high energy neutrino astronomy
TRANSCRIPT
Nuclear Physics B (Proc. Suppl.) 19 (1991) 375-387 North-Holland
375
HIGH ENERGY NEUTRINO ASTRONOMY
V.S.BEREZINSKY
Institute for Nuclear Research of the Academy of Sciences of the USSR, 60th Anniv. of October Revolution prospect 7A, 117312 Moscow, USSR
Very High Energy (VHE) and Ultra High Energy (UHE) neutrino astronomy is reviewed. The neutrino sources and detection of neutrino fluxes are considered. Much attention is given to a possibility of observations with help of "small" detectors with effective area S ~ 1000 m ~.
1. INTRODUCTION High energy neutrino astronomy can be distinctly
divided to very high energy (VHE) and ultrahigh energy
(UHE) neutrino astronomy. The threshold for the former
is 30-100 GeV, for the latter is ~ 107 GeV.
They are different in production. VHE neutrino
astronomy is related to pp-neutrinos, UHE - - to
pT-neutrinos:
p+p---~a + X p+7---~ ~ + X (1)
In contrast to pp-neutrinos, the production of
pT-neutrinos is a ttu'eshold effect: in a photon gas with
average energy s a large fraction of the neutrinos
produced have energies greater than
E0 u 4.10-2m mp/s u 6.106(1 eV/s) GeV, (2)
where m and mp are the masses of the pion and the
proton, respectively. It is interesting to note that for
many sources the pT-mechanism gives a neutrino
threshold energy E0 ~ (5-10)'106 GeV (e.g. see the
subsection "bright phase").
There is the difference in the sources.
A high energy neutrino source is compl~ed of the
accelerator (pulsar, accretion disc, black hole etc.) and
the target. For a typical VHE n e u t ~
(pp-production) the target is a gas c l o d around the
accelerator. Astrophysical observatio~ ( ~ l a r l y
X-ray observations) show that the column ~ of a
gas target is usually small, N H _( 1024cm -2- In contrast to
it, the col-ran density N 7 of photon gas is expect, ed to he
large. For example, in a case of a black hole with the
effective temperature T at the gravitational radius Rg =
3-105(M/Mo) cm and with the Eddington l ~ t y
LEd d -- 1.3-1038(M/Mo) erg/s the photon column
density
N 7=LEdd/(4~RgcT)--8. 3 . 1032(104K/T)cm -2, (3)
is considerably higher than photopion column density N = a -i = 1.102s cm -2. Such the situation is realized
7P 7P
in active galactic nuclei (AGN). In case of UHE neutrinos it becomes possible to
detect diffuse flux of extraterrestrial neutrinos, since the
flux of atmospheric neutrinos falls off rapidly with
energy. Interaction of VHE and UHE neutrinos is also
different. For VHE neutrino astronomy the basic
0920-5632/91/$3.50 © Elsevier Science Publishers B.V. (North-Holland)
376 V.S. Berezinsky / High energy neutrino astronomy
reaction is v +N----,#+X. For UHE neutrinos the
dominant reaction is Pe+C :W-----,hadrons. The
resonance energy of neutrino is
Eo = mw2/2me = 6.3-106 GeV (4)
For detection of VHE neutrino sources it is plausible
to use muons produced in y +N--~#+X -scattering. At
energy E > 30-100 GeV the angle between produced Y
muon and the parent neutrino is smaller than the typical
resolution angle for the existing muon detectors. Muons
can be registered in deep underwater detectors due to
(~erenkov radiation. This method was suggested by
M.A.Markovl in 1960. For UHE neutrino astronomy the
new methods of detection can become possible. One of
the most promising of them is the acoustic method. The
detection of particles via their acoustic radiation was
first suggested by G.A.Askaryan2 in 1957. The acoustic
neutrino detection was discussed in ref.3-o (see the
references therein). The threshold of the acoustic method
for a deep underwater detector with the reasonable grid
is estimated as Eo ~ 107 GeV.
I would like to draw the readers attention to the
surprising coincidence of neutrino energy E ~ 107 GeV for
neutrino production, eq.(2), for neutrino interaction,
eq.(4) and for neutrino detection by the acoustic method.
2. VHE NEUTRINO ASTRONOMY.
STANDARD SOURCE
Introducing the concept of the standard source7 we
can give the connecV, on between such the characteristics
of a source as proton luminosity Lp and spectrum index 7
with the number of neutrino induced muons which cross
a detector with effective area S per unit time.
Recalculations to any other source is trivial.
The standard source is comprised of the accelerator
submerged in a cloud of gas with low density nti<10ts
(Ev/1 TeV)-t cm-a and with large column density
N!!>>1025 cm'2. The accelerator generates Qp(E)
protons per unit time
Qp(E)dE = (7-2)(7-1)(E+ 1 )-'rLpdE. (5)
Here and later on E and Lp are given in GeV and GeV/s,
respectively (if not stated otherwise). The generated neutrino flux can be given with help of the neutrino
yieldsS Y • /]
Qv ÷~ (E)dE-(Yv +Y~ )(?-2)(7"/_11)LpE-~dE' tJ ~ tJ t~ 1--a
(6)
where (1-a 7-1) takes into account the secondary
collisions of a proton and an0.5 is a fraction of energy
retained by a proton in nuclear collision. The values of
neutrino yields multiplied by factor of 1000 are listed in
Table 1.
TABLE 1. Neutrino and photon yields for different 7- In
Table are given the values of 1000Y.
7 Y
/J #
Y_ //
#
Y pe
Y_ Ve
Y 7
2.1 2.2 2.3 2.5 2.7 2.9 3.0 3.2
63.1 47.3 34.9 19.6 11.5 6.96 5.52 3.49
63.1 47.3 34.9 19.5 11.3 6.83 5.37 3.34
35.1 26.3 19.5 l l .u 6.40 3.88 3.05 1.90
23.6 17.7 12.8 6.87 3.85 2.22 1.73 1.05
116 88.8 69.0 43.0
Neutrino flux underground, Fv= Qv/47rr2, where r is the
distance to the source, is accompanied by equilibrium
m u o n f lux 7'9, which can be given in terms of the ratio
r ( E ) = F ( E ) / F v , 9 ( E ). This ratio is tabulated in
Table 2 for the standard rock.
And finally in Table 3 we give the number of muons
crossing an underground detector with an effective area
S=1000 rn2 per 1 yr, if the source with luminosity Lp =
1.104terg/s is located at a distance r=10 kpc.
V.S. Berezinsky/High energy neutrino astronomy g?7
Three conclusions follow from Table 3.
(i) To detect a source at a distance r~10 kpc with
"small" detector S~103 m2 at the rate 10-100 events per
year, a luminosity Lp~104~erg/s is needed. Scaling this
value to extragalactic distances and keeping in mind that
up to distance 5-10 Mpc (which corresponds to
Lp~3-10-1046erg/s) no powerful extragalactic sources are
seen, we conclude that the horizon of small neutrino
detectors is limited by our Galaxy.
TABLE 2. The values of r ( E ) for standard rock and for
different E (in GeV) ~vd 7. The orders of
magnitude for all figures are as in the first
row.
E\7 2.1 2.2 2.3 2.5 2.7 3.0 3.2
10 69.10"]] 47 32 20 14 8.4 5.6
30 50-10-m 36 26 16 11 7.0 5.5
100 41-10 -9 30 23 14 10 6.4 5.0
300 23-10-s 18 14 8.7 6.1 4.1 3.2
600 59-10-8 45 36 24 17 11 8.5
1-103 11-10 -T 8.3 6.5 4.5 3.2 2.1 1.7
1.106 7.9.10-5 6.8 6.0 4.7 3.9 3.0 2.6
TABLE 3. The number of muons with energy higher
than E (in GeV) from the standard source
with Lp = 1.1041erg/s at a distance r=10
kpc which cross a detector in a standard rock
with area S-1000 m2 in a year.
E \7 2.1 2.2 2.3 2.4
10 120 69 31 13
30 120 66 29 12
100 110 60 26 10
300 93 49 19 7.4
600 79 40 16 5.7
1000 67 33 13 4.5
2.5 2.6 3.0
5.5 2.3 0.1
4.9 1.8 7.10 2
4.0 1.6 4.10 "2
2.8 1.0 2.10 -2
2.1 0.7 1.10 2
1.6 0.5 8.10 -3
(ii) The luminosity Lp of a detectable galactic source
is very high and it can be associated only with
supernovae or young pulsars. Mind that cosmic ray
luminosity of the whole Galaxy is L v ~ 3 - 1 ~ s .
However, a source I-minosity Lp can be ~ ff to
assume that solid angle of proton emission f l<<4r and a
source is located at ~ r<<10 kpc. For
the source with T=2.1 and fl~l sr at r---3 kpc can
marginally detected if its luminosity L , ~ I ~ erg/s.
Off) From Table 3 one may obm~.~ that for
generation spectra 2.1<q~3.0 the number of
crossing the detector with E >10 GeV ~ E ~ GeV p p
differ very little, i.e. the main contribution is ~ by
muons with E >500--600 Get/. The ~ for t ~ is t ~ p-
the flux of underground muons with a given ~ is
proportional to the number of neutrino, F ~ E - T to v p
apN~E (z,N--cross-se~ion) and to R ~E (muou path K p
length). The latter is determined by the muon eaerg~-
loss d E J d x = a + b E . It shows ~ the main
contribution to the muon flux is made by muous with
average energy E ~ a/b, which is about 0.5 TeV for the
standard rock and O.7TeV for water.
We complete this Section with the recipe for
converting the data of Table 3 from the ~andard source
to the other models.
If a source is thin and prior to escape from the source
a proton traverses a column density x<xu, where x~A0
g/cm2 is the nuclear path length, then the flux (6) has to
be multiplied by (1-aT-1)X/Xu and the same factor has to
be introduced for the numbers in Table 3.
If the model is such that during a time r the proton
beam periodically (with period T) hits a dense target, as
in the case of binary sources, then the flux averaged over
a period is obtained from (6) by multiplying by r /T and
this factor appears in Table 3.
3. VHE NEUTRINO SOURCES: SUPERNOVAE
The necessary luminosity is available in SN. We
shall consider here two possibilities: the inner and the
outer neutrino production.
3.1. Inner neutrino radiation from SN envelope
In this model protons are accelerated inside the
378 V.S. Berezinsky/High energy neutrino astronomy
expanding SN envelope (e.g. by pulsar, black hole or by
stochastic Fermi mechanism). This nmdel was suggested
in ref.m and then developed in ref.n-13. Much attention
was given to this model in connection with SN
1987AI4-1L The onset of a phase of powerful neutrino radiation is
determined by the moment t r(r) , from which on the
charged pions with Lorentz factor r decay in a nuclear
path length
t r(r ) = 2.7-102(M/3Mo)l/aug-l~ll/arl/3 s (7)
where M is the envelope mass, u9 is the velocity of
envelope expansion in units of 109cm/s and y/<l
describes the mixing of gas and accelerated particles in
the envelope. The active neutrino phase terminates at
ta u 2.3- lO7(M/3Me)l/2ug-l~}l/2 s. (8)
At t < t< ta this model coincides with the standard ~r
source and the neutrino flux is given by eq.(6). It can be
registered by small detector with S~1000 m2 if r~10 kpc
and Lp~104o---1041erg/s (see Table 3). For SN 1987A the
upper limit for the muon flux from the source is ~s
F <1.2.10-13 cm-2s -~ at E >1.7 GeV. From Table 3 one /~ p -
finds Lp<9-1041erg/s for 7=2.1 and Lp<3-1042erg/s for
7=2.3. However, VHE gamma observations give more
stringent limit on Lp, namely, from JANZOS
observations 19 F/(>3 TeV)<6.1-10-12cm-2s -l we obtain
Lp<l-1039erg/s for 7=2.1. The physical significance of
this limit depends on whether or not a fast pulsar exists
in the envelope of SN 1987A.
3.2. Neutrino radiation from the shocked shell20
Crossing the SN envelope the shock propagates
further in the ambient space filled by the stellar wind left
behind by the presupernova mass loss. It is accompanied
by rarefaction wave propagating inward in the system at
rest with the envelope gas. In the laboratory system the
shock is dragged by the gas flow and propagates together
with it outwards. In Fig.1 the shell (2) between two
shocks (o and i) is shown in the system where the shell is
at rest. There are two convergent flows of gas in this
system: one from the envelope (1), the other from the
stellar wind region (2). The accurate hydrodinamical
description of this picture is given in refs. 2~'22.
1
L :
3
0 FIGURE 1
The shocked shell (2) between outer (o) and inner (i) shock fronts.
The particles are accelerated at the both shock fronts
and dragged by the gas flows inside the shell. Therefore,
both accelerated particles and gas are accumulated inside
the shell. It results in the powerful production of gamma
and neutrino radiation.
Neutrino flux from the shell at E <Era is equal to 2o /]
1.4 ff0~Un f 1VI 12 mHc2 ft ] -(2-4) Q~÷~ (E) ~ ~ B ~ [ m H u wJ - - ~ v LFnJ (9)
where for Galactic SN: presupernova mass loss l~I =
1.10-5M®/yr, dimensionless hydrodynamical parameter
B=l.5, wind velocity Uw = 1.106cm/s, normalizing
cross-section #0=32 mb, a=0.88, ta=l.107s, un=l.109
cm/s and maximum neutrino energy Em~105GeV. At the
distance r=10 kpc the flux (9) is marginally detectable
by a neutrino telescope with area S~103km 2.
4. VHE NEUTRINO SOURCES: BINARIES
The general arrangement of a binary system as a
neutrino source involves an accelerator and the gaseous
V.$. Bereziasky /High energy neutrino astroaomy 379
target revolving around it. The atmosphere of the
companion star 23 or a bulge 24 on an accretion disc can
serve as the target. In this Section we shall confine
ourselves only to the problem of acceleration, considering
the maximum particle energy Emx and maximum
luminosity Lp. The latter, according to Table 3, serves as
an indicator of detectability of a source.
We shall discuss here three mechanisms of
acceleration: electric potential in pulsar magnetosphere,
unipolar induction in accretion disc and shock
acceleration.
Let us begin with the pulsar acceleration. The
maximum potential drop between the pulsar surface and
infinity, in case of potential field, is independent of
magnetosphere model and is equal to
1 [~_~.] 2V, pm -- H Q2R3 = 3.3-10 i0H 6 (I0)
where Hs is magnetic field on the pulsar surface, R is a
radius of neutron star and T = 2r/fl is a pulsar period.
The pulsar lnminosity for any configuration of
magnetic moment and rotation axis is
L~,e1_3Hs2f14R6~,6.104,[ Hs ]2[~__]4erg/s [10 l~GJ
(11)
Eq.'s (I0) and (II) can be considered as some indication
to possibility of acceleration to high energy with high
luminosity, required by Table 3. However, the known
models of pulsar magnetosphere provides neither this
high energy nor luminosity.
The second possibility is unipolar induction in the
accretion disc 25"27. We shall use the following model for
the thin accretion disc around neutron star. The gas in
the disc has a Keplerian distribution of the azimuthal
velocities v with radial velocity Vr<<V . The position
of the inner edge of the disc is determined by the balance
of the pressure of the pulsar magnetic field, H2/Sr, and of
the gas pressure in the disc. Thus the distance between
the neutron star and the edge of the disc is equal to
AlDen radius RA~--'2-1~; which depends ~ weakly cm
neutron star luminosity and magnetic moment ~ The
potential across the accretion ~ is
where m is g r a v i t a t ~ ~ , M is ~
mass, Hz(RA)~ /R i is the trier
of the disc and Rt is the radius d t ~ ~ edge
which we take the radius of Roche ~ ~ (12) ~ ffi
I. 103tG cm3 was used.
The luminosity Lp in accelerated partici~
exceed the energy t r a n ~ per unit t i ~ into
energy of the disc. The latter is less ~ g r a ~ ' ~
energy released per unit time on t ~ ~ ~ of the
disc: Lp "- (~eM~'A/R A where ~l is ~ ~
(<I. Using tlm Zddington l~ty,
0.1~eMIVI/R, and RA/P~}0 we
Lp ~ 10((R/RA)LEdd = 7 - 1 0 ~ ( ( M / ~ / s (13)
Therefore, unless the accretion proceeds in
super-Eddington re~i'me, the proton l u m i ~ t y is much
less than Lp~1040--1041erg/s required by Table 3. In case
of a black hole the situation is even wors~
The third possibility is shock aecelex~atio~ We shall
assume that both the inner edge of the ~ and the
position of a standing shock front are determim~d by the
Alfven radius. The maximum energy of accelerated
particles can be estimated by equating the accelerat~
time ta~D/ur 2 and the time of nuclear eaergy losses
tnuc~l/(~pnHC), where D is the diffusion coeffi~ent, Ur is
the radial velocity of the accretion flow and n H is density
of the gas. After simple calculations one obtains
1"3 aT [~-~.~] 3 [~-~] 2eHR ~ 8.1OueV , (14) Emax ~ ~
380 V.S. Berezinsky / High energy neutrino astronomy
where at the inner edge of the disc ~ = ur/u ~ 0.1 and ~/
= h/r ~ 0.1 (h is the height of the disc) and a T is the
Thompson cross--section. About a~10% of radial energy
flux of accreting gas, l~IUr2/2, is transferred to the
accelerated particles. Since only R/RA-Part of the total
gravitational energy release occurs at the position of the
shock front, the proton luminosity is
Lp u 0.5a~2(R/RA)LEd d ~ 1034(~/0.1)2erg/s (15)
We conclude this Section with a comment that from
the three acceleration mechanisms considered, only fast
active pulsars can provide (with aforementioned
reservations) the neutrino flux, which can be registered
by "small" neutrino detector with S~103m 2.
5. NEUTRINO FLUXES FROM THE OBSERVED
VHE/UHE GAMMA-RAY SOURCES
The observed flux of VHE gamma radiation from all
observed binary sources (Cyg X-3, Her X - l , Vela X- l ,
4U 0115+63) is within the range F / > I TeV)
(1-2).10-ncm-2s-L Let us first assume that a target is
gamma-transparent and 7=2.1. Then using Y - uY v +u 7
(see Table l) we arrive at Fvl/~,1(E)=(rv/rr)Fr(E ), where r and r are durations (or phase widths) of
v 7
neutrino and gamma pulses, respectively. From the
observed phase width r.~~0.1 we obtain Tt,/r.r<5 (see
Fig.2) and using the data of Table 2 we arrive at Ft~(>l
TeV) < 4. IO=I6cm=2s =I. To detect this flux at the rate ~i0
muons per year, the neutrino telescope with area
S~I05m2 is needed.
We can speculate further and assume that the target
is thick and gamma-rays are mostly absorbed. It brings
us to the hidden sources discussed in the next section,
but does not actually help to make these sources
observable by small detectors. Indeed, introducing
absorption factor ,~~100 results in increasing Lp by the
same factor. For Cyg X-3 it implies the luminosity Lp_>
2.104~erg/s and for the nearest source, Vela X- l , Lp_>
4.1039erg/s, which is extremely high for this system in
view of large period of the pulsar there (T=283 s).
6. HIDDEN SOURCES
The production of neutrinos is inevitably
accompanied by production of e.-m.-radiation, most
notably gamma radiation. If the latter is absorbed within
the source we call it a hidden source.
We shall begin with three realistic examples.
A binary system comprised of a fast active pulsar
protons ~ 7 .-: . ._
" - " - " -~1 I : '_ v
pulsar, :.. : 7 black hole }
to er
FIGURE 2 A binary as a hidden source.
and a companion star with thin atmosphere (Fig.2) can
emit large neutrino flux accompanied by small gamma
flux. The latter is produced in the thin layer of the
atmosphere, while the former - - in the atmosphere
behind the companion or inside it (prompt neutrinos).
This source was suggested in ref33 and used in ref. 2s as a
model for Cyg X-3 (see also ref39 for calculations of
neutrino production in such the system). The neutrino
flux fi'om the source can be obtained from (6)
multiplying it by ru/T, where r v is duration of neutrino
pulse and T is orbital period of the system. If neutrinos
are produced in the atmosphere behind the companion
and if the companion is transparent for VHE neutrinos,
then TJT~0.5 and the number of the detected muons
from Table 3 should be diminished by factor 2.
The second example is the hidden source 2a based on
evolutionary scenario of tel.a0. As a result of evolution of
V.S. Berezinsky / High energy neutrino astronomy 381
a binary system, the neutron star is eaten by its massive
companion, the red supergiant. The system is
characterized according to ref.3o by the following
parameters: the mass of neutron star and the mass of the
supergiant core are ~1 M e each, the distance between
them is D-~3 • 10Hcm, the mass of the supergiant envelope
is Mul0 Me, the densityof the envelope is p u (1-3). 10 .9
g/cm3 and the column density of the envelope is ~P~
(1-3).105g/cm2. The luminosity of the neutron star
powered by the accretion produces the low density cavity
above and below the accretion disc, where acceleration of
particles takes place. All kinds of electromagnetic
radiation are absorbed and thermalized in the envelope
and from outside the star looks like a usual supergiant.
The high energy neutrino emission is then a surprising
feature of such the star. The considered system is
identical to the standard source. The numbers of muons
registered by small detector are given in Table 3.
~ O w accretion d / ! \ cretion disc
black hole
star as black-body radiation. Absolute holometric
magnitude of the star is then Mbol----4.7.5--2.5~/2I W
For the detectable source with L p ~ l ( P ~ s , Mbol=-8.0.
Unless strongly obscured by the dust, such the star
would be undoubtedly known.
An exception is the burst neatrino source. The
thermal emission slowly diffuse from the center, the
is broadening and the optical luminosity ~ for
the given energy output. The outburst of acederated
particles, if it occurs within several days after SN
explosion, gives an example for such possibility.
In case of cocooned model of AGN the black-body
component of radiation gives the upper limit for the
proton luminosity Lp.
7. UHE NEUTRINO ASTRONOMY: p,~-NEUTRINO
PRODUCTION
Consider a proton beam with intensity I ~ E ) - - K ~ -7
(measured in cm-~-lsr-l) propagating in photon gas with
spectral density n (~) , where ~ is photon energy.
the number of yi-neutrinos with energy E produced per I
cm 3 per ls and per lsr in the direction of proton ~elocity
is
qvi(E) = yP'r(E,7).no~oIp(E), (16)
FIGURE 3 Massive black hole with the thick accretion disc.
The third example of a hidden source is cocooned
massive black hole as a model of active galactic nucleus
(AGN)3p32. The thick accretion disc (Fig.3) is one of the
realizations of the idea. The absorption of
gamma-radiation can also occur due to 77-collisions in
the vicinity of the black hole.
The following remarks are in order.
For a stationary hidden source some kind of
e.-m.-radiation must inevitably accompany the neutrino
flux. For example, in case of the supergiant model half of
the proton luminosity is emitted from the surface of the
where Y p7 is neutrino yield, no is the total number of vi
photons per lcm 3 and ~o-1-10-2Scm 2 is the normalizing
cross-section. In contrast to pp-production pT-neutrino
yields depend on neutrino energy and on the shape of
both proton and neutrino spectra. The detailed
calculations of neutrino yields are given in ref.~. The
yields depend crucially on angular distribution of pious in
reference system at rest with the incident proton. To
take it into account, in the low energy region ~(2.5 GeV
the binary reactions with the known angular
distributions were considered: 7+P ~ ~-++n, 7+P -- ' h+*+~ -, 7+P -'-' pO+p. At ~>2.5 GeV the scaling
inclusive distribution Ed3a/dp3=f(~,x,P T) for 7+P--"
~+X was used. The contribution of K-meson production
382 V.S. Berezinsky/High energy neutr ino as tronomy
t ~
- 1 . 5
-2.0
--2.5
-3.0
-3.5
, ! !
- ! I
! !
! !
J I
I
m
I i J I
p #
f ~ t
p /z
' ~J'~'mJ~'ml~ 1
P Ve f
! /
! u ! #
V re
Ue
I I . l ] / i I I I
-2.0 -1.0 0 1.0 2.0 IOgZ u
FIGURE 4 The yields of p7-neutrinos as a function of e for diluted /]
photon spectrum with any temperature T and for power-law spectrum of protons with 7=2.1. In the upper part of the figure are shown the total yields, in the lower - - the contribution of K-mesons.
was also taken into account.
The yields in (16) depend on the spectrum of target
photons. In particular for diluted photon spectrum with
temperature T the yields depend on T. However, in
terms of "dimensionless" neutrino energy ez,=Evxo/mp2 ,
where ~o=1.59 kT, the yields become the universal
function of ~v and 7. The yields for power-law photon
spectrum with 7=2.1 are shown in Fig.4.
In the last work listed in ref.33 the calculations of
neutrino yields are performed for arbitrary proton and
photon spectra. They are needed for the case when the
target is thick and the proton spectrum is distorted within the source.
8. UHE NEUTRINO ASTRONOMY:INTERACTIONS
At ultra high energy, uN-cross-section i n c r e a s e s 34'35
due to increasing the number of quarks with small x,
described by structure function of nucleon. The
calculated cross-sections are given in ref. 36-4o. At energy
E ~10zGeV, which is of interest here, yN--cross--section V
reaches a~10-aacm2. However, at these energies the
crucial role in neutrino detection belongs to the resonant
scattering Pe+e---,W---,hadrons 41'42 which is the close
analogue of ~e+e----~W-----,#+ P considered by #
S.L.Glashow43 in 1960. The detailed calculations for
resonant 9ee-scattering as well as for all other channels
of ue-scattering at ultra high energies are given in ref. 44.
The number of resonant events can be calculated
with great precision analytically 41. The total number of
resonant events Vres for power-law spectrum of
Pe-neutrinos I~e(E)=KE-7 is formally connected with
integral spectrum Ihe(>Eo), where
Eo=mw2/2me=6.3 • 106GeV is resonant neutrino energy:
Ures = 2~Neaeff(7-1)I~e (>E0), (17)
where aeff-(31r/4-2)GF=3.0.1032cm2 is the effective
cross---section, Ne is the number of electrons in the
detector, I~e(>Eo ) is the isotropic neutrino flux
measured in units cm-2s-lsr-1 and 2r is the solid angle
within which the resonant neutrinos reach the
underground detector without absorption (neutrinos
traveling upwards are absorbed). But actually the
number of events (17) is caused by neutrinos with
energies within width of resonant peak in laboratory
system, r=(mw/me)rw=4.4.1OBGeV, and all neutrino
produced showers are confined within the same energy
interval. The energy resolution of deep underwater
neutrino detectors, 5E, is expected to be much higher
than r. The ratio of the number of resonant events to the
number of uN-induced events, //back, ill the energy
interval ~fE is equal to44 Vres/Uback~,20 (0.2. E0/~fE).
V.S. Berezinsky / High energy neutrino astronomy 383
9. UHE NEUTRINO ASTRONOMY:
DIFFUSE FLUXES
The detection of diffuse fluxes at ultra high energies
becomes possible at ultra high energies because the flux
of atmospheric neutrinos falls off rapidly with energy.
However, the predicted fluxes can be detected only by
the gigantic arrays (M~109t, S~1 km2). Three
populations of the sources are known to be able to
produce the detectable diffuse flux: (i) quasars and
Seyfert galaxies with their evolution taken into account,
(ii) massive pregalactic objects 45 and Population HI
stars 46 and (iii) galaxies at the bright phase of their
evolution47. We shall consider here only the recent
progress in calculations of UHE neutrino fluxes from the
bright phase.
The concept of the bright phase in galaxy evolution
was put forward by R.B.Partridge and P.J.Peebles47 in
1967. They suggested that at red-shift between z=10 and
z=30 the burst of star formation can occur with the total
energy release W~3-1061erg per galaxy. The idea of
-21
---23
-25
-27
-29
-31
log F, (cm-2s-lsr-lGeV-l)
2.0 3.0 4.0 5.0 6.0 7.0 log(E/1 TeV)
FIGURE 5 Differential spectrum of v-neutrinos from the bright
phase, characterized by Wp=l. 106Oerg, nG=l. 10-75cm-3
and zf =20. The curves 1, 2 and 3 correspond to 7=2.1, 2.3 and 2.5, respectively.
galaxy formation at large red-shifts z>10 has recently found the new confirmation.4SThe calculations of UHE
neutrino production during the bright phase were
performed first in ref)9 and later in ref.r~-52. It
assumed that at the bright phase each galaxy ~ a
burst of accelerated partifles (protons) with the
power-law spectrum and with the total energy output
Wp. UHE neutrinos are produced in the ~ of
protons with the relic photons. The neutrino flux and the
characteristic features of the spectrum can be ~ with
help of the following simple estimates49-5o. In view of the
threshold character of pion photoproduction the observed
(at z=0) differential neutrino spectrum has a steepening which begins at the energy
Em = CSb/ (1 +zf)2=6.1-106(2011+zf)2GeV, (18)
where Eb=6.1.101OGeV is the energy (at z---0) where
photopion energy losses starts to dominate over pair
production energy losses, ~4-I0-2 is the fraction of
energy transferred from the proton to a neutrino and zf is
the red-shift of the bright phase epoch. The factor
(l+zf) -2 arises in eq.(18) because (i) Eb(z)=Eb(l+z) -I
and (ii) neutrino energy is red-shifted. Taking into
account that neutrinos axe produced in the epoch with
z=zf and that the energies of the parent protons _>Eb(z),
it is easy to derive:
nGWp fEb] -(7-1), (19) Iv(_>Em)=43c~/ 7 -2 ( l + z f ) r - l ~ [ E ~ o j l_.a7 -1
where ~/is the relative probability of producing charged
pions in pT--collision (1/3_<~/_<2/3, depending on energy),
a is the fraction of energy retained by the proton in
pT--collision (0.5_<a<0.85, depending on energy) and n G is
the present-day (z=0) space density of the galaxies,
which went through the bright phase.
The results of our recent accurate calculations
(V.Berezinsky, A.Gazizov, S.Grigor'eva and
B.Kanevsky) are shown "n Fig.5. For each proton
384 V.S. Berezinsky ~High energy neutrino astronomy
accelerated to energy Ep at the red--shift zf we calculated
the neutrino spectrum according to the production
neutrino functions (ref.33, 1989) and taking into account
slowing down of the proton. In the calculations we used
Wp=l.106Oerg, nG=l.10-75cm-3, zf=20 and Eo=l GeV.
The calculat~ fluxes and the energy Em are in reasonable
agreement with the estimates (18) and (19). These
results differ considerably from those of ref.52, in which
some ad hoc assumptions for pT-production of pions were made.
The calculated flux is marginally detectable by the
gigantic arrays (M~109t, S~I km2).
One cannot speculate much about the neutrino fluxes
produced in the past and in particular about the value of
Wp in eq.(19). The production of neutrinos in pp - or PT-
collisions is accompanied by the production of high
energy gamma-quanta and electrons. In collisions with
the ambient low energy photons, e.g. of microwave
radiation, they initiate e.-m.--cascade. Unless the energy
density of this cascade is less than Xx~5 • 10-6eV/cm3, the
gamma-ray flux at E ~100-200 MeV exceeds the 7
observations. Using the following chain of inequalities,
valid for any falling neutrino spectrum,
0o o0
= ~--fEIz,(E)dE> ~- E 0&>0jv(>E) 4r 4r
E E
(4r/c) EIv (>E),
f I (E)dE =
we arrive at the rigorous upper limit
Iu(>E) < (c/4r)(0&/E) < 1.10-12(107GeV/E)cm-2s-lsr-1.
This limit strengthens for the real power-law neutrino spectra.
10. SUPERHIGH ENERGY (SHE) NEUTRINOS
We suggest to refer as SHE neutrinos to those with
energies Eu>10~reV. They can produce the horizontal
extensive air showers (EAS) and EAS from under
horizon. A search for SHE neutrinos using horizontal
EAS was discussed in the past in ref. 53'54. Recently the
interest to this possibility was renewed in connection
with the observations of Fly's Eye and with the prospect
of using the satellite observations55. The new element
involved in the discussion is the absorption of SHE
neutrinos in the Earth. This problem being raised for the
first time in ref. 56 was then discussed in ref.5L According
to calculations of ref. 40 the solid angle fl~0.8 sr under
horizon is still open for SHE neutrinos. The calculations
of fluxes of SHE neutrinos and the discussion of the
prospects to detect them the reader can find in ref.59,40.
11. VHE/UHE COSMIC NEUTRINOS OF
NONACCELERATION ORIGIN
So far we have considered neutrinos produced by
accelerated particles. A question arises as to whether it is
possible to produce VHE/UHE neutrinos otherwise.
Three attempts are known in the literature.
( i) Evaporating black holes 59
In the last stages of the mini black hole evaporation,
when its mass becomes M<I g, its temperature becomes
so high that UHE neutrinos are emitted. For a mass M
(in g) the temperature T (in eV) and luminosity L (in
erg/s) of the black hole are T~I. 1022/M and L ~ 1.1046
N(M)/M2, where N(M) is the number of particle types in
equilibrium; the gravitational radius is rg ~ 1.5.10-28M.
For instance, for M~10-Sg the temperature reaches
T~1027eV and so does neutrino energy59.
However, it is easy to see that the surroundings of
the mini black hole are opaque to UHE/SHE neutrinos
due to the collisions with other neutrinos emitted in
nonradial directions. A muon neutrino with energy T
undergoes v collisions u +p --~ e÷+e -
" = r - - - '
where ~0 = 1.1'10"45cm2. For E >10 TeV, 1:>>1. The y -
total energy release in form of these neutrinos
V.S. Berezinsky /High energy neutdno astronomy 385
W <Mc2/N(M)<1029erg is too small for the detection in /J
our Galaxy.
(ii) Superconducting cosmic strings The phase transition in superconducting cosmic
strings results in the production of particles with the
masses MGUT~10Z6GeV60,6L The decay of these particles
give rise to UHE and SHE neutrinos62. However, as
shown in ref.63, all high energy particles including
neutrinos drastically degrade in energy in the strong
magnetic field around the string (e.g. ~,+I-I --.
H+v+e*+e-).
(iii) Decays of superheavy Big-Bang relics The diffuse flux of VHE neutrinos was estimated in
ref. 64'65 using ad hoc assumptions about density, nx, of
superheavy particles.
We shall begin with a remark that the Universe at
red-shift z>za(Ev) is opaque for VHE neutrinos due to
v+p --+ e÷+e - scattering on relic neutrino radiation. In
particular, for t, - a n d P -neutrinos # P
Za = 1.4.105 (E J 1 TeV)-2/Thmo 2/7
where E is neutrino energy at present epoch (z=0) and Y
h~00 is Hubble constant in units of 100 km/s Mpc.
The fluxes of neutrinos from the decay of superheavy
long-lived Big-Bang relics (X) depend on the properties
of these particles. There are also the limits on the density
of these particles from the nucleosynthesis, distortion of
2.7K-radiation and e.-m.-cascade produced by the
decay products of X-particles. We argue that if
X-particles decay via exchange of superheavy GUT
gauge bosons but annihilate (X+X --+ any) due to
electroweak interaction, then the aforementioned limits
result in undetectable neutrino flux. The calculations will
be published elsewhere.
12. CONCLUSIONS
The high energy neutrino astronomy can be
distinctly divided to VHE and UHE neutrino astronomy
with the typical energy E>0.1-1 TeV and E>107GeV,
respectively. The "small" neutrino detectors with area
S<103m 2 are mainly telescopes for VHE nemrino
astronomy. Their horizon is limited by our Galaxy.
can detect the sources with proton luminosity Lp ~
104°-104~rg/s, i.e. those connected with SN explosion: or
young pulsar. However, the detection of weaker ~
possible, if they are located at small distances 2-3 k ~ or
emit a narrow neutrino beam in the directm of the observer.
The gigantic neutrino detectors with effective
S~0.1-1 kin2, such as "Baikal" or DUMAND, can
observe the large variety of the sources, namely, y ~
SN shells, binaries, hidden sources and the ~ t AGN,
mostly in UHE neutrinos. They can as well ~ e c t
UHE neutrino spectra produced by the quasars and
Seyfert galaxies with their evolution taken into acc~mt,
by pregalactic objects and by galaxies at bright ~ of their evolution.
High energy neutrino looks forward for t ~ gigantic detectors.
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