Nuclear Physics B (Proe. Suppl.) 35 (1994) 287-289 North-Holland

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High energy neutrino background from active galactic nuclei A.P. Szabo* and R.J. Protheroe Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, South Australia 5005, Australia

We consider a model for active galactic nuclei (AGN) in which particle acceleration takes place, and interactions of accelerated protons with photons of the radiation field, and with accreting matter, result in particle production. We obtain the energy spectrum of neutrinos produced and predict the high energy neutrino intensity due to unresolved AGN.

1. I N T R O D U C T I O N

We consider the production of high energy neu- trinos as a result of particle acceleration in AGN. Details of the neutrino calculation are given in our earlier work (Szabo and Protheroe 1992a, 1992b, 1993). We have also considered the production of high energy neutrons in P7 and pp collisions and found that this could give rise to an observ- able component of the cosmic ray intensity at 1016 eV (Protheroe and Szabo 1992). In the present paper, we summarize the model and give revised neutrino intensities which result from assuming the magnetic field at the shock is equal to the ram pressure of accreting plasma.

The AGN model we adopt is that described by Protheroe and Kazanas (1983) and developed by Kazanas and Ellison (1986). The basic in- gredients of the model are summarized below. A shock of radius R = x l r s , where rs is the Schwarzschild radius, is assumed to develop in an accretion flow onto a supermassive black hole and be supported by the pressure of relativistic particles. We therefore assume that at the shock the magnetic pressure is comparable to that of relativistic particles and the ram pressure of ac- creting plasma: pu~ ~_ Up/3 "" B2/81r, where Up is the energy density in relativistic particles and ul = z'11/2c is the upstream flow velocity. We assume that relativistic particles axe responsible for the AGN continuum luminosity, Lc , and that about half their energy is lost to neutrinos, i.e. L e -- ½Lp. The luminosity in relativistic parti-

*Present address: Defence Science and Technology Orga- nization, P.O. Box 1500, Salisbury, S.A. 5108, Australia.

cles is given by Lp 1 • 2 ~_ Q ~ M u 1 where Q is the efficiency of conversion of bulk kinetic energy of accreting plasma into energetic particles at the shock (Kazanas and Ellison 1986). The black hole mass is proportional to luminosity, and from Fig- ure 5 of Kazanas and Ellison (1986) we obtain M ~_ lO-38z lLcMo where Lc is in erg s -1. The matter density at the shock is related to the ac- cretion rate by A~/= 47rR2pu1. Hence, we obtain the matter density

p ~ 1.4 x 1033Q-1x-(5/2L~ 1 g cm -3, (1)

and the magnetic field

B _~ 5.5 x 1027Q-1/2z~Z/4Lc 1/2 gauss. (2)

The radiation density in the vicinity of the shock is related to the AGN continuum luminosity by Ur~d --~ Lc/~rR2c giving

brad ~ 1.2X 1054x14Lc I erg cm -3. (3)

The available data (Wandel and Yahil, 1985), af- ter applying a bolometric correction of x5, sug- gest that xl values in the range 10 to 100 appear consistent with the model.

Making the approximation that the diffusion coefficient at the shock is some constant b times the Bohm diffusion coefficient, i.e. D = b(½rgc ) where r~ is the gyroradius, we find that

dEp ,.~ 2.5x 1039b-lQ-112x111/4Lc 1/2 eV s -I.(4) dt -

We assume two possible AGN continuum spec- tra: (a) a spectrum with negligible energy density in the infrared component from the central region

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288 A.P. Szabo, R.J. Protheroe /High energy neutrino background from active galactic nuclei

of the AGN and a n (7 - 1 " 7 photon spectrum above the UV bump, and (b) a fiat quasar-like spec- t rum which has roughly equal energy per decade from the infrared to hard X-rays, except in the UV region. In both cases equal energy density is assumed to be contained in the power-law and black body components.

2. M A X I M U M P R O T O N E N E R G Y

The main loss processes for high energy protons in the central regions of AGN are P7 collisions with photons of the infrared-X-ray AGN contin- uum resulting in either e + pair production or pion production, pp collisions with protons of the ae- creting plasma, diffusive escape from the acceler- ation region, advection onto the black hole, and synchrotron losses (Szabo and Protheroe 1992b, 1993). The maximum proton energy occurs where

d/~p accn dEp total dt = dt (5)

and we have plotted this in Figure 1 against Lc .

3. T H E H A D R O N I C C A S C A D E

In the simulations, which are described fully by Szabo and Protheroe (1992a, 1992b), the maxi- mum proton energy is adopted as a parameter, and the acceleration rate set to equal the loss rate at Emax for a given energy density. We in- ject protons into the shock accelerator and sim- ulate their acceleration, interactions and escape from the accelerator. We also deal with the in- teractions of protons which remain magnetically confined in the central region after leaving the ac- celeration region. In P7 and pp collisions, there is some probability of producing neutrons in the final state. These neutrons, not being magneti- cally confined provide a mechanism for transport- ing energy away from the intense radiation field in the central region. Below 1014 eV the bulk of the neutrons decay in a region of enhanced mat- ter density in the accretion flow and the result- ing protons are likely to suffer pp collisions. We model the 7r --~ # --+ e decay for pions produced during acceleration, after acceleration in the cen- tral region and as a result of interactions of pro-

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Figure 1. The maximum proton energy, Emax, vs. the AGN continuum luminosity, Lc , divided by b 2 where b is the ratio of the diffusion coefficient to the Bohm diffusion coefficient. The relationship is given for both types of continuum: spectrum (a) (heavy shading); spectrum (b) (light shad- ing). The upper and lower limits in each cause correspond to xl = 100 and Xl = 10 respectively.

tons from neutron decy. We then obtain the spec- tra of neutrinos produced as a result of injecting one proton into the accelerator.

4. T H E D I F F U S E N E U T R I N O I N T E N - S I T Y

The differential neutrino luminosity, d L v / d E , of an individual AGN is obtained from the spec- t rum of neutrinos produced per injected proton by assuming the AGN continuum luminosity re- suits directly from the cascading of the electro- magnetic component (e+,7) produced by accel- erated protons. The next step is to integrate over luminosity and redshift. For this, we have used the pure luminosity evolution model fits (models A to D) obtained by Morisawa et al. (1990), and the pure luminosity evolution model fit obtained by Maccacaro et al. (1991). In each case, we take

A.P. Szabo, R.J Protheroe /High energy neutrino background from active galactic nuclei 289

6

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,, .I x-%

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f ' ,

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14 16 18 20 log(E/eV)

Figure 2. The expected diffuse vg + ~u inten- sity at Earth for b=l (horizontal hatching), b=10 (oblique hatching) and b=100 (vertical hatching). In each case, the width of the band shows the ex- treme range of intensity between results obtained using the different luminosity functions and using the two AGN continuum spectra. Also shown: Stecker et al. (1991) corrected (chain line), at- mospheric neutrino intensity (dotted line).

the values of H0, q0 and Z m a x given in these pa- pers appropriate to the model used. The neutrino intensity is given by

diOdE 41rl C__E_ 1 H 0 dLx dz f(z)(1 + z) a

xp0 ~ {(1 + z )S , Lx} , (6)

where P0 is the local X-ray luminosity function of active galactic nuclei (in cm -a erg -1 s), f and g describe the evolution of luminosity and num- ber density in co-moving coordinate space, re- spectively, and ~ = 5/2 for the Einstein-de Sitter model (q0 = 0.5). Figure 2 gives our results for b -- 1, 10 and 100, and they are compared to that of Stecker et al. (1991) and the atmospheric neu- trino intensity. See Szabo and Protheroe (1993) for comparison with other work.

In conclusion, we have calculated the intensity of neutrinos produced in AGN. The pioneering calculation of Stecker et al. (1991) stimulated much interest because it predicted fluxes observ- able with DUMAND. Unfortunately, their orig- inal intensity needed to be revised down by a factor of ~ 30 making detection marginal. How- ever, our inclusion of interactions of protons down to lower energies than assumed by Stecker et at., leads to higher intensities at 1 TeV and we predict detectable neutrino intensities.

R.J.P. is grateful to V.S. Berezinsky and the conference organizers for their kind hospitality at L.N.G.S. This work is supported by a grant from the Australian Research Council.

R E F E R E N C E S

1. Kazanas, D., and Ellison, D.C., 1986, Astro- phys. J. 304, 178.

2. Maccacaro, T., et al., 1991, Astrophys. J. 374, 117.

3. Morisawa, K., el al., 1990, Astron. Aslro- phys., 236, 299.

4. Protheroe, R.J., and Kazanas, D., 1983, As- trophys. J. 265, 620.

5. Protheroe, R.J., and Szabo, A.P., 1992, Phys. Rev. Letl., 69, 2885.

6. Stecker, F.W., et al., 1991, Phys. Rev. Left. 66, 2697; erratum, 1992, 69, 2738.

7. Szabo, A.P., and Protheroe, R.J., 1992a, in Particle Acceleration in Cosmic Plasmas, eds. G.P. Zank and T.K. Gaisser, American Inst. of Physics, New York, p. 304.

8. Szabo, A.P., and Protheroe, R.J., 1992b, in High Energy Neulrino Astrophysics, eds. V.J. Stenger el al., World Scientific, Singapore, p. 24.

9. Szabo, A.P., and Protheroe, R.J., 1993, in Frontiers of Neutrino Astrophysics, eds. Y. Suzuki and K. Nakamura, Universal Academy Press, Tokyo, p. 335.

10. Wandel, A., and Yahil, A., 1985, Astrophys. J. 295, L1.