CO OC CM CD LO 193 9Ap J. co - 2 stellar hydrogenandhasexpressedtheopinion that,inanormalre- lem oftheionizationotherelementsandproblem upon theobservedintensitiesofinterstellarhydrogenemission,an discussed. relative abundanceoftheelementsininterstellarspacearebriefly state ofinterstellarhydrogen.Finally,certainaspectstheprob- of interstellarhydrogenisfirstconsideredinageneralway.Based attempt isthenmadetoarriveatapictureoftheactualphysical ionized hydrogen. of interstellarmatter.FromtheobservedstrengthZ7ain interstellar calciumandsodium,takingaccountofthepresence in theMilkyWayshowinghydrogen-hneemissionhasopenedup hydrogen. Also,hehasanalyzedtheproblemofionization new andhighlyimportantpossibilitiesforthestudyofproperties hydrogen isoftheorderA=3cm.Theextentemissionregionsatright emission regions,Struvehascalculatedthedensityofinterstellar angles tothegalacticplaneisdiscussedandfoundbesmall. problem oftheionizationotherelementsandrelativeabundance of theelementsininterstellarspacearebrieflydiscussed.Thedensity emission shouldbelimitedtocertainrathersharplyboundedregionsinspacesurround- of theactualphysicalstateinterstellarhydrogen.ItisfoundthatBalmer-line gen isfirstconsideredinageneralway.Anattemptthenmadetoarriveatpicture ing O-typestarsorclustersofstars.Suchregionsmayhavediametersabout state, inlargeregionsofspace.Theproblemtheionizationandexcitationhydro- the Balmerlinesareobservedinemissionsuggeststhathydrogenexists,ionized zoo parsecs,whichisingeneralagreementwiththeobservations.Certainaspectsof 12 3 1 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Ap./.,88,364,1938;89,119,1939.Proc.Nat.Acad. Sei.,25,36,1939. 3 M.N.,95,2,1934;Observatory,60,99,1937. Eddington hasconsideredtheproblemof ionization ofinter- In thepresentpaperproblemofionizationandexcitation The recentdiscovery,byStruveandElvey,ofextendedregions The discovery,byStruveandElvey,ofextendedareasintheMilkyWaywhich THE PHYSICALSTATEOFINTERSTELLAR BENGT STRÖMGREN HYDROGEN ABSTRACT 526 II I CO OC CM CD LO 193 9Ap J. CO f 4 f 4 5Tu pp. 593f.and612. factor ats,givenby ionizing ultravioletradiationduetoabsorption, tbeingtheoptical depth fromtheionizingstartopoints.Finally, wisthedilution weights oftheionandgroundstateatom,respectively; Here Iistheionizationpotential;q"andqarestatistical temperature Toftheexcitingstarandelectron is determinedbytheequation lar problemhasbeenconsideredbytheauthorinanotherconnec- of theionizingradiationincreases.Ultimately,radia- N"; andthatoffreeelectrons,N-Thedegreeionizationats drogen atomsperunitvolumebeN;thenumberofhydrogenions, star oftemperatureTandradiusR.Letthenumberneutralhy- region asafunctionofthetemperatureandabsolutemagnitude will beionized.Withincreasingdistancefromthestarpropor- tion. Our problemistoderiveanexpressionfortheextentofionized tion issomuchreducedthattheinterstellarhydrogenun-ionized. ri at5(cf.Rosseland);whilee~measuresthereductionin the staranddensityofinterstellarhydrogen.Asomewhatsimi- to beofimportanceinproblemsinterstellarspace. that high-temperaturestars,andespeciallyclustersofsuch being thattheionizingultravioletradiationisstronglyabsorbedby gion ofinterstellarspace,hydrogenisentirelyun-ionized,thereason Vri/ Tisacorrectionfactortoallowforthedifferencebetween tion ofneutralhydrogenatomsincreases,andhencetheabsorption are capableofionizinginterstellarhydrogeninregionslargeenough tends toconfirmEddington’sviewwiththemodification,however, the interstellarhydrogen.Theresultofanalysisgivenbelow u e e e 5 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem TheoreticalAstrophysics,chap,xxii,Oxford,1936. 4 G.P.Kuiper,O.Struve,B.Strömgren,Ap.86,570, 1937; sec.Ill,especially Consider apointininterstellarspaceatthedistance5from In theimmediateneighborhoodofastar,interstellarhydrogen ITN, _(2irmy*,T em¡h I/k 6 N' ~h*q' INTERSTELLAR HYDROGEN 527 (1) CO OC CM CD LO 193 9Ap J. co 18 18 -3 the factor3.08•10beingderivedfromchoice oftheparsecas units: iparsec=3.08•10cmfors;thesolarradiusR;and with merical values,equation(1)cannowbewrittenintheform the unitofs. Then, bydefinition, a tobeindependentofthefrequencyandequalitsvalueat tral hydrogenatombea.Wesimplifytheproblembyassuming so thatxisthedegreeofionizationhydrogen.Introducingnu- of thisassumptionforactualinterstellarspacewillbediscussedin nished byionizationofhydrogen,sothatN"=N-Thevalidity small, sothattheaccuracywillbesufficientforourpresentpurpose. absorption edge.Therelevantrangeoffrequencyisrelatively cm forN. The numericalfactorofCicorrespondstothefollowingchoice section V.Further,let 528 u u e © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Let theabsorptioncoefficientforionizingradiationperneu- We shallassumethatpracticallyallthefreeelectronsarefur- Equations (4)and(6)definethesolutionof problemofderiv- 1972 Cx =io-»-*-•^T*'R, e- —. (2) (s) INTERSTELLAR HYDROGEN 529 ing the degree of ionization as a function of the distance from the star. Solving (6) for 1 — æ and substituting in (4), we get

2 t N 2 2 x e u(Ltu — 77- % s • 3.08 • io *auds (7) Li

We introduce the following new variables:

y = e-Tu (l è ^ > O) , (8)

2 N l8 2 dz = — • 3.08 • io aM • s ds , (9) Ci with z = o for s = o, so that

= ( 3Ç, , s 2 l8 zl/} (10) \N • 3.08 • io aM/

Then (4) and (7) can be written as

dy = —Xa dz (11)

1 — X = a - z 2/3 (12)

with

a = l8 : (13) • (3.08 • io aw) r-

Since tu = o for 5 = o, we have, according to (8) and (10),

y — i for z = o . (14)

In the cases of actual interest, a is a small quantity. When a <

y = i — z for i — x <& i (iS)

© American Astronomical Society • Provided by the NASA Astrophysics Data System CO OC CM CD LO 193 9Ap J. co 4 values ofabynumericalintegrationaccording to(11),(12),and that forsmallathefollowingrelation,obtained byintegrating(11), tance sfromtheionizingstarhasbeenderived forthreedifferent quoted above.) lowing way.Oncetheproportionofneutralatomsbeginstoincrease, are giveningreaterdetailTable2.Finally, itmaybenoticed discussion ofthisphenomenonseetheinvestigationbyauthor celerated increaseofneutralatoms.(Forasomewhatmoredetailed the absorptionofionizingradiationincreases,leadingtoanac- tances greaterthans. star s,givenby(16),whilethereisalmostnoionizationfordis- (14). TheresultsareshowninTable1.For a =0.01theresults ionization isnearlycompleteuptothedistancefromionizing according to(10), that, for2slightlygreaterthan1,hydrogenispracticallyun-ionized. equal to1,sothat(cf.[15])ybecomesasmallquantity.Within- creasing 2thedegreeofionizationnowdecreasesveryabruptly,so 0 0 53° © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The exactdependenceofthedegreeionization xuponthedis- The abruptchangeoftheionizationcanbeinterpretedinfol- The resultoftheanalysiscanbestatedasfollows:forsmalla The valueofscorrespondingto2=1,whichweshallcall,is, Consequently, whenaissmall,ionizationstronguntil2nearly 0 0.2. 0.4. 0.6. 0.8. I .O. So = BENGT STRÖMGREN 2 0.000 1.004 1.003 1.002 i .000 JSÍ •3.0810 TABLE 1 3Cx l8 0.988 0.000 1.028 i .020 i .009 0) w ¿/.So 1/3 0.82 0.00 0. 9 7 1. 12 1.05 (16) CO OC CM CD LO 193 9Ap J. CO 2 5 gion betweenalmostcompleteionizationandnegligibleionization: with thepropertiesofionizingstar. 0. 9. 0.8. 0.6. O.4. 0.2. O.O. Table 3.Thetableshows,forinstance,thatwitha=0.001the and calculated,accordingto(17),asafunctionofx,areshownin a issmall,theabsolutewidthoftransition regiondoesnotvary Cu i.e.,ofthepropertiesionizingstar. Therefore, aslong tional toa.From(13)and(16)itfollowsthat asisindependentof to 0.0053,correspondingachangeinsofabout one-sixthof1per change fromr=0.5tor*0.1takesplaceforain2equal cent. 1. i. i .0. (12), and(14),putting2=1,holdsverynearlyinthetransitionre- 0 2 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Numerical valuesof2+constant,normalizedtooforx=0.5 For smallatherelativeextentoftransition regionispropor- 2 =Const—aIKzln—~—1(a<stars(hotterthanaboutB2)ismuchlarger thanthationized Kuiper’s bolometriccorrections,arealsogiven.ThevaluesofR stars. the latter.Forinstance,oneO7starionizesa volume equaltothat 0 i mag.wouldleadtoanincreaseofsbyafactor1.36. 0 7 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Table 5givessformain-sequencestarsofspectraltypesO5-B5. The increaseintheionizedvolumeasonepassesfromlow-tem- R.Trumpler,LickObs.Bull.,No.420,1930. 0 06 Ao O9. 08. O7 05 Bo B5 B4 B3 B 2 Bi Sp. INTERSTELLAR HYDROGEN 40.000 32.000 63.000 50.000 79.000 25.000 20.000 23.000 10,700 15,500 17,000 18,600 TABLE 5 m Afvis +0.9 -3-6 -4.1 — 42 -3-9 -4.0 -2.5 -3-1 —0.8 — 1.2 — 1.8 — i.0 -2 no 140 parsecsXA’/* 46 66 87 17 26 ii 0.5 3-7 5-2 7.2 533 CO OC CM CD LO 193 9Ap J. co lisional ionizationtobecomeofimportanceis checkedbyacorre- making detailedcalculations,weassumethat any tendencyforcol- ory thatwouldtaketheeffectsmentionedmoreaccuratelyintoac- unimportant comparedwithphoto-ionization. The justificationfor would not,however,presentverygreatdifficultiestodevelopathe- lated aresufficientlyaccurateforafirstsurveyoftheproblem.It per centins.Altogether,itisestimatedthatthe-valuescalcu- limit referredtoisobtainedbyneglectingtheeffectofscattering, tion fromtheionizingstarsisprimaryenergy source.Without this assumptionliesinthefactthat,interstellar space,theradia- maining one-thirdoftheabsorptionprocessesalsoacttoreduce count. thus introducinganeffectiveabsorptioncoefficientequalto|ain in removingentirelythequantumofionizingradiation.There- thirds oftheabsorptionprocessesfromgroundstateareeffective ground state,therestbeingtoexcitedstates.Therefore,abouttwo- hydrogen underthegeneralconditionsinquestionitisknownthat resulting ionization,throughthescatteringinvolved.Theupper about one-thirdofthecapturesfreeelectronsbyionsareto quency throughacaptureprocesstothegroundstate.Incaseof tion ofaquantumionizingradiationbyaninterstellarhydrogen from thiseffectisobtainedinthefollowingmanner.Uponabsorp- probably lessthan,say,20-30percent.Finally,theionizingradia- atom theremayfollowreradiationofaquantumthesamefre- very probable.Ithasalsobeenpointedoutthatacertainmean culating theionization.Anupperlimittochangeofsresulting tion emittedbytheinterstellarhydrogenhasbeenneglectedincal- edge. Itisestimatedthatthiseffectwillleadtoanincreaseofs radiation, shouldhavebeenusedinsteadofaattheabsorption value ofaytakenovertherelevantfrequencyrangeionizing So-values onthisaccountbymorethan,say,20-30percentisnot tions havebeenmade.Theeffectofapossibledecreasethefactor (16). Themaximuminfluenceisthereforeanincreaseofabout15 0 VTV Thasalreadybeendiscussed.Aresultingdecreaseofthe u 534 0 0 u U © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem We havetacitlyassumedthationizationbyelectron colhsionsis In derivingthevaluesgivenabove,certainsimplifyingassump- BENGT STRÖMGREN INTERSTELLAR HYDROGEN 535 spending decrease of the electron temperature. The mean free path of the electrons is so small as not to interfere appreciably with such an adjustment of the electron temperature. Applications of the theory developed in this section are given in sections IV and V. Ill We shall consider in this section the problem of the excitation of the higher energy-levels of hydrogen in interstellar space. We shall limit ourselves mainly to the consideration of the level n = $, which determines the emission of i7a radiation. The discussion is naturally divided into two parts, dealing with ionized and nonionized regions, respectively. In the almost completely ionized region surrounding a high-tem- perature star or a cluster of such stars, the mechanisms of excitation of one of the higher levels—say n = 3—can be classified as follows, leaving out of consideration mechanisms that are entirely negligible : {a) capture of a free electron by an ion to the state considered; (&) capture of a free electron by an ion to a higher state, followed by one or more transitions leading through the state considered; (c) Lyman-line absorption from the ground state to the state considered, and Lyman-line absorption from the ground state to higher states, followed by one or more transitions leading through the state con- sidered; (¿) Baimer-line absorption from the state n = 2y either di- rectly to the state considered or to a higher state followed by cascad- ing, as before; and (e) excitation by electron collision from the ground state to the state considered or to higher bound states, fol- lowed by cascading. In investigating these mechanisms we can largely make use of the results of investigations of the analogous problem in the case of planetary nebulae. Consider first mechanism (a). The effective cross-section 7r

8 M.N., 92, 820, 1932; 96, 771, 1936.

© American Astronomical Society • Provided by the NASA Astrophysics Data System CO OC CM CD LO 193 9Ap J. co 8 10 -20l/2 o 6 9 number Nbeingsodefinedthattheactual oftransitionsto numerical factorin(21)isincreasedbyaofabout1.5,the tion bymechanism{a)thereisnodifficultyatallintreatingthe very smalltemperatures,Jisapproximatelyequalto1;forF= Here Jdenotesthepropermeanvalueoffactorvlv~in(20).For lated easily(cf.Cillié).Forw=3onefinds ber ofatomsperunitvolumeNinanystatencannowbecalcu- where gistheGauntcorrectionfactor,whichapproximatelyequal tical weights. sition probabilityr,obtainedbyaveragingaccording tothestatis- the statew=2isgivenbyproductofNand thestandardtran- J —0.40. number ofcapturescorrespondingtoagivencapturecross-section substates ofthestatewithw=3separately.Whenthisisdone, the stateconsidered). absorption edgeandoftheradiationemittedatcapture,respec- states ofhydrogen,astabulated,forexample,byBethe,thenum- tively (sothathv=+when%nisthebindingenergyof to i(g=o.piforn3),whilevandarethefrequencyof ture cross-sectionforreverseprocesses: Milne relationbetweencontinuousabsorptioncross-sectionandcap- Jfrrrr =6.3•10r~J(excitationbymechanism[a]only).(21) 5000°, J=0.81;forT20,000,0.57;and50,000°, Gaunt formulaforthecontinuousabsorptioncross-sectionand S3 (cf., e.g.,Fowler),andusingthemeanlifetimesforvarious z Q n 32 z a 0 10 9 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Handh.d.Phys.,24,1,chap,iii,1933. StatisticalMechanics,Cambridge,England,1936. With theaidofwell-knowngas-kineticformula,giving The caseofexcitationbybothmechanisms(a) and{b)hasbeen It maybenotedthat,intheparticularlysimplecaseofexcita- 2 cr(») =i.43•io«¿^i- ;20 BENGT STRÖMGREN n V£L e CO OC CM CD LO 193 9Ap J. co (A)11 1 81 A) 12 o N"N N I() ing temperaturethefactortendstoward1. by (23)arenaturallylargerthanthosegiven(21).ForT\= where bistabulatedbyBakerandMenzel(theirhypothesisA) dynamical equilibrium.Inthermodynamicalequilibriumwehave treated byMenzelandBaker.Theseauthorsgive In thecaseofexcitationbymechanisms{a)and(b) the ratioNn/N"Nintermsofcorrespondingforthermo- Planck intensitiesforacommontemperature.Inthiscasethetran- number ofatomsinthegroundstate(fromwhichexcitationcon- considered byCilliéandMenzelBaker.FollowingZan- as afunctionoftheelectrontemperatureT\.ThevaluesNgiven JL±- =b{•10-14.44+i.sos.r-3/2 analogous tothetreatmentofcase(a)+(6),exceptthatall anced bythereverseLyman-lineexcitations,andtreatmentis sitions fromanyexcitedstatetothegroundareexactlybal- sidered takesplace),isgivenbyacommondilutionfactortimesthe tion, aswelltheionizingradiation,whichdeterminesrelative stra, theytreatedthecaseinwhichexcitingLyman-lineradia- transition probabilitiestothegroundstateareputequalzero. 5000 theincreaseisgivenbyafactoraboutequalto2;withincreas- ïQSy; J-G.BakerandD.H.Menzel,Ap.88,52,1938. e e23 e 32 (c) justconsidered, e e3 Ns 12 11 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Pub.Dom.Ap.Obs.,Victoria,4,200,1931;Zs.j.Ap.,2, 1,1931. D.H.Menzel,Ap.85,330,1937;MenzelandJ. G. Baker,Ap.86,70, The caseofexcitationbymechanisms(a),(&),and(c)hasbeen In theparticularcaseofexcitationbymechanisms(a),(&),and (particular caseofexcitationbymechanisms[a],[£], and[c]), = b^ -i • =io4-44+i-5o0.j-3/2(thermodynamicalequilibrium).(22) jQ—I4.44+I.5O0 . INTERSTELLAR HYDROGEN (excitation bymechanisms[a]and[5]), > (24) 537 CO OC CM CD LO 193 9Ap J. CO 10 -3 24 -21 17 8 lar statefromtheground(cf.Bethe). In interstellarspace, of magnitude10.When,asinthecaseunderconsideration, larger thanthecross-sectionforelectronexcitation ofthatparticu- ionization issohighthatthenumberofionsis,say,io-iotimes in question,beoftheordermagnitude10.Thecross-sectionfor moreover, weassumethatelectronionization isunimportantcom- tance, theratioNjN"Nwillapproachvalue givenbyequation of electronsthathavesufficientenergyforexcitationistheorder section forelectronionizationfromtheground stateisconsiderably cases oflesscompleteionization,whenmechanism (e)isofimpor- tant comparedwithmechanisms{a)and(&). the numberofneutralatoms,thenmechanism{e)willbeunimpor- the statew=3isofordermagnitudeio~,ifenergy excitation byanelectronofaneutralatominthegroundstateto electron ishighenoughtoexcitethestatew=3atall.Thefraction free electronbyanion,tothestatew=3,will,fortemperatures important. Theaveragecapturecross-sectionfortheofa nism (e),itiseasilyseenthatinanalmostcompletelyionizedregion, n =2,owingtothemetastabilityof25-substate,seeChandra- opaque inthefrequenciesofBalmerlines,thenrelativepopu- is supernormaltosuchanextentthattheionizedregionbecomes where istabulatedbyBakerandMenzel(theirhypothesisB) apphcations toproblemsofinterstellarspace,themechanismisun- and fortemperaturesoftheorderthosetobeexpectedinactual sekhar andStoy,asquotedbyCillié.) the ionizingstar.(Forpossibilityofsuperexcitationstate dynamical equilibrium,withthetemperatureaboutequaltothatof lation ofthestatew=3,excitedbymechanisms(a),(&),(c),and is entirelynegligible.If,however,theexcitationofstatew=3 we shallonlyconsidertwolimitingcases.Iftheexcitationof as afunctionoftheelectrontemperature. (23), thereasonbeingthat,forhigh-levelstates likew=3,thecross- state =2isnormalforinterstellarspace,theroleofmechanismd 538 e (d), approachesthevaluegivenbyexpression(22),validforthermo- © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem It isinterestingtonote,ascaneasilybeshown,thateveninsuch With regard,finally,totheimportanceofexcitationbymecha- With regardtotheimportanceofexcitationbymechanism(¿), BENGT STRÖMGREN CO OC CM CD LO 193 9Ap J. co -21 -21 of electrontemperature.Thiseffectalsolimitstheimportance pared withphoto-ionizationasaconsequenceofanadjustment lower thanthatofthestar;butherechange inthetempera- mechanisms considered,andalsofortherelevantrangeoftempera- noted above,inthespecialcaseofexcitation[a]+[b][c][d] from 3•10. o. i. 0.2. 0.4. mechanism (e)inthecaseconsidered. multiplication withthesquarerootoffactorbywhichNdiffers 0.6. 0.8. N —3•10.Forothervaluesofmaybeobtainedby analogous exampleoftheapproachcentral intensitiesofstellar NjN"N hereencounteredisnotsurprising. We maymentionthe that therelativelysmallnumbersinupper leftcornerofTable tures, thevaluesofNcomeoutapproximatelysame.(Aswas ture affectsNverylittle.)Therelativeinsensitivity oftheratio question istheelectrontemperature,andso may beconsiderably the temperatureapproachesofionizingstar,so the followingsection,valueofcalculatedwithN"=Nand ratio NjN"Ndirectly.Itgives,withaviewtotheapplicationin the variouscasesconsidered.However,tabledoesnotgive 6 areirrelevant.Formechanism[a]+[&],say, thetemperaturein I .O. z 3Zle e e e e e © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Table 6illustratesequations(21),(22),(23),and(24),validfor It isinterestingtonotethatforthewholerangeofexcitation * ThetablegivesNforN"=Nand^3=3• e 50,400 25,200 12,600 8,400 6,300 5,040 INTERSTELLAR HYDROGEN -3 um; Special Thermody- 0.55’ o. 10cm 0.28. o. 16 Excitation 2- 5 1- 3 (a)+(6) + Equilibri- namical (c) +(d) Case of (1) TABLE 6* (aj +(6)-t-(c) Excitation 3 (Eq. [24]) 2.0 i. 2 i. ocm“ 2.8 1-4 i. i Case of Special (2) 21 10 cm" Excitation 3 (Eq. [23]) 4- 3 3- 0 (a) +(6) i. 4cm 2.2 1.8 i. 6 (3) Excitation 3 (Eq. I21]) 3-8 5-2 2.0cm 2.8 2.4 2.2 (a) (4) states Con- Excitation Separately 3 (a); Sub- 4.2 31 2-3 2.0 1.8 i. 7cm sidered (4') 539 CO OC CM CD LO 193 9Ap J. CO ff 3 lem isnotquitesimple,butitsuggestedthat,inthemajorpartof which, however,aswehaveseen,isunimportantinthepresentcon- absorption linestothevalueforthermodynamicalequilibrium, in theionizedregionsaroundhigh-temperaturestars.Theprob- nection. tance fromtheionizingstar.Thisisnottrueformechanism(e), and theircombinationstheratioNjN"Nisindependentofdis- temperatures highcomparedwiththebindingenergy. in theformofLa,radiationotherLymanUneshavingbeen Paschen lines,etc.;also,thattheionizedregionistransparentin the ionizedregion,Lyman-lineradiationispresentalmostonly other hypothesesdiscussed.Theimprovedmethodforcalculating by aprocedureleadingtoequation(22)(Table6,case1),namely, 540 from thepreviousdiscussionthatvalueofratioobtainedby the useofBoltzmannandSahaformulaewithacommon converted byrepeatedfluorescenceprocessesintoLa,Bahnerlines, used hereincase3,i.e.,thewhichprobablycorrespondsmost Unes Lß,Lv,etc.,hasherebeenconvertedintoLa andlow-frequency NjN"N brieflyoutlinedbyStruveisessentiallyequivalenttothat dilution factorwhichdropsoutinformingNjNN-Itfollows culated theratioNjN"Ninanionizedregionofinterstellarspace is probablysuperexcitedbyafactorof10,very roughly,owingtothe Unes. Freeelectrons,suppliedbyelementsof lowerionizationpo- ticaUy un-ionizedregionsconsideredinsectionII.Nearlyall closely toactualconditions. Struve willnotdifferverymuchfromthoseobtainedonanyofthe the staten=3andofhigherstatesisbymechanism(a)+(b) frequencies oftheBalmerlines(cf.above),sothatexcitation Therefore, inthesepartsofintersteUarspace thereisalmostno tential thanhydrogen,willaUhaverelatively lowkineticenergy. the radiationbeyondLymanUmit,andalso thatintheLyman excitation ofthestatew=3orhigherstates. Thestaten=2 e (Table 6,case3). e e e 2 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem We shallnowconsiderbrieflytheactualmechanismofexcitation Further, itisofinteresttonotethatformechanisms(a),(&),(c), We finallyhavetodiscusstheexcitationofhydrogeninprac- In thepaperquotedatbeginningofthisarticle,Struvecal- BENGT STRÖMGREN INTERSTELLAR HYDROGEN 541 conversion of continuous radiation into La, while the metastability of the substate 25 is of no consequence here. Eddington3 has suggested that hydrogen in un-ionized regions of interstellar space is present in molecular form. It is not intended to attempt a complete solution of this problem here, but a few points may be noted. If the equilibrium between hydrogen atoms and mole- cules is determined principally by one process and its reverse proc- ess, the ratio of atoms to molecules will be given by an equation analogous to (1). (In interstellar space the lowest vibrational and rotational level only will be excited. The reduced mass fw# occurs instead of me, however.) If the frequency of the radiation absorbed in the dissociation process considered were less than that of the Ly- man limit, the factor corresponding to e~Tu would be of the order of magnitude 1. In that case the ratio of molecules to atoms would be, roughly, io~9N; i.e., the number of molecules would be negligibly small. If, however, the frequency of the dissociation process is great- er than that of the Lyman limit—and this is certainly the case if the dominant dissociation and recombination processes are the same as in the laboratory—then the number of dissociations is practically zero. On the other hand, the reverse recombination process, which involves the colhsion of one normal and one excited hydrogen atom, is extremely slow in interstellar space. Using the approximate value for the effective cross-section of this process given by Terenin and Prileshajewa13 and by Rompe,14 namely, io_s times the gas-kinetic cross-section, it is found that every hydrogen atom colhdes to form a molecule once in (very roughly) 1021 years. This means that mole- cule formation during any accepted time-scale is negligible. This, of course, does not definitely settle the question. It should be added that the mixture of material in the galactic system will tend ulti- mately to bring any molecules that may exist into ionized regions, where they will quickly dissociate. A sufficiently strong mixture will thus lead to practically complete dissociation of molecules into atoms. IV According to the analysis of the preceding sections, one would ex- pect—if the density of interstellar hydrogen is within a certain range T3 Phys. Zs. Soviet Union, 3, 337, 1932. ^ Phys. Zs., 37, 807, 1936.

© American Astronomical Society • Provided by the NASA Astrophysics Data System CO OC CM CD LO 193 9Ap J. CO o 2 -3 12 f 0 1 -21-3 chap, vi,Cambridge,Mass.,1930;J.S.Plaskett,Pub.Dom. Ap.Obs.,Victoria,2,339, Ha emissioninCepheuswiththecondensationof0starsaround low. Withanestimateddepthoftheemitting column of300parsecs, practically allthefreeelectronsresultfrom hydrogen {N"=N Ha emissionregioninCygnuswiththeclusterof0starshavingits working hypothesis. galactic longitude70. of themoregeneralhypothesisputforwardbyStruveininvesti- of uniformHaemissionastheprojectionsboundedregionsin- is probableaprioriandfurthersupported by reasonsstatedbe- N ofhydrogenisequalto2-3cm.Wehave hereassumedthat this numberweestimate,withtheaidofTable6,thatdensity effective lengthoftheemittingcolumntobe1000parsecs.Using tion. Struve’,fromtheobservedstrengthofHaemissionin to derivethedensityofinterstellarhydrogeninregionsques- sumably belongtothiscluster.Likewise,weconnecttheextended and alsoN—N,theionizationbeingnearly complete).This center atl=42,b+i°.Abouttenoftheknown0starspre- gation previouslyreferredto. 0 stars.Weshall,forthepresent,acceptthisinterpretationasa terstellar spaceionizedprincipallybyclusters,orcondensations,of gions ofHaemission,itistemptingtointerprettheobservedareas —to findBaimer-lineemissionlimitedtocertainrathersharply ance withourworkinghypothesisweconnecttheobservedextended Elvey, referredtoatthebeginningofthisarticle,extendedre- temperature starsinquestionprincipallywith0stars. 1924; O.Struve,A.N.,231,17,1927. Cygnus andCepheus,derivedA3=3*iocm,assumingthe these regions.WithaviewtotherelativeionizingefficiencyofO bounded regionsinspacesurroundinghigh-temperaturestarsor and Bstars,asdiscussedinsectionII,onewouldidentifythehigh- strength, withoutanyconcentrationtowardparticularstars,within clusters ofhigh-temperaturestars,theemissionbeinguniform 542 ei ag 15 15 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem C.H.Payne,“TheStarsofHighLuminosity,”Harvard Obs. Monograph,No.3, We cannowimmediatelymakeuseoftheanalysissectionIII Our workinghypothesismayberegardedasaspecializedversion Several clustersorclusteringsof0starsareknown.Inaccord- Comparing thispicturewiththeobservationsbyStruveand BENGT STRÖMGREN INTERSTELLAR HYDROGEN 543

instead of 1000 parsecs, one would find N equal to about 4 cm-3. The resulting N is proportional to the square root of the assumed value of N,. Assuming, for the present, that A = 3, we find, with the aid of Table 5, that the diameter of the region ionized by a cluster of n stars of the average spectral type O7 is about 80 nx/i parsecs. With n — \o (cf. above) we find a diameter of about 200 parsecs. This agrees about as well as could be expected with the estimated diam- eter of the Cygnus emission regions of, say, 200-300 parsecs. The total intensity of a hydrogen-line emission area is propor- tional to the number n of ionizing 0 stars. The total area is propor- tional to w2/3, the depth, and hence the surface intensity, to wI/3. With regard to the extension of the areas of fla emission in the direction at right angles to the galactic plane, consideration of the concentration of hydrogen toward the galactic plane is of impor- tance. Calculations based on the assumption of a static interstellar hydrogen cloud may perhaps serve as a rough guide. Using the em- pirical field of force in the direction at right angles to the galactic plane as derived by Oort,16 it is found that the density of hydrogen decreases with the height above the galactic plane approximately ac- cording to a Gaussian error law, with a dispersion of about 1.3 parsecs X Tl/2, where T is the temperature of the hydrogen gas. With T — 10,000o, a dispersion of 130 parsecs results. Though the true distribution will probably differ from this, owing to the effects of turbulence, the order of magnitude should be correct. It is, of course, very important to find how large a fraction of the relevant galactic stratum of hydrogen is ionized. From the esti- mated density of 0 and B stars, in connection with Table 5, assum- ing A = 3 cm-3, we are led to the very rough estimate that about one-tenth of the stratum is ionized. The numerical value of the fraction is inversely proportional to the square of the density of in- terstellar hydrogen. As the observational material on extended areas of hydrogen-line emission accumulates, it will be possible to test the working hypothe- sis formulated in this section. The necessity of a critical test is ob- vious, particularly in view of the fact that a revision of the tempera- ture scale might lead to a somewhat different picture of the relative 16 Bull. Asir. Inst. Netherlands, 6, 249, 1932.

© American Astronomical Society • Provided by the NASA Astrophysics Data System CO OC CM CD LO 193 9Ap J. CO -3 -3 17 -32 or moreabundantthan,hydrogen,ionizedhelium wouldberestricted ionized region(cf.sec.II).Inthecaseofsufficientlyabundantele- on theotherhand,heliumisconsiderablylessabundant thanhydro- for suchcases.Thus,itisseenthat,ifhelium wereasabundantas, ments ofhighionizationpotentialthe maybecheckedin is ionized,theelectrondensityNequaltoN.Allionizingradia- importance of0andBstarsthatadecreaseintheacceptedvalue from starswithintheionizedregion,i.e.,particularlysame of i,leadstoA=5cm. observed extentofHaemissionareasconfirmstheapproximatecor- of interstellarHaemissionleadstoavalueNaround3cm.The values inapproximatemutualagreement.First,Dunham’sdis- of therelativeextentthatpartgalacticstratuminwhich to avolumeconsiderablysmallerthanthatof ionized hydrogen.If, checked. Withobviousmodification,theanalysis insectionIIholds a wayanalogoustothatinwhichtheionization ofhydrogenis reduced byhydrogenabsorptionexceptneartheboundaryof stars whichionizethehydrogen.Thisradiationisnotverymuch tion ofwavelengthsshorterthanthattheLymanlimitcomes than hydrogen.Inthoseregionsofinterstellarspacewherehydrogen densations, whenmodifiedtocorrespondameanmolecularweight ble choiceofthevaluehydrogendensitymaximum this phenomenonbyDunhamandStruvesuggestasthemostplausi- hydrogen isionized. nonionized regions. of Nmightleadtoalesspronouncedseparationbetweenionizedand ton’s estimate,basedupontheaverageseparationofnebularcon- rectness ofthisvalue.Finally,itmaybementionedthatEdding- N =2-4cm(cf.Struve).Theanalysisbaseduponthestrength compatible withtheresultsofOort’sdynamicalinvestigations,i.e., tions, orestimates,ofthedensityinterstellarhydrogenleadto especially valuable,astheywouldleadtoanimprovedknowledge covery ofinterstellarlinesneutralcalciumandthediscussion 544 e © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem We shallconsiderbrieflythestateofionizationelementsother At thepresentmomentitcanbesaidthatanumberofdetermina- Further observationsofhydrogen-lineemissionareaswouldbe Pub. A.S.P.,49,26,1937;Nature,139,246,1937. BENGT STRÖMGREN V INTERSTELLAR HYDROGEN 545 gen, the ionization of He i to He n will usually be almost com- plete up to the boundary of the region of hydrogen ionization; but in that case, of course, helium contributes considerably less to the num- ber of free electrons than hydrogen. This argument tends to con- firm the validity of our assumption that the free electrons are con- tributed mainly by hydrogen in those regions where hydrogen is ionized. It also shows that helium D3-line emission is handicapped in comparison with hydrogen Baimer-line emission. Struve and Elvey1 observed the emission line X 3727 of [Oh] in many of the areas where Ha was seen, while Ni and N2 of [0 m] were rarely observed. As the mechanism of excitation of the fines is similar, this probably indicates that oxygen is present mainly as

O ii. Further observations on the occurrence of Nx and N2 may lead to valuable results, particularly so if it should turn out that the abun- dance of oxygen is high enough to restrict the ionization of 0 h to O in (ionization potential 34.9 volts) by a mechanism similar to the hydrogen mechanism. Ultimately, the observed relative intensity of interstellar hydro- gen and oxygen emission fines will lead to a reliable value of the rela- tive abundance of interstellar hydrogen and oxygen. A very rough estimate is easily made. The effective cross-section for the excita- tion of the upper state of X 3727 by electron collision is estimated to be somewhat smaller than 10-17 cm2. Assuming that somewhat less than one-tenth of the electrons have sufficient energy to excite X 3727, and putting the cross-section for capture of a free electron to the state n = 3 equal to about 10-21 cm2, we derive from the ob- served fact that X 3727 is somewhat fainter than Ha that there are, roughly, io2-io3 H ions to every 011 ion. Since hydrogen is largely ionized, and oxygen is mostly present as 0 11, the resulting inter- stellar abundance is io_2-io-3 oxygen atoms to every hydrogen atom. We consider next the ionization of elements with ionization po- tential less than that of hydrogen, in those regions where hydrogen is ionized. In this case the ionizing radiation comes from the entire galactic system, so that the customary calculations of the dilution factor and the effective temperature hold, while the electron density is equal to A. It should be noted that the O stars which ionize the hydrogen do not contribute especially to the ionization of such ele- ments as calcium and sodium.

© American Astronomical Society • Provided by the NASA Astrophysics Data System CO OC CM CD LO 193 9Ap J. CO 2 -2-3 -5-3 19 2 18 2-3 17 interstellar space,therelativecosmicabundancesofoxygen,calcium, the effectofrecombinationprocessestoexcitedstates,followed practicallyalwaysby of thegalacticstratumnaturallyaffectsabundancescalculated which isofthesameorderasvaluedetermined abovefromthe of calciumandsodiumfoundbyStruve(forminganaverageabun- fact thatsomeofthefactorsenteringinto this calculationwill density ofoxygenisfoundtobe5.10cm.Theresultinginter- absorption region,wearriveatadensityof3.1ocm.Adopting,for certainly needconsiderablerevision. strength ofthelineX3727.Itishardlynecessary toemphasizethe stellar abundanceis2•io~oxygenatomsto every hydrogenatom, and sodium,asdeterminedbyGoldschmidt,thecorresponding dance ofthetwoelements)onthisaccount,andusingiV=3in from theobservedintensitiesofline.Increasingabundance gen, whileCa11,Na1,andK1linesarealsomostlyabsorbedhere. Ca ilinesarealmostentirelyabsorbedintheregionsofionizedhydro- the presentvaluesfortheseconstantsitisfoundthatinterstellar sity inregionsofionizedandun-ionizedhydrogen,respectively.With stratum inwhichhydrogenisionized,andtheratioofelectronden- are knownwithgreatercertainty,namely,thefractionofgalactic discussion oftheionizationmetalsuntiltwobasicconstants oxygen, wefindthatNisaboutioiotimessmallerthaninthe extremely uncertain.Itisprobablybesttopostponethedetailed regions wherehydrogenisionized.Thisfigureis,however,asyet of thefreeelectronsarefurnishedbycarbon.Withaninterstellar lar Tiiilines. carbon abundanceofthesameorderasderivedfor is ofinterestinconnectionwithDunham’sobservationsinterstel- ized. Oftheabundantmetals,onlycalciumwillbedoublyionized. oxygen willbeun-ionized,whilecarbonandthemetalsion- It maybenoticedthattitaniumwillpresentmostlyas11.This hydrogen. Ofthemostabundantelements,helium,nitrogen,and e almost noionizationforpotentialslargerthanthatof e 546 19 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Inamorerefinedcalculationoftheionizationanelement ininterstellarspace ^Norske Videnskaps-Akademi,Oslo,Mat.-Naturv.KL,No. 4,1937. Restriction oftheabsorptionaninterstellarlinetoafraction It isquitelikelythatintheregionsofun-ionizedhydrogenmost Outside theregionsinwhichhydrogenisionized,therewillbe BENGT STRÖMGREN 1939ApJ 89. .5265 3 173 lines willdisappearwhentheeffectjustconsideredistaken intoaccount.ForCu1the ing moreaccuratecalculations,itissuggestedthattheremainder(cf.Struve)of lines aresimilarlyreduced.AccordingtoanunpublishedresultbyDr.L.C.Green, interstellar spaceisquiteconsiderablyreducedbytheeffectinquestion.Theabun- processes is,ofcourse,proportionaltothecontinuousabsorptioncoefficientfor continuous absorptioncoefficientfromthegroundstatehas notyetbeencalculated. well-known discrepancywithregardtotherelativestrengthof interstellarNa1andCa11 with regardtothecontinuousabsorptionfromgroundstate.Hence,areductionof ground state.Weconcludethatthedegreeofionizationsodiumandpotassiumin of recombinationstothegroundstate.Ininterstellarspacenumberdissociation elements thenumberofrecombinationstoexcitedstatesisfargreaterthan than thatcalculatedfromthecustomaryequation.Thiswould tendtoreconcilethe this isthecase,itfollowsthatinterstellarratioofCa1to Ca11isconsiderablylarger excited statesbeingmorehydrogen-likewithrespectto continuousabsorption.If It isveryprobable,however,thatitconsiderablysmaller thanforhydrogen,the the calculatedcalciumabundanceisindicated,butitsmallerthanforsodium.Pend- kindly communicatedtothewriter,Canisintermediatebetweensodiumandhydrogen sorption fromthegroundstateismuchsmallerthanforhydrogen,while,according per byabout30cent.Forelementslikesodiumandpotassium,however,the to decreasethedegreeofionization.Forhydrogeneffectisnotverymarked,leading dances ofsodiumandpotassiumcalculatedfromthestrengthinterstellarabsorption mately hydrogen-likewithregardtocontinuousabsorption.Itfollowsthatforthese to anunpublishedinvestigationbyMr.M.Rudkjöbing,theexcitedstatesareapproxi- effect isverymarked.Itwellknown(cf.e.g.,n.4)thatfortheseelementstheab- to J.Thiswouldcorrespondadecreaseofthes-valuescalculatedinpresentpa- to anextrafactorontheright-handsideofequation(1)estimatedbeaboutequal cascading tothegroundstate,mustbetakenintoaccount.Theeffectwillalwaystend posal theresultsofinvestigationsonsubjectthispaperbefore length region. value oftheelectronpressurederivedfromobservedstrength ofCa1and11(cf. which shownointerstellarabsorptionlinesintheaccessiblewave- Dunham andStruve)withthatfoundinthepresentinvestigation. ultimately, extremelyvaluableresultswithregardtothedetermina- with theinterstellaremission-linemethod.Evenso,itseemsalready their publication. tion oftheinterstellardensitymostabundantelements,all quite clearthattheemission-linemethodiscapableofyielding, sensitivity oftheinterstellarabsorption-linemethodascompared 0 30 20 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Zs.f.Ap.,17,316,1939. The authorismuchindebtedtoDr.0.Struveforplacingathisdis- Struve hasrecentlyemphasizedtherelativelymuchgreater Copenhagen Observatory February 15,1939 INTERSTELLAR HYDROGEN 547