- Email: [email protected]
High Energy cosmic neutrinos
I ~ L | [ I | ~-,~" i H k'&~[ L 1 "]
PROCEEDINGS SUPPLEMEHTS
Nuclear Physics B (Proc. Suppl.) 35 (1994) 185-196 North-Holland
High Energy Cosmic Neutrinos Todor Stance a* aBartol Research Institute, University of Delaware Newark DE 19716 USA W e discuss the production of neutrinos in interactionsof high energy cosmic ray nuclei acceleratedin different astrophysical objects. Neutrino fluxes of differentmagnitude and energy spectra are produced in interactions on diffuse galactic matter and possibly at or close to the accelerationsite. Different potential sources inside and outside our galaxy are discussed with an increased attention to neutrinos generated in photoproduction interactions at active galactic nuclei. The observabilityof these neutrinos with current and future generation detectors is estimated.
1. I N T R O D U C T I O N The topic of this talk is the production of neutrinos in inelastic interactions of high energy cosmic ray nuclei and the initiated by them hadronic cascades. The shape of the neutrino energy spectrum is defined by the energy spectrum of the parent cosmic rays and by the physical conditions of the medium, where the cascades are developing. One can distinguish three different general types of energy spectra for these neutrinos: (i) Atmospheric neutrinos; (ii) Diffuse galactic neutrinos; (iii) Source neutrinos. A t m o s p h e r i c n e u t r i n o s are generated in interactions of the cosmic rays particles and cascades developing in the atmosphere. Their energy spectrum is formed in the competition between interaction and decay that the secondary mesons undergo in the constantly changing atmospheric density. The contribution of pions to the atmospheric neutrino flux, for example, is given by[1]
dN,, dE,,
-
No(E`,) 1 - ZNN
× 1
A,~`, + B~rv cos t9 E`,/e,r'
where A.`, = g~r. (1
-
r)~/( 7
+
(1)
1) (r =
mt,/rr~, ZN~ = f z'r-*dn/dz dz) reflects the the zF spectrum of pions in nucleon collisions and the primary cosmic rays spectral index 7. B~`, is a normalization factor accounting for 7 and the nucleon and pion cross-sections. Eq. 1 tells us that up to energy e~ the neutrino flux is parallel to the primary nucleon flux(7 ,-~2.7), while after that it *Work supportedin part by the NationalScienceFoundation under Grant PH-Y9220990.
steepens by one power of E`, to 7 "--3.7.This reflectsthe competition between decay and interaction, and e~ is the energy at which the interaction probability equals the decay probability, e,~ --115 G e V in the atmosphere (in verticaldirection) and obviously grows for more tenuous media. For the case of atmospheric neutrinos this includes neutrino production by cosmic rays that enter the atmosphere at angles significantlydifferent from vertical. Cascades then develop in m u c h more rarified atmosphere and the neutrino spectrum is significantly harder. The atmospheric neutrino spectrum has a typical angular dependence with the m i n i m u m flux coming from vertical direction and the m a x i m u m - from horizontal. In fact the spectrum is m u c h more complicated because of the contributions of other channels and the angular dependence of the bend position. In the G e V region m u o n decay is equally important contributor for all types of neutrino. For re, where m u o n decay is a major contributor, the spectrum approaches 7 ,,,4.7at high energy. Diffuse galactic neutrinos are produced by galactic cosmic rays in interactions on the interstellar matter. These extraterrestrial neutrinos should follow the 7 ~2.7 cosmic ray spectrum up to the highest energies, since all interaction products, including muons, decay. The absolute normalization of the diffuse galactic neutrino flux depends on the column density of matter in atomic and molecular clouds in the galaxy and the cosmic ray density gradient. Under the assumption of constant cosmic ray density in the Galaxy, an estimate of the expected nearly isotropicneutrino
0920-5632/94/$07.00 © 1994 - Elsevier Science B.V. All fights reserved. SSDI 0920-5632(94)00456-6
186
T Stanev/High energy cosmic neutrinos
fluxes from cosmic ray interactions in the galaxy can be easily derived[2]. Imagine a concentration of matter of density p and linear dimension R. The flux at Earth of neutrinos generated by pions produced in cosmic ray interactions with this matter is given by
~ v - - ~ C R f A IS±nell4 2ZIv~ L mN j [pR] v +------f-'
(2)
where ~CR is the cosmic ray flux per steradian, O'inel is the total inelastic pp cross section, mjv is the nucleon mass and pR is the column density of the source. ZN~r is the spectrum-weighted moment for production of pions by nucleons as in Eq. 1. fA is a correction factor to account for the fact that some primaries and targets are nuclei heavier than protons. S o u r c e n e u t r i n o s are produced by high energy particles a~ their acceleration 8ire8 and follow the hard (V "~ 2.0-2.4) cosmic ray acceleration spectra. In principle it is possible that nuclei accelerated at an astrophysical object interact at the object and generate neutrinos, but are not able to diffuse away from the source and become cosmic rays. In practice, the existence of galactic VHE and UHE v - r a y sources was suggested as a solution of the problem of the origin of the galactic cosmic rays. If a non negligible fraction of these is accelerated at compact objects with high magnetic fields, we should observe the associated neutrinos. There is no shortage of such objects in the galaxy, the most obvious being neutron stars, black holes and young supernova remnants. The existence of extragalactic sources of high energy neutrinos is somewhat more decoupled from the cosmic ray origin. Active galactic nuclei have tremendous luminosity in all energy bands and do not have to generate a significant amount of the observed cosmic rays to be strong neutrino sources. The major assumption is that the role of particle acceleration and hadronic processes in AGN is significant. The only currently practical way to detect high energy neutrinos is by detecting muons generated in deep inelastic muon neutrino (and ant±neutrino) scattering in the rock surrounding the detector. The effective detector volume V~I! will then be the product of the actual detector area in the direction perpendicular to the muon direction S± and the muon range in the medium
R,. The muon ionization energy loss in rock is --~2 MeV g-lcm2 with a slow logarithmic energy dependence and the catastrophic loss on bremsstrahlung, pair production and photoproduct±on amounts to ..~4x10-SE, g-lcm2. Integrated over the neutrino energy spectrum this leads to an effective detector volume of ~100S±. This technique, of course, only works for muons entering the detector from below, i.e. from the direction of the Earth, because the flux of downward going neutrino induced muons is dominated by many orders of magnitude by the flux of atmospheric muons. In a more quantitative way the flux of upward going neutrino induced muons can be described
as[3]
N,(E,) = /Z ~
dE',,-~P,,(E,,, dN~, E,),
(3)
where Pv(E~,, E,) is
NA
fs~
, dav(E~, E~,)
dE.
,
(4)
~rv is the charge current cross-section, and R~j! is the effective range of muons generated with energy E~ to retain energy E.. It is very instructive to study the response of the muon rate to the neutrino spectrum, which is shown for vertical atmospheric neutrinos, neutrinos with 7--2.7, and ~/---2 in Fig. 1. Even for a high muon threshold of 100 GeV the response curve to atmospheric neutrinos peaks at Ev -.. 500 GeV. Diffuse galactic neutrinos with energies around a TeV are most important, while the response to source neutrinos is very wide and peaks at energies above 10 TeV. The contribution of ultra high energy neutrinos (Ev >10 s GeV) is not very important even for very high muon thresholds. Thus the ultra high energy behaviour of the neutrino cross-section is also not of primary
T. Starter~High energy cosmic neutrinos
importance ~r this detection technique.
, , l l , , , i , , l _
.4
~ > I 0 0 GeV :
.3 "1
2
~_
~" .2 "O I
,¢"
0 2
\
I
I
~
4
~=~1 J"'r--1..7 6
8
log10 E. (GeV) Fig. I. Response of upward going muons with energy above 100 G e V to: (I) Vertical atmospheric neutrinos - solid line; (2) Diffuse galactic neutrinos with differential spectral index 7=2.7 dashes; (3) Source neutrinos with 7=2. All three response curves are normalized to unit area. Atmospheric neutrinos have, of course, been detected and have been studied quite well. There are three statistically significant data sets on upward going muons. Since the experimental arrangements, biases, and effective areas as a function of zenith angle are quite different, it is impossible to compare these results exactly. One can roughly scale the experimental results with the average m u o n threshold energy for different detectors to the highest E~,=3 G e V of the Kamioka detector[5]. The corrections obtained in this way axe smaller than 20%. The resulting rates agree[4] quite well with each other: (2.08-60.14, Baksan[7]), (1.92±0.11, IMB[6]), and (2.04-60.13, Kamiokande) x10 -13 muons per cmZ.s.sr. Within the error bars these numbers agree with the predictions from different calculations of the atmospheric neutrino flux. The current measurements of the upward going muons axe thus well understood, and the major background for neutrino astronomy, as well as the detectable extraterrestrial neutrino fluxes are well established.
187
The expected diffuse galactic neutrino fluxes are very low. They, however, provide the only certain extraterrestrial source of high energy neutrinos, because of the normalization to the 7ray fluxes measured by SAS-218] and COS-B[9]. Most of the matter density in the galaxy is concentrated in the direction of the galactic center and the expected neutrino rate thus depends on the exact location of the galactic plane observable with a particular detector. The rate of upward going muons of energy >1 TeV within 10 degrees of the galactic disc is[2] ,,.5 events per year for a 105 m 2 detector at the South Pole which views 1.1 steradian of the outer Galaxy with an average density of 0.013 grams/cm 2 from Eq. 2. This number accounts for the fact that neutrinos are produced by the decay of muons as well as pions. In addition to the galactic plane, there are several molecular clouds in the Galaxy with sufFicient column density to generate non-negligible neutrino fluxes. Orion has column density of 2.4x 1022 cm -2 and the corresponding rate of upward going neutrino induced muons is 0.3 per year in a 105m2 detector from a solid angle of 0.07 sr around the direction of Orion. These estimates assume a cosmic ray flux that is constant and equal to the one at Earth. A recent COMPTEL[10] observation of 3 to 7 MeV fluxes from the region of Orion may suggest, however, that the cosmic ray energy density could be significantly higher in that region. The observed 7-ray line intensities (from excited lZC and 160 nuclei) would correspond to cosmic ray energy density of more than 50 eV cm -s, a factor of 100 higher than in the vicinity of the Earth. Although the lines are generated by cosmic ray nuclei of kinetic energy around 10 MeV, which are subject of strong solar modulation inside the solar system, it is quite possible that the cosmic ray density in a wider energy range is significantly higher in this active star-formation region. The limits derived from the COS-B data[11] alow a cosmic ray intensity and respectively neutrino fluxes higher by factor of 5 in the region of Orion. 2. G A L A C T I C S O U R C E S Systems combining large enough energy output with a concentration of target materials could be be sources of high energy neutrinos. Both X-ray
T. Stanev /High energy cosmic neutrinos
188
binaries and young supernova remnants (YSR) could thus be galactic neutrino sources. X-ray binaries could be powered either by accretion or by the magnetic dipole radiation of the rotating compact object. The YSR energy source could be the magnetic dipole radiation or the kinetic energy of the supernova shell. Accretion power is limited by the Eddington luminosity LEad = 4 z G M r n . p / a T erg/s,
(5)
which is the maximum X-ray luminosity which will not prevent accretion. Since the proton inelastic cross-section is lower than aT, technically the proton luminosity can exceed LEdd. On the other hand LEdd can only be achieved at the surface of the neutron star and a realistic luminosity limit depends on the ratio of the neutron star radius to the shock radius R ~ / R , . Thus a reasonably optimistic limit for the proton luminosity will be L'~ ~= = LEdd x ( R ~ o / R , ) ×
(6)
i.e. of the order of, or lower than, LEad = 1.4×103SX M / M ® erg/s. The power released by magnetic dipole radiation is Ld
=
-4 4 x 10 43 B12P(~, erg/s,
(7)
where B12 is the pulsar surface magnetic field strength in 1012 G and P,~, is the pulsar period in milliseconds. This total power has to be converted to accelerated protons using a concrete model of particle acceleration. Harding and Gaisser[12] have studied proton acceleration at X-ray binaries powered by the pulsar through a pulsar wind shock. Discussing different X-ray systems they find a maximum proton luminosity of 6X 1038 erg/s for a Cygnus X-3 with a pulsar period of 12.8 ms. A larger fraction of the magnetic dipole luminosity Ld could in principle be converted to proton luminosity in YSR because of the lack of accretion in the contact discontinuity. The kinetic energy of the shell is also very high (1051 ergs) and the conversion of even a small fraction of that into accelerated particles could power an observable neutrino source. The target material in X-ray binaries could be the companion star[13,14], the accretion disk[15],
or concentration of mass ejects from the companion star in any other shape[16]. Since any of these concentrations of matter cover only a fraction of the solid angle around the particle accelerator in the system, the neutrino production will have a duty cycle of order 0.1 of the rotational period of the system. Several calculations[17-19] were performed in the simple straightforward model of Cyg X-3114], where the pulsar is orbiting around a 4 M® companion star, which provides a duty cycle of 0.4. For a distance of 10 kpc all these calculations agree better than a factor of 2, giving an upward going muon flux of 2-3x 10 -15 cm-2s -1, i.e. 50-100 events in a 105 m 2 detector for a proton luminosity of 2x1039 erg/s. Scaled down to the optimistic value of Harding and Gaisser this gives 15-30 events in 105 m 2 detector with a muon threshold of 2 GeV or 8-16 events for a threshold of i TeV. For a more modest X-ray binary at the galactic center that accelerates 1/10 LEdd in high energy protons the upward muon rate will be 3 events above 2 GeV per 105 m 2 per year. The generic theory of the production of high energy "),-ray and neutrino signals at YSR was developed by Berezinsky and Prilutsky[20] - if protons are accelerated in a young supernova remnant, they will interact with the material of the expanding shell and produce 7-rays and neutrinos until the particle adiabatic losses exceeds the collision loss. The adiabatic losses start dominating over losses to nuclear collisions at 7-a =
(3Mc°"~v) 1/2 1.3 x 107(M~)l/us 47rmHV 3 =
(8)
The active time, during which the neutrino production is significant, is of order 1 year. If one accounts correctly for the velocity distribution of the supernova shell the u emission time increases by a factor of three. The very likely containment of protons at the acceleration site[21] increases the optical depth for inelastic interactions and extends the signal duration with a gradual decrease in intensity for up to 10 years. A YSR with proton luminosity of 1039 erg/s and flat proton spectrum at the galactic center will produce --.750 events per 105 m 2 per year for the first year and the event rate will not decrease more than a factor of 3 three years after the explosion. The difference with the rate quoted for a Xray binary is so big only because of the differ-
T. Starter~High energy cosmic neutrinos
ent energy balances of the two types of objects. The luminosity estimates are however reasonable, because an assumption that 1/10 of the highest possible bolometric luminosity goes into protons would give a Y S R Lp ...104z erg/s. The dependence of the upward m u o n rate on the proton energy spectrum is very strong. A numerical result[22] for S N 1 9 8 7 A can be expressed as a function of the differential proton acceleration spectrum - R~ -~ (.ypdiH)-Is. The big disadvantage of Y S R as observable neutrino source is, of course, that galactic supernova explosions are extremely rare events and happen not more often than once in 30 years. The one that we were lucky to observe, SNI987A, was not only quite distant, in the L M C , but also shows no signs of pulsar activity at a level above ~103z erg/s. All the estimates above are made in the assumption that the emission from the source is isotropic. The required proton luminosity for Xray binary sources will be decreased by a factor of i0, and will fit better the total energy balance of the system, ifthe proton acceleration and the production of high energy signals has a jet-like structure and only covers one steradian of solid angle. Jet-like structures have been observed in association with m a n y energetic astrophysical systems and might be c o m m o n for X-ray binaries. The emission from young supernova remnants has to be close to isotropic. 3. G E N E R I C
AGN
Active galactic nuclei are the most luminous objects in the Universe and have been long recognized as possible sources of high energy signals[23]. These first estimates were mostly based on the total A G N power and number density. The recent calculations developed the idea in two important ways. They first identified the hadronic cross sections as essential for understanding the energy transport at active galactic nuclei[24,25I. Secondly, shock acceleration models were at least crudely incorporated in the A G N models and the photoproduction process was shown to be the most important one for proton energy loss. This led to estimates of the m a x i m u m proton energy achievable in acceleration at A G N shocks and the prediction of high energy signals, both "y-ray and neutrino.
189
Active galactic nuclei have luminosities ranging from 104~ to 104s erg/s, which corresponds to black hole masses from 104 to 10 l° M e in the natural assumption that they are powered by accretion onto a black hole. A G N have been observed to have generally a very fiatemission spectra with a luminosity up to --.3x104s erg/s per decade of energy. A G N have been most extensively studied at radio frequencies, where the most general identification is as radio loud or quiet, depending on the shape of the spectrum. Roughly 10% of all observed AGN have a flat spectra and are classifted as radioloud. These have time variability on a very short scale. In the IR band a steady dust emission is observed, most probably coming from a large region far away from the core. The main thermal feature is the UV bump, which is variable on the timescale of days. Its energy source is either X-ray heating or viscous heating of the accretion disk, both sources closely related to the central engine. The UV bump is not always easy to see in radioloud AGN. X-rays have flat nonthermal spectrum, variable on even shorter timescales, which often cuts off at few MeV. To introduce most of the parameters important for the neutrino production we shall briefly describe the spherical accretion model, which is used in most of the calculations of the neutrino production at radio-quiet AGN[26-28]. It is based on work performed by Kazanas, Protheroe and Ellison[29,30] and assumes that close to the black hole the accretion flow becomes spherical and a shock is formed where the ram pressure of the black hole radiation is balanced by the accretion flow. The shock is formed at a distance R1 = z l x Rs, where Rs is the gravitational (Schwarzschild) radius of the black hole. All the continuous emission of the black hole, from IR to X-ray, is assumed to come from the radius enclosed by the shock. Since that region is optically thick, the radiation density at the shock can be estimated from the surface brightens of the AGN as
UTad ~ L x (IrRZc)-XeV/cm 3
(9)
The radiation energy density defines also the magnetic field value B at the shock in the assumption of equipartition of the radiation and magnetic energy. The proton density at the shock np can be esti-
T. Stanev /High energy cosmic neutrinos
190
mated from the accretion rate needed to support the black hole luminosity, and from the shock radius and velocity. np ~ 1.3 x lOSzl/2R-l"sL1/2Q-lcma,
(10)
ing cascades downscatter their energy to X-ray and lower energies. -10
'
I
'
'
'
I
'
'
'
I
'
7
where Q is the source efficiency, a factor of order 1. Such proton densities are not only a good injection source for proton acceleration, but also a possible target for pp interactions. The proton energy loss is dominated, however, by the photoproduction process P7 -~ n~r+(P7r°) simply because the target photon density nj, h is much higher than n~. If all target consisted of monoenergetic photons of energy (e), the density ratio would be np -9 3/2 ~_ 10 ~1 ( ( ~ ) / e V ) Q %h
--
-1
o
.
(11) 4
The high cross-section pair production process (F7 --~ Pe + e - ) is relatively unimportant because of the low proton energy loss per collision. As it turns out, the photoproduction process also limits the maximum proton acceleration energy E ~ sz, contrary to the case of cosmic ray acceleration at supernova blast shocks, where the maximum energy is limited by diffusion away from the shock. E ~ ~x is roughly proportional to the AGN luminosity, reaching a value of 1017 eV for L = 1046 erg/s. While the simple proton and photon target density arguments are still valid in the generic AGN models, an important parameter is the energy spectrum of the photon target field. Because of the minimum photon energy E ph mi" (oc E p- t) required for photoproduction by a proton of given energy, it is crucial that there are enough target photons a b o v e / ~ i ~ . This requirement is satisfied by the available data, because the main thermal feature, the UV bump, has an average energy of _ 40 eV and the hard X-ray spectrum extends to the MeV range. Neutrinos and v-rays are generated mainly in pion decays (lr° ---* 27, ~r+ -4 /~+v~) and the subsequent muon decays /~+ ---* ~, + v, + e +. In astrophysical environment all particles decay practically without any energy loss. All v-rays generated in the dense photon field immediately lose energy in 7V -* e+e- collisions and the initiated pair-production/inverse Compton scatter.
6
8
Log10 E~ (GeV) Fig. 2. Neutrino spectra generated in the central region of 3C273 in the models of Ref. [26] (thick line) and of Ref. [28] (thin lines). Neutrinos, however, freely escape from the production region. Fig. 2 shows the neutrino spectra generated at a spherical accretion shock normalized to the luminosity of 3C273. The thin lines show several of the models of Protheroe and Szabo[28], who performed their calculation for xl values from 10 to 100 and two different photon target spectra, and the thick line represents the model of Stecker et a1.[26]. The difference between the lower energy behaviour of the neutrino spectra in the two calculations is easy to understand in terms of the different astrophysical assumptions used in the calculations. Stacker et al. assume that after acceleration the protons propagate in straight lines. Low energy protons, which require high energy target photons, thus have much smaller interaction probability and a minimum proton energy E~ 'i'~ for photoproduction exists, determined by the cut-off of the target X-ray spectrum. Because of the kinematics of the photoproduction interactions and the decays involved, the neutrino spectrum below _ E~pin/20 becomes flat. Protheroe and Szabo[28], on the other hand, account for the proton diffusion in the area of the
T Stanev/High energycosmicneutrinos shock. It their model the lower energy protons are contained longer in the vicinity of the shock and have similar interaction probability. For this reason the neutrino spectrum generally follows the parent proton acceleration spectrum with a differential spectral index 2 below the high energy cutoff region. The features of their spectra around 104- 105 GeV are caused by proton energy loss on e+e - pair production. Because of the large neutrino flux in the important region around 1 TeV the models of Protheroe and Szabo generate significantly more upward going muons. The following formula gives approximately the neutrino flux[31] at Earth from an AGN of given X-ray flux and E~p== in [cm~.s.TeV] -z
FvEv ~- O.25Fx exp(-20Ev/E~p ==) x E~-2, (12) where Fx is the 2 - 10 KeV X-ray flux (erg cm-=s -z) and E~ is the neutrino energy in TeV. In their pioneering paper Stecker et al [26] proceeded to integrate the neutrino fluxes from single generic AGN's to obtain a diffuse v flux from all cosmological AGN. The integration has to account for the AGN density and luminosity distribution, as well as for the neutrino adiabatic energy loss due to the expansion of the Universe. This procedure is identical to the integration used to calculate the value of the diffuse X-ray background. As a matter of fact it uses the AGN luminosity function derived from X-ray observations and assumes that the neutrinos and the X-rays have a common source. The AGN luminosity function as a function of the redshift can be expressed as
191
with a = 5 / 2 for the Einstein-de Sitter cosmological model. Fig. 3 shows the current estimates of the isotropic v background, where the estimates of Protheroe and Szabo are made with different values of xl, photon target spectra, and integrated using two independent sets of luminosity functions. The resulting v flux extends to very high energy, where it dominates the atmospheric neutrino background by orders of magnitude. Because of the isotropic nature of the background flux, its major feature is the extremely flat energy spectrum. The thick line shows the corrected prediction of Stecker e$ a1.[26]. While the u spectra are now in very reasonable agreement at the higher energy end, the biggest difference occurs at energies below 3x105 GeV, where Stecker et a[ spectrum becomes flat and Protheroe&Szabo spectrum follows the primary proton spectrum. The difference reaches 2.5-3 orders of magnitude at E~=104 GeV which makes a big difference in the estimate of the induced upward muon signal.
7
-8
"~" -10 vi
& -12 -14
-18
p(Lx,z) = ..3g(z )
( Lx )
(13) ~
where P0 comes from measurements of the AGN luminosity, Ro is the present scale size of the Universe and g(z) and f(z) describe the number density and luminosity evolution of AGN in the comoving volume. Any AGN induced background, including X-ray and neutrino one, will then have energy spectrum [28]
d l l c4~rl fHo[ ER~
dE -
z~°"
dI, x Jo dz x dL xp(Lx, z)(1 + z ) - a ~-~{E(1 + z), Lx},
(14)
-20
4
6
8
10
Logto E,, (GeV) Fig. 3. Diffuse neutrino background from unidentified AGN. Thin lines show selected models of Protheroe & Szabo[28] and the thick line the model of Stecker et al.[26]. Fig. 4 shows the muon fluxes generated by the isotropic neutrino background as in the bracketing high and low models of Protheroe & Szabo[28] and by Stecker et a1.[26]. The angle averaged
192
T Stanev /High energy cosmic neutrinos
muon flux generated by atmospheric neutrinos is shown for comparison. The AGN backgrounds dominates at muon energies above 1 TeV. The predicted TeV muon rate in a 104 m 2 detector will be 160 to 800 p e r y e a r for Ref. [28] and ~ 30 for Ref. [26] over an atmospheric background of ~ 86 events. The highest value of Protheroe & Szabo has actually already been ruled out by an analysis of the energy distribution of the muons detected by the Frejus detector[32], which allows a flux of TeV muons not higher than 4x 10 -2 m - 2 y r -1. 0
7
--
-- ...........
..
~L A i
2 o
~)
-3
0
IllllallJlllBIllll 1 2
3
4
Log10 E~, (GeV) Fig. 4. Fluxes of upward going muons as a function of the muon threshold energy predicted by the bracketing high and low models of Ref. [28] (thin lines) and Ref. [26]. The atmospheric neutrino background is shown with a dotted line. AGN muons have a specific angular distribution because the isotropic high energy neutrinos are absorbed in propagation through the Earth, mostly in vertical direction. Surviving v~'s will produce spectacular cascading events[33] through the Glashow resonance u e e - --4 W - at E~ -6.4x 10 e GeV. Detection of other exotic phenomenal34] is also possible. Even the most pessimistic of these rates is within reach of the current generation of neutrino telescopes, which are under construction. DUMAND II[35] is scheduled to deploy its first three strings before the end of 1993. AMANDA[36] is ready for the deployment of up to six strings dur-
ing the antarctic summer. Nestor[37] has been funded to build one tower and may follow a year later. All these detectors have an effective area somewhat larger than 104 m 2 and should be able to detect the predicted isotropic backgrounds. 4. A G N J E T S
Individual radioquiet AGN will be much more difficult to detect, although the atmospheric background in 1° radius around the source is extremely small, ~ 1.6 x 10 -5 m - 2 y r -1 muons above 1 TeV. Even with optimistic luminosities the number of such events from individual sources is less than 2-3 yr -1 in a 105 m 2 detector. The recent observations of GeV "),-rays from a large number of extragalactic objects by the E G R E T instrument[38] on GRO gives a more solid basis for optimistic expectations. Most, if not all, of the E G R E T sources are radioloud AGN, which we believe are pointing their jets at us. Jets carry a reasonable fraction of the AGN luminosity, between 5 and 30%. The apparent luminosity to an observer looking into the jet along its axis is, however, increased by a factor of 1000 for a jet Lorentz factor of 10. A calculation of the neutrino production in AGN jets was first published by Biermann and Mannheim[39]. The produced neutrino flux reflects the physical conditions in the AGN jet. Because of the lower photon density protons can achieve higher energy at acceleration E ~ ax. In addition both the acceleration and proton interactions proceed in the jet frame and the neutrinos are boosted to high energy (blueshifted) with a Doppler factor of order 10. In the case of 3C273 the flux shape is almost identical to that of Stecker et al. in Fig. 2 shifted to higher energy and normalized to the jet luminosity. A model[40] of the proton acceleration and interactions envisions a bulk flow of magnetized plasma, streaming from the base of the jet towards its end (the hot spot), which can be approximated with a radiating sheet of certain radial dimension R and thickness D. The acceleration of nuclei and their interactions proceed in the frame of the flowing plasma, where the ma~ximum proton acceleration energy E ~ ~*'* _~ 2 x 101°B -1/2 GeV, B being the magnetic field strength in Gauss[24]. Both 7-ray and neutrino signals are
T. Stanev /High energy cosmic neutrinos
generated as a result of pp and mostly F7 interactions. For photoproduction the energy carried by neutrinos is directly related through kinematics to the "y-ray luminosity as L~ = ~L~r+ =
L-r,
(15)
where L-r includes a contribution from e+e pairs.
Although a fraction of the generated v-rays are able to escape from the production region, the m a x i m u m q-ray energy reaching the Earth is further limited by the absorption on the IR/optical background radiation[41,42] during propagation. Mannheim [43] has conveniently parametrised the neutrino fluxes reaching the Earth from A G N jets at blasars as a function of the total photon luminosity, redshift z, Doppler shift r, and effective magnetic field B. The neutrino output is (in
cm-28-1)
dN~ --~ 1.6 x lO_~r x L4s x Ev~-~.,
(16)
where /~4s is the total photon luminosity of the object in units of 1048 erg/s. This unit value is the peak emission of 3C279 observed by EGRET[44] in June 1992. In order to explain the variability of 3C279 on timescale of a day the radiating sheet thickness should be D .-.10ZScm, much smaller than its radius (I0 zs cm). The simultaneous observation of the BLLac source M k n 421 by E G R E T [45] and the Whipple observatory [46] is especially valuable for the understanding of the physics of A G N jets. The two observations define an energy spectrum with "y--2.06±0.04 over more than four decades in energy [47]. M k n 421 is the closest source observed by E G R E T at a redshift of 0.031. This is significant because of the absorption on propagation. The exact energy dependence of the absorption feature is uncertain because the magnitude and the energy spectra of the IR and optical background(s) are not well known. Within a factor of 2, however, 3 T e V -},-rays emitted at the distance of M k n 421 will already start being absorbed and will show an apparent steepening of the spectrum independently of the production spectrum.
193
There are at least two [48,49] models for the -/-ray emission that do not involve nucleons and generate the TeV radiation through inverse Cornpton scattering of accelerated electrons. They are, however, subjects of serious limitations and generally require higher bulk Lorentz factor of the jet. The radiation target density has to be high enough for IC scattering and, in the same time, low enough for the generated "),-rays not to be absorbed in "Y7 collisions. This is difficult to arrange for, especially when IC scattering in the Klein-Nishina regime is the relevant process. O n top of that the energy densities in soft photons (IR to X-rays) and "),-raysare comparable, which requires that the two types of radiation are generated in different locations. To prevent the electrons from loosing energy on synchrotron radiation, the energy of the magnetic field in the jet has to be of order 5% of the radiation density, far from the 0th order assumption of equipartition. It is much more natural to generate TeV 7rays through hazlronic interactions, although the ~,-ray absorption in the source is always a problem. It is almost a free parameter in any attempt to scale the observed "y-ray flux of M k n 421 to the corresponding neutrino flux. Halzen and Vasquez [50] scale the M k n 421 v-ray flux to neutrino flux in different assumptions for the v-ray absorption at source, expressed in terms of the magnetic field value B of the jet [51]. Even the order of magnitude of B is not known. Assuming one to one correspondence of the "),-ray and neutrino production, ~ they obtain 2 upward going muons of energy above 1 TeV in 105 m 2 per year for the case of no absorption (B = 10 -4 Gauss). The 10 Gauss value is 270 muons. For higher magnetic field values the neutrino flux from M k n 421 should already have been detected. Stecker et al. [52] use the "y-ray absorption on propagation to normalize the expectations from other G R O sources. They find -.~10-z3 v~ + ~ neutrinos from the 3C273 jet. Such a flux will generate 0.125 muons above i TeV in 105 m 2 per year. The corresponding flux from the 3C273 core is 40% smaller. The quiescent state of 3C279 would generate 5 muons, while the highest ob2For A + pbotoproduction only and a differentis,l energy spectrum with "7 : 2 the ratio of L,# -{-O~ to "y-rays above the same energy is slightly below I/4.
194
T, Stanev /High energy cosmic neutrinos
served "),-ray flux from 3C279 would correspond to 25 such muons. The 3C279 core contribution is only 0.125 events. These are the bracketing values for the expectations of neutrino fluxes from active galactic nuclei, it the 7-rays are indeed generated in hadronic interactions by accelerated nuclei. 5. D I S C U S S I O N A N D C O N C L U S I O N S The existing predictions of the source neutrino fluxes still suffer from uncertainties in the astrophysical input, especially for the neutrino emission from AGN. The spherical accretion model of generic AGN, which has been very successful in the analysis of the relevant astrophysical parameters, is nevertheless subject of criticism from different points of view. The model is only applicable to accretion disks with thickness comparable or exceeding the dimension of the shock radius. It has to be constructed in such a way that there is no leakage of the generated ~/-rays before their energy is downscattered to X-ray and longer wavelengths. Any significant leakage would exceed the experimental limits on diffuse extragalactic "),-rays. Some authors [53] estimate the source efficiency Q to be lower than 1/3 and ask if the conditions in the AGN nucleus are suitable for shock formation at all. Others [54] show the danger of overproducing background radiation through pair production and synchrotron radiation, which could lead to shock instability and drastically decrease All these, and other possible, problems should be a subject of further studies. Many of the problems, for example, could be avoided by placing the shocks in the bases of the AGN jets [55]. This has the advantage of providing the mechanism necessary to drive the jets and the disadvantage of only using a fraction of the total AGN luminosity. The calculations of the neutrino production in AGN jets are not less difficult. To model correctly all the jet physics one has to follow in some detail all the processes involved in the frame of the relativistic plasma flow, including particle acceleration and reacceleration at multiple shocks, v-ray production, multiplication and absorption in electromagnetic cascades in a non stationary fashion. This is very complicated problem, that involves many free parameters. The simple scaling of the
neutrino fluxes with the v-ray luminosity for individual sources may not be exact, since the conditions at the source are poorly known. The ratio of the magnetic to radiation energy density, for example, which is essential for the "),-ray absorption at the source, can vary within at least one order of magnitude. The sources are also highly variable and many might have been observed during the peak of their activity. The big question is the fraction of the AGN luminosity that goes through the nucleonic channel. Although it has been pointed out [24~25] that hadrons have suitable interaction cross sections and are a natural vehicle for the energy transport throughout the AGN disk, nucleons are not strictly necessary for the solution of this problem. Since the models of the non-nucleonic origin of the Mkn 421 ~,-rays are already struggling to extend the theory to "),-rays above 1 TeV, a possible observation of, say, 10 TeV v-rays would be a confirmation of their 7r° origin. This is hardly possible, however, because of the absorption on the IR/optical background, even if the production spectrum reaches much higher energy. There is only a slight chance that [42], for very low values of the extragalactic magnetic field, the cascading on this background will flatten considerably the spectrum observed in the GeV/TeV region. Such flattening would reveal the extension of the production spectrum to much higher energy and correspondingly confirm the ~r° origin of the "y-ray flux. The criticism above does not imply that the current predictions are not reliable. They are results of the first generation of research, which will become more exact in the near future. The differences between various estimates reflects the uncertainties of the calculations. Conclusions are that the expected fluxes of source neutrinos are well below the sensitivity of the currently active deep underground detectors with effective area less than 1000 m z. They are, however, tantalizingly close to being detectable by the new generation of detectors [35-37], especially designed for neutrino astronomy. It will not be an easy task, but as the impressive analysis of the Baikal data [56] shows, a realistic one. ACKNOWLEDGMENTS. I am grateful to V.S. Berezinsky, P.L. Biermann, J.G. Learned,
T. Stanev/High energy cosmic neutrinos
R.J. Protheroe and F.W. Stecker for helpful discussions on the subject of astrophysical neutrinos. REFERENCES
1. T.K. Gaisser, Cosmic Rays and Particle Physics (Cambridge University Press, 1990) p. 92. 2. V.S. Berezinsky, T.K. Gaisser, F. Halzen and T. Stance, it Astropart. Phys. 1, 281 (1993). 3. T.K. Gaisser and T. Stanev, PAys. Re~. D31, 2770 (1985). 4. W. Frati, T.K. Gaisser, A.K. Mann & Todor Stance, Phys. Rev. D 48 (1993) 1140. 5. M. Mori et al., Physics Letters B 210 (1991) 89. 6. R. Becker-Szendy et al., Phys. Rev. Letters 69 (1992) 1010. 7. M.M. Boliev et al., in Proc. 3rd Int. Workshop on Neutrino Telescopes (ed. M. Baldo Ceolin) (1991) 235. 8. R.C. Hartman et al. Ap. J. 230 597 (1979). 9. H.Bloemen, Ann. Reds. Astron. Astrophys. 27, 469 (1989). 10. H. Bloemen et al. COMPTEL Preprint No. 10 (1993). 11. H. Bloemen et al. Astron. Astrophys. 139, 37 (1984). 12. T.K. Gaisser and A.K. Harding, Ap. J. 358 561 (1990). 13. V.S. Berezinsky, in Proc. 1979 DUMAND Summer Conference (Univ. of Hawaii, ed. J.G. Learned, 1979) p. 235. 14. W.T. Vestrand and D. Eichler, Ap. J. 261, 251 (1982). 15. R.J. Protheroe and T. Stanev, Ap. J. 322, 838 (1987). 16. A.M. Hillas, Nature, 312, 50 (1984). 17. T.K. Gaisser and T. Stanev, PAys. Rev. Left. 54 2265, (1985). 18. E.W. Kolb, M.S. Turner and T.P. Walker, PAys. Rev D32, 1145 (1985). 19. V.S. Berezinsky, C. Castagnoli and P. Galeotti,//Nuovo Cim. 8C, 185 (1985). 20. V.S. Berezinsky and O.F. Prilutsky, Astron. Astrophys. 88, 325 (1978). 21. T.K. Gsisser, A.K. Harding and T. Sinner, Ap. J. 345 423 (1989). 22. T.K. Gaisser and T. Stance, PAys. Rev. Left. 58, 1695 (1987).
195
23. V. S. Berezinsky, in Proc. Neutrino 77 (Nauka, Moscow, 1977) 1, p. 177; D. Eichler, Ap. J. 232, 106 (1979); R. Silberherg and M.M. Shapiro, in Pro¢. 18th Int. Cosmic Ray Con/. v. 10, p.357 (1979); V.S. Berezinsky and V.L. Ginzbusrg, Mort. Not. Royal Astr. Soc., 194, 3 (1981). 24. P.L. Biermann and P.A. Strittmatter, Ap. J. 322, 643 (1987). 25. M. Sikora, M.C. Begelman and B. Rudak, Ap. J. Left 341, L33 (1989); M. C. Begelman, B. Rudak and M. Sikora, Ap. J. 382, 38 (1990). 26. F. W. Stecker et GI. Phya. Re~. Left 88, 2697 (1991); Erratum ibid 69 2738 (1992). 27. M. Sikora and M.C. Begelman, in High Energy Neutrino Astronomy, eds. V.J. Stenger et ai. (World Scientific, Singapore, 1992), p. 114. 28. A.P. Ssabo and R.J. Protheroe, in High Energy Neutrino Astronomy, eds. V.J. Stenger et al. (World Scientific, Singapore, 1992), p. 24. 29. R.J. Protheroe and D. Kazanas, Ap. J. 275, 620 (1983). 30. D. Kasanas and D.C. Ellison, Ap. J. 304, 178 (1986). 31. R.J. Protheroe and T. Stance, in High Energy Neutrino Astronomy, eds. V.J. Stenger et al. (World Scientific, Singapore, 1992), p. 40. 32. H. Meyer, in 4~h Int. Wor~hop on Neutrino Telescopes (ed. M. Baldo-Ceolin), p. 213. 33. J.G. Learned and T. Stance, in Proc. 8rd Int. Workshop on Neutrino Telescopes (ed. M. Baldo-Ceolin) p . . 34. D.A. Morris and A. Ringwald, in Proc. ~Srd ICRC, eds. D.A. Leahy et al. 4, p.407. 35. J.G. Learned and V.S. Stenger, in High Energy Neutrino Astronomy, eds. V.J. Stenger et al. (World Scientific, Singapore, 1992), p. 288. 36. S. Barwick et al. in High Energy Neutrino Astronomy, eds. V.J. Stenger et al. (World Scientific, Singapore, 1992), p. 291. 37. L.K. Resvanis, in High Energy Neutrino Astronomy, eds. V.J. Stenger et al. (World Scientific, Singapore, 1992), p. 325. 38. C.E. Fichtel et al. Preliminary EGRET Source Catalog, in Proc. Compton Symposium, in print. 39. K. Mannheim and P.L. Biermann, Astron.
196
T Stanev/High energy cosmic neutrinos
Astrophys. 253, L21 (1992); K. Mannheim and P.L. Biermann, Astron. As~rophys. 22, 211 (1989). 40. K. Mannheim, Astro~. Astrophys. 269, 67 (1993). 41. F.W. Stecker, O.C. De Jager and M.H. Salamon, Ap. J. Left. 390, L49 (1992). 42. R.J. Protheroe and T. Stanev, Mort. Not. Royal A. Soc., 264 191 (1993). 43. K. Mannheim, in High Energy Neutrino Astronomy, eds. V.J. Stenger et al. (World Scientific, Singapore, 1992), p. 105. 44. R.C. Hartman et al. Ap. J. Left. 385, L1 (1992). 45. Y.C. Lin et al. Ap. J. Left. 401, L61 (1992). 46. M. Punch et al. Nature, 358, 477 (1992). 47. G. Mohanty et al. in Proc. ~3rd ICRC, eds. D.A. Leahy et al. 1, p.440. 48. C.D. Definer, R. Schlickeiser and A. Mastichiadis, Astron. Astrophys. 258, L27 (1992). 49. A.A. Zdsiarski and J.H. Krolik, Ap. J. Left. 409, L33 (1993). 50. F. Halsen and R. A. Vazquez, in Proc. ~3rd ICRC, eds. D.A. Leahy et al. 1, p.447. 51. P.L. Biermann, in Cosmic Gamma Rays, Neutrinos arid Related Astrophysics, eds. M.M. Shapiro and J.P. Wefel (Kluwer, Dordrecht, 1988) p. 21. 52. F,W. Stecker et al. in High Energy Neutrino Astronomy, eds. V.J. Stenger et al. (World Scientific, Singapore, 1992), p. 105. 53. V.S. Berezinsky and J.G. Learned, in High Energy Neutrino Astronomy, eds. V.J. Stenger et al. (World Scientific, Singapore, 1992), p. 43. 54. A. Mastichiadis and J.G. Kirk, in High Energy Neutrino Astronomy, eds. V.J. Stenger et al. (World Scientific, Singapore, 1992), p. 63. 55. L. Nellen, K. Mannheim and P.L. Biermann, Phys. Rev. D, in print. 56. See the talks of C. Spiering and R. Wishnewski at this meeting.
PROCEEDINGS SUPPLEMEHTS
Nuclear Physics B (Proc. Suppl.) 35 (1994) 185-196 North-Holland
High Energy Cosmic Neutrinos Todor Stance a* aBartol Research Institute, University of Delaware Newark DE 19716 USA W e discuss the production of neutrinos in interactionsof high energy cosmic ray nuclei acceleratedin different astrophysical objects. Neutrino fluxes of differentmagnitude and energy spectra are produced in interactions on diffuse galactic matter and possibly at or close to the accelerationsite. Different potential sources inside and outside our galaxy are discussed with an increased attention to neutrinos generated in photoproduction interactions at active galactic nuclei. The observabilityof these neutrinos with current and future generation detectors is estimated.
1. I N T R O D U C T I O N The topic of this talk is the production of neutrinos in inelastic interactions of high energy cosmic ray nuclei and the initiated by them hadronic cascades. The shape of the neutrino energy spectrum is defined by the energy spectrum of the parent cosmic rays and by the physical conditions of the medium, where the cascades are developing. One can distinguish three different general types of energy spectra for these neutrinos: (i) Atmospheric neutrinos; (ii) Diffuse galactic neutrinos; (iii) Source neutrinos. A t m o s p h e r i c n e u t r i n o s are generated in interactions of the cosmic rays particles and cascades developing in the atmosphere. Their energy spectrum is formed in the competition between interaction and decay that the secondary mesons undergo in the constantly changing atmospheric density. The contribution of pions to the atmospheric neutrino flux, for example, is given by[1]
dN,, dE,,
-
No(E`,) 1 - ZNN
× 1
A,~`, + B~rv cos t9 E`,/e,r'
where A.`, = g~r. (1
-
r)~/( 7
+
(1)
1) (r =
mt,/rr~, ZN~ = f z'r-*dn/dz dz) reflects the the zF spectrum of pions in nucleon collisions and the primary cosmic rays spectral index 7. B~`, is a normalization factor accounting for 7 and the nucleon and pion cross-sections. Eq. 1 tells us that up to energy e~ the neutrino flux is parallel to the primary nucleon flux(7 ,-~2.7), while after that it *Work supportedin part by the NationalScienceFoundation under Grant PH-Y9220990.
steepens by one power of E`, to 7 "--3.7.This reflectsthe competition between decay and interaction, and e~ is the energy at which the interaction probability equals the decay probability, e,~ --115 G e V in the atmosphere (in verticaldirection) and obviously grows for more tenuous media. For the case of atmospheric neutrinos this includes neutrino production by cosmic rays that enter the atmosphere at angles significantlydifferent from vertical. Cascades then develop in m u c h more rarified atmosphere and the neutrino spectrum is significantly harder. The atmospheric neutrino spectrum has a typical angular dependence with the m i n i m u m flux coming from vertical direction and the m a x i m u m - from horizontal. In fact the spectrum is m u c h more complicated because of the contributions of other channels and the angular dependence of the bend position. In the G e V region m u o n decay is equally important contributor for all types of neutrino. For re, where m u o n decay is a major contributor, the spectrum approaches 7 ,,,4.7at high energy. Diffuse galactic neutrinos are produced by galactic cosmic rays in interactions on the interstellar matter. These extraterrestrial neutrinos should follow the 7 ~2.7 cosmic ray spectrum up to the highest energies, since all interaction products, including muons, decay. The absolute normalization of the diffuse galactic neutrino flux depends on the column density of matter in atomic and molecular clouds in the galaxy and the cosmic ray density gradient. Under the assumption of constant cosmic ray density in the Galaxy, an estimate of the expected nearly isotropicneutrino
0920-5632/94/$07.00 © 1994 - Elsevier Science B.V. All fights reserved. SSDI 0920-5632(94)00456-6
186
T Stanev/High energy cosmic neutrinos
fluxes from cosmic ray interactions in the galaxy can be easily derived[2]. Imagine a concentration of matter of density p and linear dimension R. The flux at Earth of neutrinos generated by pions produced in cosmic ray interactions with this matter is given by
~ v - - ~ C R f A IS±nell4 2ZIv~ L mN j [pR] v +------f-'
(2)
where ~CR is the cosmic ray flux per steradian, O'inel is the total inelastic pp cross section, mjv is the nucleon mass and pR is the column density of the source. ZN~r is the spectrum-weighted moment for production of pions by nucleons as in Eq. 1. fA is a correction factor to account for the fact that some primaries and targets are nuclei heavier than protons. S o u r c e n e u t r i n o s are produced by high energy particles a~ their acceleration 8ire8 and follow the hard (V "~ 2.0-2.4) cosmic ray acceleration spectra. In principle it is possible that nuclei accelerated at an astrophysical object interact at the object and generate neutrinos, but are not able to diffuse away from the source and become cosmic rays. In practice, the existence of galactic VHE and UHE v - r a y sources was suggested as a solution of the problem of the origin of the galactic cosmic rays. If a non negligible fraction of these is accelerated at compact objects with high magnetic fields, we should observe the associated neutrinos. There is no shortage of such objects in the galaxy, the most obvious being neutron stars, black holes and young supernova remnants. The existence of extragalactic sources of high energy neutrinos is somewhat more decoupled from the cosmic ray origin. Active galactic nuclei have tremendous luminosity in all energy bands and do not have to generate a significant amount of the observed cosmic rays to be strong neutrino sources. The major assumption is that the role of particle acceleration and hadronic processes in AGN is significant. The only currently practical way to detect high energy neutrinos is by detecting muons generated in deep inelastic muon neutrino (and ant±neutrino) scattering in the rock surrounding the detector. The effective detector volume V~I! will then be the product of the actual detector area in the direction perpendicular to the muon direction S± and the muon range in the medium
R,. The muon ionization energy loss in rock is --~2 MeV g-lcm2 with a slow logarithmic energy dependence and the catastrophic loss on bremsstrahlung, pair production and photoproduct±on amounts to ..~4x10-SE, g-lcm2. Integrated over the neutrino energy spectrum this leads to an effective detector volume of ~100S±. This technique, of course, only works for muons entering the detector from below, i.e. from the direction of the Earth, because the flux of downward going neutrino induced muons is dominated by many orders of magnitude by the flux of atmospheric muons. In a more quantitative way the flux of upward going neutrino induced muons can be described
as[3]
N,(E,) = /Z ~
dE',,-~P,,(E,,, dN~, E,),
(3)
where Pv(E~,, E,) is
NA
fs~
, dav(E~, E~,)
dE.
,
(4)
~rv is the charge current cross-section, and R~j! is the effective range of muons generated with energy E~ to retain energy E.. It is very instructive to study the response of the muon rate to the neutrino spectrum, which is shown for vertical atmospheric neutrinos, neutrinos with 7--2.7, and ~/---2 in Fig. 1. Even for a high muon threshold of 100 GeV the response curve to atmospheric neutrinos peaks at Ev -.. 500 GeV. Diffuse galactic neutrinos with energies around a TeV are most important, while the response to source neutrinos is very wide and peaks at energies above 10 TeV. The contribution of ultra high energy neutrinos (Ev >10 s GeV) is not very important even for very high muon thresholds. Thus the ultra high energy behaviour of the neutrino cross-section is also not of primary
T. Starter~High energy cosmic neutrinos
importance ~r this detection technique.
, , l l , , , i , , l _
.4
~ > I 0 0 GeV :
.3 "1
2
~_
~" .2 "O I
,¢"
0 2
\
I
I
~
4
~=~1 J"'r--1..7 6
8
log10 E. (GeV) Fig. I. Response of upward going muons with energy above 100 G e V to: (I) Vertical atmospheric neutrinos - solid line; (2) Diffuse galactic neutrinos with differential spectral index 7=2.7 dashes; (3) Source neutrinos with 7=2. All three response curves are normalized to unit area. Atmospheric neutrinos have, of course, been detected and have been studied quite well. There are three statistically significant data sets on upward going muons. Since the experimental arrangements, biases, and effective areas as a function of zenith angle are quite different, it is impossible to compare these results exactly. One can roughly scale the experimental results with the average m u o n threshold energy for different detectors to the highest E~,=3 G e V of the Kamioka detector[5]. The corrections obtained in this way axe smaller than 20%. The resulting rates agree[4] quite well with each other: (2.08-60.14, Baksan[7]), (1.92±0.11, IMB[6]), and (2.04-60.13, Kamiokande) x10 -13 muons per cmZ.s.sr. Within the error bars these numbers agree with the predictions from different calculations of the atmospheric neutrino flux. The current measurements of the upward going muons axe thus well understood, and the major background for neutrino astronomy, as well as the detectable extraterrestrial neutrino fluxes are well established.
187
The expected diffuse galactic neutrino fluxes are very low. They, however, provide the only certain extraterrestrial source of high energy neutrinos, because of the normalization to the 7ray fluxes measured by SAS-218] and COS-B[9]. Most of the matter density in the galaxy is concentrated in the direction of the galactic center and the expected neutrino rate thus depends on the exact location of the galactic plane observable with a particular detector. The rate of upward going muons of energy >1 TeV within 10 degrees of the galactic disc is[2] ,,.5 events per year for a 105 m 2 detector at the South Pole which views 1.1 steradian of the outer Galaxy with an average density of 0.013 grams/cm 2 from Eq. 2. This number accounts for the fact that neutrinos are produced by the decay of muons as well as pions. In addition to the galactic plane, there are several molecular clouds in the Galaxy with sufFicient column density to generate non-negligible neutrino fluxes. Orion has column density of 2.4x 1022 cm -2 and the corresponding rate of upward going neutrino induced muons is 0.3 per year in a 105m2 detector from a solid angle of 0.07 sr around the direction of Orion. These estimates assume a cosmic ray flux that is constant and equal to the one at Earth. A recent COMPTEL[10] observation of 3 to 7 MeV fluxes from the region of Orion may suggest, however, that the cosmic ray energy density could be significantly higher in that region. The observed 7-ray line intensities (from excited lZC and 160 nuclei) would correspond to cosmic ray energy density of more than 50 eV cm -s, a factor of 100 higher than in the vicinity of the Earth. Although the lines are generated by cosmic ray nuclei of kinetic energy around 10 MeV, which are subject of strong solar modulation inside the solar system, it is quite possible that the cosmic ray density in a wider energy range is significantly higher in this active star-formation region. The limits derived from the COS-B data[11] alow a cosmic ray intensity and respectively neutrino fluxes higher by factor of 5 in the region of Orion. 2. G A L A C T I C S O U R C E S Systems combining large enough energy output with a concentration of target materials could be be sources of high energy neutrinos. Both X-ray
T. Stanev /High energy cosmic neutrinos
188
binaries and young supernova remnants (YSR) could thus be galactic neutrino sources. X-ray binaries could be powered either by accretion or by the magnetic dipole radiation of the rotating compact object. The YSR energy source could be the magnetic dipole radiation or the kinetic energy of the supernova shell. Accretion power is limited by the Eddington luminosity LEad = 4 z G M r n . p / a T erg/s,
(5)
which is the maximum X-ray luminosity which will not prevent accretion. Since the proton inelastic cross-section is lower than aT, technically the proton luminosity can exceed LEdd. On the other hand LEdd can only be achieved at the surface of the neutron star and a realistic luminosity limit depends on the ratio of the neutron star radius to the shock radius R ~ / R , . Thus a reasonably optimistic limit for the proton luminosity will be L'~ ~= = LEdd x ( R ~ o / R , ) ×
(6)
i.e. of the order of, or lower than, LEad = 1.4×103SX M / M ® erg/s. The power released by magnetic dipole radiation is Ld
=
-4 4 x 10 43 B12P(~, erg/s,
(7)
where B12 is the pulsar surface magnetic field strength in 1012 G and P,~, is the pulsar period in milliseconds. This total power has to be converted to accelerated protons using a concrete model of particle acceleration. Harding and Gaisser[12] have studied proton acceleration at X-ray binaries powered by the pulsar through a pulsar wind shock. Discussing different X-ray systems they find a maximum proton luminosity of 6X 1038 erg/s for a Cygnus X-3 with a pulsar period of 12.8 ms. A larger fraction of the magnetic dipole luminosity Ld could in principle be converted to proton luminosity in YSR because of the lack of accretion in the contact discontinuity. The kinetic energy of the shell is also very high (1051 ergs) and the conversion of even a small fraction of that into accelerated particles could power an observable neutrino source. The target material in X-ray binaries could be the companion star[13,14], the accretion disk[15],
or concentration of mass ejects from the companion star in any other shape[16]. Since any of these concentrations of matter cover only a fraction of the solid angle around the particle accelerator in the system, the neutrino production will have a duty cycle of order 0.1 of the rotational period of the system. Several calculations[17-19] were performed in the simple straightforward model of Cyg X-3114], where the pulsar is orbiting around a 4 M® companion star, which provides a duty cycle of 0.4. For a distance of 10 kpc all these calculations agree better than a factor of 2, giving an upward going muon flux of 2-3x 10 -15 cm-2s -1, i.e. 50-100 events in a 105 m 2 detector for a proton luminosity of 2x1039 erg/s. Scaled down to the optimistic value of Harding and Gaisser this gives 15-30 events in 105 m 2 detector with a muon threshold of 2 GeV or 8-16 events for a threshold of i TeV. For a more modest X-ray binary at the galactic center that accelerates 1/10 LEdd in high energy protons the upward muon rate will be 3 events above 2 GeV per 105 m 2 per year. The generic theory of the production of high energy "),-ray and neutrino signals at YSR was developed by Berezinsky and Prilutsky[20] - if protons are accelerated in a young supernova remnant, they will interact with the material of the expanding shell and produce 7-rays and neutrinos until the particle adiabatic losses exceeds the collision loss. The adiabatic losses start dominating over losses to nuclear collisions at 7-a =
(3Mc°"~v) 1/2 1.3 x 107(M~)l/us 47rmHV 3 =
(8)
The active time, during which the neutrino production is significant, is of order 1 year. If one accounts correctly for the velocity distribution of the supernova shell the u emission time increases by a factor of three. The very likely containment of protons at the acceleration site[21] increases the optical depth for inelastic interactions and extends the signal duration with a gradual decrease in intensity for up to 10 years. A YSR with proton luminosity of 1039 erg/s and flat proton spectrum at the galactic center will produce --.750 events per 105 m 2 per year for the first year and the event rate will not decrease more than a factor of 3 three years after the explosion. The difference with the rate quoted for a Xray binary is so big only because of the differ-
T. Starter~High energy cosmic neutrinos
ent energy balances of the two types of objects. The luminosity estimates are however reasonable, because an assumption that 1/10 of the highest possible bolometric luminosity goes into protons would give a Y S R Lp ...104z erg/s. The dependence of the upward m u o n rate on the proton energy spectrum is very strong. A numerical result[22] for S N 1 9 8 7 A can be expressed as a function of the differential proton acceleration spectrum - R~ -~ (.ypdiH)-Is. The big disadvantage of Y S R as observable neutrino source is, of course, that galactic supernova explosions are extremely rare events and happen not more often than once in 30 years. The one that we were lucky to observe, SNI987A, was not only quite distant, in the L M C , but also shows no signs of pulsar activity at a level above ~103z erg/s. All the estimates above are made in the assumption that the emission from the source is isotropic. The required proton luminosity for Xray binary sources will be decreased by a factor of i0, and will fit better the total energy balance of the system, ifthe proton acceleration and the production of high energy signals has a jet-like structure and only covers one steradian of solid angle. Jet-like structures have been observed in association with m a n y energetic astrophysical systems and might be c o m m o n for X-ray binaries. The emission from young supernova remnants has to be close to isotropic. 3. G E N E R I C
AGN
Active galactic nuclei are the most luminous objects in the Universe and have been long recognized as possible sources of high energy signals[23]. These first estimates were mostly based on the total A G N power and number density. The recent calculations developed the idea in two important ways. They first identified the hadronic cross sections as essential for understanding the energy transport at active galactic nuclei[24,25I. Secondly, shock acceleration models were at least crudely incorporated in the A G N models and the photoproduction process was shown to be the most important one for proton energy loss. This led to estimates of the m a x i m u m proton energy achievable in acceleration at A G N shocks and the prediction of high energy signals, both "y-ray and neutrino.
189
Active galactic nuclei have luminosities ranging from 104~ to 104s erg/s, which corresponds to black hole masses from 104 to 10 l° M e in the natural assumption that they are powered by accretion onto a black hole. A G N have been observed to have generally a very fiatemission spectra with a luminosity up to --.3x104s erg/s per decade of energy. A G N have been most extensively studied at radio frequencies, where the most general identification is as radio loud or quiet, depending on the shape of the spectrum. Roughly 10% of all observed AGN have a flat spectra and are classifted as radioloud. These have time variability on a very short scale. In the IR band a steady dust emission is observed, most probably coming from a large region far away from the core. The main thermal feature is the UV bump, which is variable on the timescale of days. Its energy source is either X-ray heating or viscous heating of the accretion disk, both sources closely related to the central engine. The UV bump is not always easy to see in radioloud AGN. X-rays have flat nonthermal spectrum, variable on even shorter timescales, which often cuts off at few MeV. To introduce most of the parameters important for the neutrino production we shall briefly describe the spherical accretion model, which is used in most of the calculations of the neutrino production at radio-quiet AGN[26-28]. It is based on work performed by Kazanas, Protheroe and Ellison[29,30] and assumes that close to the black hole the accretion flow becomes spherical and a shock is formed where the ram pressure of the black hole radiation is balanced by the accretion flow. The shock is formed at a distance R1 = z l x Rs, where Rs is the gravitational (Schwarzschild) radius of the black hole. All the continuous emission of the black hole, from IR to X-ray, is assumed to come from the radius enclosed by the shock. Since that region is optically thick, the radiation density at the shock can be estimated from the surface brightens of the AGN as
UTad ~ L x (IrRZc)-XeV/cm 3
(9)
The radiation energy density defines also the magnetic field value B at the shock in the assumption of equipartition of the radiation and magnetic energy. The proton density at the shock np can be esti-
T. Stanev /High energy cosmic neutrinos
190
mated from the accretion rate needed to support the black hole luminosity, and from the shock radius and velocity. np ~ 1.3 x lOSzl/2R-l"sL1/2Q-lcma,
(10)
ing cascades downscatter their energy to X-ray and lower energies. -10
'
I
'
'
'
I
'
'
'
I
'
7
where Q is the source efficiency, a factor of order 1. Such proton densities are not only a good injection source for proton acceleration, but also a possible target for pp interactions. The proton energy loss is dominated, however, by the photoproduction process P7 -~ n~r+(P7r°) simply because the target photon density nj, h is much higher than n~. If all target consisted of monoenergetic photons of energy (e), the density ratio would be np -9 3/2 ~_ 10 ~1 ( ( ~ ) / e V ) Q %h
--
-1
o
.
(11) 4
The high cross-section pair production process (F7 --~ Pe + e - ) is relatively unimportant because of the low proton energy loss per collision. As it turns out, the photoproduction process also limits the maximum proton acceleration energy E ~ sz, contrary to the case of cosmic ray acceleration at supernova blast shocks, where the maximum energy is limited by diffusion away from the shock. E ~ ~x is roughly proportional to the AGN luminosity, reaching a value of 1017 eV for L = 1046 erg/s. While the simple proton and photon target density arguments are still valid in the generic AGN models, an important parameter is the energy spectrum of the photon target field. Because of the minimum photon energy E ph mi" (oc E p- t) required for photoproduction by a proton of given energy, it is crucial that there are enough target photons a b o v e / ~ i ~ . This requirement is satisfied by the available data, because the main thermal feature, the UV bump, has an average energy of _ 40 eV and the hard X-ray spectrum extends to the MeV range. Neutrinos and v-rays are generated mainly in pion decays (lr° ---* 27, ~r+ -4 /~+v~) and the subsequent muon decays /~+ ---* ~, + v, + e +. In astrophysical environment all particles decay practically without any energy loss. All v-rays generated in the dense photon field immediately lose energy in 7V -* e+e- collisions and the initiated pair-production/inverse Compton scatter.
6
8
Log10 E~ (GeV) Fig. 2. Neutrino spectra generated in the central region of 3C273 in the models of Ref. [26] (thick line) and of Ref. [28] (thin lines). Neutrinos, however, freely escape from the production region. Fig. 2 shows the neutrino spectra generated at a spherical accretion shock normalized to the luminosity of 3C273. The thin lines show several of the models of Protheroe and Szabo[28], who performed their calculation for xl values from 10 to 100 and two different photon target spectra, and the thick line represents the model of Stecker et a1.[26]. The difference between the lower energy behaviour of the neutrino spectra in the two calculations is easy to understand in terms of the different astrophysical assumptions used in the calculations. Stacker et al. assume that after acceleration the protons propagate in straight lines. Low energy protons, which require high energy target photons, thus have much smaller interaction probability and a minimum proton energy E~ 'i'~ for photoproduction exists, determined by the cut-off of the target X-ray spectrum. Because of the kinematics of the photoproduction interactions and the decays involved, the neutrino spectrum below _ E~pin/20 becomes flat. Protheroe and Szabo[28], on the other hand, account for the proton diffusion in the area of the
T Stanev/High energycosmicneutrinos shock. It their model the lower energy protons are contained longer in the vicinity of the shock and have similar interaction probability. For this reason the neutrino spectrum generally follows the parent proton acceleration spectrum with a differential spectral index 2 below the high energy cutoff region. The features of their spectra around 104- 105 GeV are caused by proton energy loss on e+e - pair production. Because of the large neutrino flux in the important region around 1 TeV the models of Protheroe and Szabo generate significantly more upward going muons. The following formula gives approximately the neutrino flux[31] at Earth from an AGN of given X-ray flux and E~p== in [cm~.s.TeV] -z
FvEv ~- O.25Fx exp(-20Ev/E~p ==) x E~-2, (12) where Fx is the 2 - 10 KeV X-ray flux (erg cm-=s -z) and E~ is the neutrino energy in TeV. In their pioneering paper Stecker et al [26] proceeded to integrate the neutrino fluxes from single generic AGN's to obtain a diffuse v flux from all cosmological AGN. The integration has to account for the AGN density and luminosity distribution, as well as for the neutrino adiabatic energy loss due to the expansion of the Universe. This procedure is identical to the integration used to calculate the value of the diffuse X-ray background. As a matter of fact it uses the AGN luminosity function derived from X-ray observations and assumes that the neutrinos and the X-rays have a common source. The AGN luminosity function as a function of the redshift can be expressed as
191
with a = 5 / 2 for the Einstein-de Sitter cosmological model. Fig. 3 shows the current estimates of the isotropic v background, where the estimates of Protheroe and Szabo are made with different values of xl, photon target spectra, and integrated using two independent sets of luminosity functions. The resulting v flux extends to very high energy, where it dominates the atmospheric neutrino background by orders of magnitude. Because of the isotropic nature of the background flux, its major feature is the extremely flat energy spectrum. The thick line shows the corrected prediction of Stecker e$ a1.[26]. While the u spectra are now in very reasonable agreement at the higher energy end, the biggest difference occurs at energies below 3x105 GeV, where Stecker et a[ spectrum becomes flat and Protheroe&Szabo spectrum follows the primary proton spectrum. The difference reaches 2.5-3 orders of magnitude at E~=104 GeV which makes a big difference in the estimate of the induced upward muon signal.
7
-8
"~" -10 vi
& -12 -14
-18
p(Lx,z) = ..3g(z )
( Lx )
(13) ~
where P0 comes from measurements of the AGN luminosity, Ro is the present scale size of the Universe and g(z) and f(z) describe the number density and luminosity evolution of AGN in the comoving volume. Any AGN induced background, including X-ray and neutrino one, will then have energy spectrum [28]
d l l c4~rl fHo[ ER~
dE -
z~°"
dI, x Jo dz x dL xp(Lx, z)(1 + z ) - a ~-~{E(1 + z), Lx},
(14)
-20
4
6
8
10
Logto E,, (GeV) Fig. 3. Diffuse neutrino background from unidentified AGN. Thin lines show selected models of Protheroe & Szabo[28] and the thick line the model of Stecker et al.[26]. Fig. 4 shows the muon fluxes generated by the isotropic neutrino background as in the bracketing high and low models of Protheroe & Szabo[28] and by Stecker et a1.[26]. The angle averaged
192
T Stanev /High energy cosmic neutrinos
muon flux generated by atmospheric neutrinos is shown for comparison. The AGN backgrounds dominates at muon energies above 1 TeV. The predicted TeV muon rate in a 104 m 2 detector will be 160 to 800 p e r y e a r for Ref. [28] and ~ 30 for Ref. [26] over an atmospheric background of ~ 86 events. The highest value of Protheroe & Szabo has actually already been ruled out by an analysis of the energy distribution of the muons detected by the Frejus detector[32], which allows a flux of TeV muons not higher than 4x 10 -2 m - 2 y r -1. 0
7
--
-- ...........
..
~L A i
2 o
~)
-3
0
IllllallJlllBIllll 1 2
3
4
Log10 E~, (GeV) Fig. 4. Fluxes of upward going muons as a function of the muon threshold energy predicted by the bracketing high and low models of Ref. [28] (thin lines) and Ref. [26]. The atmospheric neutrino background is shown with a dotted line. AGN muons have a specific angular distribution because the isotropic high energy neutrinos are absorbed in propagation through the Earth, mostly in vertical direction. Surviving v~'s will produce spectacular cascading events[33] through the Glashow resonance u e e - --4 W - at E~ -6.4x 10 e GeV. Detection of other exotic phenomenal34] is also possible. Even the most pessimistic of these rates is within reach of the current generation of neutrino telescopes, which are under construction. DUMAND II[35] is scheduled to deploy its first three strings before the end of 1993. AMANDA[36] is ready for the deployment of up to six strings dur-
ing the antarctic summer. Nestor[37] has been funded to build one tower and may follow a year later. All these detectors have an effective area somewhat larger than 104 m 2 and should be able to detect the predicted isotropic backgrounds. 4. A G N J E T S
Individual radioquiet AGN will be much more difficult to detect, although the atmospheric background in 1° radius around the source is extremely small, ~ 1.6 x 10 -5 m - 2 y r -1 muons above 1 TeV. Even with optimistic luminosities the number of such events from individual sources is less than 2-3 yr -1 in a 105 m 2 detector. The recent observations of GeV "),-rays from a large number of extragalactic objects by the E G R E T instrument[38] on GRO gives a more solid basis for optimistic expectations. Most, if not all, of the E G R E T sources are radioloud AGN, which we believe are pointing their jets at us. Jets carry a reasonable fraction of the AGN luminosity, between 5 and 30%. The apparent luminosity to an observer looking into the jet along its axis is, however, increased by a factor of 1000 for a jet Lorentz factor of 10. A calculation of the neutrino production in AGN jets was first published by Biermann and Mannheim[39]. The produced neutrino flux reflects the physical conditions in the AGN jet. Because of the lower photon density protons can achieve higher energy at acceleration E ~ ax. In addition both the acceleration and proton interactions proceed in the jet frame and the neutrinos are boosted to high energy (blueshifted) with a Doppler factor of order 10. In the case of 3C273 the flux shape is almost identical to that of Stecker et al. in Fig. 2 shifted to higher energy and normalized to the jet luminosity. A model[40] of the proton acceleration and interactions envisions a bulk flow of magnetized plasma, streaming from the base of the jet towards its end (the hot spot), which can be approximated with a radiating sheet of certain radial dimension R and thickness D. The acceleration of nuclei and their interactions proceed in the frame of the flowing plasma, where the ma~ximum proton acceleration energy E ~ ~*'* _~ 2 x 101°B -1/2 GeV, B being the magnetic field strength in Gauss[24]. Both 7-ray and neutrino signals are
T. Stanev /High energy cosmic neutrinos
generated as a result of pp and mostly F7 interactions. For photoproduction the energy carried by neutrinos is directly related through kinematics to the "y-ray luminosity as L~ = ~L~r+ =
L-r,
(15)
where L-r includes a contribution from e+e pairs.
Although a fraction of the generated v-rays are able to escape from the production region, the m a x i m u m q-ray energy reaching the Earth is further limited by the absorption on the IR/optical background radiation[41,42] during propagation. Mannheim [43] has conveniently parametrised the neutrino fluxes reaching the Earth from A G N jets at blasars as a function of the total photon luminosity, redshift z, Doppler shift r, and effective magnetic field B. The neutrino output is (in
cm-28-1)
dN~ --~ 1.6 x lO_~r x L4s x Ev~-~.,
(16)
where /~4s is the total photon luminosity of the object in units of 1048 erg/s. This unit value is the peak emission of 3C279 observed by EGRET[44] in June 1992. In order to explain the variability of 3C279 on timescale of a day the radiating sheet thickness should be D .-.10ZScm, much smaller than its radius (I0 zs cm). The simultaneous observation of the BLLac source M k n 421 by E G R E T [45] and the Whipple observatory [46] is especially valuable for the understanding of the physics of A G N jets. The two observations define an energy spectrum with "y--2.06±0.04 over more than four decades in energy [47]. M k n 421 is the closest source observed by E G R E T at a redshift of 0.031. This is significant because of the absorption on propagation. The exact energy dependence of the absorption feature is uncertain because the magnitude and the energy spectra of the IR and optical background(s) are not well known. Within a factor of 2, however, 3 T e V -},-rays emitted at the distance of M k n 421 will already start being absorbed and will show an apparent steepening of the spectrum independently of the production spectrum.
193
There are at least two [48,49] models for the -/-ray emission that do not involve nucleons and generate the TeV radiation through inverse Cornpton scattering of accelerated electrons. They are, however, subjects of serious limitations and generally require higher bulk Lorentz factor of the jet. The radiation target density has to be high enough for IC scattering and, in the same time, low enough for the generated "),-rays not to be absorbed in "Y7 collisions. This is difficult to arrange for, especially when IC scattering in the Klein-Nishina regime is the relevant process. O n top of that the energy densities in soft photons (IR to X-rays) and "),-raysare comparable, which requires that the two types of radiation are generated in different locations. To prevent the electrons from loosing energy on synchrotron radiation, the energy of the magnetic field in the jet has to be of order 5% of the radiation density, far from the 0th order assumption of equipartition. It is much more natural to generate TeV 7rays through hazlronic interactions, although the ~,-ray absorption in the source is always a problem. It is almost a free parameter in any attempt to scale the observed "y-ray flux of M k n 421 to the corresponding neutrino flux. Halzen and Vasquez [50] scale the M k n 421 v-ray flux to neutrino flux in different assumptions for the v-ray absorption at source, expressed in terms of the magnetic field value B of the jet [51]. Even the order of magnitude of B is not known. Assuming one to one correspondence of the "),-ray and neutrino production, ~ they obtain 2 upward going muons of energy above 1 TeV in 105 m 2 per year for the case of no absorption (B = 10 -4 Gauss). The 10 Gauss value is 270 muons. For higher magnetic field values the neutrino flux from M k n 421 should already have been detected. Stecker et al. [52] use the "y-ray absorption on propagation to normalize the expectations from other G R O sources. They find -.~10-z3 v~ + ~ neutrinos from the 3C273 jet. Such a flux will generate 0.125 muons above i TeV in 105 m 2 per year. The corresponding flux from the 3C273 core is 40% smaller. The quiescent state of 3C279 would generate 5 muons, while the highest ob2For A + pbotoproduction only and a differentis,l energy spectrum with "7 : 2 the ratio of L,# -{-O~ to "y-rays above the same energy is slightly below I/4.
194
T, Stanev /High energy cosmic neutrinos
served "),-ray flux from 3C279 would correspond to 25 such muons. The 3C279 core contribution is only 0.125 events. These are the bracketing values for the expectations of neutrino fluxes from active galactic nuclei, it the 7-rays are indeed generated in hadronic interactions by accelerated nuclei. 5. D I S C U S S I O N A N D C O N C L U S I O N S The existing predictions of the source neutrino fluxes still suffer from uncertainties in the astrophysical input, especially for the neutrino emission from AGN. The spherical accretion model of generic AGN, which has been very successful in the analysis of the relevant astrophysical parameters, is nevertheless subject of criticism from different points of view. The model is only applicable to accretion disks with thickness comparable or exceeding the dimension of the shock radius. It has to be constructed in such a way that there is no leakage of the generated ~/-rays before their energy is downscattered to X-ray and longer wavelengths. Any significant leakage would exceed the experimental limits on diffuse extragalactic "),-rays. Some authors [53] estimate the source efficiency Q to be lower than 1/3 and ask if the conditions in the AGN nucleus are suitable for shock formation at all. Others [54] show the danger of overproducing background radiation through pair production and synchrotron radiation, which could lead to shock instability and drastically decrease All these, and other possible, problems should be a subject of further studies. Many of the problems, for example, could be avoided by placing the shocks in the bases of the AGN jets [55]. This has the advantage of providing the mechanism necessary to drive the jets and the disadvantage of only using a fraction of the total AGN luminosity. The calculations of the neutrino production in AGN jets are not less difficult. To model correctly all the jet physics one has to follow in some detail all the processes involved in the frame of the relativistic plasma flow, including particle acceleration and reacceleration at multiple shocks, v-ray production, multiplication and absorption in electromagnetic cascades in a non stationary fashion. This is very complicated problem, that involves many free parameters. The simple scaling of the
neutrino fluxes with the v-ray luminosity for individual sources may not be exact, since the conditions at the source are poorly known. The ratio of the magnetic to radiation energy density, for example, which is essential for the "),-ray absorption at the source, can vary within at least one order of magnitude. The sources are also highly variable and many might have been observed during the peak of their activity. The big question is the fraction of the AGN luminosity that goes through the nucleonic channel. Although it has been pointed out [24~25] that hadrons have suitable interaction cross sections and are a natural vehicle for the energy transport throughout the AGN disk, nucleons are not strictly necessary for the solution of this problem. Since the models of the non-nucleonic origin of the Mkn 421 ~,-rays are already struggling to extend the theory to "),-rays above 1 TeV, a possible observation of, say, 10 TeV v-rays would be a confirmation of their 7r° origin. This is hardly possible, however, because of the absorption on the IR/optical background, even if the production spectrum reaches much higher energy. There is only a slight chance that [42], for very low values of the extragalactic magnetic field, the cascading on this background will flatten considerably the spectrum observed in the GeV/TeV region. Such flattening would reveal the extension of the production spectrum to much higher energy and correspondingly confirm the ~r° origin of the "y-ray flux. The criticism above does not imply that the current predictions are not reliable. They are results of the first generation of research, which will become more exact in the near future. The differences between various estimates reflects the uncertainties of the calculations. Conclusions are that the expected fluxes of source neutrinos are well below the sensitivity of the currently active deep underground detectors with effective area less than 1000 m z. They are, however, tantalizingly close to being detectable by the new generation of detectors [35-37], especially designed for neutrino astronomy. It will not be an easy task, but as the impressive analysis of the Baikal data [56] shows, a realistic one. ACKNOWLEDGMENTS. I am grateful to V.S. Berezinsky, P.L. Biermann, J.G. Learned,
T. Stanev/High energy cosmic neutrinos
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T Stanev/High energy cosmic neutrinos
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