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Astrophysical sources of high energy neutrinos
Nuclear Physics B (Proc . Suppl .) 14A (1990) 17-27 North-Holland
17
ASTROPHYSICAL SOURCES OF HIGH ENERGY NEUTRINOS Todor STANEV Bartol Research Institute, University of Delaware, Newark, DE 19716, USA The observations of VHE and UHE -y-ray signals from compact astrophysical sources have suggested that cosmic rays are accelerated at these objects . Corresponding neutrino fluxes ought to be produced too. The paper discusses the neutrino production in astrophysical plasma and estimates the magnitude of the expected neutrino signals . Two types of possible compact sources : X-ray binary systems and young supernova remnants are discussed in specific models . A special attention is paid to the absorption of the -y-ray signals both at the sources and during the propagation in the interstellar medium .
tors of extraterrestrial neutrinos were still not feasible .
1 . INTRODUCTION Both neutrinos and -y-rays are copiously produced
The current experimental situation is quite different .
in inelastic proton interaction . Neutrino production is
The large underground detectors, originally built for
strongly enhanced in tenuous targets, which we expect
proton decay, have already$ studied the main back-
to find in astrophysical systems, where most secon-
ground - neutrinos produced by cosmic rays in the at-
daries decay rather than interact . In an approximate
mosphere . The first module of MACRO' is running at
and idealised picture, where incoming protons give
Gran Sasso, and the whole detector (along with LVD 4 )
their total energy to secondary pions, and all particles
will be operational soon.
The following generation
decay with no energy loss, neutrinos and photons(and
of detectors, typified by DUMANDS and GRANDE',
electrons) share equally the energy of the parent nu-
will certainly be able to start observing high-energy
cleon .
neutrino signals from astrophysical sources if our cur-
Thus at every site, where protons generate
-y-rays, a comparable neutrino flux will be created .
rent estimates are not dramatically wrong. This is the
Furthermore, -y-rays and electrons interact readily on
time to have a more detailed look at the possible neu-
matter, thermal and magnetic fields and quickly lose
trino sources from a different viewpoint - the analysis
energy. Neutrino cross-sections are smaller by many
of the forthcoming experimental results .
orders of magnitude and potential neutrino signals ar-
The neutrino detection technique employed by cur-
rive at Earth pretty much as produced . These gen-
rent and future experiments is detection of upward
eral considerations gave an early boost' to the idea
going muons, induced by
of neutrino astronomy in an era when realistic detec-
teractions in the Earth . For two basic reasons this
Ep
+
2/3 nch
L
charge current in-
technique is sensitive mostly to neutrinos with very high energy :
1/3 7r° --3, 2y
3/4 p
L
+
1/4
1/3 v,, + 1/3 v e + 1/3 e
Figure 1 : Sharing the energy of the primary proton between photons and neutrinos in a simple interaction/decay picture
0920-5632/90/$03 .50 © Elsevier Science Publishers B .V . (North-Holland)
a) . neutrino cross-section is proportional to the energy up to 1VIW and continues to increase logarithnically after that, and b) .
muon range also depends strongly on the muon
energy. As a result the energy spectrum of the neutrinos that produce observable upward going moons is flattened by almost two powers of Ev , which drastically
T. Stanev/Astrophysical sources of high energy neutrinos
18
decreases the rates but provides a very good angular resolution, because at high energies the angle between the muon direction and the trajectory of the parent neutrino is negligible. In this talk we shall concentrate on the astrophysical production ofneutrinos with energy >1 TeV, which carry directional information about the production site. Since our current knowledge on sources, where generationofsuch neutrinosignals is expected, is based on observations of TeV and PeV -y-ray fluxes, a large fraction of the talk is devoted to comparison of the expected -y-ray and neutrino fluxes and on necessary and possible corrections of the estimated proton luminosity at the source . All the advantages of neutrino astronomy, as defined in earlier papers (larger duty cycle for neutrino production, non absorption of the neutrino signal, possibility for observation of hidden sources) are at least qualitatively preserved. The effects that we discuss here are second order corrections, that are necessary for better estimates of the expected neutrino signals. 2. ESTIMATES OF THE SOURCE LUMINOSITY The cosmic ray luminosity, which is responsible for the production of signals at the source, can be estimated following the recipe, which A.M. Hillas8 used to calculate LOR of Cygnus X-3. LCtt = ~ X 1D1 X
X [11 X
47rR®
X PE
(1)
The first term fl/47r describes the solid angle in which cosmic rays are accelerated at the source, a parameter we are not likely to ever know. PE is the energy density of the detected signal, an experimental quantity. The geometrical factor 4xR® is usually derived from measurements of the source distance through the absorption of radiation in other frequency bands. The three terms in square brackets are of special interest to us, because they characterize the production of high energy signals at source and their absorption at source and during propagation . D is the duty cycle, i.e. the fraction of time during which cosmic rays at source produce signal_ visible from the Earth. A is the fraction of the signal that survives absorption, both at source and during propagation in the interstellar medium. e is the efficiency for production of the signal, i.e. the fraction of the cosmic ray luminosity LcR that is present in the generated signal. Using c=1/S, A=1/3, D=1/50, R,=12 kpc and the -y-ray flux measured by the Haverah Park 1° detector, Hillas estimated the proton luminosity of the good ole Cyg
X-3 + to LCR
= 4a
X
1 .7 x 10x9 ergs/s
(2)
In case of isotropic acceleration this luminosity is a factor of 10 higher than the Eddington luminosity for a standard 1.4 Me neutron star. The Eddington limit, however, applies to X-ray emission and there are ways" to circumvent it in the case of cosmic ray acceleration. Hillas may have also overestimated LCR of Cygnus X-3 by adopting too small value for the duty cycle, which is not supported by other experimental data. We shall nevertheless accept the value of 1039 x (R,/12 kpc)- Z ergs/s as a standard cosmic ray luminosity for an astrophysical source znd use it throughout this paper. This is, within the experimental uncertainties, the cosmic ray luminosity required to produce all reported UHE -y-ray signals" (Cygnus X3, Hercules X-1, Vela X1, LMC X-4) . An interesting feature of all confirmed sources is their flat energy spectrum - a E-z power law. Although -yp=2 is predicted to be the spectral index of shock acceleration at shocks with large compression ratios (>_4), it is not yet clear if flat spectra are inherent tt-, all powerful cosmic ray accelerators or our observations are limited by detector sensitivity to sources with flat spectra. Cosmic ray luminosity of 1039 erg/s is not in direct contradiction with the power balance of astrophysical systems. Both accretion and magnetic dipole radiation, the two main power sources, can provide that much energy. The maximum accretion luminosity is Lacer ^-' 10"" X (M/MO)
ergls
(3)
where 11~ is the accretion mass rate. Magnetic dipole radiation gives LMD = 4 X 1043P;; Bis
ergls,
(4)
where Pm, is the pulsar period in milliseconds and B12 is its surface magnetic field in units of 1011 Gauss. It is not trivial, however, to have a large fraction of this energy output in the form of high energy protons and nuclei . The extremely high efficiency of astrophysical particle accelerators is still a mistery and requires a lot of work .
"The good ole Cyg J%8 is a stable cosmic ray accelerator that yields PeV 7-rays at the rate reported by the Kiel9 and Haverah Park shower arrays .
T. Stanev/Astrophysical sources ofhigh energy neutrinos 3. PRODUCTION OF GAMMA-RAYS AND NEUTRINOS . It is easy to understand the relation between -yray and neutrino signal from a power spectrum -y-ray source. From the -y-ray spectrum dN Const x E,~a dE.1 =
(5)
one can reconstruct the primary w° and xoh spectrum and then use the relation between E l. and pion decay neutrino energy a E = (1- ~)E, mA
(6)
to obtain the spectrum of muon neutrinos from pion decay. a dN Const x (1- mz) 0-1 x E-0 dE,
(7)
which for a=2 gives v,, flux equal to 1/2 of the -yray flux. To obtain the total flux one has to add the contribution from muon decay to the muon neutrino flux. The exact numbers, however, depend on the amount of muon energy loss before decay, i.e. are sensitive to the target density, and on the amount of electromagnetic cascading that -y-rays suffer before leaving the target, i.e. on the total thickness of the target . These are easy to account for in a Monte Carlo simulation . Fig. 2 shows the fraction of the primary proton beam energy (E;2 spectrum) that is converted into -grays and v,, with energy >1 TeV in astrophysical slabs of different thickness and density. Neutrino efficiency grows with the slab thickness until all the proton beam energy is dissipated in the cascades . For column densities > 300 g/cm2 it stays constant. There is also a rather strong dependence on the slab density as at p=10'3 g/cm3 some charged pions still interact rather than decay, and muon lose significant energy before decay. In tenuous targets (p <10-1 ° g/cms) the density dependence becomes negligible. It is worth noting that such density corresponds to significant astrophysical number density of 6 x 1013 CM-3 . -y-ray efficiency has entirely different trends . Secondary interactions in denser targets increase the energy fraction transferred to photons . The maximum is achieved at column density of -100 g/cni2. Then electromagnetic cascading takes over and cy decreases to become negligible at column density comperable to the thicknes of Earths atmosphere. The trends on
19
Fig. 2 are enhanced by only counting the energy in partcles with energy above 1 TeV. If all energies were taken into account the turnover of the -y-ray efficiency would happen at -x300 g/cm2 and the overal normalization would have been higher . There are several conclusions to be drawn from this picture: 1. Simultaneous observation with good statistics of -gray and v,. signals from a hypothetical astrophysical source would reveal all characteristics of the production site - density and column density and one would be able to fully reconstruct the pourer and energy spectrum of the primary proton beam. This has been said before. . 2. There is a favourable target thickness for production of -y-ray signals which varies from 2 to 4 radiation lengths depending on the -y-ray energy and the density of the target. There is no such depth for v signals once the energy of the primary proton beam is dissipated in particle collisions . This is the basis for the qualitative statement that the duty cycle for neutrino production can be significantly larger than for -x-ray production. This also opens the possibility" for observation of cosmic ray acceleration sites that are enshrouded in matter so thick that all other signals are absorbed. Such "hidden" sources may include objects enshrouded by thick dust clouds in the Galactic Center region or very young supernova remnants hidden behind a thick shell. This has also been said before . 3. Fig . 2 also shows that one does not need tremen-
1s
aoo
column depthscm ( %° ')
°w
low
Figure 2: Fraction of the proton beam energy converted into neutrinos and ,y-rays of energy >1 TeV in astrophysical slabs as a function of the column depth . The density is: (a) 10' 1 a; (b) 10-1°; (c) 10'3; and (d) 10-6 g/cm3.
20
T. Stanev/Astrophysical sources of high energy neutrinos
dous concentration of matter to produce sizeable high energy 7-ray and neutrino signals. A good fraction of the full efficiency is achieved already at column depths of 25-50 g/cm2, which are typical for common astrophysical features, such as accretion disks. This is at least partially due to the rising proton inelastic crosssection, which may reach 120 - 180 mb at 109 GeV in the Lab. Even thin features, such as accretion disk coronae 14, may produce -10% of the maximum signal if the primary proton beam extends to ultra high energy. All this discussion shows that it is difficult, if not impossible, to generalize the relation between the effficiencies for .y-ray and v production at astrophysical sources. One could use results as the one shown on Fig . 2 to make rough estimates for different assumptions for the conditions at source. A more ambitious calculation will always require accounting for the geometry, matter distribution and dynamics of the source . Two examples of such calculations are discussed in the next section . 4. POSS LE NEUTRINO SOURCES . .1. X-ray binary systems . X-ray binaries are systems consisting of a compact object (neutron star or a black hole) and a more ordinary companion star. The dynamics of such systems, and especially of compact binaries, is very complicated and involves mass transfer from the companion onto the compact object . Neutron stars, on the other hand, are known to have very strong surface magnetic fields and to rotate very fast. Both the accretion and magnetic dipole radiation can be the onergy source. The existence of high magnetic fields and plasma flows should may magnetic irregularities, that are needed for particle acceleration. Finally the companion itself, the accretion flow or accretion disk, even the induced stellar wind, might be targets for inelastic proton interactions and production of secondaries . Fig . 3 gives several possible configurations of a close binary system . The first one (Fig. 3a) is a most natural scenario proposed by Vestrand and Eichlerls (and independently by Berezinsky") for explanation of the radiation of Cygnus X-3. Although for several reasons (which we shall discuss further down) it is not likely to be a valid model of this system, it provides an extremely useful illustration of the high energy signal production phenomena. Let us assume that the neutron star is a strong emitter of X-rays. Then the X-ray flux will be visible from the Earth while the neutron
neutron star
. . ' . . ._. . . . . > 0-0.75
n
b
0-0 .2 c
d
Figure 3: Possible configurations of targets for inelastic proton interactions . star is between the observer and the companion star. When the neutron star starts getting eclipsed by the companion the X-ray flux will be gradually absorbed and will become zero at full eclipse. This is the position of the X-ray phase zero. The shape of the X-ray light curve will be a broad sinusoidal curve, where the width of the emission peak reveals the orbit of the neutron star, which in the Cygnus X-3 case has to be only sligtly above the companion photosphere (the separation between the two stars is 1.05 stellar radii) .
T. Stanev/Astrophysical sources If one fits a Keplerian orbit to this configuration the orbital period of 4.8 hours yields a total mass of the system of ^_r4 Re . It is easy to calculate the neutrino production from this picture and a good ole Cyg X-3 luminosity. The calculation was performed independently with different methods 18,1r-18 and results agree within the uncertainties of the calculational techniques and the details of the assumptions . We shall briefly describe the approach of Ref. 17. Assuming a standard neutron star mass of 1.4 Me the the density profile of the companion star was taken to be that of a main sequence hydrogen star with M/Mo=2 .8, R/Ro=2, and a surface temperature of 10 000 K. The inner density distribution and the outher atmosphere of such a star are extensively modeled 11.2°, and a density profile can be compiled from the stelar evolution calculations . The density profile used in the calculation is given in Table I. Such a quiescent and symmetric picture is, of course, unrealistic, but useful, as it contains the range of densities and distances characteristic for more realistic models . A Monte Carlo cascade simulation was carried for protons hitting the companion at different inpact parameters and the muon neutrino yields collected as function of the proton beam energy and the impact parameter . The neutrino yields were folded with different primary spectra and inegrated to obtain the v,(-v,.) flux at production. At the next step of the calculation the absorption of the neutrinos in the companion star was estimated . Finally the flux at Earth was used with the charge current neutrino cross-section to calculate the resulting upward muon rate shown on Fig . 4 together with the X-ray light TABLE I. Assumed density profile of the companion star used to illustrate neutrino production in Cygnus X-3. Xt and h t are the total column density and length of a chord at inpact parameter r, and wt is the corresponding phase angle of the neutron star. r (106 km) 0 0 .721 1 .249 1 .355 1 .399 1 .420 1 .428 1 .434 1 .442
p (g/cm 3 ) 38 0.31 1 .3x 10 -4 Lox 10 -5 1 .1 x 10 -6 1 .3 x 10 -7 3 .1 x 10 -8 5 x 10 -9 . 0
h, (cm) 2 .884 x l 0l' 2 .498 x 10 11 .442X1011 1 9 .86x 10 1, 7 .46 x 10'0 5 .01 x 10i° 3 .52x 10 10 2 .51 x 10 10 0
X, (g/cm 2 ) .10x1()12 2 2 .16 x 10" .8X106 9 4 .8x 105 3 .34 x 104 2760 534 64 0
(degrees) 00 29.3 57 .9 66 .8 71 .7° 74 .5° 75 .6° 76 .6° 78"
of high
energy neutrinos
21
Phoso
Figure 4: Phase dependence of upward muons from Cygnus X-3 neutrinos : 108 GeV beam, solid curve; power law spectrum, dashed curve. The thin line shows the light curve in X-rays. curve . The beautiful butterfly shape reflects the density profile of the companion star. Highest flux corresponds to the impact parameter value where total proton beam energy is absorbed at the lowest density (wt = 76°). Neutrino fluxes that have to pass through the center of the companion star are heavily absorbed. The absorption effects are greater for the case of monoenergetic proton beam than for the power law case because of the harder spectrum of the secondaries from a 108 GeV monoenergetic proton beam. The total upward muon flux for a source distance of 10 kpc is 2-3 x 10 -15 cm-'s-', i.e. 0.5-1 upward muons per year per 1000 m2 for a fully efficient detector . An inspection of the density profile ofTable I shows that if the high energy .y-ray flux were calculated following the same procedure only two very narrow angular regions (wt > 75°) would have yielded any -y-ray flux. Thus the ratio of the 7-ray and neutrino duty cycles would have been of order 1/20. The symmetric picture comes, of course, from the assumption that the system is viewed from the plane of orbit. Any deviation from this viewing position would have distorted the symmetry, moved the position of the dip in the v light curve (making the ,-ray peaks assymetric), or for high viewing angles eliminate the v dip and produce a single -y-ray peak. It is obvious that even in a well defined simple model of a binary system the ratio of the duty cycles is not unique, and can vary by as much as a factor of 10. The rest of Fig . 3 shows three other possible configuration of the matter responsible for inelastic proton
99
T. Stanev/Astrophysical sources of high energy neutrinos
interactions . Figs. 36-* show two suggestions by A.M. Hillas where mass loss by the companion forms clouds due to gravitational forces. Models are adjusted to fit different UHE -y-ray light curves and the column density of the clouds is of order of 2-4 radiation lengths required to minimize the proton luminosity needed for production of these signals. The neutrino and -y-ray duty cycles would be the same in these configurations. Fig . 3a is a schematic drawing of the model originally suggested by White and Holt21 for the binary source X1822-371, very similar to Cygnus X-3 and applicable 22 to the latter . The matter accreting from the stellar companion onto the neutron star forms an accretion disk with bulges on the rim. X-ray and IR emission from the accretion disk corona are modulated by obscuration by the bulges and the companion. The model fits well the similar X-ray and IR light curves of Cygnus X-3 and provides sufficient targets 14 for VHE and UHE .y-rays and neutrino production. The accretion disk has a column density of 50-100 g/cm2 , bulges are comparable. The duty cycles for -y-ray and v production would be the same. The brief inspection of several different production models for high energy signals at X-ray binary signals does not give us convincing evidence for a big ratio of the v to -y-ray duty cycles. Although the general idea of D >D., appears to be true, there is only a limited number of models where the ratio could be large. An educated guess would put the ratio at 2 or 3 or, for convenience, x. 4.2. Young supernova remnants. All conditions that are inevitably present at young supernova remnants make them prime candidates for production of high energy neutrino signals. The stellar collapse produces either a fast rotating neutron star or a black hole, both of which could be powerful central engines, providing the energy for cosmic ray acceleration . The accretion scenario is also possible - the reverse shock in the supernova shell could drag back to the central region enough mass" to create luminosity up to 1040 erg/s. The main feature, however, is the supernova shell itself, the outer envelope of the collapsed star that is ejected by the blast shock and is a natural target for production of secondaries . A lot of knowledge on the supernova explosions was acquired in theoretical studies, which were proven correct with the explosion of the 'nearby' SN1987A . The experimental observations enriched our knowledge and allowed detailed models some of which might be essential for the high energy processes we are interested in.
An already classical treatment of cosmic ray interactions in young supernova :emnants was made by Berezinsky and Prilutsky". They define two characteristic times important for the production of -y-ray signals. r,, is the time when thickness of the supernova shell becomes less than one radiation length, and the produced -y-ray signals become visible to the observer . For an uniform shell expanding with velocity v T
=
(_'M )1/2 s 47rv3X,.ad
which for v=109 cm/s and Xrad=60 g/cm2 becomes 2.8x10 g (M/Mo) 1/2 s. The other important time is ra when the adiabatic energy losses start dominating over losses to nuclear collisions. Ta
(4
~covs ) 1/2 = 1 .3 x 10r( X
Me )1 2 s /
for v=109 cm/s. A third important time, r,, when the decay time of charged pions is much shorter than the nuclear collision time, can be defined in a similar way and is much shorter than r.,. The scenario is that all protons accelerated inside the supernova shell lose practcally all of their energy to nuclear collisions . At time r < r r (which is of course function of the pion Lorentz factor) pions reinteract and only soft v fluxes leave the shell. When r > rr charged pions start decaying and the v fluxes follow the primary proton flux up to 1/10 of the maximum proton energy Epaz . At r,, the shell becomes transparent for -y-rays . The production of both the .y-ray and neutrino signals happens as outlined in Section 3 in the case when all particles decay, because density of 10 -12 g/cO is achieved several days after the explosion for envelopes of 10-20 Me. After ra only a fraction of the accelerated protons interact to produce -y-rays and v's and the power in proton induced secondaries begins to decrease quadratically with time. The detailed features of the emission can be obtained in this frame when the uniformly expanding shell is replaced with a specific realistic model with imbedded proton acceleration mechanism. Gaisser, Harding and Stanev made26 such an attempt for SN 1987A, using a wind shock acceleration in the IOHM shell of Pinto and Woosley 26. In this model cosmic rays are accelerated by first order Fermi mechanism in the pulsar wind shock . The pulsar wind is relativistic MHD electron-positron wind driven by the pulsar when the plasma frequency wp is greater than the pulsar angular frequency A. The wind luminosity can be approximated by the total
T. Stanev/Astrophysical sources of :jigh energy neutrinos pulsar luminosity of Eq.(4) . The pulsar wind shock forms at a radius R, where the wind ram pressure is balanced by the accumulated energy density of the shocked wind. Numerically R, is R.
/Umi ^-' scnumtnt
3.5 x 1013cm ty,uSoo
(10)
where ty, is the age ofthe supernova in years and umin in units of 500 km/s is the velocity of the inner edge of the supernova shell. The shock is contained in the central cavity of the remnant, where matter density is very low . The shock position determines the pulsar generated magnetic field strength at the shock B, and one could use it to estimate the maximum energy of the accelerated protons El","' - F(r) e B,R
(11)
where F(r) is a function" ofthe shock compression ratio and the characteristic energy e BR, = 105TeV B12 p,02 depends on the surface magnetic field of the pulsar wad on its period (in units of 10 ms) . Cosmic rays can be accelerated to ultra-high energies with this mechanism. The highest energy particles will diffuse away from the acceleration site, while the bulk of the protons will be confined inside the contact discontinuity for a time comperable with the supernova age . The model requires a mixing of the accelerated proton beam with the shell material for inelasic interactions and production of -y-ray and neutrino signals . The most likely mixi:.,,, mechanism is the growth of Rayleigh-Taylor instability at the wind-shell interface . The account for a realistic shell model significantly modifies the values of the characteristic times derived by Berezinsky and Prilutsky. Instead of using an uniformly expanding shell with v=109 cm/s, one has to numerically integrate through a shell, where density and velocity are in reverse proportion. For a shell with total ejected mass M 150 23 r., becomes -1 year and ^_r
Ta
Xrad 112
1
C_- 10 (12) 71 where AN is the nucleon interaction length and Q=v/c is the effective velocity of the expanding shell. Combined with the containment of the accelerated cosmic rays inside the ejecta this yields a constant v flux for the first several years of the supernova. The value of the neutrino induced upward muon signal is the same muon per 100 m2 detector per week is in Ref. 28, x Lok/(1043 erg/s) for a supernova at 50 kpc . Unfortunatelly the upper limit of the pulsar luminosity AN
^_rl
#1/2
23
of SN1987A is fewx 1038 erg/s and only a fraction of this is expected to appear in the form of accelerated cosmic rays. The low pulsar luminosity of SN1987A seems to preclude the possibility for observation ofneutrino signal from this source . The theoretical work inspired by the recent supernova, however, established new, more details limits of the production of high energy -y-ray and v signals. The containment hypothesis, described above, is e.g. another valuable extreme that brackets the expected signal duration from yound supernova remnants . The other extreme hypothesis is the straightforward propagation of the accelerated cosmic rays through the nebula as in the models of Sato29. These calculations also give us hints for the relative strength of v and -y-ray signals from sources that are fully enshrouded in matter, which is not (or is only partially) transparent toy-rays . 5. GAMMA-RAY ABSORPTION. An important factor for establishing the ratio of v to y-ray signal is the absorption of the -y-ray signals in interactions with thermal fields. The process is y7 -i- e+e - and the threshold is EE.v > 1 .3 x 1011/(1 - cos9)eV2,
(13)
where 0 is the angle between the directions of the two photons. To obtain the absorption length one has to integrate over the photon spectrum f(E) and over all direction. For blackbody radiation the maximum absortions° then occurs at E., - 5 x 1015 eV/(T, K) and the corresponding absorption length is X., - 6.8 x 1012T-3Ro. Both the absorption at source and in the interstellar medium will then 'lie important, although in different E, ranges. 5.1. Absorption at source. There are models for -1-ray production at sources where no matter is required for inelastic proton interactions . A suggestion" has been made that high energy -y-rays are produced in photoproduction interactions of the accelerated protons on the X-ray radiation at source . Indeed for isotropic X-ray emission with temperature of 2 KeV the photoproduction threshold is 10 TeV and the X-ray luminosity of Cygnus X-3 might provide several APhoe for protons above 10 TeV . It is, however, important that the protons are accelerated outside the X-ray emission site. Otherwise the protons and the X-rays might move in parallel directions and will never reach the CM photoproduction threshold . We can turn the argument around and ask what
T. StanevlAstrophysical sources of high energy neutrinos
24
10'4
V
- -.
6
--
V
f
1 1
1 1
t 107®K 0
Ô
O I.o (h
Id 1%
6X107 'K "-N. %% 101® 107
1017 ENERGY (OV)
Figure 5: 7-ray absorption length in thermal bremsstrahlung radiation of the accretion disk corona of temperature 107 and 6x10 7 K. fraction of a -y-ray flux will survive if the -y-ray production site does not coincide with the X-ray emission site. In the binary system model of Fig . 3" the X-ray emission happens in the accretion disk corona. The corona temperature derived from the emission measure is between 107 and 6x10 K . Fig . 5 shows the absorption length of -y-rays with energy E., in such fields". The maximum ofthe absorption is in the TeV range and for an accretion disk corona of 0.7Ro the survival probability might be as small as e-1°=5x 10-5 for certain directions of TeV -y-rays . This is gust an example of possible -y-ray absorption . All binary systems that are candidates for acceleration sites of cosmic rays and correspondingly for sources of high energy -y-ray and v signals are strong X-ray emitters. The intense radiation may heat not only the accretion disks and create a hot corona, but also increase significantly the temperature of the 'hot' face of the companion star. Hot faces has been seen in astronomical observations . They might be the main reason for the modulation of the -y-ray emission, and if this is the case, we may gain large factors in neutrino fluxes, which are not affected by the thermal fields at the source .
Figure 6: Ratio of v to PeV -y-ray signal as a function of the source distance . 5.1. Absorption in the interstellar space. While the absorption at source depends strongly on the temperatures and the dynamics at the source, the absorption on the 3 K background is universal - it depends only on the source distance . It has been discussed previously 32 and has to be accounted for when -y-ray and v signals are compared. Fig . 6 shows the correction factor for deriving the neutrino flux from the UHE -y-ray flux above certain threshold . The distances to several popular sources are indicated with arrows . Because the maximum absorption in the blackbody background is at E., =2 x 1015 eV the flux ratio is the biggest for E7 >10" eV. It is a factor of 5 for the 12 kpc distance to Cygnus X-3, and more than 100 for the 50 kpc to the Large Magelanic Clouds . This is what G. Cocconi 33 pointed out immediately after LMC X-4 was reported as a PeV 7-ray source. The absorption of PeV 7-rays from extragalactic sources will be many orders of magnitude and any confirmation of such a source will certainly indicate an extremely strong neutrino signal . 6. HOW DIFFICULT IS IT? We have derived the neutrino induced flux of upward muons for our standard source the good ole Cyg X-5 to be 1 in 1000 m2 detector per year. Is the detection of such fluxes realistic? What are the back-
T. Stanev/Astrophysical sources of high energy neutrinos grounds? The main background are of course the upward muons generated by cosmic rays in the atmosphere . Fig . 7 compares"' the atmospheric v flux with the calculated for Cygnus X-3. The dotted line shows the atmospheric flux within 1° from the source. At low energy the two lines are not distinguishable as the angle between the muon and the parent neutrino is too big . It is at energy around a TeV where this angle becomes smaller than the multiple scattering angle of the muon and helps the resolution of the source signal. While the total atmospheric flux is still (bigger than the signal from Cygnus even at 105 GeV the cross-over with the the flux in 1° cone is at about a TeV. The effect is further amplified by the detection technique. The magnitude ofthe neutrino induced signal" is Sp(> 10 E ) -dE dEV P(E , E,J, JE,.
E
v (crti2 .s 10-4 10 6 10 8 10~~ 10 2 1014 d6
(14)
where P(E , E.) is the probability that a neutrino directed at the detector will produce a muon with energy above E,, at the detector. P(E , E.) is a steep function of the neutrino energy and grows like E,2, for energies below MW/2 and continues to increase as E,-8 at higher energy. Thus the relative importance of the highest end of the neutrino energy spectrum is very large. Furthermore, the magnitude of the signal, being dominated by the very high energy neutrinos, does not depend strongly on the minimum muon energy. This fact has important consequences for detector design, which has been discussed in detail by Stenger36 . Finally the exact form of the neutrino cross-section at ultra high energy is not important for the magnitude of the signal. Gaisser and Grillo37 have studied the P(E,,, E.) dependence on the form of the structure functions . Their conclusion is that although it is important to use forms including QCD evolution, the exact form of the structure function does not appreciably change the result. The detection of UHE -r-ray signals from point sources has indicated that cosmic rays are accelerated at compact astrophysical systems . Although we cannot think of any other way for generating PeV ,y-rays, only the observation of point neutrino sources will be a proof for this phenomenon . This is, however, a formidable experimental task. Fig . 8 compares the magnitude of different already detected v sources with the expected for Cygnus X-3 . The lines show the energy spectrum of the neutrinos, that contribute to the signal. The rates are given in parantheses . The v, from SN1987A
25
1
10-2
10 0
2
4
Ey (GeV )
Figure 7: Neutrino flux from Cygnus X-3 compared with the neutrino flux of atmospheric origin. The dashed line shows the background within 1° of the source.
w b
-~
Contained v's (kt.yr) -1 (0 .2-0 .3 per day)
z b
w
Figure 8: Comparison of the neutrino fluxes contributing to different observed neutrino signals with the expected signal from Cygnus X-3.
26
T. Stanev/Astrophysical sources of high energy neutrinos
produced 18 events in IMB and Kamiokande for 10 seconds, roughly 1 event is seen every day in contained Vs and in upward going muons. To observe high energy neutrino signal from a point source we have to able to observe fluxes of 1 event per year with the same area. We need large detectors to do it. We need GRANDE and DUMAND to be able to see different regions of the Galaxy and to study it in the highest energy band of the astronomy. In conclusion, it is not possible to give a recipe for calculating the ratio of the expected .y-ray and v signals from different poin sources. Neutrino astronomy has to be an experimantal science. The comparison of a neutrino signal with the -y-ray signal from a given source will give us the instrument to study type of the source and the conditions at it. Different VHE and UHE ,y-ray sources are certainly not the same. Every source has its unique configuration and dynamics . We already know that from the comparison ofthe high energy -y-ray signals to the X-ray signals and periodicities in the X-ray and GeV -y-ray bands. Already the first detection of neutrino signal from a cosmic accelerator will give us invaluable clues on the dynamics of such sources and the acceleration of PeV cosmic rays. ACKNOWLEDGEMENTS The author grafully acknowledges the contributions of T.K. Gaisser, R.J. Protheroe and F. Halzen to this paper, which is based on the research performed with them and many other collegues. My research is supported in part by the U.S. National Science Founda tion. REFERENCES 1. M.A. Markov, in: Proceedings of the 1960 Interna tional Conference on High Energy Physics (Rochester, 1960), p. 578 2. T.J. Haines et al. (IMB Collaboration), Phys . Rev . Letters 57 (1986) 1986; K.S. Hirata et al. (Kamiokande), Phys. Letters 205 (1988) 416. 3. M. Calicchio et al. (MACRO Collaboration), Nucl. Istr. Meth. A264 (1988) 18. 4. C. Bari et al. (LVD Collaboration), Nucl. Instr. Meth. A264 (1988) 5. 5. For the most recent design see V.J. Stenger, this volume. 6. H. Sobel (GRANDE Collaboration) this volume . 7 . T.K. Gaisser and T. Stanev, Phys. Rev .D30 (1984) 985 . 8. A.M. Hillas, Nature 312 (1984) 50.; A .M. Hillas,
in: Proceedings of the 19th International Cosmic Ray Conference, vol . 9, eds. F.C. Jones, J. Adams and G.M. Mason (NASA Conference Publication 2376, Washington D.C. 1985) p. 409. 9. M. Samorski and W. Stamm, Ap. J. Letters 268 (1983) L17 . 10. J. Lloyds-Evans et al., Nature 305 (1983) 784. 11. K. Brecher and G. Chanmugam, in: Proceedings of the 19th International Cosmic Ray Conference, vol . 1, eds. F.C. Jones, J. Adams and G.M. Mason (NASA Conference Publication 2376, Washington D.C. 1985) p. 103 . 12. D.E. Nagel, T.K. Gaisser and R.J. Protheroe, Ann. Rev . Nucl. Part. Sci 38 (1988) 609 . 13. V.S. Berezinsky, C. Castagnoli and P. Galeoti, Il Nouvo Cim. 8C (1985) 185; see also M.M. Shapiro and R. Silberberg, in: Relativity, Quanta and Cosmology (vo1.2, ed. Pantaleo and DeFinis, Johnson Corp., Harcourt, Brace and Jovanovich, New York, 1979) 745 . 14. R.J. Protheroe and T. Stanev, Nature 328 (1987) 136. 15. W.T. Vestrand and D. Eichler, Ap.J. 261 (1982) 251 . 16. V.S. Berezinsky, in: Proceedings 1979 DUMAND Summer Conference (University of Hawaii, ed. J.G . Learned, 1979) p. 235 . 17. T.K. Gaisser and T. Stanev, Phys. Rev. Letters 54 (1985) 2265. 18. E.W. Kolb, M.S. Turner and T.P. Walker, Phys. Rev. D32 (1985) 1145. 19. D.D. Clayton, Principles of Stellar Evolution and Nucleosynthesis (McGraw Hill, New York, 1968) . 20. R. Kurucz, D.F. Carbon and D. Gingerich, in: Theory and Observation of Normal Stellar Atmospheres (ed . by D. Gingerich, MIT Press, Cambridge, Mass., 1969) . 21. N.E. White and S.S. Holt, Ap. J. 257 (1982) 253 . 22. K.O. Mason, F.A. Cordoba and N.E. White, Ap. J. 309 (1986) 700 . 23. S .E. Woosley, in: Supernova 1987A in the Large Magelanic Clouds (eds. K . Kafatos and A. Michalistianos, Cambridge, 1988) p. 289. 24. V.S. Berezinsky and O.F . Prilutsky, Astr. Astrophys. 66 (1978) 325 . 25 . T.K. Gaisser, A.K. Harding and T. Stanev, Nature 332 (1988) 1695; T.K. Gaisser, A.K. Harding and T. Stanev, Ap. J. in print . 26. P.A. Pinto and S.E. Woosley, Nature 333 (1988) 534. 27. P.O. Lagage and C.J. Cesarsky, Astr. Astrophys .
T. Stanev/Astrophysical sources of high energy neutrinos
125 (1983) 249 . 28. T.K. Gaisser and T. Stanev, Phys. Rev . Letters 58 (1987) 1695. 29. H. Sato, Progr . Theor. Phys. 58 (1977) 549; Y. Yamada et al., Progr.Theor .Phys. 79 (1987) 426. 30. R.J. Protheroe and T. Stanev, Ap. J. 322 (1987) 838. 31 . R.J. Gould and G.P. Schreder, Phys. Rev 155 (1967) 1404. 32. R.J. Protheroe, M.N.R.A.S. 221 (1986) 769. 33. G. Cocconi, CERN Preprint PRE 85-021.
27
34 . T.K. Gaisser and T. Stanev, in: Proceedings of the 19th International Cosmic Ray Conference, vol. 8, eds. F.C. Jones, J. Adams and G.M. Mason (NASA Conference Publication 2376, Washington D.C. 1985) p. 156 . 35. T.K. Gaisser and T. Stanev, Phys. Rev. D31 (1985) 2770. 36. V.J. Stenger, Ap. J. 284 (1984) 810 . 37. T.K. Gaisser and A.F. Grillo, Phys. Rev. 36 (1987) 2752.
17
ASTROPHYSICAL SOURCES OF HIGH ENERGY NEUTRINOS Todor STANEV Bartol Research Institute, University of Delaware, Newark, DE 19716, USA The observations of VHE and UHE -y-ray signals from compact astrophysical sources have suggested that cosmic rays are accelerated at these objects . Corresponding neutrino fluxes ought to be produced too. The paper discusses the neutrino production in astrophysical plasma and estimates the magnitude of the expected neutrino signals . Two types of possible compact sources : X-ray binary systems and young supernova remnants are discussed in specific models . A special attention is paid to the absorption of the -y-ray signals both at the sources and during the propagation in the interstellar medium .
tors of extraterrestrial neutrinos were still not feasible .
1 . INTRODUCTION Both neutrinos and -y-rays are copiously produced
The current experimental situation is quite different .
in inelastic proton interaction . Neutrino production is
The large underground detectors, originally built for
strongly enhanced in tenuous targets, which we expect
proton decay, have already$ studied the main back-
to find in astrophysical systems, where most secon-
ground - neutrinos produced by cosmic rays in the at-
daries decay rather than interact . In an approximate
mosphere . The first module of MACRO' is running at
and idealised picture, where incoming protons give
Gran Sasso, and the whole detector (along with LVD 4 )
their total energy to secondary pions, and all particles
will be operational soon.
The following generation
decay with no energy loss, neutrinos and photons(and
of detectors, typified by DUMANDS and GRANDE',
electrons) share equally the energy of the parent nu-
will certainly be able to start observing high-energy
cleon .
neutrino signals from astrophysical sources if our cur-
Thus at every site, where protons generate
-y-rays, a comparable neutrino flux will be created .
rent estimates are not dramatically wrong. This is the
Furthermore, -y-rays and electrons interact readily on
time to have a more detailed look at the possible neu-
matter, thermal and magnetic fields and quickly lose
trino sources from a different viewpoint - the analysis
energy. Neutrino cross-sections are smaller by many
of the forthcoming experimental results .
orders of magnitude and potential neutrino signals ar-
The neutrino detection technique employed by cur-
rive at Earth pretty much as produced . These gen-
rent and future experiments is detection of upward
eral considerations gave an early boost' to the idea
going muons, induced by
of neutrino astronomy in an era when realistic detec-
teractions in the Earth . For two basic reasons this
Ep
+
2/3 nch
L
charge current in-
technique is sensitive mostly to neutrinos with very high energy :
1/3 7r° --3, 2y
3/4 p
L
+
1/4
1/3 v,, + 1/3 v e + 1/3 e
Figure 1 : Sharing the energy of the primary proton between photons and neutrinos in a simple interaction/decay picture
0920-5632/90/$03 .50 © Elsevier Science Publishers B .V . (North-Holland)
a) . neutrino cross-section is proportional to the energy up to 1VIW and continues to increase logarithnically after that, and b) .
muon range also depends strongly on the muon
energy. As a result the energy spectrum of the neutrinos that produce observable upward going moons is flattened by almost two powers of Ev , which drastically
T. Stanev/Astrophysical sources of high energy neutrinos
18
decreases the rates but provides a very good angular resolution, because at high energies the angle between the muon direction and the trajectory of the parent neutrino is negligible. In this talk we shall concentrate on the astrophysical production ofneutrinos with energy >1 TeV, which carry directional information about the production site. Since our current knowledge on sources, where generationofsuch neutrinosignals is expected, is based on observations of TeV and PeV -y-ray fluxes, a large fraction of the talk is devoted to comparison of the expected -y-ray and neutrino fluxes and on necessary and possible corrections of the estimated proton luminosity at the source . All the advantages of neutrino astronomy, as defined in earlier papers (larger duty cycle for neutrino production, non absorption of the neutrino signal, possibility for observation of hidden sources) are at least qualitatively preserved. The effects that we discuss here are second order corrections, that are necessary for better estimates of the expected neutrino signals. 2. ESTIMATES OF THE SOURCE LUMINOSITY The cosmic ray luminosity, which is responsible for the production of signals at the source, can be estimated following the recipe, which A.M. Hillas8 used to calculate LOR of Cygnus X-3. LCtt = ~ X 1D1 X
X [11 X
47rR®
X PE
(1)
The first term fl/47r describes the solid angle in which cosmic rays are accelerated at the source, a parameter we are not likely to ever know. PE is the energy density of the detected signal, an experimental quantity. The geometrical factor 4xR® is usually derived from measurements of the source distance through the absorption of radiation in other frequency bands. The three terms in square brackets are of special interest to us, because they characterize the production of high energy signals at source and their absorption at source and during propagation . D is the duty cycle, i.e. the fraction of time during which cosmic rays at source produce signal_ visible from the Earth. A is the fraction of the signal that survives absorption, both at source and during propagation in the interstellar medium. e is the efficiency for production of the signal, i.e. the fraction of the cosmic ray luminosity LcR that is present in the generated signal. Using c=1/S, A=1/3, D=1/50, R,=12 kpc and the -y-ray flux measured by the Haverah Park 1° detector, Hillas estimated the proton luminosity of the good ole Cyg
X-3 + to LCR
= 4a
X
1 .7 x 10x9 ergs/s
(2)
In case of isotropic acceleration this luminosity is a factor of 10 higher than the Eddington luminosity for a standard 1.4 Me neutron star. The Eddington limit, however, applies to X-ray emission and there are ways" to circumvent it in the case of cosmic ray acceleration. Hillas may have also overestimated LCR of Cygnus X-3 by adopting too small value for the duty cycle, which is not supported by other experimental data. We shall nevertheless accept the value of 1039 x (R,/12 kpc)- Z ergs/s as a standard cosmic ray luminosity for an astrophysical source znd use it throughout this paper. This is, within the experimental uncertainties, the cosmic ray luminosity required to produce all reported UHE -y-ray signals" (Cygnus X3, Hercules X-1, Vela X1, LMC X-4) . An interesting feature of all confirmed sources is their flat energy spectrum - a E-z power law. Although -yp=2 is predicted to be the spectral index of shock acceleration at shocks with large compression ratios (>_4), it is not yet clear if flat spectra are inherent tt-, all powerful cosmic ray accelerators or our observations are limited by detector sensitivity to sources with flat spectra. Cosmic ray luminosity of 1039 erg/s is not in direct contradiction with the power balance of astrophysical systems. Both accretion and magnetic dipole radiation, the two main power sources, can provide that much energy. The maximum accretion luminosity is Lacer ^-' 10"" X (M/MO)
ergls
(3)
where 11~ is the accretion mass rate. Magnetic dipole radiation gives LMD = 4 X 1043P;; Bis
ergls,
(4)
where Pm, is the pulsar period in milliseconds and B12 is its surface magnetic field in units of 1011 Gauss. It is not trivial, however, to have a large fraction of this energy output in the form of high energy protons and nuclei . The extremely high efficiency of astrophysical particle accelerators is still a mistery and requires a lot of work .
"The good ole Cyg J%8 is a stable cosmic ray accelerator that yields PeV 7-rays at the rate reported by the Kiel9 and Haverah Park shower arrays .
T. Stanev/Astrophysical sources ofhigh energy neutrinos 3. PRODUCTION OF GAMMA-RAYS AND NEUTRINOS . It is easy to understand the relation between -yray and neutrino signal from a power spectrum -y-ray source. From the -y-ray spectrum dN Const x E,~a dE.1 =
(5)
one can reconstruct the primary w° and xoh spectrum and then use the relation between E l. and pion decay neutrino energy a E = (1- ~)E, mA
(6)
to obtain the spectrum of muon neutrinos from pion decay. a dN Const x (1- mz) 0-1 x E-0 dE,
(7)
which for a=2 gives v,, flux equal to 1/2 of the -yray flux. To obtain the total flux one has to add the contribution from muon decay to the muon neutrino flux. The exact numbers, however, depend on the amount of muon energy loss before decay, i.e. are sensitive to the target density, and on the amount of electromagnetic cascading that -y-rays suffer before leaving the target, i.e. on the total thickness of the target . These are easy to account for in a Monte Carlo simulation . Fig. 2 shows the fraction of the primary proton beam energy (E;2 spectrum) that is converted into -grays and v,, with energy >1 TeV in astrophysical slabs of different thickness and density. Neutrino efficiency grows with the slab thickness until all the proton beam energy is dissipated in the cascades . For column densities > 300 g/cm2 it stays constant. There is also a rather strong dependence on the slab density as at p=10'3 g/cm3 some charged pions still interact rather than decay, and muon lose significant energy before decay. In tenuous targets (p <10-1 ° g/cms) the density dependence becomes negligible. It is worth noting that such density corresponds to significant astrophysical number density of 6 x 1013 CM-3 . -y-ray efficiency has entirely different trends . Secondary interactions in denser targets increase the energy fraction transferred to photons . The maximum is achieved at column density of -100 g/cni2. Then electromagnetic cascading takes over and cy decreases to become negligible at column density comperable to the thicknes of Earths atmosphere. The trends on
19
Fig. 2 are enhanced by only counting the energy in partcles with energy above 1 TeV. If all energies were taken into account the turnover of the -y-ray efficiency would happen at -x300 g/cm2 and the overal normalization would have been higher . There are several conclusions to be drawn from this picture: 1. Simultaneous observation with good statistics of -gray and v,. signals from a hypothetical astrophysical source would reveal all characteristics of the production site - density and column density and one would be able to fully reconstruct the pourer and energy spectrum of the primary proton beam. This has been said before. . 2. There is a favourable target thickness for production of -y-ray signals which varies from 2 to 4 radiation lengths depending on the -y-ray energy and the density of the target. There is no such depth for v signals once the energy of the primary proton beam is dissipated in particle collisions . This is the basis for the qualitative statement that the duty cycle for neutrino production can be significantly larger than for -x-ray production. This also opens the possibility" for observation of cosmic ray acceleration sites that are enshrouded in matter so thick that all other signals are absorbed. Such "hidden" sources may include objects enshrouded by thick dust clouds in the Galactic Center region or very young supernova remnants hidden behind a thick shell. This has also been said before . 3. Fig . 2 also shows that one does not need tremen-
1s
aoo
column depthscm ( %° ')
°w
low
Figure 2: Fraction of the proton beam energy converted into neutrinos and ,y-rays of energy >1 TeV in astrophysical slabs as a function of the column depth . The density is: (a) 10' 1 a; (b) 10-1°; (c) 10'3; and (d) 10-6 g/cm3.
20
T. Stanev/Astrophysical sources of high energy neutrinos
dous concentration of matter to produce sizeable high energy 7-ray and neutrino signals. A good fraction of the full efficiency is achieved already at column depths of 25-50 g/cm2, which are typical for common astrophysical features, such as accretion disks. This is at least partially due to the rising proton inelastic crosssection, which may reach 120 - 180 mb at 109 GeV in the Lab. Even thin features, such as accretion disk coronae 14, may produce -10% of the maximum signal if the primary proton beam extends to ultra high energy. All this discussion shows that it is difficult, if not impossible, to generalize the relation between the effficiencies for .y-ray and v production at astrophysical sources. One could use results as the one shown on Fig . 2 to make rough estimates for different assumptions for the conditions at source. A more ambitious calculation will always require accounting for the geometry, matter distribution and dynamics of the source . Two examples of such calculations are discussed in the next section . 4. POSS LE NEUTRINO SOURCES . .1. X-ray binary systems . X-ray binaries are systems consisting of a compact object (neutron star or a black hole) and a more ordinary companion star. The dynamics of such systems, and especially of compact binaries, is very complicated and involves mass transfer from the companion onto the compact object . Neutron stars, on the other hand, are known to have very strong surface magnetic fields and to rotate very fast. Both the accretion and magnetic dipole radiation can be the onergy source. The existence of high magnetic fields and plasma flows should may magnetic irregularities, that are needed for particle acceleration. Finally the companion itself, the accretion flow or accretion disk, even the induced stellar wind, might be targets for inelastic proton interactions and production of secondaries . Fig . 3 gives several possible configurations of a close binary system . The first one (Fig. 3a) is a most natural scenario proposed by Vestrand and Eichlerls (and independently by Berezinsky") for explanation of the radiation of Cygnus X-3. Although for several reasons (which we shall discuss further down) it is not likely to be a valid model of this system, it provides an extremely useful illustration of the high energy signal production phenomena. Let us assume that the neutron star is a strong emitter of X-rays. Then the X-ray flux will be visible from the Earth while the neutron
neutron star
. . ' . . ._. . . . . > 0-0.75
n
b
0-0 .2 c
d
Figure 3: Possible configurations of targets for inelastic proton interactions . star is between the observer and the companion star. When the neutron star starts getting eclipsed by the companion the X-ray flux will be gradually absorbed and will become zero at full eclipse. This is the position of the X-ray phase zero. The shape of the X-ray light curve will be a broad sinusoidal curve, where the width of the emission peak reveals the orbit of the neutron star, which in the Cygnus X-3 case has to be only sligtly above the companion photosphere (the separation between the two stars is 1.05 stellar radii) .
T. Stanev/Astrophysical sources If one fits a Keplerian orbit to this configuration the orbital period of 4.8 hours yields a total mass of the system of ^_r4 Re . It is easy to calculate the neutrino production from this picture and a good ole Cyg X-3 luminosity. The calculation was performed independently with different methods 18,1r-18 and results agree within the uncertainties of the calculational techniques and the details of the assumptions . We shall briefly describe the approach of Ref. 17. Assuming a standard neutron star mass of 1.4 Me the the density profile of the companion star was taken to be that of a main sequence hydrogen star with M/Mo=2 .8, R/Ro=2, and a surface temperature of 10 000 K. The inner density distribution and the outher atmosphere of such a star are extensively modeled 11.2°, and a density profile can be compiled from the stelar evolution calculations . The density profile used in the calculation is given in Table I. Such a quiescent and symmetric picture is, of course, unrealistic, but useful, as it contains the range of densities and distances characteristic for more realistic models . A Monte Carlo cascade simulation was carried for protons hitting the companion at different inpact parameters and the muon neutrino yields collected as function of the proton beam energy and the impact parameter . The neutrino yields were folded with different primary spectra and inegrated to obtain the v,(-v,.) flux at production. At the next step of the calculation the absorption of the neutrinos in the companion star was estimated . Finally the flux at Earth was used with the charge current neutrino cross-section to calculate the resulting upward muon rate shown on Fig . 4 together with the X-ray light TABLE I. Assumed density profile of the companion star used to illustrate neutrino production in Cygnus X-3. Xt and h t are the total column density and length of a chord at inpact parameter r, and wt is the corresponding phase angle of the neutron star. r (106 km) 0 0 .721 1 .249 1 .355 1 .399 1 .420 1 .428 1 .434 1 .442
p (g/cm 3 ) 38 0.31 1 .3x 10 -4 Lox 10 -5 1 .1 x 10 -6 1 .3 x 10 -7 3 .1 x 10 -8 5 x 10 -9 . 0
h, (cm) 2 .884 x l 0l' 2 .498 x 10 11 .442X1011 1 9 .86x 10 1, 7 .46 x 10'0 5 .01 x 10i° 3 .52x 10 10 2 .51 x 10 10 0
X, (g/cm 2 ) .10x1()12 2 2 .16 x 10" .8X106 9 4 .8x 105 3 .34 x 104 2760 534 64 0
(degrees) 00 29.3 57 .9 66 .8 71 .7° 74 .5° 75 .6° 76 .6° 78"
of high
energy neutrinos
21
Phoso
Figure 4: Phase dependence of upward muons from Cygnus X-3 neutrinos : 108 GeV beam, solid curve; power law spectrum, dashed curve. The thin line shows the light curve in X-rays. curve . The beautiful butterfly shape reflects the density profile of the companion star. Highest flux corresponds to the impact parameter value where total proton beam energy is absorbed at the lowest density (wt = 76°). Neutrino fluxes that have to pass through the center of the companion star are heavily absorbed. The absorption effects are greater for the case of monoenergetic proton beam than for the power law case because of the harder spectrum of the secondaries from a 108 GeV monoenergetic proton beam. The total upward muon flux for a source distance of 10 kpc is 2-3 x 10 -15 cm-'s-', i.e. 0.5-1 upward muons per year per 1000 m2 for a fully efficient detector . An inspection of the density profile ofTable I shows that if the high energy .y-ray flux were calculated following the same procedure only two very narrow angular regions (wt > 75°) would have yielded any -y-ray flux. Thus the ratio of the 7-ray and neutrino duty cycles would have been of order 1/20. The symmetric picture comes, of course, from the assumption that the system is viewed from the plane of orbit. Any deviation from this viewing position would have distorted the symmetry, moved the position of the dip in the v light curve (making the ,-ray peaks assymetric), or for high viewing angles eliminate the v dip and produce a single -y-ray peak. It is obvious that even in a well defined simple model of a binary system the ratio of the duty cycles is not unique, and can vary by as much as a factor of 10. The rest of Fig . 3 shows three other possible configuration of the matter responsible for inelastic proton
99
T. Stanev/Astrophysical sources of high energy neutrinos
interactions . Figs. 36-* show two suggestions by A.M. Hillas where mass loss by the companion forms clouds due to gravitational forces. Models are adjusted to fit different UHE -y-ray light curves and the column density of the clouds is of order of 2-4 radiation lengths required to minimize the proton luminosity needed for production of these signals. The neutrino and -y-ray duty cycles would be the same in these configurations. Fig . 3a is a schematic drawing of the model originally suggested by White and Holt21 for the binary source X1822-371, very similar to Cygnus X-3 and applicable 22 to the latter . The matter accreting from the stellar companion onto the neutron star forms an accretion disk with bulges on the rim. X-ray and IR emission from the accretion disk corona are modulated by obscuration by the bulges and the companion. The model fits well the similar X-ray and IR light curves of Cygnus X-3 and provides sufficient targets 14 for VHE and UHE .y-rays and neutrino production. The accretion disk has a column density of 50-100 g/cm2 , bulges are comparable. The duty cycles for -y-ray and v production would be the same. The brief inspection of several different production models for high energy signals at X-ray binary signals does not give us convincing evidence for a big ratio of the v to -y-ray duty cycles. Although the general idea of D >D., appears to be true, there is only a limited number of models where the ratio could be large. An educated guess would put the ratio at 2 or 3 or, for convenience, x. 4.2. Young supernova remnants. All conditions that are inevitably present at young supernova remnants make them prime candidates for production of high energy neutrino signals. The stellar collapse produces either a fast rotating neutron star or a black hole, both of which could be powerful central engines, providing the energy for cosmic ray acceleration . The accretion scenario is also possible - the reverse shock in the supernova shell could drag back to the central region enough mass" to create luminosity up to 1040 erg/s. The main feature, however, is the supernova shell itself, the outer envelope of the collapsed star that is ejected by the blast shock and is a natural target for production of secondaries . A lot of knowledge on the supernova explosions was acquired in theoretical studies, which were proven correct with the explosion of the 'nearby' SN1987A . The experimental observations enriched our knowledge and allowed detailed models some of which might be essential for the high energy processes we are interested in.
An already classical treatment of cosmic ray interactions in young supernova :emnants was made by Berezinsky and Prilutsky". They define two characteristic times important for the production of -y-ray signals. r,, is the time when thickness of the supernova shell becomes less than one radiation length, and the produced -y-ray signals become visible to the observer . For an uniform shell expanding with velocity v T
=
(_'M )1/2 s 47rv3X,.ad
which for v=109 cm/s and Xrad=60 g/cm2 becomes 2.8x10 g (M/Mo) 1/2 s. The other important time is ra when the adiabatic energy losses start dominating over losses to nuclear collisions. Ta
(4
~covs ) 1/2 = 1 .3 x 10r( X
Me )1 2 s /
for v=109 cm/s. A third important time, r,, when the decay time of charged pions is much shorter than the nuclear collision time, can be defined in a similar way and is much shorter than r.,. The scenario is that all protons accelerated inside the supernova shell lose practcally all of their energy to nuclear collisions . At time r < r r (which is of course function of the pion Lorentz factor) pions reinteract and only soft v fluxes leave the shell. When r > rr charged pions start decaying and the v fluxes follow the primary proton flux up to 1/10 of the maximum proton energy Epaz . At r,, the shell becomes transparent for -y-rays . The production of both the .y-ray and neutrino signals happens as outlined in Section 3 in the case when all particles decay, because density of 10 -12 g/cO is achieved several days after the explosion for envelopes of 10-20 Me. After ra only a fraction of the accelerated protons interact to produce -y-rays and v's and the power in proton induced secondaries begins to decrease quadratically with time. The detailed features of the emission can be obtained in this frame when the uniformly expanding shell is replaced with a specific realistic model with imbedded proton acceleration mechanism. Gaisser, Harding and Stanev made26 such an attempt for SN 1987A, using a wind shock acceleration in the IOHM shell of Pinto and Woosley 26. In this model cosmic rays are accelerated by first order Fermi mechanism in the pulsar wind shock . The pulsar wind is relativistic MHD electron-positron wind driven by the pulsar when the plasma frequency wp is greater than the pulsar angular frequency A. The wind luminosity can be approximated by the total
T. Stanev/Astrophysical sources of :jigh energy neutrinos pulsar luminosity of Eq.(4) . The pulsar wind shock forms at a radius R, where the wind ram pressure is balanced by the accumulated energy density of the shocked wind. Numerically R, is R.
/Umi ^-' scnumtnt
3.5 x 1013cm ty,uSoo
(10)
where ty, is the age ofthe supernova in years and umin in units of 500 km/s is the velocity of the inner edge of the supernova shell. The shock is contained in the central cavity of the remnant, where matter density is very low . The shock position determines the pulsar generated magnetic field strength at the shock B, and one could use it to estimate the maximum energy of the accelerated protons El","' - F(r) e B,R
(11)
where F(r) is a function" ofthe shock compression ratio and the characteristic energy e BR, = 105TeV B12 p,02 depends on the surface magnetic field of the pulsar wad on its period (in units of 10 ms) . Cosmic rays can be accelerated to ultra-high energies with this mechanism. The highest energy particles will diffuse away from the acceleration site, while the bulk of the protons will be confined inside the contact discontinuity for a time comperable with the supernova age . The model requires a mixing of the accelerated proton beam with the shell material for inelasic interactions and production of -y-ray and neutrino signals . The most likely mixi:.,,, mechanism is the growth of Rayleigh-Taylor instability at the wind-shell interface . The account for a realistic shell model significantly modifies the values of the characteristic times derived by Berezinsky and Prilutsky. Instead of using an uniformly expanding shell with v=109 cm/s, one has to numerically integrate through a shell, where density and velocity are in reverse proportion. For a shell with total ejected mass M 150 23 r., becomes -1 year and ^_r
Ta
Xrad 112
1
C_- 10 (12) 71 where AN is the nucleon interaction length and Q=v/c is the effective velocity of the expanding shell. Combined with the containment of the accelerated cosmic rays inside the ejecta this yields a constant v flux for the first several years of the supernova. The value of the neutrino induced upward muon signal is the same muon per 100 m2 detector per week is in Ref. 28, x Lok/(1043 erg/s) for a supernova at 50 kpc . Unfortunatelly the upper limit of the pulsar luminosity AN
^_rl
#1/2
23
of SN1987A is fewx 1038 erg/s and only a fraction of this is expected to appear in the form of accelerated cosmic rays. The low pulsar luminosity of SN1987A seems to preclude the possibility for observation ofneutrino signal from this source . The theoretical work inspired by the recent supernova, however, established new, more details limits of the production of high energy -y-ray and v signals. The containment hypothesis, described above, is e.g. another valuable extreme that brackets the expected signal duration from yound supernova remnants . The other extreme hypothesis is the straightforward propagation of the accelerated cosmic rays through the nebula as in the models of Sato29. These calculations also give us hints for the relative strength of v and -y-ray signals from sources that are fully enshrouded in matter, which is not (or is only partially) transparent toy-rays . 5. GAMMA-RAY ABSORPTION. An important factor for establishing the ratio of v to y-ray signal is the absorption of the -y-ray signals in interactions with thermal fields. The process is y7 -i- e+e - and the threshold is EE.v > 1 .3 x 1011/(1 - cos9)eV2,
(13)
where 0 is the angle between the directions of the two photons. To obtain the absorption length one has to integrate over the photon spectrum f(E) and over all direction. For blackbody radiation the maximum absortions° then occurs at E., - 5 x 1015 eV/(T, K) and the corresponding absorption length is X., - 6.8 x 1012T-3Ro. Both the absorption at source and in the interstellar medium will then 'lie important, although in different E, ranges. 5.1. Absorption at source. There are models for -1-ray production at sources where no matter is required for inelastic proton interactions . A suggestion" has been made that high energy -y-rays are produced in photoproduction interactions of the accelerated protons on the X-ray radiation at source . Indeed for isotropic X-ray emission with temperature of 2 KeV the photoproduction threshold is 10 TeV and the X-ray luminosity of Cygnus X-3 might provide several APhoe for protons above 10 TeV . It is, however, important that the protons are accelerated outside the X-ray emission site. Otherwise the protons and the X-rays might move in parallel directions and will never reach the CM photoproduction threshold . We can turn the argument around and ask what
T. StanevlAstrophysical sources of high energy neutrinos
24
10'4
V
- -.
6
--
V
f
1 1
1 1
t 107®K 0
Ô
O I.o (h
Id 1%
6X107 'K "-N. %% 101® 107
1017 ENERGY (OV)
Figure 5: 7-ray absorption length in thermal bremsstrahlung radiation of the accretion disk corona of temperature 107 and 6x10 7 K. fraction of a -y-ray flux will survive if the -y-ray production site does not coincide with the X-ray emission site. In the binary system model of Fig . 3" the X-ray emission happens in the accretion disk corona. The corona temperature derived from the emission measure is between 107 and 6x10 K . Fig . 5 shows the absorption length of -y-rays with energy E., in such fields". The maximum ofthe absorption is in the TeV range and for an accretion disk corona of 0.7Ro the survival probability might be as small as e-1°=5x 10-5 for certain directions of TeV -y-rays . This is gust an example of possible -y-ray absorption . All binary systems that are candidates for acceleration sites of cosmic rays and correspondingly for sources of high energy -y-ray and v signals are strong X-ray emitters. The intense radiation may heat not only the accretion disks and create a hot corona, but also increase significantly the temperature of the 'hot' face of the companion star. Hot faces has been seen in astronomical observations . They might be the main reason for the modulation of the -y-ray emission, and if this is the case, we may gain large factors in neutrino fluxes, which are not affected by the thermal fields at the source .
Figure 6: Ratio of v to PeV -y-ray signal as a function of the source distance . 5.1. Absorption in the interstellar space. While the absorption at source depends strongly on the temperatures and the dynamics at the source, the absorption on the 3 K background is universal - it depends only on the source distance . It has been discussed previously 32 and has to be accounted for when -y-ray and v signals are compared. Fig . 6 shows the correction factor for deriving the neutrino flux from the UHE -y-ray flux above certain threshold . The distances to several popular sources are indicated with arrows . Because the maximum absorption in the blackbody background is at E., =2 x 1015 eV the flux ratio is the biggest for E7 >10" eV. It is a factor of 5 for the 12 kpc distance to Cygnus X-3, and more than 100 for the 50 kpc to the Large Magelanic Clouds . This is what G. Cocconi 33 pointed out immediately after LMC X-4 was reported as a PeV 7-ray source. The absorption of PeV 7-rays from extragalactic sources will be many orders of magnitude and any confirmation of such a source will certainly indicate an extremely strong neutrino signal . 6. HOW DIFFICULT IS IT? We have derived the neutrino induced flux of upward muons for our standard source the good ole Cyg X-5 to be 1 in 1000 m2 detector per year. Is the detection of such fluxes realistic? What are the back-
T. Stanev/Astrophysical sources of high energy neutrinos grounds? The main background are of course the upward muons generated by cosmic rays in the atmosphere . Fig . 7 compares"' the atmospheric v flux with the calculated for Cygnus X-3. The dotted line shows the atmospheric flux within 1° from the source. At low energy the two lines are not distinguishable as the angle between the muon and the parent neutrino is too big . It is at energy around a TeV where this angle becomes smaller than the multiple scattering angle of the muon and helps the resolution of the source signal. While the total atmospheric flux is still (bigger than the signal from Cygnus even at 105 GeV the cross-over with the the flux in 1° cone is at about a TeV. The effect is further amplified by the detection technique. The magnitude ofthe neutrino induced signal" is Sp(> 10 E ) -dE dEV P(E , E,J, JE,.
E
v (crti2 .s 10-4 10 6 10 8 10~~ 10 2 1014 d6
(14)
where P(E , E.) is the probability that a neutrino directed at the detector will produce a muon with energy above E,, at the detector. P(E , E.) is a steep function of the neutrino energy and grows like E,2, for energies below MW/2 and continues to increase as E,-8 at higher energy. Thus the relative importance of the highest end of the neutrino energy spectrum is very large. Furthermore, the magnitude of the signal, being dominated by the very high energy neutrinos, does not depend strongly on the minimum muon energy. This fact has important consequences for detector design, which has been discussed in detail by Stenger36 . Finally the exact form of the neutrino cross-section at ultra high energy is not important for the magnitude of the signal. Gaisser and Grillo37 have studied the P(E,,, E.) dependence on the form of the structure functions . Their conclusion is that although it is important to use forms including QCD evolution, the exact form of the structure function does not appreciably change the result. The detection of UHE -r-ray signals from point sources has indicated that cosmic rays are accelerated at compact astrophysical systems . Although we cannot think of any other way for generating PeV ,y-rays, only the observation of point neutrino sources will be a proof for this phenomenon . This is, however, a formidable experimental task. Fig . 8 compares the magnitude of different already detected v sources with the expected for Cygnus X-3 . The lines show the energy spectrum of the neutrinos, that contribute to the signal. The rates are given in parantheses . The v, from SN1987A
25
1
10-2
10 0
2
4
Ey (GeV )
Figure 7: Neutrino flux from Cygnus X-3 compared with the neutrino flux of atmospheric origin. The dashed line shows the background within 1° of the source.
w b
-~
Contained v's (kt.yr) -1 (0 .2-0 .3 per day)
z b
w
Figure 8: Comparison of the neutrino fluxes contributing to different observed neutrino signals with the expected signal from Cygnus X-3.
26
T. Stanev/Astrophysical sources of high energy neutrinos
produced 18 events in IMB and Kamiokande for 10 seconds, roughly 1 event is seen every day in contained Vs and in upward going muons. To observe high energy neutrino signal from a point source we have to able to observe fluxes of 1 event per year with the same area. We need large detectors to do it. We need GRANDE and DUMAND to be able to see different regions of the Galaxy and to study it in the highest energy band of the astronomy. In conclusion, it is not possible to give a recipe for calculating the ratio of the expected .y-ray and v signals from different poin sources. Neutrino astronomy has to be an experimantal science. The comparison of a neutrino signal with the -y-ray signal from a given source will give us the instrument to study type of the source and the conditions at it. Different VHE and UHE ,y-ray sources are certainly not the same. Every source has its unique configuration and dynamics . We already know that from the comparison ofthe high energy -y-ray signals to the X-ray signals and periodicities in the X-ray and GeV -y-ray bands. Already the first detection of neutrino signal from a cosmic accelerator will give us invaluable clues on the dynamics of such sources and the acceleration of PeV cosmic rays. ACKNOWLEDGEMENTS The author grafully acknowledges the contributions of T.K. Gaisser, R.J. Protheroe and F. Halzen to this paper, which is based on the research performed with them and many other collegues. My research is supported in part by the U.S. National Science Founda tion. REFERENCES 1. M.A. Markov, in: Proceedings of the 1960 Interna tional Conference on High Energy Physics (Rochester, 1960), p. 578 2. T.J. Haines et al. (IMB Collaboration), Phys . Rev . Letters 57 (1986) 1986; K.S. Hirata et al. (Kamiokande), Phys. Letters 205 (1988) 416. 3. M. Calicchio et al. (MACRO Collaboration), Nucl. Istr. Meth. A264 (1988) 18. 4. C. Bari et al. (LVD Collaboration), Nucl. Instr. Meth. A264 (1988) 5. 5. For the most recent design see V.J. Stenger, this volume. 6. H. Sobel (GRANDE Collaboration) this volume . 7 . T.K. Gaisser and T. Stanev, Phys. Rev .D30 (1984) 985 . 8. A.M. Hillas, Nature 312 (1984) 50.; A .M. Hillas,
in: Proceedings of the 19th International Cosmic Ray Conference, vol . 9, eds. F.C. Jones, J. Adams and G.M. Mason (NASA Conference Publication 2376, Washington D.C. 1985) p. 409. 9. M. Samorski and W. Stamm, Ap. J. Letters 268 (1983) L17 . 10. J. Lloyds-Evans et al., Nature 305 (1983) 784. 11. K. Brecher and G. Chanmugam, in: Proceedings of the 19th International Cosmic Ray Conference, vol . 1, eds. F.C. Jones, J. Adams and G.M. Mason (NASA Conference Publication 2376, Washington D.C. 1985) p. 103 . 12. D.E. Nagel, T.K. Gaisser and R.J. Protheroe, Ann. Rev . Nucl. Part. Sci 38 (1988) 609 . 13. V.S. Berezinsky, C. Castagnoli and P. Galeoti, Il Nouvo Cim. 8C (1985) 185; see also M.M. Shapiro and R. Silberberg, in: Relativity, Quanta and Cosmology (vo1.2, ed. Pantaleo and DeFinis, Johnson Corp., Harcourt, Brace and Jovanovich, New York, 1979) 745 . 14. R.J. Protheroe and T. Stanev, Nature 328 (1987) 136. 15. W.T. Vestrand and D. Eichler, Ap.J. 261 (1982) 251 . 16. V.S. Berezinsky, in: Proceedings 1979 DUMAND Summer Conference (University of Hawaii, ed. J.G . Learned, 1979) p. 235 . 17. T.K. Gaisser and T. Stanev, Phys. Rev. Letters 54 (1985) 2265. 18. E.W. Kolb, M.S. Turner and T.P. Walker, Phys. Rev. D32 (1985) 1145. 19. D.D. Clayton, Principles of Stellar Evolution and Nucleosynthesis (McGraw Hill, New York, 1968) . 20. R. Kurucz, D.F. Carbon and D. Gingerich, in: Theory and Observation of Normal Stellar Atmospheres (ed . by D. Gingerich, MIT Press, Cambridge, Mass., 1969) . 21. N.E. White and S.S. Holt, Ap. J. 257 (1982) 253 . 22. K.O. Mason, F.A. Cordoba and N.E. White, Ap. J. 309 (1986) 700 . 23. S .E. Woosley, in: Supernova 1987A in the Large Magelanic Clouds (eds. K . Kafatos and A. Michalistianos, Cambridge, 1988) p. 289. 24. V.S. Berezinsky and O.F . Prilutsky, Astr. Astrophys. 66 (1978) 325 . 25 . T.K. Gaisser, A.K. Harding and T. Stanev, Nature 332 (1988) 1695; T.K. Gaisser, A.K. Harding and T. Stanev, Ap. J. in print . 26. P.A. Pinto and S.E. Woosley, Nature 333 (1988) 534. 27. P.O. Lagage and C.J. Cesarsky, Astr. Astrophys .
T. Stanev/Astrophysical sources of high energy neutrinos
125 (1983) 249 . 28. T.K. Gaisser and T. Stanev, Phys. Rev . Letters 58 (1987) 1695. 29. H. Sato, Progr . Theor. Phys. 58 (1977) 549; Y. Yamada et al., Progr.Theor .Phys. 79 (1987) 426. 30. R.J. Protheroe and T. Stanev, Ap. J. 322 (1987) 838. 31 . R.J. Gould and G.P. Schreder, Phys. Rev 155 (1967) 1404. 32. R.J. Protheroe, M.N.R.A.S. 221 (1986) 769. 33. G. Cocconi, CERN Preprint PRE 85-021.
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34 . T.K. Gaisser and T. Stanev, in: Proceedings of the 19th International Cosmic Ray Conference, vol. 8, eds. F.C. Jones, J. Adams and G.M. Mason (NASA Conference Publication 2376, Washington D.C. 1985) p. 156 . 35. T.K. Gaisser and T. Stanev, Phys. Rev. D31 (1985) 2770. 36. V.J. Stenger, Ap. J. 284 (1984) 810 . 37. T.K. Gaisser and A.F. Grillo, Phys. Rev. 36 (1987) 2752.