5xE5 HH Fe   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 HH>AR  ` # Star Formation ;` $ 'Lots of questions, not all the answers X` %   u` ' tn'The Birthplace: Giant Molecular Clouds ` ( Cold  (T  10 K) ` ` ) 0Dense  (n  10 6  / m 3 ) ڀ` * 3Massive  ( M 10 4   M SUN ) M` + BLarge  (R  [ M / n ] 1/3  100  pc) ` , ˪Clumpy 1` -  N` 5  k` . The Onset: Pressure changes ` /  Decrease internal pressure ` 0 Decrease temperature or density ` 1 Atoms   Molecules ` 2  Increase external pressure ` 3 Pressure shocks 6` & !Ionization of surrounding medium HH5RDHHlUQQ ` #d5SLoUUhensHH5TS HHce ^ Z^U  ` 4 K)When Collapse Occurs ;` 6 The Jeans Mass mX` 7  u h 9  (Start with hydrostatic equilibrium:  : 1Assume a uniform density  atomic hydrogen  @ : ˀcloud of radius R: mpy` ; -  r =  nm H ;` < *  M(r)  = (4p r 3 /3) r X` =  8  P  = 2p G(nm H ) 2 R 2 /3 eau` > de t @ 1.Now, assume this pressure is greater than the  H @ e2internal pressure from the cloud temperature: & h ? 2Therefore, the mass of a collapsable cloud is HH5USHHlRXTT d5VXXHH5WV HHZ^X  ` 8 CValues for the Jeans Mass ;` A s  sX` B 7General interstellar gas ` E st n =10 6 / m 3 ` F u T =10 K a` G >  M J  = 10 33   kg  = 500  M SUN ` I  $Is this why stars form in clusters? ` J  #` K = @` M  +What density for a single solar mass star? k` C < M J   =  M SUN  = 210 30   kg e ` O e T =10 K e ` N pe(  n  = 310 11 / m 3 e,` H la Dense cloud! 6d D  HH5XVHHlUaWW ݀ 5YZ;3 ʼn9݀ ,'equal[(*q"Green"q*)over[(*q"Green"q*)times[(*q"Green"q*)char[(*q"Green"q*)d],char[(*q"Green"q*)P]],times[(*q"Green"q*)char[(*q"Green"q*)d],char[(*q"Green"q*)r]]],minus[(*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],id[(*q"Green"q*)char[(*q"Green"q*)r]],char[(*q"Green"q*)rho],id[(*q"Green"q*)char[(*q"Green"q*)r]]],power[(*q"Green"q*)char[(*q"Green"q*)r],num[(*q"Green"q*)2.00000000,"2"]]]]]]NR5Z\SYYT f a5[\CwE Wv>210'geq[(*q"Red"q*)over[(*q"Red"q*)times[(*q"Red"q*)num[(*q"Red"q*)2.00000000,"2"],char[(*q"Red"q*)pi],char[(*q"Red"q*)G],power[(*q"Red"q*)id[(*q"Red"q*)times[(*q"Red"q*)char[(*q"Red"q*)n],indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)m],char[(*q"Red"q*)H]]]],num[(*q"Red"q*)2.00000000,"2"]],power[(*q"Red"q*)char[(*q"Red"q*)R],num[(*q"Red"q*)2.00000000,"2"]]],num[(*q"Red"q*)3.00000000,"3"]],times[(*q"Red"q*)char[(*q"Red"q*)n],char[(*q"Red"q*)k],char[(*q"Red"q*)T]]]nNZ5\Z^Sn*)[[T(*Gr5]^e"qa wB2im'geq[(*q"Blue"q*)char[(*q"Blue"q*)M],approx[(*q"Blue"q*)indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)M],char[(*q"Blue"q*)J]],times[(*q"Blue"q*)power[(*q"Blue"q*)id[(*q"Blue"q*)over[(*q"Blue"q*)times[(*q"Blue"q*)char[(*q"Blue"q*)k],char[(*q"Blue"q*)T]],char[(*q"Blue"q*)G]]],over[(*q"Blue"q*)num[(*q"Blue"q*)3.00000000,"3"],num[(*q"Blue"q*)2.00000000,"2"]]],over[(*q"Blue"q*)num[(*q"Blue"q*)1.00000000,"1"],power[(*q"Blue"q*)char[(*q"Blue"q*)n],over[(*q"Blue"q*)num[(*q"Blue"q*)1.00000000,"1"],num[(*q"Blue"q*)2.00000000,"2"]]]],over[(*q"Blue"q*)num[(*q"Blue"q*)1.00000000,"1"],power[(*q"Blue"q*)indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)m],char[(*q"Blue"q*)H]],num[(*q"Blue"q*)2.00000000,"2"]]]]]](*qNvS5^\S,m[]]T],med5_d*)aaHH5`_ HHOGr]cca"q ` L Conservation of C ` P chAngular Momentum pf` Q nd s` R ha,Consider collapse of a one solar mass cloud q"` T Bl7 Radius  0.1  pc  = 3.110 15   m harˀ` U ar4 Rotational velocity at surface  1  km/sec *)` V 00,(Recall: v ARM    220  km/sec) ov` S [(5 Collapse to solar radius  710 8   m l"` X Bl q? h W 1.&Must have L = mvr conserved, so ` Y Bl qӀ` Z 1..  The process must shed angular momentum! ` [ lu Accretion and axial jets num ` ] 00Magnetic fields are important! *` \  Fragmentation ]G` ^ me Clusters and planetary systems! HH5a_HHlX`` O6-bc,RSI(0ti'equal[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)v],string[(*q"Red"q*)"AFTER"]],cross[(*q"Red"q*)times[(*q"Red"q*)num[(*q"Red"q*)1.00000000,"1"],string[(*q"Red"q*)" km/sec"]],id[(*q"Red"q*)over[(*q"Red"q*)sn[(*q"Red"q*)num[(*q"Red"q*)3.10000000,"3.1"],num[(*q"Red"q*)15.00000000,"15"]],sn[(*q"Red"q*)num[(*q"Red"q*)7.00000000,"7"],num[(*q"Red"q*)8.00000000,"8"]]]]],times[(*q"Red"q*)num[(*q"Red"q*)15.00000000,"15"],char[(*q"Red"q*)c]]]NZ6.c_ = bb` Yd51.Lefte d6moRightd7io ReferenceedDMa fdSdV]d_ p a 1msf a Body. f b ]]( RBulleted\tn. 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