THE RADIO-FREQUENCY LINE SPECTRUM OF ATOMIC HYDROGEN AND ITS APPLICATIONS IN ASTRONOMY
J. P. Wild Division of Radiophysics, Commonwealth Scientific and Industrial Research Organization, Australia Received September 8, 1951 ABSTRACT Formulae are obtained for the frequencies, transition probabilities, and natural widths of the dis- crete lines of atomic hydrogen that fall within the radio spectrum. Such lines are due to transitions within either the fine structure or the hyperfine structure of the energy levels. The conditions necessary for the formation of observable emission and absorption lines are examined. Thence an inquiry is made into which of the hydrogen lines are likely to be observable from astronomi- cal systems. It is found that the sun may give a detectable absorption line at about 10,000 Mc/sec, corre- 2 2 sponding to the 2 Si/2-2 P3/2 fine-structure transition, but that other solar fines are not likely to be observable. From the interstellar gas, the emission line already observed (i.e., the 1420 Mc/sec hyper- fine-structure line) is probably the only detectable hydrogen line. The importance of this fine in the study of the interstellar gas is discussed. Some general conclusions are drawn from the preliminary evidence regarding the motion and kinetic temperature of the regions of un-ionized hydrogen. The ratio data are used to obtain a measure of the product of “galactic thickness” and average hydrogen concentration. I. INTRODUCTION The first astronomical observation of a spectral line in the radio-frequency band has recently been announced by Ewen and Purcell1 and has had independent confirmation by two other groups of workers.2,3 The observed line is an emission line of frequency 1420 Mc/sec due to the transition between the hyperfine-s truc ture substates in the ground state of atomic hydrogen. It is observed from the general direction of the galaxy. The likelihood that this line is detectable from the galaxy was first pointed out by van de Hulst.4 In a subsequent discussion, Shklovsky5 concluded that no atoms other than hydrogen are likely to produce observable lines, although certain molecules could. The possibility of observing radio-frequency lines has also been discussed briefly by Reber and Greenstein6 and by Saha.7 The discovery of Ewen and Purcell now arouses new interest in the subject. The present paper has two objectives. The first is a detailed investigation of the radio- frequency line spectrum of atomic hydrogen. The second is an inquiry into which of these lines are likely to be observable from astronomical systems. Included in this part is a discussion of the 1420 Mc/sec galactic line and its importance to astronomy. The conclusions of the paper are summarized in the final section.
II. THE RADIO-FREQUENCY LINE SPECTRUM OF ATOMIC HYDROGEN A radio-frequency spectral line originates in transitions between a pair of closely spaced energy states of an atom or molecule. In the case of atomic hydrogen sufficiently close spacing exists (1) between the main levels of high quantum number, (2) between 1 Nature, 168, 356, 1951. 2 C. A. Muller and J. H. Oort, Nature, 168, 357-358, 1951. 3 W. N. Christiansen and I. V. Hindman, reported by J. L. Pawsey, Nature, 168, 358, 1951. * Nederlandsch. Tijdschr. v. Natuurkunde, 11, 201, 1945. *AJ. U.S.S.R., 26, 10, 1949. 6 Observatory, 67, 15, 1947. 1 Nature, 158, 717, 1946. 206
© American Astronomical Society • Provided by the NASA Astrophysics Data System 1952ApJ. . .115. .2 O 6W 9 43 consider onlythefine-structureandhyperfine-structurelines. garded merelyascontributingtowardacontinuousspectrum.Wehavethereforeto are ofnoparticularinterestinthestudydiscretelinesbecausetheysonumerous ture substatesofaparticularfine-structurestate.Transitionsthefirstthesekinds the fine-structurestatesofaparticularmainlevel,and(3)betweenhyperfine-struc- where hisPlanck’sconstant,cthevelocityoflight,RRydberg’sanda ferent l)quantumnumberscoincide.Theenergylevelsaregivenwithsufficientaccuracy discussed later. fine-structure constant.Thequantumnumbersland7canassumethefollowingvalues: by theory ofthehydrogenatom.Theeffectsknowndeparturesfromthiswillbe ties oftheelectron.Indescribingfinestructure,weshallinitiallyassumeDirac’s that, withoutthepresenceofsomeselectiveexcitationmechanism,theymaybere- between fine-structurestatesofthesamenaretype into afinestructureisascribedtothecombinedeffectofspinandrelativisticproper- equations givenbyCondonandShortley,namely, theirequationsnumbered75,118, The frequenciesofthefine-structurelinesassociatedwithmainlevelsupton=4,calcu- where7 mayassumethevaluesf,.,^Numerically^ apart fromdegeneratetransitionsofthetypein,l,j)—(n,l1,7),allowed The selectionrulesforelectricdipoleradiationallowtransitionstotakeplacewhen state 2andalower1,isgivenby transition probabilityofspontaneousemission,^421, foratransitionbetweenanupper lated byequation(2),aregiveninTable1. The frequency,v,ofthetransitionsthistypeisgiven,fromequation(1),by the land7ofinitialandfinalstatesdifferbyAZ=±1,A70,1.Itfollowsthat, Mod. Rhys.,13,233,1941. The strengthsofthefine-structuretransitionsmay becalculatedbycombiningfour where g=27+1,thestatisticalweightofstate2, andS21isthe“strength”ofline. 2 8 9 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The splittingofeachmainlevel(characterizedbytheprincipalquantumnumbern) An outcomeofDirac’stheoryisthatpairsstateshavingthesamenand7(butdif- We shallnowcalculatethetransitionprobabilities ofthisserieslines.TheEinstein Thevaluesofphysicalconstants usedthroughoutthispaperarethosegivenbyR.T. Birge,Rev. TheTheoryofAtomicSpectra (Cambridge:AttheUniversityPress,1935). nd1 1.7 510Xn~{(7-è)--(i+è)" 2 hv TUyWj-i—(,*_1.-11)’ 7... _ww_Rhco(\1^ n W= , nj RADIO-FREQUENCY SPECTRUM (n, l,j)-l—1,71). a) THEEINE-STRUCTURELINES j =l±h- 1=0, 1,2,.,n—1; 2 Rh cca/I3 ¿ n A 21 óIttV c c c n n (tV¿) 2 J~r2/ sec -1 207 (i) 0) (2) 1952ApJ. . .115. .2 O 6W 2 6 width oftheline(definedastotalbetween half-maximumpoints).Thehalf- frequency interval(v,v+dv),fisthecenter oftheline,andôvishalf- width isrelatedtothelifetimestiandT2oflower andupperlevelsby where/(f) dpdenotestheprobabilitythatatransition ofthetype(1,2)occurswithin spectroscopy thisnaturalwidthisrarelyofpracticalimportancebecauseinstrumental limitations andothercausesoffinebroadeningtend tomakeitinsignificant.However, of alineisgivenby and maybethechieffactorindeterminingwidths ofactuallines.Thenaturalshape has afinite“natural”widthduetothelifetimeofexcitedstate.Inoptical extraneous causesoflinebroadening(e.g.,Dopplereffectandcollisions),aspectral the naturalwidthsofradio-frequencyfine-structure linesarerelativelyverylarge Transition probabilitiesofthefine-structurelinesassociatedwithlevelsuptow=4, where aoistheradiusoffirstBohrorbitandeelectroniccharge.Also,for 0 calculated fromequations(5)and(4¿z),areincludedinTable1. Since 521isexpressedintermsofale,themostconvenientnumericalformequation the degeneratetransitionsoftype{n,l,j)—(n,l,l,y)>weobtain 63, and2.Fortransitionsofthetype(n,l,j)—ll,j1)weobtain (3) is 208 J.P.WILD © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Finally, wecalculatethenaturalwidthsoftheselines.Eveninabsenceall 2 2 2 2 2 2 2 2 2 4F 7/2- 4F5/2- 4D/2- 4D/2- 4P3/2- 3D/2- 3P/2- Fine-Structure Linesforn=2,3,and4,According 3D5/2- 2P3/2- 5 3 3 3 Designation 2 2 2 2 2 2 1 ■ 4D/2. -4D/2. -4P/. -42SÍ/2. -3P/. -3P/2. -3S/2. 5 3 32 32 1 1 ,421= 7.521X10-38—sec“.) (5 2 (l) = (6> 521(nl )ae S21 =(4f-1)(wP)a¡e,(4a) ' TôîIITTT(v-vo)T&P\’ =i6ÿT+T-°' 2 9n 2j\ to Dirac’sTheory Frequency (Me/Sec) 10,944 3243 3243 1368 1368 1081 456 456 228 TABLE 1 2 g2 VaeV 0 -7 11 8 -9 8 8 10 9 7 8.9X10 9.6X10- 3.5X10- 3.9X10 8.7X10" 2.8X10" 7.2X10- 1.2X10- 1.4X10“ Probability Transition -1 (Sec) Half-width (Mc/Sec) 100 Natural 40 40 30 17.2 17.2 13.6 6.6 6.6 <=/ ,p. Tt" ? •< 1952ApJ. . .115. .2 O 6W 9 10 2 12 11 6 / =j±Itfollowsfromequation(7)thattheseparationbetweenapairofhyperfine- used tocalculatethehalf-widthsoffine-structurelinesgiveninTable1. This equationandvaluesoflifetimestabulatedbyCondonShortleyhavebeen fine-structure splitting.FollowingthefirstcalculationsofFermi,Bethederivedfol- lowing expressionforthehyperfine-structureenergyshifts: levels. Thishyperfine-structuresplittingissmallbutnotnegligiblecomparedwiththe upon theelectron.Whenthisistakenintoaccount,eachlevel{nlj)splittwosub- where Here iisthespinofnucleus,/totalquantumnumbergivenbysum the iandyvectors,g(i)isLandéfactorforproton.Forhydrogen,=J note that,forthegroundstate,1Si/2,separationis structure sublevels,/=+èandj—isgiveninfrequencyunitsby This equationgivesthefrequenciesofhyperfine-structurelines.Todeterminevo,we and Zacharias,usingtheatomic-beammagneticresonancemethod.Thevalue,asgiven The valueofvhasbeenmeasureddirectlybyNafeandNelsonNagle,Julian, Hence, byequation(10), by NafeandNelson,is cent). Thefrequenciesoftheselines,calculatedfromequation(9),forthen=1and Of the.hyperfine-structurelines,byfarthemostimportant inastrophysicalapplications therefore magneticdipoletransitions.Thetransition probability,foratransitionof is thatoffrequency1420Mc/secassociatedwiththe groundstate.Thefirstderivationof the type(w,/,/,/)—{n,l,j,f1)isagaingiven intérmsofthelinestrength,S21,by (the valueofvocalculatedfromeq.[8]differstheabovebylessthan0.3per equation (3),butnowwemustregardthestatistical weightofstate2as the strengthofthislinewasmadebyShklovsky, whoobtained(inournotation) 2 levels,aregiveninTable2. G 11 n 10 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem In theabovediscussionwehaveignoredeffectsofnuclearmagneticmoment The transitionsoccurbetweenstateshavingthesamelquantumnumberandare Phys.Rev.,73,718,1948. Phys. Rev.,72,971,1947. HandbuchderPhysik,Vol.24/1,chap,iii,pp.385ff.,1933. fk hyperfii RADIO-FREQUENCY SPECTRUM b) THEHYPEREINE-STRUCTURELINES H ^/(/+D-i(i+D-j(j+D n* (j(j+1)(2/+1) V2 „ =JL-i±±1"(9) 1420.410 ±0.006Me/sec. vq =532.65Me/sec ns +■ 2 J'o =g(f)CLcR. = £2 2/-f-1.(ii) 2 £21 =fß, j) ^O 209 (7) (8) 1952ApJ. . .115. .2 O 6W 134 15 where ßdenotestheBohrmagneton, permissible, Purcellpointedoutthatinthisinstanceitwasincorrect,sinceimplied 210 strength ofthislinetobe In Shklovsky’sderivationaquantum-mechanicalresultofCondonandShortley,origi- Recently, however,EwenandPurcell(personalcommunication)havefoundthe with L,S,andJreplacedby/,I,Z,respectively.Althoughthissubstitutionisoften nally expressedintermsoftheelectronicquantumnumbersZ,S,andJ,wasused,but able totheauthorpriorpublication. 1951). fine structure. must bemodified,owingto(1)knowndeparturesfrom Dirac’stheoryand(2)thehyper- broadening underallconditionsencounteredinpractice. as theorbitalandspincomponentsofelectronicmagneticmomentbearto by LambandRetherford.Theyfoundthat,whereas theseparationof2Pi/2and quantities Land2S.(Infact,theratiosdifferbyfactorm/M,wheremMdenote that themagneticmomentofnucleusbearssameratiotoquantumnumberI 27r) andwouldbequiteinsignificantincomparisonwithextraneouscausesofline electron.) Wethereforeadoptresult(12)and,inconjunctionwithequations(3)and the massofelectronandproton,itfollowsthat,incalculatinglinestrength, 2P/2 levelswasinaccordancewiththetheory, 2Si/2leveldidnotcoincidewiththe the magneticmomentofnucleusmaybeneglectedincomparisonwiththat (11), obtainforthetransitionprobabilityof1420Mc/secline, 3 13 15 14 -16 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem “RadiationfromGalacticHydrogenat1420Mc/Sec” (Ph.D. thesis,HarvardUniversity,May, Phys.Rev.,79,549,1950,and 81,222,1951. ThanksareduetoProfessor E.M.Purcellformakingthisresultandtheensuingdiscussion avail- The naturalhalf-widthofthislinehastheminutevalue5X10c/sec(=^42i/ We nowconsiderhowtheseriesoffine-structure linesdiscussedinsubsectionlia The frequencyseparationofthe2sand2pstateshas recentlybeenmeasureddirectly c) theeffectsofdeparturesfromdirac’stheory uponthefine-structurelines 2 2 2 2 2P/2. 2Pi/. 2Si/ • lS. 3 2 2 l/2 Level 15- Hyperfine-Structure Lines A\ =2.85X10“sec. 2 FOR W=1AND2 2 ß = J. P.WILD Si=ß. (12) 2 Frequency (Mc/Sec) TABLE 2 1420.4 177.5 23.7 59.2 ^irm c’ eh 15 2.85X10" Probability Transition -1 (Sec) 1952ApJ. . .115. .2 O 6W 2 2 9 2 strengths ofthesecomponentsareindicatedbelowthearrows. splitting. Thearrowsincshowtheallowedtransitionsbetween2P/2andSi/levels.relative theory; b,correctedfortheLamb-Retherfordshift;c,finalscheme,includinghyperfine-structure 2P ^S, 32 for Russell-Saunderscoupling.Figure2showsthetheoreticalprofileofthismultiplet, is seentoconsistofthreecomponents(theappropriateselectionruleA/=0,±1). is showninFigure1,b.Theshiftofthe2Si/2levelhasbeenexplainedbyBetheand The relativeintensitiesofthesecomponentsmaybecalculatedbytheusualsumrules The finalschemeofthen=2sublevelsisshowninFigure1,c.P/2—2Si/2line others intermsoftheinteractionelectronwithquantizedelectromagneticfield. 2Pi/2 level,aspredicted,butlayhigherby1062±5Mc/sec.Themodifiedlevelscheme 2 s 2P, © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The energyshiftsduetothehyperfinestructuremaybecalculatedfromequation(7). Fig. 1.—Thestructureofthen=2levelatomichydrogen:a,schemepredictedbyDirac’s Dirac theory un corrected y (a) I O) O 2 2S, levelshift Corrected for RADIO-FREQUENCY SPECTRUM 5b) 1062 Mc/s 2[ 2 \ 2 P/ 2P, { { \ ili Final schemewith hyperfine structure -f-OAV=H33Mc/s — Relativestrengthsof —f=0,AV =-44Mc/s ^-f= t,av=+I5Mc/s t = M, av=“15Mc/s f2, av»+9Mc/s components hyperfine-structure (c) = av+44Mc/s 211 1952ApJ. . .115. .2 O 6W Kd8 Vf". ^^,.v,-.I(v)—fje ^ ¿S'(13 16 lowed transitionsoffinitefrequency(^1000Mc/sec)canoccurbetweenthem.The equation applicableatradiofrequencies seeS.F.SmerdandK.C.Westfold,Phil.Mag., 40,831,1949. tion arecompletelyspecified. tion) andmagnitudeofaspectrallinewhenthephysicalconditionsaffectingitsforma- sociated withconsiderablyhighernlevels. strengths ofsuchlinesaregivenbyequation(4b);theymuchlessthanthosethe The solutionis in thefrequencyelement(vjvdv)atthe'pointlineofsightdistancesfrom these lines. subsection liamaybeusedtocalculatethefrequencyandtransitionprobabilityof arise inthen—Zandhigherlevels.Asafirstapproximation,however,resultsof type (n,Z,j)—(nl1,j1)ofcomparablefrequency,becausethelatterareas- and thetransitionprobability,usingabovevalueofv,isfoundtobe we canexpresstheemission coefficientintemperatureunits(degreesper centimeter) or “brightness”temperature,definedby radiation atanypointisgivenbytheequationoftransfer, through someassemblyofatoms.Letthevolumecoefficientsabsorptionandemission and the“linewidth,”definedbyequation(27)asreciprocalof/(v),maybecalcu- which isnegligiblydifferentfromPlanck’sexactformula atradiofrequencies.Similarly, Intensities atradiofrequenciesareoftenexpressed intermsoftheequivalentblack-body the observerbeK(v)&ndj(v)dv,respectively.Thenspecificintensity,I(v)dv,of 212 J.P.WILD where kisBoltzmann’sconstant.Thistransformation isjusttheRayleigh-Jeansformula, lated tobe the frequencyofmaximumoccursat taking accountofthenaturalshapecomponentsgivenbyequation(6)withdv= 100 Mc/sec(seeTable1). y 0 0 2 16 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The removalofthedegeneracybetween2Si/2andPi/2levelsimpliesthatal- We havefirsttoconsiderthetransferofradiationalonganylinesightpassing In thissectionweconsidertheproblemofcalculatingnature(emissionorabsorp- Asgivenheretheequation referstomediaofunitrefractiveindex.Forthegeneral formofthe These remarkshavebeenconfinedtothen—2levels.Similareffectswill,ofcourse, If the2P/2—2Si/2multipletisregardedasasinglelinewithasymmetricalprofile, 3 III. THEFORMATIONOFEMISSIONANDABSORPTIONLINES 1; T —=/WK(v)I0).A'- a s a) THEEQUATIONOFTRANSFER Av =—-T-=210Mc/sec, 71 ^i =6.5X1C“sec“. vo= 9847+5Mc/sec, 2 J M 2 _I(v) c T 1 2 kv’ 1952ApJ. . .115. .2 O 6W 17 and 2,thecoefficientsofabsorptionemission forthelineradiationaregivenby where Similarly, thenegativeexcessbrightnesstemperature ofanabsorptionlinecannotexceed the value value may simplybeshownthat,ifweneglecttheveryspecialcasesofexcitationforwhichK Evidently, positiveATimpliesanemissionlineandnegativeabsorptionline.It is negative,theexcessbrightnesstemperatureofanemissionlinecannotexceed The differencebetweenthetwowillbereferredtoas“excessbrightnesstempera- and thatofthebackgroundis ture,” AT: hood oftheline“background”coefficientsJbandKbareconstant. denotes thecontributionofallothertransitions.Thenweassumethatinneighbor- where thesubscriptadenotescontributionoftransitionstype(1,2)andb a be statedformallyasfollows:LetthecoefficientsJ(v)andK{v)writtensumof two terms, no oneofwhichpredominates)and(2)the“line”duetotransition(1,2).Thismay a continuousuniform“background”(duetolargenumberofunspecifiedtransitions, neighborhood ofthefrequencyz^o,spectrumradiationmayberesolvedinto(1) frequency, vq(thelinewill,ofcourse,havefinitewidth).Itwillbeassumedthat,inthe between someupperstate“2”andalower“1”correspondingtolineofnominal Equation (13)maythenbewritten thus, 17 See,e.g.,E.A.Milne,Handbuch derAstrophysik,Vol.3,chap,ii,pp.159ff.,1930. In termsofthetotalnumbersatomspercubic centimeter,niand^2,instates1 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem In accordancewithequation(14),thebrightnesstemperatureinlineis Let usnowsupposethatsomeoralloftheatomsinviewarecapableatransition b) EVALUATIONOETHECOEFFICIENTSOFABSORPTION AND EMISSION [KU,+Kts Totiv) =["{Jai?)+J}e-?“’‘ds,(15) J {v)=Ja(y)+/,K(v)K(v)+ b bah —-T ( AT)=1—ea)^rT, (18) max6a RADIO-FREQUENCY SPECTRUM K (v)=a(^!—n ),(19) a2 T = Kbds T= f™Je~?'ds.(16) (Ar)= /J(v)ds.(17) hb max T =/K(v)ds. a J{v) AT =Tab—T.~^- b Z' 00 \ £2/ S jjv)_cz : d 2 0 — fKinds'-i 2kv S . 213 (14) 1952ApJ. . .115. .2 O 6W - give íí, Here a(v)istheatomicabsorptioncoefficient,definedby 214 where f(v)dvdenotestheprobabilitythatatransitionoftype(1,2)occurswithin 6, definedby frequency range(v,vdv).Thefunction/(v)thusdeterminestheshapeandwidthof librium, disidenticalwiththetemperature. atoms betweenstates1and2.Inparticularcircumstances,suchasthermodynamicequi- In general,theexcitationtemperatureexpressesmerelyrelativedistributionof the line. and We notethat brightness temperatureisgivenbythefollowingapproximation,providedthatKJ<$C1 This isKirchhofi’slawandquitegenerallyvalid. of thelineisclearlyjustreciprocalwidth,Ay,whendefinedby and 0»TV Finally, wehavetoconsidertheline-shapefunctionf(v).Itsvalue,/(ï'o),atcenter a When thelinewidthisdeterminedentirelyby naturalwidth,/(y)isgivenbyequa- a then frequency v'=yo(l+[y/c]),where^isthemeanvelocity oftheatomsalongline tion (6).WhenDopplerbroadeningpredominates, thecenteroflineisshiftedto the velocitydispersion,Av,isdefinedby sight. Ifni(v)dvdenotesthenumberofatomswith velocitybetweenvanddvif a 0 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem It isoftenconvenienttoexpressthecoefficientsintermsofexcitationtemperature, When hv<£kd(whichisusualatradiofrequencies),equations(19),(20),and(22) It isshownintheAppendixthat,auniformmediumofthicknessZ,excess a Kl T “T,AT~0(1—ß-a).(26) a n(v)A= Ini(v)dvni, 1 Ja (y)=a0)—?Z2^. / (y)Ay= 0 a K (p)=an,~(23) K 00 Ja O') a a Ja (v)=aM—.(24) („) =lL4|iü -m- ,\.kV Ay =—A, — =Sl(22) ni gi J. P.WILD c O TTvgi 00 n co g2 k /w, (21) (20) (25) (27) 1952ApJ. . .115. .2 O 6W 2 192 0 18 2 state 2Pi/2becausethelatter transitionhasalifetimeofsome40years. radio-frequency hydrogenlines,thevalueofNzor (N\—^[gi/^])requiredtoproduce second isthemetastabilityof2Si/2state;this resultsinanoverpopulationofthe the chromosphere,whereneutralhydrogenisfarmore abundantthaninthecorona.The The firstisitshighfrequency:radiationof10,000Me/sec canpenetratequitedeeplyinto tion. Twocircumstancescombinetomakethisline themostfavorablefordetection. a measurablevalueofAT(~1(jK,say)isinconceivably high. With theuseoftheseequationsitmayreadilybe shownthat,forallbutoneofthe frequency, i>o,ofthetransition(1,2).Thenitfollowsfromequations(17),(18),(19), properties ofthesolaratmosphereanddependscriticallyonfrequency.Ingeneral, and (20)thatthemaximumpossibleexcessbrightnesstemperatureoflineisgivenby Let NiandNzdenotethenumberofatomsinstates12containedacylinder absorbing layerabovethephotosphereisdeterminedbyrefractiveandadsorptive follows that,unlesslinesofgreatstrengthcanbeobtainedfromthesun(regardedasa ground continuumofgalacticradioradiationisbelievedtobenonstellarinorigin.It of 1cmcross-sectionbetweentheobserverandabsorbinglayercorrespondingto to someextentwithin,theabsorbinglayercorrespondingfrequencyofline. which cancontributetotheformationofaspectrallinearethoselieabove,and of radio-frequencyhydrogenlines. typical star),itisunlikelythatanylineswouldbeobservableintheaggregateradiation to thephotospherebutsomediffuselayerinsolaratmosphere.Theheightofthis the lowerfrequency,higherabsorbinglayer.Itisclearthatonlyatoms of otherstars.Apartfromtheinterstellargas,therefore,sunismostlikelysource occupy onlyaminutefractionofthesolidangleaerialbeam.Thegeneralback- cause theangularresolutionofpracticableaerialsystemsisextremelylow.Theonly star thatcanberesolvedasasinglesourceisthesun.Theaggregateofotherstars stellar gas.Both,therefore,maybesourcesofradio-frequencyhydrogenlines. where Mistheatomicmassand0kinetictemperature. When themotionofatomsisentirelythermal, and e 18 19 2 2 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem See,e.g.,S.F.Smerd,Australian J.Sei.Res.,A,3,34,1950. Themetastabilityofstate2 Si/2 isnotsignificantlyaffectedbytheallowedtransition tothelower The exceptionisthefine-structureline2P/2—2Si/2 (near10,000Mc/sec)inabsorp- When thesunisviewedatradiofrequencies,diskwhichseencorrespondsnot Radio-frequency techniquesareunsuitedtotheobservationofindividualstars,be- Atomic hydrogenisknowntobetheprevalentconstituentofbothstarsandinter- 3 ( —Ar)^Ta(^o)^-A^iAforanabsorption line.(3D maxh2 (AT) max RADIO-FREQUENCY SPECTRUM 1 = a(^o)-—r-Nz IV. ASTRONOMICALAPPLICATIONS g2 k Ap vo a) THESUN /2 ( Mv for anemissionline, 215 (29) (30) (28) 1952ApJ. . .115. .2 O 6W 4 220 2 12-2 9 -3 2 20 4-3 12-2 1-3 1 4 21 6-1 7-3 prominences aresomewhatsmallerthanthisvalue.Furthermore,theobservationof disk isknownfromobservationstobeabout2X10°K.Takingthisvalueofand The averagebrightnesstemperatureof10,000Mc/secsolarradiationovertheoptical at thecenterofthislineisfound,fromequation(21)andnumericalvaluesgiven Thus, toobtainanabsorptionlinewithexcessbrightnesstemperatureof—50°K, neglecting {gi/g^NzincomparisonwithWi,weobtainfromequation(31) the endofsubsectionlie,tobe 2Si/2 State(cf.Giovanelli)—i.e.,ahighvalueofNi.Theatomicabsorptioncoefficient lower kinetictemperatures.)Itisgenerallybelievedthathydrogenconcentrationsin atoms willbeconcentratedintothelastthousandkilometersorsoneartopof and theabsorptionlayerof10,000Mc/secbackgroundradiation.Mostthese atoms instate2Si/2containedacylinderof1cmcross-sectionbetweentheobserver we requireN\^10cm.Nowinthepresentcasedenotesnumberofabsorbing 216 spectroscopic studyofothermuchlessabundantelements,notablysodiumandcalcium. a uniformsheetofgasbeyondthesolarlimbthickness10cmandkinetictemperature in theseregionsisgenerallytakentobeabout1cm . Thegasdistributionisknownto for thedirectinvestigationofinterstellarhydrogen. Theimmediatevirtuesofthisnew such alinewouldprobablyrequiretheuseofanaerialextraordinarilyhighdirectivity. corona, suchasprominencematerial,producingsignificantlineabsorptionnearthe be detectableandthatasearchforitseemsworthwhile. atoms inthestate2Si/2underchromosphericconditionsindicatevaluesbetweenabout total thicknessofthechromosphere).EstimatesbyGiovanelliconcentration concentration ofni=10cmoveralength1000kilometers(aboutone-tenththe chromosphere. ItmaybenotedthatthevalueWi=10cmcorrespondstoamean the groundstatewere+^2—4X10cm.(Lowerconcentrationswouldsufficefor center ofthesolardiskorlineemissionnearlimb.Themostlikelywasfound distances oftheorder100parsecsoneitherside. Themeandensityofhydrogenatoms hydrogen linefromthegalaxyhasinitiatedwhat promisestobeapowerfulnewtool The hydrogeninallcloudsexceptthosenearOand Bstarsisun-ionized.Thekinetic 5-10 km/sec(rootmeansquare),thoughmuchhigher velocitiesaresometimesobserved. be highlyirregular,mostoftheatomsbeingconcentrated incloudswhichoccupyperhaps the groundstate,and,second,inrelativelyhigh accuracywithwhichDopplershifts The pioneeringobservationbyEwenandPurcellofthe1420Me/sechyperfine-structure of theinterstellargas,mostourknowledgeonsubjecthasbeenderivedfrom to betheground-statehyperfine-structureline(1420Mc/sec)inemission.Forexample, and linewidthsmaybemeasuredbymeansofradio techniques. technique arise,first,inthepeculiarcircumstance thattheemissionisduetoatomsin 10° Kwouldgivea1420Mc/secemissionlineofexcessbrightnesstemperatureAT= 5 percentofspacenearthegalacticplane.Theclouds haverandomvelocitiesofabout 10° K(theDopplerwidthAv=1.1X10sec)ifthetotalconcentrationofatomsin 10 andcm.Thuswithpresentknowledgeitcanbeconcludedonlythatthelinemay 21 20 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Although ithasbeenknownforsomeyearsthathydrogenistheprincipalconstituent B.Strömgren,Ap./.,108, 242, 1948. The possibilityhasbeenconsideredofcloudsrelativelydense,coldmatterinthe AustralianJ.Sei.Res.,4,1, 289,1948. The interstellargasisconfinedmainlytoregionsnear thegalacticplaneextendingto -12 ( —AT)~5XlO^!(indegreesKelvin,whenismeasuredincm). max -152 a (v)=2.3X10cm. 0 b) INTERSTELLARGAS J. P.WILD 1952ApJ. . .115. .2 O 6W 22 o yet unpublished. points, itwasassumedthatthemaximumoccurred atthegalacticequator.Thesame provided thatdislargecomparedwiththebrightnesstemperatureofgeneralback- ponderance ofneutralinterstellarhydrogeninthegroundstate.Someaspectsthis galaxy (about20kiloparsecs),thepossibilityofobservinganyradio-frequencyhydrogen ized totheassumedmaximumandabscissas converted intogalacticlatitudes. experimental pointsarereplottedinFigure3,which theordinateshavebeennormal- probability, the1420Mc/seclinegainsoverallothersbecauseofoverwhelmingpre- about 60°K.Usingthesedatatomakecalculationsofthekindemployedabovefor temperature oftheun-ionizedcloudshasbeenestimatedbySpitzerandSavedofftobe measure ofbrightnesstemperature.Indrawing the curvethroughexperimental aerial temperaturethroughthegalacticcenter.The observationsweretakenalongthe lowest curveplotted. ground radiation(about10°Ktowardthegalacticcenteratthesefrequencies).The from opticálobservations. interstellar lineanditsimportancetostudieswillnowbediscussed. line otherthanthatat1420Mc/secisextremelyremote.Inspiteofitslowtransition sun, itisfoundthat,evenifthecloudsareassumedtoexistthroughoutextentof of theaerialbeam(about2J°betweenhalf-power points)wasnarrowincomparison Kd. Theeffectofthefiniteextentgalaxyismerelytocutofftopscurves when thelineisobservedindirectionsoflowopticalthickness;otherwise,self-absorp- where ^(^4%)isthetotalnumberofground-statehydrogenatomspercubiccentimeter, with thatofthesource,someasured(aerial) temperatureshouldgiveatrue line ofdeclination—30°,whichpassesobliquelyacross thegalacticequator.Thewidth near =0overafractionofdegree;theeffectshould bequitenegligibleforallbutthe show thevariationofAT/6with6,accordingtoequation(33),forvariousvalues latter conditionwilltentativelybeassumedtosatisfied.ThefullcurvesofFigure3 thickness willbe In anydirectionthroughthegalacticlongitudeofcenter,lineoptical each paralleltoanddistantdfromthegalacticplane.Forsimplicity,weassumesun to beinthegalacticplane,thoughthisassumptionisnotessentialmainargument. 5 km/sec.Thevalueisingeneralagreementwiththerandomcloudvelocitiesderived tion andhenceadditionalbroadeningoccur.Thepreliminaryobservationsindicatethat by theapproximation(26), the galaxyisopticallythinforgeneralbackgroundradiationatfrequenciesaround Ay isabout60kc/sec,correspondingtoaroot-mean-squarevelocitydispersionof d theexcitationtemperaturein°K,andkv“linewidth/’senseofequation (where bisgalacticlatitude),exceptforverysmallangles(probablylessthanI)near (27), incyclespersecond.ThevalueofAycorrespondstotheobservedlinewidthonly 1400 Mc/sec.Underthisconditiontheexcessbrightnesstemperatureoflineisgiven a a a a 23 23 = 0,wherealimitisimposedbythefiniteextentofgalaxy.Nowitknownthat © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Figure 4showsanexperimentalplot,obtainedby W.N.Christiansen,oftheexcess TheauthorisindebtedtoMr. Christiansenformakingavailabletheseobservations which areas ™Ap. ill,593,1950. Let usnowsupposethattheregionofinterstellarhydrogenisboundedbytwoplanes, The absorptioncoefficientoftheline,givenbyequations(21),(23),and(27),is K^ M a T AT ~0(1—e~a)=-Kdcoeob),(33) aeS RADIO-FREQUENCY SPECTRUM a (v)n-^hvo 0 T =Kdcosecb a kd a 3-1 = 8.0X1C-parsec, fl 217 (32) 1952ApJ. . .115. .2 O 6W 15 24 7 near thegalacticplaneislarge,andsobrightnesstemperatureatmaximuma and PurcelliscontrarytothepredictionofShklovskythatgalaxyshouldbe optically thinthroughthegalacticcenter.EwenandPurcellfoundabsolutevalue true measureoftheexcitationtemperature.ThisdeductionwasfirstmadebyEwen 218 of thetemperature(presumablyaerialtemperature,whichwouldberatherlessthan of thesource)tobeabout35°K. upper andlowerlevelsislikelytobedeterminedalmostentirelybycollisions;inthis the brightnesstemperaturewhenwidthofaerialbeamiscomparablewiththat tion hasanenormouslengthoftheorder10years,distributionatomsin extends). TheexperimentalpointscorrespondtothoseinFigure 4. galactic regionofun-ionizedhydrogen,anddthedistance from thegalacticplanetowhichthisregion brightness temperature(AT-f 7^)isequaltoQwhent=«>. perature (inunitsof0)the1420Mc/sechydrogenline alongthelongitudeofgalacticcenter. Curves correspondingtoseveralvaluesofKdareplotted{K denotestheline-absorptioncoefficientin a0 O a a 5 24 œ The largeangularwidthoftheobservedsourceindicatesthatopticalthickness © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem It wassuggestedbyShklovskythat,sincethelifetimeofupperleveltransi- Accordingtotheapproximate relation(26),AT~Qwhenr=.Precisely,however, thetotal Fig. 3.—Thecurvesshowthecalculatedvariationwithgalactic latitudeoftheexcessbrightnesstem- a J. P.WILD 1952ApJ. . .115. .2 O 6W 4 -32 -3 22 1 frequency) ofthelineobservedtowardgalactic center,Figure5,b,showsthekind of profiletobeexpectedfrom45°eitherside the galacticcenter(itmaybenearly is about18km/sec/kiloparsec.Insuchdirections themonochromaticemissionandab- galaxy arenotopentoobservationbythistechnique.Awayfromthegalacticcenter, value ofKdabout0.15.Hence,substituting=40°K,6X10c/secin angles, theobservedprofile (i.e.,aerialtemperatureversusfrequency)willbe ofthekind “flat-topped” overseveralmegacyclespersecond). However,sincethemoredisplaced as locally,then,ifFigure5,a,representstheprofile (brightnesstemperatureversus the atomicconcentration,averagedoverlargevolumes, isthesameininnerregions and soweshouldexpecttoobserveconsiderable line broadening.Ifitissupposedthat sorption ofdistantatomsoccuratfrequencieswell displaced fromthenominalfrequency, magnitude intheoptimumdirections(45°awayfrom thegalacticcenterandanticenter) 300 parsecs.Henceitseemsthat,towardthegalacticcenter,innerregionsof positive andnegativegalacticlatitudeareshownbycirclestriangles,respectively,tofacilitatecom- i.e., nd=45(nincm,dparsecs).MullerandOortconsiderthat,owingtothelow 60° K. method ofmeasuring,inordermagnitudeatleast,thekinetictemperature In anycaseitisnotunlikelythatthebrightnesstemperatureprovidesuswithadirect frequencies arereceived fromgreaterdistancesandthereforethrough smaller solid be greaterthanabout50parsecs.Takingwto1cm,thiswouldgivend<50,which parison withFigure3. sion alongdeclination—30°,observedbyW.N.Christiansen(unpublished).Pointscorrespondingto random velocitiesoftheatomsproducingemissionline,meanvaluedcannot Purcell isinorder-of-magnitudeagreementwithSpitzerandSavedoff’sestimateof clouds ofun-ionizedhydrogen.ItisnoteworthythattheobservedvalueEwenand and thatthekinetictemperaturemayberatherhigherthanexcitationtemperature. Purcell havesuggestedthatradiativeprocessesmayplayasignificantbutminorrole case theexcitationtemperatureisjustkineticofgas.Ewenand differential rotationofthegalaxytointroducesystematic variationsinvelocityalong however, theinnerregionsshouldbeopentoinvestigation,owingeffectof equation (32),weobtain is consistentwiththeaboveresult. the lineofsight.Nearsunradialvelocity variesdirectlyasthedistance;its a -3 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Returning, now,toFigure3,wenotethattheexperimentalpointscorresponda If ^istakentobe1cm,anopticaldepthofunityreachedinadistanceabout Fig. 4.—Thevariationofexcessaerialtemperatureinthe1420Mc/sechydrogenlinewithrightascen- 3