Aa5d HH $ @d HHHHff@  d/ Footnote TableFootnote**.\t.\t/ - :;,.!?0 `    `!TOCHeading1Heading2  EquationVariables7M6Zd5] ) 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 All!7Table<$paranumonly>, <$paratext>, on page<$pagenum> =Table Number & Page'Table<$paranumonly> on page<$pagenum>  FFAe HHAM JJ LL NN PP RA$  5y  soe>5|  s > 5  ui> 5 t"5 ! u/um5 " ta5 # ~n$d5 $ ~ se5 % w s>/5 &  s$ea5 ' v sfi5 ( s 5 ) } v 5 * v vele5 + vte5 , v v]5 - } vg5 . v va5 / va5 0 v vod)5 1 v v+t 5 2 vu<$5 3 vn5 4 vnge5 5 v vx p5 6 vu5 7 veen5 8 vHe5 9 ve<5 : v e5 ; v v 5 < v!e5 = vl$p5 > vo<5 ? v vTa5 @ v&'5 A vay>5 B vp>5 C v5 D vF5 E ve5 F v v5 G v v5 H vJ5 I  v5 J v v5 K x v5 L y v5 M v5 N v vR5 O x v$ 5 P y vs5 Q v vs5 R vu5 S t5 T u5 U t5 V ~5 W ~5 X v w5 Y v5 Z vv5 [ v7* \ }6 ] vv6 ^ v6 _ vv6 ` v}6 a vv6 b v6 c vv6 d vv6 e v7+ f 7, g v6 h v6# i 6$ j 60 k 6) l 6* m 6+ n v6< o v v6 p | v6? q z6V r v vv6 s v6@ t w w6 u  v6 v v v6 w v v6 x v6 y vv6 z vv6 { v6 | v v6 }  vv6 ~ } vx6  | vy6 v v6 | |v6 |x6 x y6 } vv6 | v6 v v6 v v6 | |6 |6 6 vv6 v6 v6 v6 v6 v6 v6 6 6 6 6 7 6 7: 6 7 7 v7 v7 v7 v7 7 7 v7 |7 7 {v7 7 w7 7! v7$ v73 5g6dq5PF6dq6|yLH6dq7xy8C6Hm3R q897 vHm3R H RH R FootnoteHr@ q98:7 Hr@ HzHz  Single LineH'q:9<7 ;;Footnote  5_;:     HD q<:=7 6HD HH  Double LineH q=<@77>? Double Line 5c>?=|5e?>=7 7! H q@=B7AA Single Line5hA@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 HHA  R  ` # Variable Stars  and UVC ` $ Planetary Nebulae f` %  ` & /Loss of (Hydrostatic) Equilibrium with Old Age ` '  ` )  Evolutionary importance ` *  ` + &Clues to details of stellar structure ` , K 1` 0  N` -  Practical importance k` .  ` / Distance and age indicators !HH5RDHHlUQQ MMd5SUUHH5TS  HH "5U ` ( Types of Variable Stars ;` 1  X` E Stars with Varying Brightness u` F  ` 3 Ϊ Eclipsing Variables ` 4 Binary star systems nd` 5 $ ` 6 e  Pulsating Variables ` 7 Regular period variables i#` 8 geCepheids (Type I and II) @` 9 RR Lyrae stars imp]` : Long period variables z` ;  i` < ct Eruptive Variables K` = 0Novae ` > Supernovae im` ?   ` @  Other Variables (` A orT Tauri stars E` B Flare stars b` C Magnetic variables ` D M... HH5USHHlRXTT d5VXXHH5WV ae HHq 1 St]]Xng ` 2 F Naming Stars ;` G li nX` I %Identify Stars within Constellations u` J  ` K ץ  General Scheme ` L .Greek letters in order of  brightness . ` M a0Example:  a   Orionis (aka Betelgeuse) ` N Lo p` O ' Variable Stars: Weird and diabolical  #` P K5Latin letter sequence in order of  discovery : n@` Q  ?]` R 'Numbers  1 ... 9   R ... Z ` Az` S s +Numbers  10 ... 18   RR ... RZ ` T v Next  8   SS ... SZ ..` U ...Next  1   ZZ ` V 4Next  25  AA ... AZ  (Dont use J) ` W $...Last  10  QQ ... QZ !; ( X This allows for  stars e L@ X ˈwithin a constellation i` Y   V335, V336, ... HH5XVi nHHlU[WW ud5Y ne[[ LHH5ZY . HHExonis (ak[UTUT ` H Cepheid and RR Lyrae Variables s: 5` Z al R` ^ K Giant stars o` a f Cepheids: F and G spectral type Q` b *-2 >  M V  > -6  Population I ` c = 0 >  M V  > -3  Population II (aka W Virginis) ` d /RR Lyrae: A and F spectral type; Population II ..` e M V  0.5 ` ` t  ` _ .  Regular pulsation periods :` \ La0Cepheids:  1  day to  100  days W` f 1RR Lyrae:    1.5 hours to   1  day at` g  Y` ] V3 Distance indicators  j ,Strong correlation between pulsation period @ j Wand intrinsic brightness. ` h !Period-Luminosity Relationship L` i  "` l Identify variable ?` k   measure period k\` m !  Look up absolute magnitude ny` n   Find the distance HH5[YHHlX`ZZ v:5\] v:v:!3'equal[plus[num[9.00000000,"9"],sum[char[i],equal[char[i],num[1.00000000,"1"]],num[25.00000000,"25"]]],plus[num[9.00000000,"9"],over[times[num[25.00000000,"25"],id[plus[num[25.00000000,"25"],num[1.00000000,"1"]]]],num[2.00000000,"2"]]],num[334.00000000,"334"]] 3,Cv<5]Vf;\\Whos d5^Y``cendHH5_^ aonHHfPioand indd`ne ` [ PPulsation Mechanism ioAfPfP` q The He +  Valve l^fP` t ia {fP h o 5Key: Star brightens just after radius at minimum k[fPfP` r tu1Depth of He +  zone very sensitive to mass xfP` p -  Period-Luminosity   Relationship HH5`^HHl[c__ d63am.0ccqu[cHH64ba ,5"HH0,0000000,cnu UU` s 00Period-Luminosity Relationship ]]]8` v "3 ]U` u ӈ/Distinct for Type I & II Cepheids and RR Lyrae r` w  ` ~ Cepheids Y`  C Nearly linear in  M  (i.e. log  L ) versus log  P H` ) Tracks nearly parallel for Type I & II e` *Type I  4  brighter than Type II `   ` RR Lyrae a=` o3  M  +0.5  independent of Period P  mZ` r$ Important distance indicators for enw` fPGlobular Clusters ` it$  RR Lyrae gap on HR Diagrams `  ` /  You have to know what youre looking at! `  3HH66caHHl`bb HHfP6Yd^00,B3g_l-6e|kdp]]l-"3 ]ll )fgqA6fd L )fgqA 9 9  Star surface>?YY6igidlea>?YYD6hqrdr~Drac nDDXZ%#6migjdIXZ%#`c6ojild`c;-6kend .5;-of ri;;6mm6rljmdor6mm? 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(A) Zeilik Fig.18-3: Visual Luminosity ` 8Find L/L SUN   10 7/2  for log  P =1 ks ` .(Bolometric correction small for F & G stars) 9` St/  M   +4.72 - 2.5  (7/2)  = -4.0 dV` ʛ s` 4or  (B) Karttunen Fig.14.6: M V  directly `   Read  M   -4.2 ` ck .`  ` "(2) Convert Magnitude to Distance `  !` >Zeilik Eq.11-6:  m - M  =5  log  d  - 5 >`  [` WoAm - M  = +7.0 - (-4.0) = 11.0 = 5  log  d  - 5 Ix` *  d  =10 16/5  = 1.6  kpc HH6HHlc frod6 la HH6 i18HH nd L/L   ` { =Planetary Nebulae ;` | co cX` } G*Atmosphere permanently out of equilibrium u` /2 ` 4 Typical end stage for  1  solar mass stars tu` V ` F Mass loss rate  10 -4 -10 -5   M SUN /year `  ` (2&  Lifetime   50,000  years #` (Not so many of them around.) @`   =]`   Central star very hot z` Wo ` .00  Ionizes gases and emission lines observed `  ` = + May be preceded by long period variables `   ` * Possible ingredients for new star birth HH6HHl  i d5Leftd6 Rightd7 ReferencedD GdSutuidV/2dYl agd^s tudad  dM a Dr f a Body. f b ve Bulleted\t. f c CellBody. f d  CellHeading. f e V 2Footnote. 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. f   Body. 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