Aa=d HH $ @d HHHHff@  d Footnote TableFootnotee*m*.\td.\t/ - h:;,.!?c `1`TOCHeading1Heading2    EquationVariables(5E8 &5&6&7'9'q:5'z;7'<8'=(>'?'@<$lastpagenum><$monthname> <$daynum>, <$year>"<$monthnum>/<$daynum>/<$shortyear>;<$monthname> <$daynum>, <$year> <$hour>:<$minute00> <$ampm>5Y>"<$monthnum>/<$daynum>/<$shortyear><$monthname> <$daynum>, <$year>"<$monthnum>/<$daynum>/<$shortyear> <$fullfilename> <$filename> <$paratext[Title]> <$paratext[Heading1]> <$curpagenum>  <$marker1> <$marker2> (Continued)+ (Sheet <$tblsheetnum> of <$tblsheetcount>)tdHeading & Page <$paratext> on page<$pagenum>Pagepage<$pagenum>OSee Heading & Page%See <$paratext> on page<$pagenum>. Table All7Table<$paranumonly>, <$paratext>, on page<$pagenum>qTable Number & Page'Table<$paranumonly> on page<$pagenum>AADA$orAdmgyem*:ten)o'ndap(rq)oe>r( >'!s//"hnt'moru+ fuv, w+ax-a[Ty- paz-i{.uum|/ er}/ er~/ in0Sh1e o2t)1e& 3r 3a3$p4SeM Se6x p/u7 Ta8u, 8>pa9m9bag9$mo/een78::;/A/ 8 88MA./5=or6=9/d:>*H/)l?'x8(}8)/(@//'M+6,/+G-H-I-/.//K/L/'8N/0'ZN/1'[//2'=661'\//3'LM/3'UB/3'_C/4'//M's1/6'~///'//7'//8'P/8'//9'//9(PP9(PP/( CA7'//8'PO:'M/:'P/;'PO/'///'//8'//8'//8'//M'///'//='//='///'//>IE\HdqM(dqM/'N"fPH?N"G-#56e>O//6e6e$'equal[dangle[times[over[num[1.00000000,"1"],num[2.00000000,"2"]],char[m],power[char[v],num[2.00000000,"2"]]]],times[over[num[3.00000000,"3"],num[2.00000000,"2"]],char[k],char[T]]]'sfPnN"/7f#6'$U}( HD.oO/9*>(BZ$U}( HD.OP'equal[over[indexes[0,1,char[N],char[B]],indexes[0,1,char[N],char[A]]],times[over[indexes[0,1,char[g],char[B]],indexes[0,1,char[g],char[A]]],exp[id[(*i1i*)minus[over[times[char[Delta],char[E]],times[char[k],char[T]]]]]]]]'hZ6e'O/=hZ6ehZ6e$'mequal[times[over[char[d],times[char[d],char[lambda]]],indexes[0,1,char[R],char[lambda]]],num[0.00000000,"0"]]Nf`H'N01=?^ , :@L(O^ , :@L^ , :@L6f`'equal[indexes[0,1,char[lambda],times[char[m],char[a],char[x]]],over[cross[num[2.89800000,"2.898"],times[indexes[1,0,num[10.00000000,"10"],minus[num[3.00000000,"3"]]],bullet[char[m],char[K]]]],char[T]]]2Nf`k(N0P3@1>/PP(N HPPlHH$ (N1haH$ l  s[0d'Mr]][tesHUa (N]]]HUa l  hZHH(N[meHHl  R],PP'N `PP}fP1= dLaw of Stefan and Boltzmann L;dHow Bright is a Star? Xda] mud,c1It depends on Temperature and Radius nd00 0"l3.Integrated intensity9 cfPfPd]2swhere s = 2p5k4/15c2h3 = 5.6710-8 W/m2K4 7fPd TfPd qfP"l2Total luminosity (for a star of radius R)? fPd fPd fP"l1Detected Flux (for star at a distance r)@ ufPd[t'Later: Connect flux with magnitude VH'N9Urr3j'OUrr3jUrr3j$'equal[times[char[I],id[char[T]]],int[(*i2i*)times[indexes[0,1,char[R],char[lambda]],id[char[T]],diff[char[lambda]]],num[0.00000000,"0"],char[infty]],times[char[sigma],indexes[1,0,char[T],num[4.00000000,"4"]]]]oVfPH'Nm?dsn \ %p'O\ %p\ %p$ed'equal[char[L],times[id[times[num[4.00000000,"4"],indexes[1,0,times[char[pi],char[R]],num[2.00000000,"2"]]]],char[I]],times[num[4.00000000,"4"],char[pi],indexes[1,0,char[R],num[2.00000000,"2"]],char[sigma],indexes[1,0,char[T],num[4.00000000,"4"]]]]or VhfPH'N @fP'e59'Ot d'e59'e59$r:'cequal[char[F],over[char[L],times[num[4.00000000,"4"],char[pi],power[char[r],num[2.00000000,"2"]]]]]H$ (NH$ lal[HUa (N[deHUa l,nuHH(Nia]HHlHH(NHHl\ HH(N eqHHlA!!mes`a@N,h[IT3-7"]ha R",c Z6_ fPZ6NZ?lHu?l6u$?TOu$~$u$?Z?DV^  rha?DV?T?TdA~Gt U  ~Gt~~Blackbody surfacet ^ 2 l[t$$Power radiatedH$  N H$  iUUdn HUa  N NHUa  UUdp HH N HH a@Ndty 3H$ N RH$  UU`q NHUa N HUa  $uUU`r ^HHN HH G Gdoy bdqM2tH3R `@qN H3R `@H RH RFootnoteHq3@ `@qN Hq3@ `@HzHz Single LineH'qNaFootnote  &Vp     H3D `@qP H3D `@HH Double LineH qNN Double Line&W`q&WaH qNr Single Line&WHZqNMq TableFootnoteEGVR `@qN EGVR `@EPwEPw TableFootnoteod5pMHHN HH>a `mPrevious Class ;`u X`v3+Began discussing Electromagnetic Radiation 3u`w `x General properties `yN Astronomical sources `z& Optical line emission from hydrogen `{ Balmer series in visible `|W #`} @`~ e `Todays Class ` `,Finish discussing Electromagnetic Radiation W` ` More on lines `N Blackbody radiation ` Temperature 6`q Application to stars GVd MoHH!N HHjNH `Other Line Sources ;`(Zeilik Sec 8-3) X`&Theres more than hydrogen out there! u` R a`Multielectron atoms `l , Nothing as easy as hydrogen to understand al`* Characterize by Ionization Potential: `Hydrogen13.6 eV m`leHelium24.5 eV `|#`Calcium6.1 eV @` ]`yIonic spectra z`' New spectrum after electrons removed rom`W Symbols:I is neutral atom `re#II is one electron removed, ...  `n Examples: HI, HII, HeII, ... p`  `at%Molecular spectra: Three classes (`o. Electronic (complicated; loptical) E`= Vibrational (equally spaced levels; lIR) b`5 Rotational (Ej(j+1), bands; lcm) d("MA$ tn HH)#N" aHHtfPie`Ag  `erEnergy and Temperature ;`y  nX`: +Thermal Energy  kT per particle {fPfP`um=k=1.38010-23 J/K Boltzmanns constant fP` fP ec*Example: Mean kinetic energy per molecule fP Hedin an ideal gas5 is  7fP`tr aTfP hBoltzmanns Equation6 rfP`.N = number of particles in each level fP`g = level multiplicity ar 2fP` c sOfP`Sahas Equation (lfP`(Generalize to include ionization energy ioQ~M$XA"I%+ ta Z&%Y&$c  Z( c lZ&&Y%'$ lZ#N lclu x^P'Z&($ u x^uuEBuZw1R(Z')$ uZw1ujfujfEA<8Z\(W)Z(*$ P<8Z\(<I <I DE?&*[)+$? ec?6??Q&+[*$ed?Q5is?Q?ld,MEqBBHH-N, cleHH{f_iplicityB dBlackbody Radiation (;d%Beware of Zeiliks notation & typos! gXd ud$If you make something hot it glows: tadHot Yd Hotter Zd Even hotter dY 'd2Intensity I = Power (energy/sec) radiated #dover all wavelengths ^@"lthrough unit surface area7 ds d.Units ofLareJoule/sec=Watt (W) 9f_fPd$Units ofIareW/m2  Vf_d sf_d+ d.MCC&[HH/N. sHHy858CB d Radiance ;"l4Intensity sorted by wavelength or frequency: d "lPlancks Formula; oId f"lsGeneral shape:< Xd'M0MfouDDwstaHH'N1N0 HHD ' dnsWiens Displacement Law rg;dWhat Color is a Star? Xd udug'It depends on Temperature  d  f`"lBFind l=lmax by taking derivative of Rl(T)= f`d  _5f`"l and you find that> +t&2^ 3 +t<< through dA isC_(\(&3^2 C_(\(TTdL = I dAT/<6 '9\:8/6 jq66 6M':\9;8q6Meq66 ';d:<8[q"6 m@q"R"q6HHLQQZclcllHu$u$y~~$--Hcc~V5;\('<W;=8 eq*5;\(^5^5Wavelength (l)4>tK'=W<?8 "d"+^5Kt+^5+^5 Radiance (R)*)u.<&|'>b@8 *qu.<&|uulmaxd"~c'?`=@8.00~cN~~~~?'@b?>8~?~~HH(AN$"HHlB##HH(BN,'HHlAC--HH(CN.[q"HHlBD//HH(DN0HHlC11H dLeftdRightd Reference8d\(^5d )d"Wd,td.*)d0 dU56lf Body. f  Bulleted\t. 'f CellBody. f  CellHeading. f   Footnote. fT Heading1Body. fT  Heading2Body. fT   HeadingRunInBody. f l yIndented. f g Numbered.\t. fE  Numbered1.\tNumbered. f  f TableFootnote. f!T   TableTitleT:Table : .  f"P TitleBody. f#|T   TableTitleT:Table : . f$y  CellHeading. f%y CellBody. f&y  CellFooting. f'y Body. @(  l Footer. @) bl a Header. f*$ Body. f+Body. f,Body. $$f-Body. HHf.Body. f/Body. f0$ Body. f1Body. f2Body. $$f3Body. HHf4Body. f6Body. f7 Body. $$f8Body. llf92 Body. $$f: Body. llf;Body. f=Body. $f>Body. f? Body. f@ Body. fA$Body. fB$ Body. fCBody. fG Body. fH Body. fI Body. ~~fKBody. ~fLBody. fM$ Body. fNc.~..Body. fO$Body. fPBody. yz! ڝy )| ~ Emphasis EquationVariablesڝ [ ڝw ڝ$) ڝtu w$) ڝtu w$ڝtu ) ڝwwtu ) ) ) ) ڝ ڝw$tu uo& MQMNOPRT ZUV ZW ZXY ZZ[ Z\ Z^_` Zb Zd ZAQFAThinBMediumCDoubleDThick@E Very Thin AAAAAAAAAC#H$%&H$%&H$%&H$%&H$%&Format A ABAAAAAB#H$%&H$%&H$%&H$%&H$%&Format B   Commentd BlackT!WhiteddARedddGreendd Blue dCyandMagentad Yellow Times-Roman Times-Bold Times-ItalicHelvetica-BoldSymbolSymbolTimes-BoldItalicTimesE HelveticaeSymbol RegularRegular BoldRegularItalichK0}BafwTf삯X½8ɿ0BH M: EBG"tjɎĀ׆4m8`cAF7rs,CO.͊o(h3t-lUi؃Va