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The components of the extragalactic γ-ray background (EGB) have been a puzzle since its discovery four decades ago10. Recently, the Large Area Telescope (LAT) on Fermi provided a fifty-month measurement of the integrated emission from γ-ray sources, with photon energies extending from 0.1 to 820 GeV (ref. 2). The latest analysis of Fermi-LAT data implies that both resolved and unresolved blazars account for ∼50−11+12% of the EGB in the energy range of 0.1–10 GeV, leaving the origin of the remaining component in question3.

Active galactic nuclei (AGN) are observed to exhibit strong outflows, with velocities of ∼0.1c, as manifested by broad absorption lines5,7. The ratio between the input kinetic luminosity of the outflows Lin and the bolometric luminosity of quasars Lbol, fkin, is observationally inferred to be fkin ∼ 1–5% (refs 4,5,6,7). The shock wave produced by the interaction of a quasar-driven outflow with the surrounding interstellar medium is expected to accelerate protons to relativistic energies, similarly to the shocks surrounding supernova (SN) remnants, where observations of γ-ray emission due to decay of neutral pion (π0) indicate relativistic proton–proton (pp) collisions via pp → π0 → 2γ (ref. 11). Here, we calculate the analogous γ-ray emission from quasar-driven outflows.

The energy distribution of accelerated protons per unit volume can be written as N(Ep) = N 0 E p - Γ p , where Ep is the proton energy, N0 is a normalization constant, and the power-law index Γp ∼ 2–3, based on theoretical models12 and observations of shocks around SN remnants11,13. We adopt a fiducial value of Γp ∼ 2.7 and show that our results are not very sensitive to variations around this value (see Supplementary Fig. 1 for details). N0 can be constrained by the total energy condition εntEth = ∫ E min E max N(Ep)Ep dEp, where Eth is the thermal energy density of the shocked particles and εnt ∼ 10% is the fraction of the shock kinetic energy converted to accelerate protons14. The minimum energy of the accelerated protons, Emin, is set to be the order of the proton rest energy mpc2 and their maximum energy, Emax, is obtained by equating the acceleration time of protons, tacc, to either the timescale of pp collision, tpp ∼ (npσppc)−1 ≈ 108np, 0σpp, −26 yr, or the dynamical timescale of the outflow shock tdyn ∼ Rs/vs ≈ 106Rs, kpcvs, 3−1 yr. For typical values of the outflow parameters, Emax is of the order of 106 GeV. The e-folding time to accelerate protons to relativistic energies is tacc ∼ Epc/eBvs2 ≈ 300Ep, TeVB−6−1vs, 3−2 yr, where Ep, TeV = (Ep/TeV), e is the electron charge and B = 106B−6 G is the magnetic field strength15. We assume a fraction of the post shock thermal energy, ξB, is carried by the magnetic field and adopt ξB ∼ 0.1, in analogy with SN remnants16, and we have verified that our results are not sensitive to variations around this value. Here, np, 0 = (np/1 cm−3) is the proton number density, σpp, −26 = (σpp/10−26 cm2) is the inelastic cross section of pp collision, and Rs, kpc = (Rs/1 kpc) and vs, 3 = (vs/103 km s−1) are the radius and velocity of the outflowing shell, which can be obtained by solving the hydrodynamics of the outflows17 (see Methods for details).

The contribution from quasar outflows to the EGB can be estimated by summing the γ-ray emission over the known quasar population of all bolometric luminosity at all redshifts. The cumulative specific intensity is given by:

where Eγ′ = Eγ(1 + z) is the intrinsic photon energy, ϕ(Lbol, z) is the quasar bolometric luminosity function18 and DL(z) is the luminosity distance to redshift z. is the time-averaged γ-ray luminosity of an individual quasar outflow, where tSal ∼ 4 × 107 yr is the Salpeter time for a radiative efficiency of 10% (ref. 19; see Methods for details). The diffuse extragalactic background light (EBL) associated with the cumulative ultraviolet–optical–infrared emission by star-forming galaxies and AGN over the wavelength range of 0.1–103 μm, attenuates high-energy photons via e+e− pair production. The high-energy γ-ray spectrum is therefore attenuated by photon–photon scattering on the EBL, through a factor of exp(−τγγ), where τγγ(Eγ, z) is the EBL optical depth20 for photons with energy Eγ at a redshift of z.

Figure 1 shows the cumulative γ-ray emission from quasar-driven outflows. We set upper and lower limits on the contribution from radio galaxies to the EGB on the basis of the most recent Fermi-LAT catalogue (3FGL)21 and find that radio galaxies can account for ∼7 ± 4% of the EGB at Eγ ≲ 10 GeV, roughly two to five times less than previous estimates based on sources identified in the first and second Fermi-LAT catalogue (1FGL22 and 2FGL23). Insufficient knowledge of the γ-ray emission’s origin and core variability of radio galaxies lead to uncertainties in the estimation of their contribution to the EGB (see Methods for details). Star-forming galaxies have been evaluated to constitute ∼13 ± 9% of the EGB24. We show that the contribution from quasar outflows takes up the remaining ∼20–40% of the EGB, which is dominant over the total of radio galaxies and star-forming galaxies, and can naturally account for the amplitude and spectral shape of the remaining EGB, while at higher energies the EGB is dominated by blazars3. We have verified that the cumulative contribution from radio galaxies and star-forming galaxies does not match the spectral shape of the EGB, in that the EGB would be overproduced at Eγ ≳ 10 GeV if the sum of radio galaxies and star-forming galaxies makes up the missing component at Eγ ≲ 10 GeV. We find that the break in the spectral energy distribution (SED) of quasar outflows at ≲10 GeV is independent of the parameter choices for the outflow dynamics. This generic cutoff in the emission spectrum of quasar outflows naturally fits the missing EGB component.

Figure 1: Spectral energy distribution of the integrated γ-ray background.
figure 1

Fermi-LAT data of the extragalactic γ-ray background is shown as the red points with error bars taken from Ackermann and colleagues2. The green dashed line corresponds to the contribution from blazars as estimated by Ajello and colleagues3. The purple dashed line shows the contribution from radio galaxies, following Inoue22 and Di Mauro et al.23, derived from the most recent sample in the Fermi-LAT catalogue21 (Ackermann et al. 2015). The orange dotted line corresponds to the contribution from star-forming galaxies as estimated by Ackermann et al.24, assuming the γ-ray emission spectral shape follows that of the MW. The dot-dashed blue line represents the contribution from our quasar-driven outflow model with η−3 = 3.98, where η−3 = (η/10−3). The total contribution to EGB from all sources is shown as the solid black line. The shaded regions indicate the uncertainties of each component.

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The fraction of the shock kinetic energy used to accelerate protons εnt and the fraction of the quasar’s bolometric luminosity that powers the outflow fkin are free parameters whose product η = εntfkin can be constrained by the EGB data. We search for the minimum of χ2 = ∑ i=1N(Iobsi − Imodi)2/Δi2 throughout the parameter space, where N is the number of data points, Δi is the error bar of the ith observed point, and Iobsi and Imodi are the EBG intensity of the observed and expected values, respectively. We find the best fit value of η = (3.98 ± 0.76) × 10−3 at 90% significance. For εnt ∼ 10%, as inferred from observations of SN remnants11 and theoretical models12,14, we deduce a value of fkin ∼ 1–5%, which agrees well with observations of outflows5,6,7 and theoretical predictions8,9.

The bright phase of the γ-ray emission from an individual quasar ends abruptly when the outflow exits from the surrounding galactic disk, as shown in Fig. 2, making it difficult to detect afterwards. Outflows embedded in Milky Way (MW) mass halos propagating to 10-kpc scale are expected to produce GeV γ-ray emission of ∼1039–1040 erg s−1. In the local Universe (z < 0.1), we find that only ≲0.1% of quasars host γ-ray bright outflows that are detectable by Fermi-LAT at GeV energies. These outflows are too faint to be detected in γ-rays individually, explaining why they have not been identified so far. A possible candidate for a galactic outflow relic is the Fermi bubbles at the Galactic centre25, whose γ-ray emission has been explained by a hadronic process similar to our model26,27. Our interpretation can be tested through observations of quasar outflows at other wavelengths. Radio emission is simultaneously produced via synchrotron radiation from accelerated electrons by the same outflow shocks (see black solid line in Fig. 2). Radio telescopes such as the Jansky Very Large Array and the Square Kilometre Array provide high sensitivity to detect this emission and confirm the parameters of outflows17 at redshifts of up to ∼5. For most AGN, the radio emission is free of contamination from the central source or scattering of its light by surrounding electrons. Source stacking28 could be performed in the future to find direct evidence for the cumulative γ-ray signal from multiple outflow-hosting quasars. The calibration of the outflow parameters based on their γ-ray emission can be used to forecast their contribution to the neutrino background through pion production in pp collisions (X. Wang and A. Loeb, manuscript in preparation).

Figure 2: Light curve of γ-ray emission from AGN-driven outflows and its radio counterpart, for a halo mass Mhalo = 1012 M⊙ and redshift z = 0.1.
figure 2

The solid black line represents the radio synchrotron emission at 1 GHz from electrons accelerated at the outflow shock front17. The dotted and dashed blue lines show the γ-ray emission from accelerated protons with photon energies at 1 GeV and 10 GeV, respectively. The dot-dashed vertical line marks the transition of the outflow from the disk to the halo of its host galaxy. The radio and γ-ray luminosity are shown as a function of time, t, and outflow shock radius, Rs, on the lower and upper horizontal axes, respectively. Above the lower horizontal axis, we express the time as a fraction of the Salpeter time tSal, indicating roughly the probability of finding a quasar at each time or position. The vast majority of the quasar outflows are too faint to be detected individually, explaining why their contribution to the EGB had not been recognized.

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Methods

Hydrodynamics of quasar-driven outflows.

Outflows are injected into the ambient medium with an initial velocity of ∼0.1c. As they propagate in the ambient medium, a double shock structure forms. The outer forward shock accelerates the swept-up medium, while the inner reverse shock decelerates the wind itself. The equations describing outflow hydrodynamics are given by17,29:

where Ms is the swept-up mass of the outflowing shell. Mtot is the gravitational mass decelerating the expansion of the shell, including the mass of dark matter, host galaxy, central black hole (BH) and the self gravity of the shell. The thermal pressure in the shocked wind, PT, declines at a rate determined by the work done on the medium and radiative losses in the shocked wind, described by the heating/cooling luminosity Λ, composed of energy injection Lin, free–free emission Lff, synchrotron cooling Lsyn, inverse Compton scattering LIC and proton cooling Lp. Hydrostatic equilibrium gives the thermal pressure in the ambient medium P0. We assume that quasars radiate at Eddington luminosity , providing BH mass for a given Lbol. The prescription for assigning to host halo mass Mhalo follows Guillochon and Loeb30, with a fixed bulge to total stellar mass ratio of 0.3. We set an upper limit of Mhalo to be ∼1013M⊙, which is the maximum halo mass that allows the propagation of outflows to halo scale as found in numerical results17. We make the assumption of spherical symmetry for the density distribution of the surrounding gas and the mass profile of the galaxy where the outflows are embedded. The gas density distribution is assumed to be a broken power law, expressed as:

where α and β are different indices for the disk and halo components, and Rdisk and Rvir are the radius of the disk and halo, respectively. We fix α = 2, assuming an isothermal sphere for the gas within the disk component and β can be self-consistently constrained by halo mass Mhalo, redshift z and disk baryonic fraction fd (taken to be 0.5 in the calculation).

γ-ray spectrum from quasar-driven outflows.

We compute the spectral energy distribution (SED) of gamma-ray emission produced by neutral pion (π0) decay. For Ep ≲ 0.1 TeV, the γ-ray luminosity is given by31:

where Emin = Eγ + mπ2c4/4Eγ, mπ and Eπ are the mass and energy of π0, and V is the volume of the outflow. qπ(Eπ) is the emissivity of π0, given by31:

where x = mpc2 + Eπ/κpp, κpp ∼ 17% is the fraction of the relativistic proton energy that goes to neutral pions in each interaction, N(x) is the energy distribution of accelerated protons, and ng = ρg/mp is the number density of the ambient medium. The inelastic cross section of pp collision σpp is approximated by31:

for Ekin ≥ 1 GeV, and σpp = 0 is assumed at lower energies, where Ekin = Ep − mpc2 is the kinetic energy of protons. This implies that the γ-ray emission is produced by relativistic protons with energy ≳2 GeV. We have verified that the variation in results adopting other approximations of σpp is negligible32. We estimate that the timescale of Coulomb collisions33 is ∼10 times longer than tpp, meaning that pp collisions are the dominant proton cooling process. The γ-ray SED of an individual quasar outflow for different power-law indices of accelerated protons Γp is shown in Supplementary Fig. 2. For a quasar with halo mass ∼1012 M⊙ at redshift z ∼ 0.1, the expected GeV γ-ray luminosity is ∼1039–1040 erg s−1, which falls off the detection limit of Fermi-LAT by ∼2–3 orders of magnitude.

Integrated γ-ray background.

The bolometric luminosity function of quasars is given by18:

where Lbol is the bolometric luminosity, L⋆ varies with redshift, described by logL⋆ = (logL⋆)0 + kL, 1ξ + kL, 2ξ2 + kL, 3ξ3, ξ = log[(1 + z)/(1 + zref)], zref = 2 and kL, 1, kL, 2 and kL, 3 are free parameters. We adopt parameter values of the pure luminosity evolution model, where log(ϕ⋆/Mpc−3) = −4.733, (log(L⋆/L⊙))0 = 12.965, L⊙ = 3.9 × 1033 erg s−1, kL, 1 = 0.749, kL, 2 = −8.03, kL, 3 = −4.40, γ1 = 0.517 and γ2 = 2.096. We integrate the γ-ray emission over the bolometric luminosity range 1042–1048 erg s−1 and redshift range 0–5. The comoving volume per unit redshift is given by34:

where DH = c/H0 and . We adopt H0 = 70 km s−1 Mpc−1, ΩM = 0.30 and ΩΛ = 0.7.

Constraints on radio galaxies’ contribution to the EGB.

We estimate the contribution to the EGB by radio galaxies (RGs) using samples identified in the most recent Fermi-LAT catalogue, 3FGL21. Compared with previous Fermi-LAT catalogues, PKS 0943-76 has been removed due to misassociation21. The association of Fornax A (NGC 1316) has not been confirmed by 3FGL21. Newly identified FRI (Fanaroff–Riley type I) sources include 4C+39.12 and 3C 264, and FRII sources include 3C 303, 3C 286 and 3C 275.1. Consequently, 19 objects constitute our RG sample; their parameters are summarized in Supplementary Table 1. We note that some FRI sources such as IC 310, PKS 0625-35 and NGC 1275 show blazar-like variabilities, which could lead to debatable source classification with BL Lac objects. TXS 0348+013, 3C 207, 3C 275.1, 3C 286 and 3C 380 are classified as steep-spectrum radio quasars (SSRQs) and thus are non-standard FRIIs23. However, FRI/BLL and SSRQ sources are also included in the sample selection of Inoue22 and Di Mauro and colleagues23. Therefore, we keep them in our source selection, to be consistent with previous analysis, and we have verified that their removal leads to negligible changes in radio–γ-ray correlation, as discussed later.

Previously, the contribution of RGs to the EGB has been evaluated based on the γ-ray luminosity function of RGs, which is established from a correlation between γ-ray and 5 GHz ‘core-only’ radio luminosities of RGs22. However, the origin of the γ-ray emission from RGs remains uncertain. γ-ray emission could be produced by ultrarelativistic electrons of high density in the radio lobes by scattering soft photons via self-synchrotron Compton or external Compton processes. Such γ-ray emission has been resolved and confirmed in the lobes of a nearby FRI RG, Cen A, by Fermi-LAT35. Due to the lack of simultaneous radio and γ-ray observations of RGs, core variabilities could invalidate this correlation. In our calculation below, we choose radio data closest in date to γ-ray observations. The correlation between the ‘core-only’ radio luminosity and the total γ-ray luminosity would be distorted if some of the unresolved γ-ray emission originates outside the core of the corresponding galaxies. In such a case, the γ-ray emission from the core would be overestimated, and the radio–γ-ray correlation would provide an upper limit on the contribution of RGs to the EGB. The actual contribution would be between this upper limit and the result one gets when correlating the total radio and γ-ray emission of these galaxies.

We recalculate the Lγ–Lrad correlation for both ‘core-only’ and total radio luminosity cases using the most recent samples. We follow the BCES (bivariate correlated errors and intrinsic scatter) method by Akritas and Bershady36 to fit regression parameters and uncertainties. Using the BCES(Lγ ∣ Lrad) slope estimator, we find that the best fit Lγ–Lradtot and Fγ–Fradtot correlation can be expressed as:

where Lγ, 40 and Lrad, 40tot are Lγ and total radio luminosity Lradtot in units of 1040 erg s−1. Similarly, the best fit Lγ–Lradcore and Fγ–Fradcore are given by:

where Lradcore is the core-only radio luminosity in units of 1040 erg s−1. γ-ray–radio correlations based on 1FGL22 and 2FGL23 samples are given by:

We compare our fitted Lγ–Lradtot and Lγ–Lradcore correlation with previous results, shown in Supplementary Figs 3 and 4, respectively. We calculate the corresponding Spearman coefficients and partial correlation coefficient of Lγ and Lrad, Fγ and Frad, and the corresponding p-values, summarized in Supplementary Table 2.

Following Inoue22 and Di Mauro et al. 23, we calculate the contribution of RGs to the EGB using our updated γ-ray–radio correlation. The γ-ray luminosity function (GLF) can be obtained by:

where ρrad is the radio luminosity function (RLF) of the RGs, and κ is the fraction of γ-ray loud RGs, constrained by source-count distribution, as discussed later in the text. For the total-radio–γ-ray luminosity correlation, we adopt the total RLF and corresponding parameters given by model C of Willott et al. 37 and convert it to the cosmological constants in this work. For the ‘core-only’ radio luminosity correlation, we convert the total RLF to core RLF, following the method proposed by Di Mauro et al. 23, according to the core–total radio luminosity correlation of RGs38:

where core radio luminosity at 5 GHz Lrad, core5 GHz and total radio luminosity at 1.4 GHz Lrad, tot1.4 GHz are in units of W Hz−1. We adopt a radio spectral index αr = 0.8 for conversion of radio luminosities at different frequencies in our calculation37.

The intrinsic γ-ray photon flux per unit energy is obtained by:

where Γ is the γ-ray photon index. Therefore, we obtain the integrated γ-ray SED from RGs, expressed as:

where dNΓ/dΓ is the distribution of γ-ray photon index Γ, which is assumed to be Gaussian, in an analogy to blazars, with an average value of 2.25 and a scatter of 0.28, based on our RG sample. ω(Sγ) is the detection efficiency of Fermi-LAT at a photon flux of Sγ. However, ω(Sγ) is not given in 3FGL, so we adopt the derived detection efficiency for detection threshold TS > 25 and |b| < 10° derived for 2FGL23. We adopt Γmin = 1.0, Γmax = 5.0, zmin = 0.0, zmax = 5.0, Lγ, min = 1038 erg s−1 and Lγ, max = 1050 erg s−1 in our calculation.

The expected cumulative flux distribution can be obtained by:

where Sγ is the photon flux above 0.1 GeV and Lγ(Sγ, z) is the corresponding γ-ray luminosity at a redshift of z. The observed source-count distribution of our sample is given by39:

where we sum up all RG sources with photon flux Sγ, i > Sγ. κ can be constrained by normalizing Nexp to Nobs. We find the best fit at 1σ significance is κ = 0.081 ± 0.008 by using total-radio–γ-ray luminosity correlation (equations (12) and (13)), and κ = 2.32 ± 0.15 by using core-radio–γ-ray luminosity correlation (equations (14), (15) and (19)). This indicates that the core-only radio–γ-ray correlation overproduces γ-ray loud RGs constraint by the observed source-count distribution. In this case, we fix κ = 1 in our calculation, following Di Mauro and colleagues23.

We obtain the resulting integrated γ-ray spectrum for both cases, which set the upper and lower limits of contribution of RGs to the EGB. In our calculation, we adopt the mid-value of this range as the contribution of RGs and show the full range as uncertainty.

We find that the RGs make up ∼7 ± 4% of the EGB. We have verified that if RGs accounts for the rest of the EGB besides blazars and star-forming galaxies at Eγ ≲ 10 GeV, then the EGB would be overproduced at higher energies. However, quasar outflow’s SED has a generic break at <10 GeV, which naturally accounts for the missing component of the EGB. We note that although our model explains the data, it may not be the only contributor to the missing γ-ray sources, due to uncertainties in its input parameters.

Data availability.

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.