Cosmic neutrino fluxes — scaling from UHE gamma rays

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<ul><li><p>38</p><p>COSMIC NEUTRINO FLUXES -- SCALING FROM UHE GAMMA RAYS</p><p>Michael L. CherryDept . of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 USA</p><p>Nuclear Physics B (Proc. Suppl.) 14A (1990) 38-46North-Holland</p><p>Gamma ray and neutrino observations are closely coupled : in energetic astrophysical objects wherecopious production of pions takes place, both gammas and neutrinos are produced . Although y rays canbe produced as a result of either electron or hadron acceleration processes, however, the neutrinos area clean and unequivocal tracer of the hadrons . Assuming that UHE y rays are produced by energetichadrons in astrophysical "beam dumps", it is possible to estimate fluxes of cosmic neutrinos based onthe UHE .y ray observations . These estimates are made for Cygnus X-3 and applied to a variety of othersources . Throughout, an attempt is made to parametrize the results so that they can easily be normalizedto other detector areas or UHE -f ray fluxes, and so that they can easily be modified for more or lessoptimistic assumptions about gamma ray attenuation and relative v -- y intensity levels.</p><p>1 . IntroductionOur information on energetic hadron production in</p><p>cosmic sources comes from direct cosmic ray studies andgamma ray observations . The interpretation of chargedcosmic ray measurements is complicated, however, bythe presence of the galactic magnetic field, which makesisotropic the arrival directions of all but the highest en-ergy particles, and by the production of secondary par-ticles in interactions with the interstellar medium. Mea-surements of gamma ray lines at low energies (near 1MeV) give direct evidence of proton acceleration to MeVand GeV energies in active regions on the sun, in theearth's atmosphere, and toward the galactic center' . Andat energies of 50 MeV to 10 GeV, the diffuse gamma rayemission from the galactic disk can be modeled as a com-bination of an electron component (due to bremsstrah-lung, synchrotron and Compton emission, and pair pro-duction in the interstellar medium) and a pro meson decaycomponent z .</p><p>At very high energies (VHE, 100 GeV to 100 TeV),binary neutron stars, individual pulsars, and the radiogalaxy Cen A have been detected sporadically, but atthese energies there is no obvious way to separate theelectron and hadron components of the signal'' . At ul-trahigh energies (UHE, 100 TeV to 100 PeV), however,</p><p>0920-5632/90/$03.50 O Elsevier Science Publishers B.V .(North-Holland)</p><p>where positive signals have been reported from four bi-nary neutron stars and the Crab pulsar s, ", energy lossesgenerally proceed too rapidly to allow the required accel-eration of electrons . Although special geometries and thecurvature radiation model of Cohen and MustafaP mayprovide a plausible electron mechanism, the usual pic-ture is that the UHE emission is presumably due to highenergy hadrons .</p><p>The only alternative to the UHE -y rays as a tracer ofPeV hadrons is the high energy neutrino emission fromcharged meson decay. If the UHE gamma ray emissionis due to 7r" decays, then the corresponding 7r - -decay vflux must be comparable to or larger than the gammaray flux, and can be calculated straightforwardly. Scal-ing from the gamma ray measurements allows us to pre-dict expected v flux rates with some reasonable degree ofconfidence . Observation of the neutrinos then will pro-vide the clearest and most unambiguous measurementswe have of high energy cosmic hadrons at their source .</p><p>High energy air showers, presumably from 10" to2 x 10"' eV photons, were first detected 7,H with the char-acteristic 4 .8 hr orbital period from Cygnus X-3 in 1976-80, and since then signals have been reported from threeother binary x-ray sources (Her X-1`'-12 , Vela. X-1", and</p></li><li><p>LMC X-41 '1 ) and the Crab Pulsar" . Neutron stars havelong been recognized as attractive sites for the accelera-tion of exceptionally energetic cosmic rays, and the highproportion of interacting binary star systems on the listof UHE emitters strongly suggests that the UHE luminos-ity is fed by accretion' . Although the acceleration mecha-nism is poorly understood, the production of high energyphotons (and th:-~ accompanying neutrinos) is straightfor-ward if a beam of energetic protons accelerated at theneutron star is allowed to strike either the atmosphereof a companion star or an accretion wake or tail stream-ing behind the neutron star" . At those points in theorbit where the target material lies between the neutronstar and the earth, and where the accelerated beam isdirected toward the earth, episodes of 7r-decay photonemission and a}- and Ft}-decay neutrino emission canbe expected .</p><p>The emission in the HE, VHE, and UHE ranges ap-pears to be highly sporadic both in time and in phase .Above 100 MeV, SAS II reported a 4o- signal from CygX-3 in 1973", but COS B could provide only upper limitsin 1975". At VHE energies, Cyg X-3 has been detectedsometimes in the range of binary phases 0 - 0.15 - 0.3,at other times near phase 0 .5 - 0.7, and at some timesnot at all . At UHE energies, at least through 1985, thesignal has been detected near phases 0.25 or 0.6 1" . Since1986, Cyg X-3 has generally been undetectable (althoughthe CYGNUS experiment2" has reported a brief periodof activity in April-May 1986, and Fly's Eye21 has pre-sented evidence for a 10 18 eV signal during the period1981-1988) . In general, the emission has not been seenjust before or after- eclipse (,0 = 0) or simultaneously atboth low and high phases (as would be expected if thetarget were the limb of the companion's atmosphere) . Inthe case of the VHE signal from Her X-1, emission hasbeen seen over the entire orbital period including duringx-ray eclipse)" . The implicaticn is that the photons (andcorresponding neutrinos) produced by highly relativisticprotons interacting in the environment of a closely or-</p><p>M.L . Cherry/Cosmic neutrino fluxes</p><p>biting binary star system are generated in a turbulent,non-static medium where the geometric conditions re-quired for a detectable signal are not neatly reproducibleor always satisfied .</p><p>In Sec . 2, neutrino fluxes are estimated based on themeasured gamma rays . These neutrino (and neutrino-induced muon) fluxes are normalized by the proton lu-minosity at the source in Sec . 3, and in Sec . 4 these esti-mates are extended to several varieties of specific sources .Finally, in Sec . 5, the potential for simultaneous y ray-v observations is discussed, including the possibility fordetecting neutrino emission during transient gamma rayevents .2 . Flux Estimates - Scaling from UHE GammaRay Observations</p><p>Numerous authors22-25 have made predictions of cos-mic neutrino flux rates . The connection between the ob-served .y ray flux and the accompanying neutrino fluxis made very clearly by Kolb et al . 2s With the assump-tions that the photons are the result of 7r decay, that thecharged 7rf mesons decay in flight before they interact,and that the K and charmed meson contributions can beneglected, then the measured UHE ,y ray spectrum</p><p>A art decay in flight produces a neutrino of maximumenergy</p><p>E,, = (I - -' ) EM,rand gives a resulting 7r-decay neutrino spectrum</p><p>d.5,,(</p><p>M</p><p>dE</p><p>'' )</p><p>-I</p><p>dS,C</p><p>1</p><p>,m2</p><p>E;;" '</p><p>.2 - .4dE</p><p>4"</p><p>a</p><p>for spectral indices in the range a - 2 -- 3.</p><p>39</p><p>Kolb et alr' assume mc, !.oenergetic photons are emitted at en-ergy EA/2 . Here a flat spectrum is assumed from 0 to EA. Theresults here, and also in Eq . (4), therefore differ from theirs byapproximately a factor of 2.</p><p>dS.,"_ CE (1)</p><p>dE, '</p><p>implies a pion spectrum'</p><p>d_S,+ +.- dS,r ._=</p><p>dE,r2dE~</p><p>aCE,r" . (2)</p></li><li><p>40</p><p>In a close binary system, the neutrino emission pre-</p><p>sumably lasts through most of the time during which the</p><p>neutron star is eclipsed :</p><p>where a (E) is a neutrino energy-dependent absorption</p><p>factor, T is the binary period, a is the binary separa-tion, and R, is the dimension of the target region (e.g.,</p><p>the radius of the neutron star's larger companion) . Theabsorption factor a(E) may be close to unity for a rea-sonable fraction of the eclipsed4-26 . For the -y rays,</p><p>r, = a,(E)hd</p><p>(6)</p><p>where h is a characteristic dimension of the target mate-rial (e .g ., the companion star's atmospheric scale height) .For both the neutrinos and the gammas, the target mustbe thick enough (&gt; 50 g cm-2) to generate secondarymesons efficiently. For the gammas, if the target thick-ness is much greater than -200 g cm-2 , absorption willdecrease the flux ; for the neutrinos, absorption by themain body of the companion star may set in above a fewTeV2'i . As pointed out by numerous authors23-2.1 the rel-ative v--+ duty factor A = r/r, may be large : In the caseof the Haverah Park Cyg X-3 observations, r, /T - 0.02,so that if 25 a - 1.058, and a;,(_E) - 0.4, then A - 20t .The emitted v-decay v spectrum is then</p><p>dS dS,dE</p><p>ti .3A(E)dE</p><p>An energetic muon produced by a neutrino interac-tion in the rock around the detector has a range</p><p>P(E) -= N.jaR,jj</p><p>M.L. Cherry/Cosmic neutrino fluxes</p><p>R,, = 3x10'ln(1+iTV)gcm-2. (8)</p><p>The probability that a neutrino of energy E headed to-ward the detector interacts in the rock within a distanceR,,(E) of the detector, and produces a muon which thentraverses the detector, is</p><p>This is in fact only a lower limit ifone allows for smearing ofanintrinsically narrower r, at the source . At VHE energies (where themechanism may be electronic rather than hadronic), the Whipplemeasurements give r,/T - 0.1, or A &gt; 4.</p><p>where the v cross section is taken from Ref. 26 . The7r-decay v-induced muon event rate in a detector of areaA is then</p><p>n,,</p><p>ti</p><p>.3N,,Af A(E) dE a,Rp dEEA</p><p>S,(E, &gt;_ 3 x 10" eV)ti r(a)C0.4 x 6 x 104 M2)(1.5 x 10-lacm-2sec-t )</p><p>x ( X )(1/3</p><p>- 120 fn-u~a~P yr(10)</p><p>normalized to the observed Haverah Park Cygnus X-3flux and a detector area A = 6 x 104 m2 . (The detectorarea A = 6 x 10'm2 is taken to be that of GRANDE,since this is the largest of the proposed new detectors .The calculation can be scaled to DUMAND or any otherdetector by using the appropriate value of eA.) The func-tion r(a) is the result of the actual integration (in eventsyr- ') performed over the range 10 GeV - 1000 TeV andscaled to the case of GRANDE. It is assumed that a typ-ical Southern hemisphere source is visible for a fractione = 0.4 of the time, where the on-source duty factor E isthe ratio of the effective area to the detector's geometricarea (E is a function of the detector and source location,and the time of year.), and that the observed 10' 5 eVCygnus X-3 y ray flux has been attenuated on the mi-crowave background by a factor of 1/3 . Therange of expected rates as a function of spectral index isthen :</p><p>a</p><p>r(a) yr- '1 .5 32 502.1 902.5 20002.75 18,000</p><p>The muon rate increases rapidly with a steepening spec-trum. We have normalized to the y ray flux above 3 x 10"'eV and assumed a power law spectrum all the way downto TeV energies . Since most of the neutrino contributionarises from energies near 10 TeV, an increasing spectralindex with a fixed rate above 3 x 10 15 eV leads to arapidly increasing 10 'TeV neutrino event rate . The y raymeasurements suggest ct - 2.1 for Cygnus X-3 . 1</p><p>lit should be made clear that, although this is the usual as-</p></li><li><p>Based on Hillas' model'' of a monoenergetic 10'7 eVproton spectrum at the source, Gaisser and Stanev27 pre-dict an upward-moving muon flux above 2 GeV of 2 x10- ' 5Cm-2sec-', or 16 yr- ' in 6 x 10" M2(assuming thesame e = 0.4 duty factor) . For the same power in anE-2 proton spectrum, their results give 20 yr-', a factorof 2.5 below this estimate . These rates vary by no morethan a factor of 2 over the entire range of densities in thetarget region 10-12 to 10-6 g cm-3 .</p><p>The calculations of Berezinsky et al .23 , assuming thesame energy-independent v - -y duty factor A = 20, inde-pendently give the number of upward-moving muons in0.4 x6x~0'm2 tobe</p><p>n,,(&gt; 10 GeV)</p><p>=</p><p>30yr-'</p><p>n,,(&gt; 1000eV) = 24yr-'</p><p>n,,(&gt; 1 TeV)</p><p>=</p><p>16yr-'</p><p>Again, these results are in reasonable agreement with thepresent estimates.</p><p>The normalization to Haverah Park used above is notcrucial to the argument, and has been used only for con-venience . The expected muon rate can be calculated fromEq. 10 based on any desired normalization . In the firstline of the table below, the values of n,, as a function of</p><p>sumption, such a flat spectrum is not particularly well established .At UIfE energies, Samorski and Staminr derive a = 2.2 f 0 .3 fromtheir data based on 13 events above 2 PeV and 4 events above 10PeV . In very few other cases is spectral information given in a sin-gle experiment . Rather, the results of many experiments (at both'PeV and PeV energies) are typically lumped together, based ondata taken at different times, sometimes time-averaged and some-times from transients, with different thresholds, and often no errorbars given for intensities or energy ranges ; and then a power lawspectrum is drawn through the data . Although it is difficult tosuggest a better technique, the universal adoption of such an ex-tremely hard spectrum must at least be treated with caution . Onthe other hand, the underground IMB detector is a factor of 150smaller than the proposed GRANDE detector, so the upper limitsfrom IMB rule out a stee (a :_" 2.5) steady-sta.fe spectrum at thelevel of several x 150 yr - in 6 x 10W from Cygnus X-3 .</p><p>M.L. Cherry/Cosmic neutrino fluxes 41</p><p>a based on the 1979-1982 Haverah Park flux levels fromCyg X-3 are repeated . The results are also calculated bynormalizing to the 1976-1980 Kiel flux7 and the CYGNUSresult 2" based on a 45-day period in 1986. In each casethe reported .y ray flux level S,,(&gt; Em; ) is given on whichthe scaling is based .</p><p>Unfortunately, although Cyg X-3 may be a reason-able standard candle for normalization purposes, it is aNorthern Hemisphere source which may not be visiblein neutrinos from Northern Hemisphere detectors. It istherefore interesting to scale to the Southern Hemispheresources LMC X-4 and Vela X-1, as well: The observedUHE flux from the Southern Hemisphere source LMCX-4 is'" 4.6 x 10- ' 5cm-2sec- ' above 10 PeV . Assuming</p><p>f,,-wave. - 0.1 here, Eq. 10 gives n,, - 150 yr- ' for a = 2,and n,, - 330 yr- ' for a = 2.1, comparable to or abovethe rates suggested for Cyg X-3 . Similarly, the Adelaidegroup'" have reported a time-averaged -f ray flux from</p><p>Vela X-1 of S7 (Ey &gt; 3PeV) = 9 x 10- ' 5cm-2sec'' . Tak-ing = 1 for the case of this nearby source, wefind predicted neutrino-induced muon fluxes at - 20%of the level predicted for Cygnus X-3 (based on the orig-</p><p>inal Haverah Park normalization) .Summarizing the above, various theoretical mod-</p><p>els and normalizations to UHE -f ray observa-</p><p>Lions yield expected muon event rates in detec-tors of the scale currently being discussed, fromsources such as Cyg X-3 (at the level observedprior to 1986), LMC X-4, and Vela X-1, in ex-cess of ten events per year for differential spectralindices in the range of 2 to 2 .5 . The results have beenparametrized in terms of the measured UHE .y ray flux,the detector area, on--source duty factor, relative v - Y</p><p>Em.rn S,(&gt; Em.r....</p></li></ul>


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