A model is proposed to describe the observed shelf in the cosmic diffuse radiation spectrum just above 1 MeV. This model is based on induced positronium annihilation, which at incident photon energy 2 mc^2 gives rise to enhancement of the radiative field. It is proposed that this amplification may occur in double radio sources or other accreting objects. Recent observation of γ-ray line emission from the double radio sources SS 433 at 1.2 and 1.5 MeV is in good agreement with the proposed model

Heffernan, Daniel M.

Liboff, Richard L.

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-(tc_:onr-.-Th—ca-a:—C-c)a---i1&)—(-A-)VAeSTRAC]A morhl is ir:susd to d”scdbc th observed shc-lf in thecosmic thf2Le rdire.ion sprct,u.1; just hbovc 1 11eV. This modelis based on ig:ducecl pusitroniumar1nihilatio., which at incidentphoton e..orgy 2 r1c2 givcs rise to enhn’em2nt of the radiativefield, it j provised Ihat tl4s amplification mLy occur in doubleradio sot’rcer or ether accreting objects. Recont observation ofy—ray lin c1rission from the dot*le radio source 55 433 at 1.2and 1.5 11eV is ii good agre.!n..nt with the proposed model.I. II4TRODUCTIOiIIt is believed that the lobes of doublc radio sources contain acontinually regenerated electron-positron plasma. This explains theanomalously small Faraday rotation of experimentally observed radiation from the cenral region.1 It is further argued that suchsources contain a black hole at the center of an accreting disk.2’3Elecbti-positron showers are continuously produced in jets near theinner lobe, travel outward and eventually are annihilatedin theouter lobes (providing thcy htie not already done so onthe outwardjourney). The jet--like structure of such sources has beenobservedin the rac’io map of the double radio source 3C449.4’5The electron-positron plasi.ia in the outer lobes is relativelycold and approximately 80% of elcctrpns and positrons form positronium.1’6 It will be shown that a flux of 1MeV photons passingthrough such a plasn1a may be enh.nced by induced two-photon decay ofpositronium providing the positronium density exceeds a certainvalue. Whereas photons of all frequencies are produced in the innerlobe by synchrotron emission of electrons and positrons in their outward motion, only the 1MeV photons are enhanced by the processdescribed herein.II. ANALYSISConsidar that a photon of frequenry to and wavelength A interactswith a positroniura atc.n at rest and annihilates it to yield twophotons o? frequ..ncy to1 and to2. These photons emerge atangles 01and 02 respectively, with respect tothe incident photon direction.Taking the positronium atom to be a particle of mass 2m(m is electron mass), a siuple Compton-like calculation yields thefollowingrelation for the wavelength A3,r 201A1 - A = A&5fl T - (1)•LAcJwhete Ac r h/1nc, it thr Coiiq ton :evelengti, h is Planck’s constantand c is thc. specst oP light. Ccriservatiun equations indicate thatwhen ‘Tho 2mc and 01 600,ww12 (2)correspønding to2lKO = 1 K’ (3)The cqual-frequency photons of (2) emerge at 1200 to each other.These photnas in turn can induce two other positronium atoms toannihilates to yield two phito:is each wit!; energy 1MeV. Thus, aftertwo prth lingthc, at; incidu;. flux of I McV photons will be doubled.Hence, for contitnally rc9Dn:rated clcctron—positron plasma ofextc1:sicn %, greater than the ;..2an free path of the .1 MeV photon inthe plas;a, an incident flux of such photons may be amplified by thisprocess. It should be born in mind that such amplification wouldlikely he diminished due to pair production.6 However, we also notethat such ;2&ir prod’iction would serve to maintain the rapidly decaying posironium density.A full quantun electrodynamical calculation for the photon-induced arnihilation of positronium yields (1) and the followingcross section as a function of incident photon frequency7a(w) = 7ra4rgf(C) (4)Here r is the classical electron radius, a is the fine structureconstant and is the dimensionless parameter,. fico/mc . The functionf() is given by the following monotonically decreasing expression:f(Fj = -__-_ [(-i-2)(23f72+12c÷c)(5)— 2(c+1)(5c+)2a8)2n(+1)]In the preceding analysis we refer to the positronium atom in thetriplet state as dictated by the principle of charge conjugationinvarianci when the atom undergoes inducr-d annihilation.The c..id prol I let c Lion of I i4 photons occurs at scatt9rinointo co° th incident 3 It-V phoion b:am. For order-of—regriitu& ‘stimDt€’ w.a i;y ta:e the differential cross section ti’ hegivet; by U.s isotropc form:da/d12 o(w)/4 (6)A typic.;i dorble rajio sou.”ce4 is of size 1 Xpc. Hence it11 act as a sot’rc’ of 1 14eV photons if the mean electron-positron&nsiy exceeJs I/%u(”wc) : 1O cr13. In obtaining this value wehrve used the preceding threc. formulas. The electron-positron densities in such objects can vary anw1’ere between io14 cr13 in theinner region to 1O cr13 in the outer lobes)’8How”ctr we note th&t the energy contained in a lobe of density4O cr1’ is u;ncDlistic..ally large. Thus, for example, the volume ofa lobe of length g and half apex angle e0 is• V g3tan2o0 (7)The wnrgy n this lobe, coiltaining nc pairs/cm3 is2nlcncV(8)E0 2m’ng3%With nc i0 cr13 and 5° = 0.1 radian, we find E0 lO erg.10 remedy this situatiun it is &oposed that the critical density lie within a filamentary cone of apex angle 0 0.010 2x304radian. The energy in this cone isE = E0 (o/o)2 io67 erg (9)Whereas this energy is still not entirely realistic, it renders thepropostd scheme somawhat more plausible.For configurations wherein the positroniu:n plasma moves outwardfrom the central region, it is found that the x-ray spectrum isshifted to higher values. Our peculiar frequency then becomeskT6) w 2wc11+b—!I 10L mcj:here tliti coastatic b 1 and LT represents the mean kinetic energyof the dv&’ Cfl9 j1; s:uo.9 ror Ii mc2, c’ 2 Me?. In general,the line:idth for a ron—i’axr’liia;i plasma is given by1°AL 0.97 (ki in eV)1’2keV (11)which for ItT = inc2 gives tE 0.7 14eV.If one a$sur,:2s tI1 the diffuse gaiaua radiation in the universepartially slejas from a randon distrivutiori of such objects as doubleradio sourcEs, pulsars etc., then one would expect thc diffuseradiation to exhibit a shelf just above 1 11eV. This shelf has becnclearly rev.saled in a extensive review article of previous observational dFtta by Fichtel et al.11R:cntly [zmb et al.12 ob...erved 1r’ty line emission from thedouble rtiio snurce SS 433 at 1.2 and 1.5 KeV. These lines canbe explaia’-d in this model as shifts in the 1 NeV line due to outward iintic’n of the relativistic jets. First we writekT = (y-1)mc2_______(12)V 1/A•(V/c)2“here V rc(,rese:;ts tin mean velocity of the relativistic jet. Substituting these expressions into (10) and setting_v = 0.5 c gives1.2 Nc’i. If we assumo a secondary jet with v = 0.75 c, then(10) gives GJ = 1.5 14eV. Line widths calculated from (11) givelsE/tw’ 20% for both lines which agrees with observation to withina factor of 10.In summary, a model has been proposed based on stimulatedannihilation of positronium to explain the shelf in the diffusey-ray spectrum just above 1 11eV. Specific application of the modelto the double radio source SS 433 was found to be in good agreementwith observed spectral emission.AC KNOLILEDGEMENTSFruitful discussions on this subject with Michael Burns, RichardLovelace, K. C. Liu, 14. A. Guillen, and David Hammer are gratefullyacknowledged.RFFL JU NCES1. P. Nc3vdlingor,Phys. Rev. Løtt. ê.1, 135 (1978)2. R. Blz’rford and J. Priiyle, Month. Not. Roy. Asbon. Soc.176, 443 (i97C)3. R. Lovelac, Nturc, 26?, 649 (1976)4. It Perky, A. Willis and J. Scott, Nature, 281, 437 (1979)5. R.D. Blanford, 14. Begelma and N.J. Rees, Sd. Am. 246, No. 5,124 (3982) —6. it Tucker, Radiation ProreTsos in Astrophysics (MIT, CLmbridge,175)7. U.N. Hcftcman Lrid R.L. Liboff, mt. J. Theo. Physics, 22(1983) —8. 11. Ri’r.s, The4is. Cornell University (1980)9. F. AWn nian, A. Atoyan aid“. Sunyacv, Yerevan Physics Inst.’Pt’ei;rii;t rN—6s2(z9) (1980)10. C. Cror.!el, CL Joyce, R. Rarmty and C. Werntz, Astrophys.J.?L3 (1976)11. C. rirhtel et ol., in Rccert Ad. in y—Ray Astron., ed.R. Willsand H. Battick (ESA Sci. and Tech. Pub., Netherlands, 1977)12. R.C. Lamb, J.C. Ling, N. Mahoney, G. Riegler, W. Wheaton andS. Jacobson, Nature, 305, 37 (1983)

A Model for the Diffuse γ-Ray Spectrum

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A Model for the Diffuse γ-Ray Spectrum

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