We show that inverse Compton scattering of cosmic-microwave-background and
starlight photons by cosmic-ray electrons in the interstellar and intergalactic
space explains well the spectrum and intensity of the diffuse gamma-ray
background radiation (GBR), which was measured by EGRET aboard the Compton
Gamma Ray Observatory (CGRO) in directions away from the Galactic disk and
centre. The Gamma Ray Large Area Space Telescope (GLAST) will be able to
separate the Galactic foreground from the extragalactic gamma-rays, and to
provide stringent tests of the theory

Dado, Shlomo

Dar, Arnon

De Rujula, A

English

arXiv

We show that inverse Compton scattering of cosmic-microwave-background and starlight photons by cosmic-ray electrons in the interstellar and intergalactic space explains well the spectrum and intensity of the diffuse gamma-ray background radiation (GBR), which was measured by EGRET aboard the Compton Gamma Ray Observatory (CGRO) in directions away from the Galactic disk and centre. The Gamma Ray Large Area Space Telescope (GLAST) will be able to separate the Galactic foreground from the extragalactic gamma-rays, and to provide stringent tests of the theory

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arXiv:astro-ph/0607479 v1   20 Jul 2006On the origin of the diffuse gamma-ray background radiationShlomo Dado and Arnon DarDepartment of Physics and Space Research Institute, Technion, Haifa 32000, IsraelA. De Ru´julaTheory Unit, CERN, 1211 Geneva 23, Switzerland; Physics Department, Boston University, USA(Dated: July 21, 2006)The spectrum and intensity of the diffuse gamma-ray background radiation in directions awayfrom the Galactic disk and centre were measured by EGRET. We show that the observations are wellexplained by inverse Compton scattering of cosmic-microwave-background and starlight photons bythe cosmic-ray electrons produced in our Galaxy, in external galaxies and by active galactic nuclei.PACS numbers: 98.70.Sa, 98.70.Rz, 98.70.VcI. INTRODUCTIONThe existence of a diffuse gamma background radia-tion (GBR) was first suggested by data from the SAS 2satellite [1]. Data from the EGRET instrument of theCompton Gamma Ray Observatory supported this find-ing [2]. We call “the GBR” the residual of measurementsmade by EGRET by subtracting point sources, maskingthe Galactic disk at latitudes |b| ≤ 10o, and the Galacticcentre at |b| ≤ 30o for longitudes |l| ≤ 40o, and by extrap-olating the data outside this mask to zero column den-sity, which should eliminate the Galactic contributions ofbremsstrahlung from cosmic-ray electrons (CREs), andπ0 production by CR nuclei. Outside the mask, the GBRflux in the observed range of 30 MeV to 120 GeV, shownin Fig. 1, is well described by a power law:dFγdE≃ 2.74× 10−3[EMeV]−2.101cm2 s sr MeV. (1)The spectral index of the GBR is the same, 2.1± 0.03,in all sky directions [2]. The normalization of the GBRflux was found to be normally distributed around the cen-tral value given by Eq. (1). These two results were usedto argue for a cosmological (extragalactic) origin of theGBR [2]. A large number of putative sources have beenproposed. Perhaps the most conservative hypothesis forthe origin of an isotropic GBR is that it originates fromunresolved active galactic nuclei (AGNs) [3]. The factthat blazars have a γ-ray spectrum with an average index2.15± 0.04, compatible with that of the GBR, supportsthis hypothesis [4], but later studies have shown that≤ 25% of the GBR can result from unresolved AGNs [5].Geminga-type pulsars, expelled into the Galactic halo byasymmetric supernova explosions, could also be abun-dant enough to explain the GBR [6]. Other suggestionsinclude cosmic-ray interactions in galaxy clusters andgroups [7], and fossil radiation from shock-acceleratedCRs during structure formation [8]. More exotic hy-potheses are a baryon-symmetric Universe [9], now ex-cluded [10], primordial black-hole evaporation [11], su-permassive black holes at very high redshift [12], and theEnergy (MeV)Photons/(cm2 s sr MeV)10-1310-1210-1110-1010-910-810-710-610-5102103104105E-2.1FIG. 1: The GBR spectrum, inferred by EGRET [2]. Theline is their best power-law fit.annihilation of dark-matter particles [13].The EGRET GBR data in directions away from theGalactic disk and centre show a significant deviationfrom isotropy, clearly correlated with the structure of theGalaxy and our position relative to its centre [14]. Thisadvocates a large Galactic contribution to the GBR. In-dications of such a contribution were found by means ofa wavelet-based “non-parametric” approach that makesno reference to a particular model [6]. Other authors[15] also found that the contribution of inverse Comptonscattering (ICS) of starlight (SL) and microwave back-ground radiation (MBR) photons by Galactic CREs ispresumably much larger than expected. Earlier evidencethat ICS of SL and of the MBR by CREs in the Galactichalo contributes significantly to the GBR at large Galac-tic latitudes was reported in [16]: ∼ 30% of the intensity2of the GBR at large latitudes is correlated to the Galac-tic radio emission at 408 MHz, which is dominated bysynchrotron radiation from the same CREs as produce∼ 100 MeV γ-rays by ICS from the Galactic SL.In [14] we went a step further, showing that the GBRcould be dominated by ICS of MBR and SL by Galac-tic CREs, provided that the Galactic CR halo is largeenough. A later analysis [17] led to the same conclusion.Here we reinforce this conclusion by showing how the in-tensity and directionality of the GBR can be predictedfrom our detailed understanding [18] of the distributionand spectra of CR electrons and nuclei in the Galaxy.A large Galactic contribution to the GBR —correlatedwith the structure of the galaxy’s halo and our positionrelative to its centre— and the uniformity of its spectralindex over the whole sky suggest similar origins for theGalactic and extragalactic contributions. We shall arguethat ICS of radiation by CREs in our Galaxy, in exter-nal galaxies and in the intergalactic space, is that origin.The extragalactic component is calculated directly fromthe CR luminosity of the main cosmic accelerators: su-pernova explosions and the massive black holes of AGNs.We show that the observed spectrum, intensity and an-gular dependence of the GBR are correctly predicted.The energy spectrum of CREs near Earth [19], withenergy Ee > 5 GeV, is well described by:dFedEe= A[EeMeV]−3.2±0.101cm2 s srMeV. (2)This spectrum is predicted by the Cannonball (CB)model, wherein CRs are particles of the interstellarmedium accelerated by relativistic “cannonballs” —emitted in core-collapse SN explosions— to a “source”spectrum with a power-law index, βs = 13/6 ≈ 2.17[18]. Energy loss by synchrotron emission in magneticfields and ICS of radiation change βs for CREs to βe =βs + 1 ≈ 3.17. Radio observations of synchrotron radi-ation emitted by CREs in the Galaxy, external galaxies,galaxy clusters and active galactic nuclei (AGNs) supportthis predicted universal spectrum of high-energy CREs.The temperature and mean energy of the MBR areT0=2.725 K and ǫ0≈ 2.7 k T0≈ 6.36meV [20]. Starlighthas an average energy ǫ1 ∼ 1 eV. Consider the ICS ofthese radiations by CREs. The mean energy E¯γ of theCompton upscattered photons is:E¯γ(ǫi) ≈43(Eeme c2)2ǫi. (3)The ICS of the MBR and SL photons by CREs producesa GBR with a spectrum which is a convolution [25] of theCRE spectrum with the thermal spectrum of the MBRand of SL. The result can be well approximated by:dFγdE∝dEedE[dFedEe]Eie, Eie ≡ mec2√3 E¯γ4 ǫi, (4)with Eie obtained from Eq. (3) by inverting E¯γ . Intro-ducing the electron flux of Eq. (2) into Eq. (4), we obtain:dFγdE∝ E−(βe+1)/2 ≃ E−2.083. (5)The predicted photon spectral index coincides with themeasured one, 2.10± 0.03 [2]. Next, we calculate theintensity of the extragalactic GBR produced by ICS ofMBR and SL photons by CREs in external galaxies andthe intergalactic medium (IGM).Adopt a standard cosmology with a Hubble con-stant H ≈ 70 km s−1 Mpc−1 and (Ω, ΩM , ΩΛ) =(1, 0.27, 0.73), for which the age of the Universe is ap-proximately the Hubble time H−1 ≃ 14 Gy. Let σT≈0.65×10−24 cm−2 be the Thomson cross-section. Let Uγbe the energy density of the radiation field (MBR+SL),and UB = B2/(8π) the energy density of a magnetic fieldB. Given Eq. (3), CREs with energy ≥ 3 GeV are neededto produce the GBR above 30 MeV by ICS of the MBR.Even for B = 0, the radiative lifetime of these electrons:τrad =3m2e c34 σTEe (Uγ + UB)(6)is much shorter than the Hubble time. In the CR haloof galaxies and in galaxy clusters B < 3µG, and in theIGM, where B ∼ 50 nG [26], ICS of the MBR dominatesover synchrotron losses on the magnetic field. Therefore,we shall calculate the intensity of the extragalactic GBRfrom the conclusion that practically all the kinetic energyof CREs in the Universe has been converted by ICS to γ-rays of the GBR, with the predicted spectrum of Eq. (5).The main accelerators of high-energy CREs are su-pernovae (SNe) and AGNs [18]. Consider SNe first.The SN rate is proportional to the star-formation rateRSN(z) ∝ RSF(z), with RSN(0) ≈ 10−4Mpc−3 yr−1 [21].The observed rate is well represented by RSF(z)/RSF(0)≈(1+z)4 for z<1.2 and RSF(z)=RSF(1.2) for z ≥ 1.2 [22].Let Ek≈2× 1051 erg be the mean energy release in CRsper SN [18] and let fe be the fraction of the luminosityin CREs out of the total luminosity LCRin CRs. TheCB model does not predict fe, we shall assume that it isequal to the ratio of the Milky Way’s luminosity in CREsto its total luminosity in CRs:fe ≈∫dFe[MW]dEE dEτrad/∫ dFCR[MW]dEE dEτdif≈140(7)where τdif ≈ 2× 108 (E/GeV)−0.6 yr is the mean escapetime of CR protons and electrons from the Galaxy bydiffusion in its magnetic field [18].Given our inferred 100% ICS conversion of CRE energyto photon energy, the GBR spectrum satisfies:∫dFγdEE dE≈c Le4πH RSF(0)∫dz (1 + z)−βs RSF(z)√ΩM (1 + z)3 +ΩΛ,(8)where Le = feLCR ≈ feRSNEk is the mean luminositydensity of CREs in the Universe. Inserting Le into Eq. (8)3yields the contribution to the GBR from extragalacticSNe:dFγdE≃ 0.97× 10−3[EMeV]−2.081cm2 s sr MeV. (9)Powered by mass accretion onto massive black holes,AGNs eject powerful relativistic jets whose kinetic en-ergy is transferred mainly to CRs. The kinetic powerof these jets has been estimated from their radio lobes,assuming equipartition between CR- and magnetic fieldenergies and an energy ratio fe similar to that observedin our Galaxy. It was estimated [23] that AGNs with acentral black hole of M ≃ 108M⊙ inject ≈ 1061−62 erginto the intergalactic space, mostly during their ∼ 108y bright phase around redshift z = 2.5. In search foran upper bound, we assume that the kinetic energy re-lease in relativistic jets is the maximal energy releasefrom mass accretion onto a Kerr black hole (≈ 42% of itsmass), and that this energy is equipartitioned betweenmagnetic fields and cosmic rays [18] with a fraction feof the CR energy carried by electrons. These CREs alsocool rapidly by ICS of the MBR and SL. The energy ofCREs with γe>∼185, whose cooling time is shorter thanthe look-back time to z = 2.5, is converted to γ-rayswhose energy is redshifted by 1 + z by the cosmic ex-pansion. We assume the Galactic ratio of the mass ofthe central black hole, 3.5 × 106M⊙, to the luminosity,L∗[MW] ≈ 2.3 × 1010L⊙, to be universal. The Univer-sal luminosity density, ρL= 1.2 × 108L⊙Mpc−3, thenimplies that ρBH(z = 0) ∼ 1.82 × 104M⊙Mpc−3 in thecurrent Universe (see however [24]) and that AGNs havecontributed an extragalactic GBR flux:dFγdE≃1.75× 10−2 c fe ρBH c24 π (1 + z)MeV[EMeV]−2.08. (10)With the above priors this contribution is:dFγdE≃ 2.1× 10−4[EMeV]−2.081cm2 s sr MeV. (11)Because of Feynman scaling, the GBR from π0 produc-tion and decay in hadronic CR collisions in the ISM andIGM has the same power-law index as that of CRs [7],i.e. −2.77 in the ISM of galaxies and −2.17 in the IGMinside and outside galaxy clusters [18]. This contributionto the extragalactic GBR is much smaller than that ofCREs and need not be discussed here.The GBR contains a considerable Galactic foregrounddue to ICS of MBR, SL and sunlight photons by GalacticCREs [18]. The convolution of a CRE power-law spec-trum with a photon thermal distribution [25] can be ap-proximated very simply [14]. Using the index i to labelthe CMB, SL and sunlight fluxes, we have:dFγdEγ≃ Ni(b, l) σTdEiedEγ[dFedEe]Ee=Eie, (12)0.050.10.150.20.250.30.350.40.450.5-150 -100 -50 0 50 100 1500.050.10.150.20.250.30.350.40.450.5-150 -100 -50 0 50 100 1500.050.0750.10.1250.150.1750.20.2250.25-150 -100 -50 0 50 100 1500.050.0750.10.1250.150.1750.20.2250.25-150 -100 -50 0 50 100 1500.060.080.10.120.140.160.180.2-150 -100 -50 0 50 100 1500.060.080.10.120.140.160.180.2-150 -100 -50 0 50 100 150b = + 45ob = − 45ob = − 20ob = +20ob = + 75ob = − 75oLongitudeExtragalactic Extragalactic104×Fγ(E>100MeV)/[cm2ssr]FIG. 2: The flux of GBR photons above 100 MeV: compar-ison between EGRET data and our model for he = 8 kpc,ρe = 35 kpc, as functions of longitude l at various fixed lat-itudes b. The shaded domain is EGRET’s mask. The AGNcontribution is subdominant: compare Eqs. (9) and (11).where Ni(b, l) is the column density of the radiation fieldweighted by the distribution of CREs in the direction(b, l), and Eie is given in Eq. (4). The distribution of the(non-solar) SL is approximated as ∝ 1/r2, with r the dis-tance to the Galactic centre, and the CREs are assumedto be distributed as a Gaussian “CR halo” [14]. Natu-rally, the results depend crucially on the size and shapeof this halo. In this note we use our updated estimate ofthe halo properties [18]: a Gaussian distribution with ascale length of ρe = 35 kpc in the Galactic disk, as weused in [14], but a scale height of he = 8 kpc perpendicu-lar to the disk [18] instead of the he = 20 kpc used before[14]. The justification for this change is as follows:The radio emission of “edge-on” galaxies –interpretedas synchrotron radiation by electrons on their magneticfields– offers direct observational evidence for CREs wellabove galactic disks (e.g. [27]). For the particularly wellobserved case of NGC 5755, the exponential scale heightof the synchrotron radiation is O(4) kpc. If the CRs4and the magnetic field energy are in equipartition, theyshould have similar distributions, and the Gaussian scaleheight he of the electrons ought to be roughly twice thatof the synchrotron intensity, which reflects the convo-lution of the electron- and magnetic-field distributions.The inferred value is he ∼ 8 kpc. The correspondingvolume of the Galactic CR halo is VCR= (π)3/2 ρ2e he =1.6×1069 cm3. The SN rate in the Galaxy is RSN[MW]∼2 per century, and its predicted total luminosity in CRsis LCR≈Ek RSN [MW] ≈ 4 × 1049 erg y−1. The CR con-finement volume must obey the constraint:LCR∼ VCR×4πc∫dEτdifEdFpdE. (13)Our estimated τdif and the observed (or fitted) spec-trum of CRs [19, 29] yield the expected VCR≈1.6×1069cm3. The volume inferred from a leaky-box model fit tothe Galactic GBR [28] is smaller by a factor ≈ 2.5 thanour estimate, reflecting the shorter confinement time ofCRs estimated in leaky-box models from the abundanceof unstable CRs [30], and the higher contribution as-sumed in [28] for the extragalactic GBR.In Fig. 2 we compare the observed GBR with our pre-dictions, as functions of Galactic coordinates. The pre-diction is a sum of a (b, l)-dependent Galactic foregroundproduced by ICS of the MBR, SL and sunlight, and a uni-form extragalactic GBR. The result has χ2/dof = 0.85, avast improvement over the constant GBR fit by EGRET,for which χ2/dof = 2.6. We conclude that the GBR canbe explained by standard physics, namely, ICS of MBRand SL by CREs from the two main CR sources in theuniverse: SNe and AGNs. At Eγ>100 GeV, most of theextragalactic GBR photons are absorbed by pair produc-tion on the cosmic infrared background radiation [31] andthe diffuse GBR reduces to the Galactic foreground. 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On the origin of the diffuse gamma-ray background radiation

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