1973ApJ. . .180. .5315 25_1 -3 1 32 3126 9 0-3211 The AstrophysicalJournal,180:531-546,1973March1 cluding special-andgeneral-relativityeffects)ofboththefluidmechanicsradiationprocesses © 1973.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. has beenused.Theprincipalradiationmechanismsareelectron-protonandelectron-electron onto anonrotatingblackholeatrestintheinterstellarmedium.Afullyrelativistictreatment(in- onto ablackholearecalculated.Themodelisthatofsphericallysymmetric,steady-stateaccretion total luminosityL=3x10ergss.ThespectrumhasabremsstrahlungshapewithT~ medium isanHiornregion.Forregionwith«=1cmandT100°K,the The spectrumisagainbremsstrahlunginappearancewithT~10°K.Inbothcasesonlyasmall bremsstrahlung. TheresultsforablackholeofmassM=1M©dependonwhethertheinterstellar spectral distributionremainsthesamewhiletotalluminosityLccMTo~n,provided gas accretingontotheobject.Knowingfromtheoreticalconsiderationscharac- fraction oftheavailablethermalenergyisradiated.Fordifferentvalues«,To,andM Subject headings:blackholes—interstellarmatterradiativetransferrelativity discussed. H iiregion.Thepossibilityofdetectingthisradiationandtherebyidentifyingblackholesis (MlM)(T100° K)-n«10fortheHiregionand(M/M)(r/,00°t from observationswhetherornotablackholehasindeedbeenlocated. teristic frequencyspectrumoftheemittedradiation,onecanpresumablydetermine has beenexaminedbyBondi(1952)inthenonrelativisticlimit.Michel(1972)con- to theaccretionofmatterontocondensedobjects. Electromagneticemissionfromthe sidered thegeneral-relativisticversionofsameproblemandappliedhisanalysis space isbyobservingtheelectromagneticradiationspectrumemittedinterstellar 10 K.AnHiiregionwithn=1cmandT10,000°KproducesL2xergss. gas wasnotconsideredintheseinvestigations.The possibilitythatgasaccretingonto Zel’dovich (1964)andSalpeter(1964).Shvartsman (1971)employednonrelativistic a blackholemightbeanimportantsourceofradiant energywasfirstsuggestedby total energyradiatedbyafullyionizedgasaccreting ontoablackhole. luminosity andfrequencyspectrumthatemerges frominterstellargasaccretingonto approximations forboththefluiddynamicsand radiativeprocessestoestimatethe 0 the blackhole.Weanalyze twocases,oneinwhichthemediumisanH iregionat a blackhole.Weconsiderthecaseofspherically symmetric,steady-stateaccretion loss andionizationof the gasareconsidered.Thetreatmentofboth thefluid assumed toconsistofpurehydrogengasuniform densityandtemperaturefarfrom 0 onto anonrotatingblackholeatrestintheinterstellar medium.Themediumis 0 o0 0 100° Kandanotherinwhich themediumisanHiiregionat10,000°K.Internal heat The luminosityandfrequencyspectrumofradiationresultingfrominterstellargasaccreting © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem One ofthemorepromisingwaysidentifyingacollapsedstarorblackholein Spherically symmetric,steady-stateaccretionontostarsforsimplepolytropicgases The purposeofthisinvestigationistoprovidea relativistic calculationofthetotal Princeton UniversityObservatory,Princeton,NewJersey ACCRETION ONTOBLACKHOLES:THE EMERGENT RADIATIONSPECTRUM Received 1972August21 Stuart L.Shapiro I. INTRODUCTION ABSTRACT 531 532 STUART L. SHAPIRO Vol. 180 mechanics and radiation processes is fully relativistic, incorporating both special and general relativity. The basic assumptions and equations used in this paper are set forth in § II. In §111 the results of the numerical integrations are presented and analyzed. The pos- sibility of detecting black holes in space by observing the radiation emitted by accreting gas is discussed in § IV.
II. BASIC EQUATIONS
a) Assumptions In the model, hydrogen gas surrounding a black hole flows radially inward toward the hole under the influence of the gravitational field. In falling toward the hole the gas is heated and compressed as gravitational energy is converted into internal plus kinetic energy. A portion of this internal energy ultimately escapes in the form of radiation which is emitted when the gas particles collide inelastically with each other. We adopt in this paper the field equations of general relativity in a Schwarzschild metric and a fluid description of the accreting gas. The adoption of a continuum model to describe the inflowing gas may seem inappropriate since one can show that, as each gas element falls inward, the mean free path of gas particles, /c, with respect to Coulomb collisions becomes larger than the characteristic dimension r of the region. Here r is the radius of the fluid element from the black hole. However, the presence of a very weak magnetic field frozen into the hydrogen plasma serves to couple particles together and effectively provide collisions. Zel’dovich and Novikov (1971) have shown that even for field strengths many orders of magnitude less than the mean interstellar field of 10_ 6 gauss the Larmor radius of protons moving at thermal velocity remains much smaller than r everywhere throughout the fluid. More- over, observations of the solar wind and experience with high-temperature laboratory plasmas provide further evidence for the general validity of fluid picture even when lc » r (Perkins 1972). We henceforth assume the existence of a very weak magnetic field frozen into our plasma to hold particles together. We neglect all other dynamical and radiative effects of the magnetic field, postponing a discussion of these topics for a subsequent report. In the model we suppose the gas to be pure hydrogen. We assume spherical sym- metric, steady state flow onto a nonrotating black hole of mass M at rest in the interstellar medium. Shvartsman (1971) has argued that the assumption of spherical symmetric flow is also appropriate for a black hole moving with an arbitrary velocity V through the medium. If F > cs, where cs is the sound velocity in the gas, a conically shaped shock wave forms behind the black hole. After compression in the shock wave 2 the gas increases in temperature so that kT0 ~ mpV . For any F, gas particles within 2 2 a distance rc ~ GM/(V + cs ) from the black hole will be captured. Gas pressure serves to symmetrize the flow, and for r « rc the motion of the gas can be considered radial. We assume the gas pressure to be isotropic at each point in the fluid. In an H n region the gas is assumed to be completely ionized by ultraviolet photons from an exciting star. In an H i region collisional ionization of neutral hydrogen by electrons is assumed to predominate over other ionization processes, including ionization by cosmic rays and photoionization by the outgoing radiation flux. The principal heating and cooling mechanisms in the gas depend on whether the medium is an H i or H n region and are discussed in detail in § lib. Reabsorption and scattering in the fluid of the outgoing X-ray and y-ray flux, as well as the production of electron-positron pairs, are shown to be unimportant.
© American Astronomical Society • Provided by the NASA Astrophysics Data System 1973ApJ. . .180. .5315 -3_1 1 2 relations thatcharacterizetheinternalproperties ofthegas,namely,equation integration. Specifically, we findthatthetemperatureofhydrogenplasma inan state, theequationforproperinternalenergy density, andtheequationsdescribing gas accretingontoablackhole.Inadditiontothese threeequations,werequirethe equal totheenergylostthroughinelasticcollisions, A(P),minustheenergygainedby In theaboveequationdecreaseinentropy oftheinflowinggashasbeenset identity these expressions,weanticipate aresultthatisdeterminedlaterbydirect numerical the energygainandlossfunctions.Toobtain thecorrectrelativisticformfor reproduces equation(6)above. absorption, F(P).HereA(P)andF(P)areboth measured inergscms. energy. For/=1,equation(5)reducesto For i=2,3,equation(5)reducestothetrivialidentity0whilefor/it where Pisthepressure,ou=e+internalenthalpyperunitpropervolume, and eistheproperinternalenergydensity,includingrestmassionization where 11/!=u¡c.TherelativisticgeneralizationsofEuler’sequationsare or rounding plasmaonthestaticlineelement;increaseinMduetoaccretionis state flow,equation(2)becomes the fluidelementisatrest.Sinceweareassumingsphericallysymmetricandsteady- where m=GM/c.Inwritingequation(1)wehaveignoredtheinfluenceofsur- where the4-velocityvectoroffluidU'=dx'/dsandnisscalarnumberdensity of relativisticfluiddynamicsaregivenbyLandauandLifshitz(1965).Theequation shown belowtobenegligibleoveranyrelevanttimescale.Thefundamentalequations of particles(neutralhydrogenatomsplusprotons)measuredintheframewhich of continuityis No. 2,1973ACCRETIONONTOBLACKHOLES533 Equations (4),(6),and(7)representthethreebasic fluidequationsthatcharacterize Finally, wehavetheentropyequationwhichisgivenbythermodynamic © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem A blackholeofmassMisrepresentedbytheSchwarzschildlineelement, 2r2sn ds =(1—2m/r)cdt^2m¡r)~(d0+i6d(f>),(1) 2 + 2 2 dr\c/(P+e) Id/u\ _1dPiu ± _idn_PdnA(P)-F(P) dr nu . ' = jlnUW-g) =0, r k ojUU =-UiU* Uk b) RelativisticFluidEquations 2 Annur =Aconstant, (nU% =0,(2) 1 dx 2 dp dr k dx dP_ (4) (5) (3) 1973ApJ. . .180. .5315 2 2 9 1 ionize eachneutralhydrogenatomassumingtheelectronisingroundstate.We the nonrelativisticelectronenergyregimewehaveP=(1+x)nkTand teristic relationsforthetwolimitingtemperatureregimes,0«1and»1.In tion. InthesamelimitP=\EnkT.Wenotethatinthisapproximationequation have adoptedthenotationn==+,=xn.Inultrarelativisticelectron where xisthedegreeofionizationandequals13.59eV,energyrequiredto thermal energyoftheelectronsbecomesrelativisticas0=kTlmc»1forT» the gasremainsessentiallynonrelativisticsince0==kTlmc«1.However, photoionization rateduetotheabsorptionofultravioletphotonsfromoutgoing ionization processes.Wethereforeneglectthelowrateduetocollisions computed asafunctionoftemperatureonlybysettingtheionizationratedueto is heatedandbecomesionized.Thedegreeofionizationatanypointinthefluid remains continuousasafunctionoftemperatureat0=f. We notethatinthisapproximationthetotalinternalenthalpydensityofgas limit byE=3nkT.Thisresultfollowsdirectlyfromaveragingtheinternalenergy energy regimethegasisfullyionizedandproperdensitybecomes radiation flux.Thelatterrateisshowntobeunimportantin§IIIc.Wemaythenwrite the ionizationofneutralhydrogenbyelectroncollisionspredominatesoverallother electron collisionsequaltotherecombinationrate.Asstatedabove,itisassumedthat adequate touseequation(8)whenever0
Fig. 3.—Cooling rate and heating rate in an H h region as functions of temperature. The solid curves show A/«2, where A is the cooling rate per unit volume for the processes radiative recombination (RR), electron-proton bremsstrahlung (e-p), and electron-electron bremsstrahlung (e-e) and n is the total hydrogen num- 2 2 ber density. The dashed curve shows the total cooling rate, An/« . The dotted curve shows Fn/zz , where rn is the heating rate per unit volume due to the absorp- tion of ultraviolet photons from an exciting star. The stellar color temperature, TCi is taken to be 10,600° K; the gas is assumed to be completely ionized. 1973ApJ. . .180. .5315 2 _1-3 dr\ r)(s) aretobedeterminedasfunctionsoftheindependent variables.Thesolutionis neglected mcincomparisonwith.Wehave allowedforchangesinthedegree uniquely determinedgiven definiteboundaryvaluesforw,r,andr¡atsome finitepoint in accordancewithequations(8)and(9).Inwriting theaboveequations,wehave may writethefluidequationsinform relationships intoequations(4),(6),(7),andbyutilizingtheabovedefinitionswe level abouttheblackhole.Thenwedefinefollowingdimensionlessquantities: 5 =Thesolutionmust beconsistentwiththeconditionthatinfinitely faraway ds I where x*=xfor0
3 d(M/MQ) 2 / Tn \ - /2 / 2 \ 3/2 = 1.3 X 10 Ac«0(M/Mo) (]0 00()O Kj (j + XJ (19) d(t/lQ10 years)
For stellar-mass black holes and typical interstellar conditions, M is effectively con- stant over time scales less than 1010 years.
d) The Observed Frequency Spectrum In this section we discuss the determination of the continuous-emission spectrum that originates from radiative processes in the infalling gas and is measured by a distant observer. Given the quantities n(r), T(r), and u(r) as functions of radius r from numerical integration of the fluid equations, it is straightforward to compute -1 1 LVo, the observed luminosity measured in ergs s Hz' . For the cases we examine, most of the radiation is in the X-ray and y-ray portion of the spectrum. The accreting gas is optically thin to this outgoing radiation flux. The contribution of each fluid element to this radiation field may therefore be computed from known emission coefficients for hydrogen gas, and the individual contributions of each element may then be summed over the entire accreting volume to obtain LVo. In performing this calculation care must be taken to use relativistically correct expressions for the emission coefficients which are appropriate for a high temperature plasma (i.e., 0e » 1) and to account for all other special- and general-relativistic effects that influence the observ- ed frequency spectrum. In order to obtain LVo from the known quantity jv, the isotropic emissivity of the fluid in ergs s'1 cm"3 sterad"1 Hz"1 measured in its own rest frame, we proceed in several steps. First we obtain the emissivity of the plasma as measured by a stationary observer in the Schwarzschild frame, j'v>. This is merely a local special relativistic transformation which gives
2 2 2 1/2 ■ (1 - ^ /c ) ,, r (1 - ^ ) 7 v' ■/v (1 - (v/c) cos 0')2 ’ (1 - (v/c) COS ©')
(Thomas 1930). In the above expression v is the proper velocity of the fluid as measured by a stationary observer and is given by
dr 1 v(r) = u(r) (21) dt \ — 2m/r [u2(r)/c2 + 1 — Im/r]112
The angle 0' is the angle between the velocity v, which points radially inward, and the line of sight. Next we consider the amount of energy received at infinity in the time interval St0 and frequency interval 8v0 from a gas element of proper volume 8V' emitting for a period St' in the frequency interval SF and in the solid angle SQ'. We may write
112 SLVoSt0Sv0 = fv,8V'8£l'8t'(l - Im/r) , where the last factor accounts for the gravitational redshift of the emitted energy. 112 Using spherical symmetry and the familiar relations St0 = St'/(I - Im/r) , Sv0 = 8^(1 — 2m/r)112, and 8V' = Awr2Sr/(1 — 2m/r)112, we obtain
2 SLVo = j'vA7Tr 8r8£l'.
© American Astronomical Society • Provided by the NASA Astrophysics Data System 1973ApJ. . .180. .5315 123 -3 2 y_1 7 13 5 4/9 2/39 312 10 1 1-3 Integrating theresultoverrandO'substitutingequation(20),weobtain where No. 2,1973ACCRETIONONTOBLACKHOLES rays thatemergeatananglelessthan0*asmeasuredinthestationaryframewillbe performing theintegrationoversolidangle,wetookintoaccountfactthatlight ation emittedbythegaswithinSchwarzschildradiusistrappedandneverescapes. captured bytheblackholeand,consequently,willneverescapetoinfinity.Theangle Beyond r=atheemissionofhigh-frequencyX-ory-radiationisnegligible.In (Zel’dovich andNovikov1971). i(2GM/r), givingn(r)^n(r/r).Throughouttheaccretingvolumeadiabatic 4, 5,and6,respectively. first theaccretionofionizedhydrogenwithn=1cmandT10,000°Konto the infallingfluidareplottedasfunctionsofradiusfromblackholeinfigures a 1Afblackhole.Thevelocityu(r),thedensity/?(r),andtemperatureT(r)of n(r) ~nandT(r)^TConsequently,thevelocityu(r)variesasr~inthisregion perature increasesadiabaticallywiththedensity orT(r)oc«(V).Intheregion 0(r*) ^1),u(r)increasestonearlyone-halfofthefree-fallvelocity.Hence~ r* ~6x10cmdenotestheradiusatwhichelectronsbecomerelativistic,i.e., according tothecontinuityequationandissubsonic.Inregionr^*(where Beyond theaccretionradiusr=5x10cmgravitationalfieldisbarelyfeltand heating ofthefluiddominatescoolingduetoinelasticprocesses.Hencetem- r ^r*,y~5/3,whichgivesT(r)T(r /r). Thegasflowremainssubsonic plasma inwhichtheprotonsarenonrelativisticwhile theelectronsareultrarelativistic. pressure playsadiminishingrolewithdecreasing radiusandthegasflowapproaches in thisregionalthoughu(r)slowlyapproachesthe soundvelocityasrdecreasestor*. In thissupersonicregionr*^r>2m,where r=2m2.95x10cm,thegas 0* isafunctionofradiusanddeterminedfromtheformula Thus T(r)variesas/?(r)or^T*(r*)(r*/r) , whereT*(r*)^4x10°K. the free-fallvelocity.Thedensityn(r)^n(rlr) whiley^13/9,appropriatefor e-p bremsstrahlung,and e-ebremsstrahlung.Bysubstitutingthecorresponding with equation(21). 2.8 x10cms".Thepropervelocityofthefluid ¿;=catr—2minaccordance At theSchwarzschildradiusT=1.0x10° K,m =3.9x10cm,andu 0c Q0 0 00/ e c c c0 c s 0c s s s The radialintegralintheaboveexpressionhasalowerlimitatr=2msinceradi- The generalvariationoftheabovequantitieswithradiusiseasilyunderstood. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem In thissectionwepresenttheresultsofournumericalintegrations.Weconsider As theelectronsbecomerelativisticandyfallsbelow 5/3,u(r)becomessupersonic. Radiation isemittedfrom theplasmainformofradiativerecombination, 2 L =8t7 Vo d2m J-1 COS 0*1 r* a/»cos©* 2 rdr\ ./, 21 III. NUMERICALRESULTS y[(l -v/c)(l2m/r)] a) HiiRegion [1 -(v/c)cos0'] (T) (1 —(v/c)COS0')^ 2 (1 -u/c) ¿/(cos 0'), (22) (23) 539 (24) 1973ApJ. . .180. .5315 © American Astronomical Society Provided bytheNASA Astrophysics DataSystem 1973ApJ. . .180. .5315 -1 121 2_3 + 3 2 24 2 3 21-1 emissivities intoequation(22)wecomputetheobservedfrequencyspectrumofemitted radiation numericallyandplottheresultsinfigure7.Thespectrumhasacharacteristic ergss. bremsstrahlung shapewithT~10°KandthetotalluminosityL—1.5x holes andtypicalinterstellarconditionstheopticaldepthoffluidr«1from scattering. Theopticaldepthatrisgivenby cross-section forthisprocessisoforder<7~Zx10c7(Clayton1968).Hence positron pairinthefieldofanucleuschargeZviay+Z->Zee~, r =2mtoa,andthegasisopticallythinemergentradiationflux.Finally, in ourhydrogenplasmar~10"«1andpairproductioncanbeignored. we notethatalthoughphotonswithenergyhv>2mccancreateanelectron- Here theThomsoncross-sectionv=0.665x10"cm.Forstellar-massblack of thermalenergytransport,Ê^47rrwwf(l+x*)kTisgivenby of thenetcoolingrateatanypointrinfluid,È^^Trr(A—F),to and accretion, andconsequentlymostoftheenergyislosttoblackhole.Theratio pairT pair e T emission spectrum.Theintegrated luminosityL=1.5x10ergss. solid curvesshowthecontributions fromradiativerecombination(RR),electron-proton brems- th c strahlung (e-p),andelectron-electron bremsstrahlung(e-e).Thedashedcurveshows thetotal ¿th The dominantsourceofopacityinthefluidforX-andy-rayphotonsisThomson © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Only asmallfractionoftheavailablethermalenergyisradiatedincourse Fig. 7.—ThecontinuousemissionspectrumfromanH n regionwitha1M©blackhole.The - 3x10 r(r) x 10_, (l(»Tc) ACCRETION ONTOBLACKHOLES541 71/203 10 “(2m/r)(r/10,000K)-M/MK• o0 r ^> c r* >r2m. (26) (25) 1973ApJ. . .180. .5315 9 32 312 23 26 3,2 12 10 152 regime ournumericalresultsapplyuptoasimplescalingfactoraccretionmodels the plasmaandonly10"ofavailablethermalenergyisemittedasradiationin the adiabaticvalueof0.25inaccordancewithequation(18).Equations(25)and(26) the high-temperature,high-densityregionnearSchwarzschildradius. given theconditionswehavespecifiedinourmodel.Wefind«1throughout demonstrate theextremeinefficiencyofaccretionontoblackholesasanenergysource perature oforderunityandaretabulatedbySpitzer(1968).Equations(25)(26) proportional toM.HencewefindthatLccnT~Theobservedfrequency with arbitraryr,«andM.ThusthequantitynvariesasT~whileu adiabatically. AsaresultthemaximumaccretionparameterAisverynearlyequalto lations byShvartsman(1971)indicatethatinthisregimetheinfallinggaswillbevery distribution oftheinfallinggasremainsunchanged. as nMsincetheemissionratepercmvarieswhileemittingvolumeis are independentoftheseinputparameters.ThetotalobservedluminosityLvaries indicate thatingeneralÉ¡É«1provided72(To/10,000°K)"(M/M)10.Inthis In theaboveexpressionsxi(T)>^(Tc)?andareslowlyvaryingfunctionsoftem- temperature, anddegreeofionizationtheinfallinggasareplottedasfunctions in theopticalrangeofspectrum. nearly isothermalatT~5000°Kandthattheobservedluminositywillfallmainly spectrum willhavethesamegeneralshapeasshowninfigure7sincetemperature zoner ^rr'wefindasbefore«(r)~n(/r),T(r)whilethevelocity the radiusfromblackholeinfigures4,5,6,and8,respectively. and r=100°KontoablackholewithmassM\.Thevelocity,density, u(r) increasesto%(2GM/r)andremainsslightlysubsonic.Thedimensionless adiabatically withy^5/3.Intheouterzoneofthisregion,co>r,=9.65x Throughout theionizationzoner'^r",wherer"~2x10cmandT"(r") accretion parameterA=0.255. 542 STUARTL.SHAPIROVol.180 0 0s c 10 cm,n(r)nandT(r)^Twhileu(r)variesasr~issubsonic.Intheinner ctYi0 c0 0 by electroncollisionsandradiative recombination. The fractionaldegreeofhydrogen ionizationisplottedasafunctionofradius,assuming ionization c c 0i 3 13 4 The factthatÊ/£«1throughouttheentirefluidexplainswhygasbehaves © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem We considerinthissectiontheaccretionofneutralhydrogenwithn=1cm" We shallnotconsiderinthispapercasesforwhichÊ/È^1.Preliminarycalcu- Throughout theregionco>r^r',wherer'4x10cm,gasbehaves At r~\TXr')^1x10°Kandthegasbeginstoionizeviaelectroncollisions. cth Q cth Fig. 8.—Ionizationequilibrium ingasaccretingontoa1Mblackholean H iregion. 0 b) HIRegion 1973ApJ. . .180. .5315 9 5 9 251 210 3/2 7 153 25-1 energy isconvertedpredominantlyintoionizationratherthanthermalenergy. velocity. Inthefullyionizedinnerregionr"^r>2mgasagainexhibitsadiabatic unity whiletheflowvelocityu(r)becomessupersonic,approachingfree-fall In theionizationzoneeffectiveadiabaticindexyfallsbelow5/3andapproaches behavior withy~5/3.AttheSchwarzschildradiusT=1.5x10°K,1.1 3 x10°K,thegastemperaturerisesslowlywithdecreasingradiusasgravitational No. 2,1973ACCRETIONONTOBLACKHOLES543 frequency spectraobservedfromaccretioninHnandiregions.Thelowertempera- electrons followedimmediatelybyradiativede-excitationarenotshown.Themost bution isagainfromradiativerecombination,e-pbremsstrahlung,ande-ebrems- potential energyisutilizedtoionizetheneutralgasinHiregionratherthanheat density neartheSchwarzschildradius.However,asignificantamountofgravitational ture oftheHigasresultsinalargercaptureradiusforparticlesandhigher it up,resultinginalowertemperatureforthegasnearr=2m.Consequently, again bremsstrahlunginappearancewithT^10°K. at 10.2eV.ThetotalobservedluminosityL=3.2x10ergss“.spectrumis significant ofthesediscretetransitionsarethe1^-2^and\s-2pwhichoccur strahlung. Additionallinefeaturesduetothecollisionalexcitationofhydrogenby roughly 5x10“inthemiddleofionizationzoneatr^910cm.This in anHigastheyremainnonrelativistic(thoughathigherdensity).Thesedifferences main radiatingregionnearr=2mtheelectronsinanHngasarerelativistic,whereas indicating theextremeinefficiencyofaccretionasanenergysource.Wenoteagainthat fig. 2).TheratioÈJÈ^thendecreasesastheradiusinionizedzone increase isduetothehighlossratefromcollisionalexcitationatT^10,000°K(see that therelevantratioÈ!Èisalmostzeroinneutralregionbutincreasesto account forthedifferentemissionspectra. models withdifferentvaluesofn,TandMprovided(r/100°K)“(M/M)««10 accordance withequation(25)(hereT=0).Atr2m,ÈJÈ^6x10“,again our modelappliesequallywelluptoasimplescalingfactorotherHiaccretion 10 cm“,andu~c. strahlung {e-p),andelectron-electron bremsstrahlung{e-e).Thedashedcurveshows thetotal s solid curvesshowthecontributions fromradiativerecombination(RR),electron-proton brems- emission spectrum.Theintegrated luminosityL=3.2x10ergss. cth 0o c s The observedcontinuousemissionspectrumisplottedinfigure9.maincontri- A comparisonoffigures7and9clearlyindicatesasignificantdifferenceinthe © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Fig. 9.—ThecontinuousemissionspectrumfromanH iregionwitha1M©blackhole.The In examiningtheefficiencyofthisHiaccretionmodelasanenergysource,wefind 1973ApJ. . .180. .5315 3 12 1932 9 234 32_1 3/22 21 o26 1 13 flowing neutralgasisionizedbyelectroncollisionsaloneandnotthereabsorption visual partofthespectrum. the gastocontinueinwardisothermallyatabout10,000°K,emittingchieflyin that photoionizationbytheoutgoingradiationfluxisunimportantinneutral ensuring ÈJÈ^«1.Formodelsinwhich£/£^1theionizationzone,weexpect L ^(i'/i').Thelastrelationisobtainedfrominspectionoffigure9foryi^. where theintegrationisfromvtoooand