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Double Line w5c>?=5e?>=7z7~ wH q@=B7AA Single Line|5hA@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  ` # X-Ray Binary Systems ;` $  X` 6 Weird Stars u` %  ` ' F Ingredients: ` ( 3 One  compact object  and one normal star ` ) $e.g.  Neutron star or black hole ` * & Small separation (near Roche limit) ` + +  Short orbital period ( ~ days) 1` ,  N` - Today: Three Examples k` . +  Cygnus X-1 ` 0 (Our best isolated black hole candidate ` 1 +  Centaurus X-3 ` 2 A pulsar eclipsed by a big star ` 3 +  SS433 ` / A  very  weird object 6` 4 5 S` 5 4We will use  kinematics  to understand these. OHH5RDHHlUQQ d5SX-UUHH5TS a HH gredientYqU h & t !Motion of Binary Systems u  h ; wherew t h < ck+Newtons Second Law (F=ma) says thaty ion h 9 ) >Assume circular motion, so with  i=C  or  X ,x }` : ,'where  P  is the orbital period. e EHH5USX HHlRXTT  d6VXX eipHH6WV HHj /rd objecX ` 7 5 Cygnus X-1 us;` 8  X` ? O%A Black Hole in Orbit around a Star? u` =  ` @  Very bright X-Ray source ` A 57L  (2 E 11  keV ) = 210 30   W H` F 5=  5000  L SUN ` B  ` C  Radio signal gives position #` E t =  O9Iab star (M 33 M SUN ) at that location @` M <'Note: Massive star, so large mass loss hat]` D  9z` G la, Doppler shift in stars spectrum: Binary!  ` H ,$Period  P   = 5.6  Days d.` I 2Max velocity  v MAX   = 76  km/sec ` J  ` K % No evidence of eclipsing in X-rays  ` L X'  Probably steep inclination angle 6(` N  E` O Why a black hole? b` P 9Consider the mass ( M X ) of the unseen object. HH6XV acHHlUvWW Hl5YoS ZmTu hZZ5Z[YhZZ?6$$5[Z\YB ?6$$6$5\[]Y6$ Ia6ZH$5]\^YH$asse HHQ~$5^]_YQ~$er ifQ~Q~$5_^`Yd ~$ ay~~5`_aY76~~;Z5a`bYn ;Z L;~5bacY N~ O 5cbdYms of e Q5dceY acQlQ5edfY5Q5fegY[QhQ lZ#26gfhY lZ#2 ljdZ ljdZ M XD$"$g6hgiY D$"$gD4dZD4dZ M Chfg6ihjY hfgxx ql~q6jikY ql~qqlkqlk a X%l~qvR6kjlY %l~qvR%lk%lk a CX 6lkmY X XdZXdZ a Q+$6mlY Q+$adZadZ Center of Mass6no"jA6'list[(*q"Red"q*)equal[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)a],char[(*q"Red"q*)X]],times[(*q"Red"q*)char[(*q"Red"q*)a],over[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)M],char[(*q"Red"q*)C]],plus[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)M],char[(*q"Red"q*)X]],indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)M],char[(*q"Red"q*)C]]]]]],equal[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)a],char[(*q"Red"q*)C]],times[(*q"Red"q*)char[(*q"Red"q*)a],over[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)M],char[(*q"Red"q*)X]],plus[(*q"Red"q*)indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)M],char[(*q"Red"q*)X]],indexes[(*q"Red"q*)0,1,char[(*q"Red"q*)M],char[(*q"Red"q*)C]]]]]]]N9n6 oYrSCnnTwm6pqdZ$FD$>'equal[(*q"Blue"q*)string[(*q"Blue"q*)"Acceleration"],over[(*q"Blue"q*)power[(*q"Blue"q*)indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)v],char[(*q"Blue"q*)i]],num[(*q"Blue"q*)2.00000000,"2"]],indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)a],char[(*q"Blue"q*)i]]],times[(*q"Blue"q*)indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)a],char[(*q"Blue"q*)i]],power[(*q"Blue"q*)char[(*q"Blue"q*)omega],num[(*q"Blue"q*)2.00000000,"2"]]],times[(*q"Blue"q*)indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)a],char[(*q"Blue"q*)i]],power[(*q"Blue"q*)id[(*q"Blue"q*)over[(*q"Blue"q*)times[(*q"Blue"q*)num[(*q"Blue"q*)2.00000000,"2"],char[(*q"Blue"q*)pi]],char[(*q"Blue"q*)P]]],num[(*q"Blue"q*)2.00000000,"2"]]]]ReNKe6qrS)deppTxq"d"Nj6%roqS*,1ssTy*qed6&srr%j|e>Bm'equal[(*q"Green"q*)char[(*q"Green"q*)F],times[(*q"Green"q*)char[(*q"Green"q*)G],over[(*q"Green"q*)times[(*q"Green"q*)indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)M],char[(*q"Green"q*)C]],indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)M],char[(*q"Green"q*)X]]],power[(*q"Green"q*)char[(*q"Green"q*)a],num[(*q"Green"q*)2.00000000,"2"]]]],cross[(*q"Green"q*)string[(*q"Green"q*)"Mass"],string[(*q"Green"q*)"Acceleration"]]]d63te*)vv0000HH64ut ")0HH,cr[(*q"Blzvlu h > s[8We do not know the inclination angle  i : v q* h T e"3Some algebra with binary motion formulas gives{ * h U (Now put in the numbers and you find| q"} h Q 7The easiest way to solve this is by making a plot:z *q^` R )  Far too massive for a neutron star {` V   Must be a black hole! HH66vthaHHlXyuu s[(d6ew*Gryyen*)HH6fxw X],HHjr[Green"q*y"] ` S inCentaurus X-3 ;` W GrAn eclipsing pulsar ]]X` X  3u` Z e'Similar to Cygnus X-1 in some ways ... H` [  Very bright X-rays ` ^ ,c4L  (2 E 11  keV )= 10,000  L SUN ` ] s[/ Companion is O6II giant ( mass loss! )  ` \ ' Doppler shifts in companion spectrum fo` _ P   = 2.087  Days in#` a ou"v MAX   = 415  km/sec @` ` ol t]` b p... and different in others z` c ss Eclipses! ro` d '  Inclination angle not very large H` e 66 X-ray pulses every 4.84 sec ` f $  Suggest X is a neutron star ` g 6e  ` h Gr,Enough information to determine both masses (` i )  Find M X  1.5  M SUN E` j ee *b` k Consistent with a neutron star! s HH6hywa]]HHlvxx us H`t6izt {uv 6Q@Z'<6m{z|000&9$ *8&"H m~K<6t|~z}) I4?{ J4OK<6y}zoFe6p |H @X'<6v~|zaouf6 f6HJ@X'<6s{|z{|.andr3Y h3YHZ K 3@['<6w~z~ (X; (X;"HZ J~K<6x}z|}c G8~ Y|6z}z Y|  c7p,M|6{z7p,M|) 7pdp[\&6D6z*&6D Cois&6j6Z6 6zQ6Z6 ZZlDfgO6z lDfgOlTlT iTEDfgR[6z TEDfgR[TETTET To Earth8&fg[6z t&fg[&'&' 2Measure  v MAX  =  v C  sin i6vJG2X8'equal[(*q"Blue"q*)equiv[(*q"Blue"q*)times[(*q"Blue"q*)char[(*q"Blue"q*)f],id[(*q"Blue"q*)comma[(*q"Blue"q*)indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)M],char[(*q"Blue"q*)X]],indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)M],char[(*q"Blue"q*)C]]]]],over[(*q"Blue"q*)power[(*q"Blue"q*)id[(*q"Blue"q*)times[(*q"Blue"q*)indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)M],char[(*q"Blue"q*)X]],sin[(*q"Blue"q*)char[(*q"Blue"q*)i]]]],num[(*q"Blue"q*)3.00000000,"3"]],power[(*q"Blue"q*)id[(*q"Blue"q*)plus[(*q"Blue"q*)indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)M],char[(*q"Blue"q*)X]],indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)M],char[(*q"Blue"q*)C]]]],num[(*q"Blue"q*)2.00000000,"2"]]]],times[(*q"Blue"q*)over[(*q"Blue"q*)char[(*q"Blue"q*)P],times[(*q"Blue"q*)num[(*q"Blue"q*)2.00000000,"2"],char[(*q"Blue"q*)pi],char[(*q"Blue"q*)G]]],power[(*q"Blue"q*)id[(*q"Blue"q*)times[(*q"Blue"q*)indexes[(*q"Blue"q*)0,1,char[(*q"Blue"q*)v],char[(*q"Blue"q*)C]],sin[(*q"Blue"q*)char[(*q"Blue"q*)i]]]],num[(*q"Blue"q*)3.00000000,"3"]]]]Fl6zti(*u{*)ar6uq*B< LCJ!fGM]'equal[(*q"Green"q*)power[(*q"Green"q*)id[(*q"Green"q*)times[(*q"Green"q*)indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)M],char[(*q"Green"q*)X]],sin[(*q"Green"q*)char[(*q"Green"q*)i]]]],num[(*q"Green"q*)3.00000000,"3"]],cross[(*q"Green"q*)num[(*q"Green"q*)0.26000000,"0.26"],power[(*q"Green"q*)id[(*q"Green"q*)plus[(*q"Green"q*)indexes[(*q"Green"q*)0,1,char[(*q"Green"q*)M],char[(*q"Green"q*)X]],num[(*q"Green"q*)33.00000000,"33"]]],num[(*q"Green"q*)2.00000000,"2"]]]])CNz66te(*u|)cr[H6tuq*4uzBl"q 6qid s[("B 6"uelue*)zc6zc6 uulul^QQ2?_-_-~6~eqHuHuc^~H~H>6Qi ,6 r*q>6Qi ,>L>L 0.26(M X +33) 2re}6]cr}num*qbt6Nbt6N]%GG2}6")02}"q*],t6Xt6X],GGD^IiG6 ^IiGuu (*q#26 q#2kk M X$ IievF ,6 $ IievF ,$$$$ (M X sin  i ) 3H1(65bM6 H1(65bMH1(FdZH1(FdZ  i =90 QZ666QZ6lQZQ1($5bM6 1($5bM1(4dZ1(4dZ  i =75 1(5bM6 1(5bM1("dZ1("dZ  i =60 Q$6Q$  QQc6 rccc )Must have M X   1 6 M SUNd60HH6 HH^Ii ` Y ӎSS433 ;` l A Very Weird Object f` m MRelativistic Jets ` n  ` p ,! Not particularly strong X-rays n` q 1( Rather strong radio signal ` r  Bizarre optical spectrum i1` s Strong emission hydrogen lines N` t Moving  hydrogen lines z` u 6 Two periods ` v H-lines move with 164 day cycle  ` x bM%  Precessing Relativistic Jets ` w 1('Weaker Doppler shift with 13 day cycle ` y   Close binary system HH6HHly t hd60HH6 HH h o $The Complete Doppler Effect } SS h { lGFor wavelengths emitted ( l 0 ) and observed ( l ), =` z  Z h | ڥ , At  q=0  find ~ Blue shift qw` on a`   h e - At  q=180  find  Red shift g` l s` t  h ge At  q=90  find  wo %`  vB` w1This is the  Transverse Doppler Effect . c_` ic$It is due to time dilation and is a op|` d purely relativistic effect . HH66HHl d66HH6 6HHx h  0Solving for the Angles and Jet Velocity  ec` 'Dopper shift is from  v JET . l1` ~ er N` 6 At  q=90  see only Transverse Doppler Effect k` J  Find  v JET   = 77,000  km/sec  = 0.26  c (!) ` q 0` . 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