Oscillating Neutrinos from the Galactic Center Roland M

OSCILLATING NEUTRINOS FROM THE GALACTIC CENTER ROLAND M. CROCKER,1 FULVIO MELIA,2,3 AND RAYMOND R. VOLKAS1 Received 1999 November 11; accepted 2000 June 1 ABSTRACT It has recently been demonstrated that the c-ray emission spectrum of the EGRET-identiÐed central Galactic source 2EG J1746-2852 can be well Ðtted by positing that these photons are generated by the decay of n0Ïs produced in p-p scattering at or near an energizing shock. Such scattering also produces charged pions which decay leptonically. The ratio of c-rays to neutrinos generated by the central Galac- tic source can be accurately determined, and a well-deÐned and potentially measurable high-energy neutrino Ñux at Earth is unavoidable. An opportunity, therefore, to detect neutrino oscillations over an unprecedented scale is o†ered by this source. In this paper we assess the prospects for such an observation with the generation of neutrinoC‹ erenkov telescopes now in the planning stage. We determine that the next generation of detectors may well Ðnd an oscillation signature in the Galactic center (GC) signal. Subject headings: acceleration of particles È cosmic rays È elementary particles È galaxies: nuclei È Galaxy: center È radiation mechanisms: nonthermal

1. INTRODUCTION synchrotron Ñux radiated by these charges is consistent 1.1. T he Neutrino Source with the radio spectrum of Sgr A East observed with the The dominant radio-emitting structures at the Galactic VLA. In fact, such relativistic electrons and positrons would center (GC) are the supernova remnant (SNR)Èlike shell Sgr also radiate by bremsstrahlung and undergo inverse A East, a three-armed spiral of ionized gas dubbed Sgr A Compton scattering in such a way as to self-consistently West, and, embedded at the center of Sgr A West, the explain the entire broadband emission spectrum of Sgr A Galactic dynamical nucleus, Sgr A*, thought to be a East, ranging from GHz frequencies all the way up to the ^ ] 6 massive (M 2.6 10 M_) black hole (Haller et al. 1996; TeV energies observed by Whipple (Buckley et al 1997). For Genzel et al. 1997; Ghez et al. 1998). Sgr A East has a major the purposes of this paper, then, we take it that the EGRET axis length of about 10.5 pc, and its center is located 2.5 pc source 2EG J1746-285 is identical with Sgr A East (Melia et from Sgr A* in projection, and probably behind the latter al. 1998). We note in passing that the maximum energy (Goss et al. 1989). Lo et al. (1998) have recently determined attained by the shocked protons at Sgr A East, given the the intrinsic size of Sgr A* to be less than 5.4 ] 1011 mat energy-loss rate via collision in the shock, is D5 ] 1015 j7 mm. eV \ 5000 TeV (Melia et al. 1998). Also located at the GC is the EGRET-identiÐed c-ray Regardless of the ultimate identity of the EGRET source source 2EG J1746-2852 (Mayer-Hasselwander et al. 1998). 2EG J1746-285, given that the process producing the high- It has been shown that the high-energy (0.1È10 GeV) c-ray energy emission is pionic, there should be an associated emission spectrum of this source is very likely due to the neutrino Ñux from the GC (Blasi & Melia 1999). These decay of n0Ïs (Melia et al. 1998; Marko†, Melia, & Sarcevic neutrinos are due to both direct pion decay(nB ] kl ) and B ] k 1997). These pions are produced by p-p collisions, which the decay of muons to electrons and positrons (k ele lk), might plausibly take place at either of two shock regions: (1) where we take l to mean l andl here (as we often do in the the shock at Sgr A* due to gas accretion from ambient remainder of this paper). Prima facie, then, we expect the winds, or (2) the shock produced by the expansion of the Ñavor composition of the neutrino ““ beam ÏÏ generated at the SNR-like nonthermal shell of Sgr A East into the ambient GC to be essentially 67% k-like and 33% e-like by na• ve gas of the interstellar medium. Thus, a priori, either Sgr A* channel counting (cf. atmospheric neutrinos in the GeV or Sgr A East or both might be the source of the c-rays that energy range). Note that there is alq background produced constitute 2EG J1746-285. It has recently been shown, at the source due to nonpionic processes such as charmed however, that the identiÐcation of Sgr A* with 2EG J1746- hadron decay. This background is, however, small (see 28 is disfavored, because charged leptons produced in nB below). Of course, in the absence of neutrino Ñavor oscil- decays would emit too much synchrotron Ñux in Sgr A*Ïs lations, one would expect to observe GC neutrinos at Earth intense magnetic Ðeld at GHz frequencies to be consistent with the same Ñavor composition as that generated at the with the well-studied radio spectrum of this object (Melia et source. al. 1998; Blasi & Melia 1999). We do not distinguish between l andl, because present On the other hand, given the physical conditions in Sgr A and planned terrestrial detectors do/will not distinguish East, the putative charged leptons generated there have a between the two. There is one interesting proviso to this ^ ] 3 \ distribution that mimics a power law with index D3. The statement, however: ale Ñux atEle 6.4 10 TeV 6.4 ] 1015 eV can be detected by resonant W ~ boson pro- 1 ~ ] ~ School of Physics, Research Centre for High Energy Physics, The duction viale e W with the electrons in the detector University of Melbourne, 3010 Australia; r.crocker= medium. The resonance energy, however, is just above that physics.unimelb.edu.au, r.volkas=physics.unimelb.edu.au. 2 Physics Department and Steward Observatory, The University of attained by neutrinos generated in the processes described Arizona, Tucson, AZ 85721; melia=physics.arizona.edu. above at the GC (Glashow 1960; Berezinsky & Gazizov 3 Presidential Young Investigator. 1977; Gandhi et al. 1996, 1998). 339 340 CROCKER, MELIA, & VOLKAS Vol. 130

Given our detailed knowledge of the basic physical pro- These are (1) the e†ectively point-source nature of the GC, cesses producing the GC c-rays, we are able to determine an and (2) a GC neutrino spectrum that is signiÐcantly Ñatter ~3.7 expression for the total neutrino emission at the source, than that of atmospheric neutrinos (which scales as El ). 0 Ql(El), in terms of the c-ray emission there,Qc(Ec), the If we preliminarily adopt an angular resolution of hres D 2¡ numerical power of the proton spectrum at the source, a for the proposed large-scale detectors (1 km2 e†ective detec- (such as would result from shock acceleration at either Sgr tor area), the condition for the detection of the GC neutrino 2 2 A East or Sgr A*), andr 4 (mk/mn) (Blasi & Melia 1999). Ñux is'l(El)/)res [ Iatm(El), where)res Bnhres is the solid The quantity a has been empirically determined to lie angle corresponding to the angular resolution of the experi- between 2.1 and 2.4 (Marko† et al. 1997; Blasi & Melia ment, andIatm(El) is the Ñux of atmospheric neutrinos per 1999), using a procedure to Ðt the EGRET spectrum of 2EG unit solid angle. This condition is fulÐlled above a few TeV, J1746-2852 with a detailed calculation of the particle and the expected event rate from this preliminary analysis is cascade using an extensive compilation of pion-multiplicity D4km~2 yr~1 for a \ 2.4 to D70 km~2 yr~1 for a \ 2.1 cross sections. In the energy range between the * resonance (Blasi & Melia 1999). Note that a fuller analysis of event (s1@2 D 1 GeV) and the intersecting storage rings (ISR) range rates (presented later) must also consider the problems (D23È63 GeV), simple scaling (Feynman 1969) does not posed by the atmospheric muon background and Earth adequately take into account the strong dependence of the neutrino opacity. cross section on the rapidity at lower energy, and the pion We see therefore that preliminary calculations reveal that distribution is not adequately described by a power-law there is a well-determined and potentially observable neu- mimicking the injected relativistic proton distribution trino Ñux at the Earth from the Galactic center. We now between D1 and D100 GeV. Instead, the distribution brieÑy list the motivations behind this work before going on steepens in this region and is curved, which is consistent to consider whether any sort of neutrino oscillation signa- with the suggested spectral shape measured by EGRET. ture might be detectable in the GC signal. Above about 10 GeV, however, the pion distribution settles into the ““ asymptotic ÏÏ form suggested by scaling, in which 1.2. Summary of Motivations the power-law index is a direct reÑection of the underlying The main motivations behind the present work are: relativistic protons. Thus, an EGRET spectrum with an e†ective spectral index of D[3 below 10 GeV is produced 1. Sgr A East is arguably the most thoroughly under- by a pion distribution whose power-law index lies in the stood extrasolar astrophysical source of very high energy range 2.1È2.4 above this energy. In other words, a relatively neutrinos identiÐed to date. It is thus of fundamental impor- steep and curved c-ray spectrum below 10 GeV is consistent tance for the embryonic science of neutrino astronomy. with a Ñatter neutrino spectrum at TeV energies. The rela- 2. It is important for general scientiÐc reasons to explore tive normalization between the c-ray and neutrino distribu- the neutrino oscillation phenomenon in a wide variety of tions is e†ected at 10 GeV, where the pions take on a regimes. Because of the high energy scales and the very long power-law form. baselines involved, astrophysical sources such as Sgr A East We take the neutrino spectrum at Earth to be, in general, provide a novel regime not investigated in previous and given by current solar, atmospheric, reactor, and accelerator neutrino-detection experiments. Previous works that have E ~a ' (E ) \ ' (10 GeV)A l B . (1) considered propagation-e†ect signatures in Galactic and l l l 10 GeV extragalactic high-energy neutrino signals include Learned & Pakvasa (1995), Weiler et al. (1994), Pakvasa (1995), Roy Normalizing to the observed c-ray Ñux at Earth at 10 GeV, (1996a, 1996b),P• riz, Roy, & Wudka (1996), Minakata, & one arrives at the following values for the total neutrino Ñux Smirnov (1996), Enqvist,Kera nen, & Maalampi (1998), here (Blasi & Melia 1999): Husain (1999), Halzen & Saltzberg (1998), Bento, Kera nen, ~2.1 & Maalampi (2000), Iyer, Reno, & Sarcevic (2000), Mann- \ ] ~9A El B ~2 ~1 ~1 'l(El) 1.1 10 cm s GeV (2) heim (1999), and Ra†elt (1998). 10 GeV 3. Given that solar and atmospheric neutrino obser- for a \ 2.1, and vations have essentially established the existence of neutrino oscillations, it is important to incorporate this E ~2.4 propagation e†ect when examining possible sources for ' (E ) \ 9.6 ] 10~10A l B cm~2 s~1 GeV~1 (3) l l 10 GeV study through neutrino astronomy. Neutrino signals from astrophysical sources are an important complement to elec- for a \ 2.4, where we have taken the absolute upper bound tromagnetic signals from the same, and they will serve to to the energy spectrum of GC neutrinos to be given by the improve our understanding of the dynamics of important highest energy (5 ] 1015 eV) of the shocked protons. astrophysical objects such as supernova remnants, gamma (Kinematical calculations show that neutrinos created by ray bursters, and active galactic nucleii. the decay of charged pions produced in scattering of a ““ beam ÏÏ proton o† a stationary ““ target ÏÏ proton can attain 2. NEUTRINO OSCILLATIONS BETWEEN energies very close to the beam proton.) Note that in the Sgr A EAST AND EARTH above calculations we make the very reasonable assump- tion that high-energy cÏs and lÏs travel to Earth equally 2.1. Distance Considerations unimpeded by the ambient matter they encounter (which For purposes of calculational expediency, we take the has a column number density of barely 1023 cm~2). neutrino source Sgr A East to have a linear dimension of 10 Two factors improve the odds for the detection of the GC pc ^ 3 ] 1017 m. This distance is relevant because we need neutrino Ñux above the atmospheric neutrino background. to know how the neutrino oscillation lengths compare with No. 2, 2000 SGR A EAST NEUTRINOS 341 the size of the emitting object to determine whether the the MSW e†ect; Smy 1999). In summary, then, the atmo- neutrino source is Ñavor-coherent. If the former are small spheric anomaly deÐnitely requires a large mixing angle compared to the latter, then, because neutrinos are emitted solution, while the solar problem can be solved by large- from all points within the source, the oscillations will be angle oscillations. averaged out. Alternatively, if the latter are large compared We now brieÑy review the various possible solutions to to the former, then no averaging due to the Ðnite size of the the atmospheric and solar neutrino problems, and then source will be needed, and the source is essentially Ñavor- apply the various scenarios to the GC neutrino Ñux. coherent for neutrinos of a given energy. Note that two types of averaging generally need to be done: over distance 2.3. Atmospheric Neutrinos and over energy. Thus far, we have only considered distance SuperKamiokande detects a 50% deÐcit of k-like atmo- averaging, due to the Ðnite size of the l source. One must spheric neutrinos coming up through the Earth (Fukuda et also take into account distance (and energy) averaging due al. 1998a, 1998b, 1998c). They see no deÐcit of either to the detector. For Sgr A East, the source distance scales upward- or downward-going e-like neutrinos. The lower involved are at least 6 orders of magnitude larger than those energy downward-going k-like events are deÐcient, whereas for the detector (1 AU ^ 1.5 ] 1011 m). Detector-based dis- their high-energy counterparts are not. These data can be tance averaging, then, will not impact on calculations con- explained by close-to-maximall ] l oscillations with cerning Sgr A East. We do not address the issue of energy k x x D e and x \ q or x \ s (sterile). These two alternatives averaging due to the Ðnite energy resolution of the detector both require parameters in the range in great detail in this paper. The distance between source and detector is about ] lk lx , 8 kpc ^ 2.5 ] 1020 m . (4) 2\ ~3 ] ~2 2 2 \ with *mkx 10 10 eV and sin 2hkx 1 . (9) 2.2. Introduction to Neutrino Oscillations (To be strict, the *m2 ranges are a little di†erent for the two % possibilities because of the ““ matter e†ect ÏÏ in the Earth, but We consider only two-Ñavor oscillation modes, la lb, for simplicity and deÐniteness. Suppose a beam of Ñavor a is this will be irrelevant for us; see Foot, Volkas, & Yasuda produced at x \ 0. Then at a point x distant from the 1998; Scholberg 1999.) SuperKamiokande currently favors source, the oscillation probability is oscillations tolq over oscillations to a sterile neutrino at the 2 p level (Fukuda 2000). x P(a ] b) \ sin2 2h sin2 An B , (5) L 2.4. Solar Neutrinos ] whereas the ““ survival probability ÏÏ is obviously The solar neutrino problem can be solved by le ly oscillations, where y \ k, q, s are all allowed, with one P(a ] a) \ 1 [ P(a ] b) . (6) important proviso: if the Los Alamos Liquid Scintillator Neutrino Detector (LSND) experiment is correct, then The parameter h is the ““ mixing angle,ÏÏ which determines ] the amplitude of the oscillations. The value h \ n/4, which le lk oscillations, with parameters that cannot solve the leads to the largest possible amplitude, is termed ““ maximal solar neutrino problem, have already been detected (White 1999). Thus, if the still-controversial LSND result is correct, mixing.ÏÏ The parameter L is the ““ oscillation length,ÏÏ and is \ given by then y k is ruled out. The MiniBOONE and BOONE experiments at Fermilab should eventually settle this issue 4nE (Bazarko 1999). L \ , (7) *m2 The precise oscillation parameter space required to account for the solar data depends on which of the solar in natural units + \ c \ 1. Note that the oscillation neutrino experiments are held to be correct. The two length increases linearly with energy. This is important, parameter ranges deÐned below, however, are broadly con- because the high energy scale under consideration sistent with all solar data; (E [ TeV) stretches the oscillation length. The parameter 2 2[ 2 1. l ] l with a small mixing angle (SMA)h is possible *m 4om1 m2 o is the squared-mass di†erence between e y ey the two mass eigenstate neutrinos. through the MSW e†ect. If this pertains, then the oscillation For totally averaged oscillations, the second sin2 factor amplitude will be far too small to a†ect Sgr A East neu- in equation (5) is set equal to 1/2, leading to trinos. ] 2. le ly with a very large mixing angle (LMA) SP(a ] b)T \ 1 sin2 2h . (8) 2 ^ 2 sin 2hey 1 is an interesting possibility for the range This, to reiterate, can be due to either distance or energy *m2 spread or both. ~3 ey ~10 10 Z 2 Z 10 . (10) Given the poor statistics of the proposed neutrino tele- eV scopes, only modes with large mixing angles, h, can be 2 ~10 2 probed (unless the MSW phenomenon takes place; see The immediate vicinity of*mey D 10 eV deÐnes ““ just- below). The atmospheric neutrino anomaly (forl Ïs) seen by so ÏÏ oscillations, where the oscillation length for solar neu- k 2 SuperKamiokande and other experiments clearly indicates trinos is of the order of 1 AU. For larger*mey values, large-angle vacuum oscillations, however (Fukuda et al. completely averaged oscillations, with a Ñux suppression 2 1998a, 1998b, 1998c; Apollonio et al. 1998). Furthermore, factor of0.5sin 2hey, result. Maximal mixing explains the solar neutrino anomaly (forleÏs) can be solved by large- almost all the data with averaged oscillations (excepting the angle oscillations (or by small-angle oscillations through Homestake result [Cleveland et al. 1998] and the contro- 342 CROCKER, MELIA, & VOLKAS Vol. 130 versial SuperKamiokande spectral anomaly). Values of vary (over and above the variation given by the spectral 2 ~3 2 *mey [ 10 eV are ruled out by the nonobservation of le shape) between maximally suppressed and unsuppressed. disappearance from reactors (CHOOZ and Palo Verde Imagining, then, that we had both a neutrino detector able experiments; Bemporad 1999; Boehm 1999). to determine the energy of an incoming neutrino to arbi- trary accuracy, and a very long time to accumulate sta- 2.5. Atmospheric and Solar Neutrino Data Combined tistics, we should be able to Ðnd an experimental signature In summary, for GC neutrinos, the following are well- of the Ñavor coherence in the form of this spectral distortion 2 motivated scenarios that are composed of two-Ñavor sub- (and thus determine whether*mey were in the just-so energy systems: range able to lead to such coherence, and, if it were, exactly what value it takes). Pragmatically, given the small statistics 1. Large-anglel ] l ] large-angle l ] l@ (scenario 4 e s k s that will accrue from the GC source and the limited energy 1). resolution expected to be achieved by any of the proposed 2. Large-anglel ] l ] large-angle l ] l (scenario 2). e ] s ] k ] q neutrino telescopes, one expects no observational conse- 3. Large-anglele lq large-angle lk ls (scenario 3). quence of the Ñavor coherence. This is because the energy 4. Small-anglel ] l ] large-angle l ] l (scenario 4). e ] y ] k ] s dependence of the Ñux suppression washes out with the 5. Small-anglele ly large-angle lk lq (scenario 5). inevitably large size of the energy bins into which particular neutrino events are accumulated. The beam, therefore, is We are now in a position to perform a number of simple indistinguishable from one in the distance-averaged oscil- calculations for neutrino oscillations between the GC and lation regime. ] the Earth motivated by the above list of two-Ñavor pos- Note also that thele ly oscillation length would sibilities. Note here that bimaximal (Vissani 1997; Barger become of the order of the GCÈEarth distance for E D 1016 2\ ~9 2 1998; Baltz, Goldhaber, & Goldhaber 1998; Jezabek & eV for*mey 10 eV . Thele Ñux would then rise from Sumino 1998; Alterelli & Feruglio 1998; Mohapatra & being suppressed below 1017 eV to being unsuppressed 17 Nussinov 1998) and trimaximal (Nussinov 1976; Giunti, above 10 eV if thele attained this energy. Of course, given Kim, & Kim 1995; Harrison, Perkins, & Scott 1994, 1996a, that the maximum energy of the shocked protons does not 1996b) mixing scenarios, which are intrinsically three- surpass D5 ] 1015 eV, this phenomenon does not occur for Ñavor, will not be considered in this paper. the GC source. Using the atmospheric problem parameters, we see that At the opposite extreme of the acceptable parameter ] 2 ^ ~3 2 thelk lx oscillation length is given by space, i.e.,*mey 10 eV , the oscillation length is E/(1 TeV) E/(1 TeV) ^ ] 8 L ^ 2.5 ] 109 m . (13) L kx 2.5 10 2 ~2 2 m . (11) ey 2 ~3 2 *mkx/(10 eV ) *mey/(10 eV ) Therefore, the oscillation length is orders of magnitude less This is back in the totally distance-averaged oscillation 2 than the size of Sgr A East for the entire neutrino spectrum regime. In conclusion, for the entire allowable*mey regime, (which only reaches up to 5 ] 1015 eV \ 5 ] 103 TeV). we pragmatically expect a situation similar to the muon- This means that the oscillations will be distance averaged, type neutrino case: totally averaged oscillations, i.e., a 50/50 and hence at Earth we expect a 50/50 mixture oflk and lx, mixture ofle andly for maximal mixing. where x \ q or x \ s, depending on which solution to the atmospheric problem turns out to be correct. 2.6. Matter E†ects? Using the solar problem parameters, one determines the A brief calculation is sufficient to show that for the GC, ] le ly oscillation length to be matter e†ects (refractive indices for neutrinos) do not impinge signiÐcantly on the oscillation probabilities. The E/(1 TeV) L ^ 2.5 ] 1015 m . (12) quantities that have to be compared are *m2/2E and ey *m2 /(10~9 eV2) ey DGF n, whereGF is the Fermi constant, and n is the electron The reference*m2 is in the ““ just-so ÏÏ range. The oscillation minus positron number density for the medium. Right at ] ey the source, we expect n D 0 because of the equal production length ofle ly oscillations in this range, therefore, becomes larger than Sgr A East for E [ 10È100 TeV or so. of electrons and positrons there. Concerning propagation of This means that the more energetic component of the l the neutrinos from source to detector, we Ðnd that the inter- e 3 beam from the source is Ñavor-coherent. stellar medium consists of approximately 1 H atom per cm , ^ ~5 ~2 ] ~14 3 In principle, such coherence would evidence itself by an so thatGF n (10 GeV )(2 10 GeV) , converting energy-dependent spectral distortion; thel Ñux at a partic- the number density to natural units. This number works out e ~46 2 ular energy (E ] E ] *E) would depend on the part of the to be about 10 GeV. The smallest *m we consider is ~10 2\ ~28 2 neutrino oscillation wave (for that particular energy) 10 eV 10 GeV , and for the highest attainable ] 15 \ ] 6 encountered by the Earth at its distance from Sgr A East, neutrino energy of 5 10 eV 5 10 GeV, we get 2 ] ~35 i.e., the neutrino Ñux at a particular energy might be any- *m /E D 2 10 GeV, so we are 11 orders of magnitude thing from maximally suppressed to unsuppressed, depend- away from having important matter e†ects due to the inter- 2 stellar medium. We do not consider matter e†ects due to ing exactly on*mey and the source-observation point distance. Certainly, ranging over the expected energy spec- dense intervening objects between the GC and Earth, since their covering fraction for Sgr A East is trivially negligible. trum (and therefore ranging overL ey), we should see the Ñux 2.7. Observational Consequences: In T heory 4 This is the situation predicted by the mirror matter or exact parity model. (See Foot, Lew, & Volkas 1991, 1992; Foot 1994; Foot & Volkas We now consider the observational consequences of sce- 1995). narios 1È5 listed above in terms of the neutrino Ñux at No. 2, 2000 SGR A EAST NEUTRINOS 343

Earth (we remind the reader that alllk mixing scenarios are Note also that, unfortunately, none of the Ðve scenarios LMA). considered here realistically exhibits the energy-dependent Ñux suppression (within an appropriate energy range) that ] ] 1. Scenario 1 (LMAle ls andlk ls@): 50% reduction would be the most telling signature of neutrino oscillations. of bothle andlk Ñux, and nolq appearance above back- Furthermore, even assuming that we possess a detector ground. with near perfect neutrino identiÐcation capability, so that ] ] 2. Scenario 2 (LMAle ls andlk lq): 50% reduction we can determine the ratios deÐned above and hence dis- ofle Ñux, and equallk andlq Ñuxes. tinguish between the Ðve broad scenarios, we still cannot 3. Scenario 3 (LMAl ] l andl ] l ): Equall and l 2 2 e q k s e q pin down*mkx or*mey further than has already been Ñuxes, and 50% reduction ofl Ñux. achieved with the terrestrial solar, atmospheric, reactor, and ] k ] 4. Scenario 4 (SMAle ly andlk ls): Unreduced le accelerator neutrino experiments.5 The allowable mixing- Ñux, 50% reducedlk Ñux, nolq appearance above back- angle parameter space might only be constrained in the ground. sense that the above ratios distinguish between a large and 5. Scenario 5 (SMAl ] l andl ] l ): Unreduced l e y k q e a small hey. Ñux, and equallk andlq Ñuxes. In the next section we examine the prospects for deter- The scenarios above imply the ratios (and ratios of ratios) mining the neutrino Ñux of each Ñavor at Earth. of neutrino Ñavor Ñuxes given in Table 1. In the table, the 3. DETECTION OF OSCILLATIONS superscript ““ obs ÏÏ denotes the Ñux ratios observed by a neutrino telescope, while ““ theor ÏÏ denotes the ratio 3.1. T he Detectors expected from the no-oscillation theoretical calculation. In this work we consider only theC‹ erenkov neutrino Deviation away from the value predicted for the no- telescopes now in planning and construction stages as oscillation case in any of the ratios deÐned in Table 1, observation platforms. Other proposed astronomical neu- beyond experimental uncertainty, would constitute a prima trino detection methods tend to require neutrino energies in facie case for whatever neutrino oscillation scenario most excess of that possessed by Sgr A East neutrinos (see closely predicts the experimental Ñuxes. Deviation in the Appendix C of Rachen &Me sza ros 1998 for a brief third-last ratio would constitute the strongest evidence for review).6 oscillation, because errors due to uncertainties in the deter- TheC‹ erenkov detectors are planned to operate through mination of the total theoretical neutrino Ñux tend to cancel the instrumentation of very large volumes (D1km3 is in taking the ratio of the theoreticalle andlk Ñavor ratios, thought to be optimal for astronomical neutrino detection; given thatleÏs andlkÏs are produced by the same mecha- Halzen 1998) of some transparent medium (in practice nism at the source. water or ice) with photomultiplier tubes (PMTs). These On the other hand, there is considerable uncertainty con- tubes will detect theC‹ erenkov light generated by super- theor cerning thelq background (see below), so estimates of 'lq luminal charged leptons traversing the detector volume. may not be particularly meaningful. For this reason, we do TheC‹ erenkov light is generated at a characteristic angle obs theor not list('lq /'lq ). As displayed in Table 1, however, in the (for the medium) away from the direction of travel of the absence of oscillations we still expect thelq Ñux to be con- charged particle. Note that only muons and extremely ener- siderably smaller than the other Ñavor Ñuxes in the absence getic tauons have path lengths through water and ice sig- of oscillations to this Ñavor type. Furthermore, deviation niÐcant on the scales of the PMT separation of these from 1 in the Ðrst two ratios deÐned could only provide detectors (tens of meters). Electrons are arrested very strong evidence of oscillations if the uncertainties in the quickly (within a meter or so), even at the highest energies power of the neutrino spectrum a and'l(10 GeV) were we are considering, O(PeV). Lower energy tauons (produced both signiÐcantly reduced by future c-ray observations 14 bylq primaries withElq \ 10 eV) decay within meters. using instruments with better energy resolution and cover- We remark in passing that, at considerably higher ener- age. The Gamma-Ray L arge-Area Space Telescope (GL AST ) gies still (i.e., D20 PeV), the Landau-Pomeranchuk-Migdal mission may be the Ðrst to provide the necessary improve- (LPM) e†ect starts to cause a measurable reduction to the ments over the next few years (Gehrels & Michelson 1999). pair-production and bremsstrahlung cross sections of the electron. This increases the radiation lengths of eB (Alvarez- Mun8 iz & Zas 1997). TABLE 1 C‹ erenkov neutrino telescopes of course encounter back- RATIOS OF NEUTRINO FLAVOR FLUXES ground generated by atmospheric muons (i.e., muons generated directly by cosmic-ray interactions in the atmosphere), Scenario as well as the atmospheric neutrino background. In fact, O N . this background overwhelms the genuine neutrino signal RATIO OSCILLATIONS 12 3 4 5

('obs/'theor) ...... 1 1 1 1 11 le le 2 2 2 5 As noted previously, however, with perfect energy resolution, the ('obs/'theor) ...... 1 1 1 1 1 1 2 lk lk 2 2 2 2 2 potential Ñavor coherence of Sgr A East over at least some of the *mey ('obs/'obs)...... 1 1 1 1 11 le lk 2 2 2 2 parameter space would have an experimental signature. ('obs/'obs)...... >1 >111 >11 6 lq lk 2 The two most interesting alternative neutrino detection techniques are (' /' )obs 1 11122 the use of air-shower arrays and radio detection of neutrino interactions in le lk ...... (' /' )theor ice. Air-shower arrays, which probably o†er the best hope forle detection le lk and identiÐcation, are limited to energies in excess of D1017 eV by the (' /' )obs 12?1 ?12?1 lq lk ...... atmospheric background (Capelle et al. 1998). Radio detection of neutrinos (' /' )theor lq lk will probably require energies at or in excess of the GC neutrino energy (' /' )obs 1 1 >1 >11>1 upper limit (i.e., 5 ] 1015 eV) because of signal-to-noise ratio problems le lq ...... 2 (' /' )theor (Gaisser et al. 1995;Alvarez-Mun8 iz, Va zquez, & Zas 1999; Alvarez-Mun8 iz le lq & Zas 1999). 344 CROCKER, MELIA, & VOLKAS Vol. 130 due to any conceivable astronomical object at sea level, and high-energy atmospheric muon background, we take these hence neutrino telescopes must be shielded somehow. This Ñuxes over a sensible range of telescope angular resolutions requirement (as well as the requirement for sufficient clarity (from2¡.0 to 0¡.3, say). Subsequently, we compare these of the medium) is what has driven all proposed sites for (angular-resolutionÈdependent) rates with the genuine, working neutrino telescopes deep (few kilometers) into the neutrino-generated event rate found by convolving the GC Antarctic ice cap or under water. neutrino spectrum with reasonable estimates for the neu- Even at these depths, however, the atmospheric muon trino detection probability. background is far from negligible. The simplest way to The probability that a high-energy muon-type neutrino is ensure exclusive selection of genuine neutrino-generated detected in a km3-scale neutrino telescope depends on two leptons against this background is to have a C‹ erenkov factors, viz., approximately inversely on the interaction detector register only ““ upcoming ÏÏ leptonsÈthose that length of the neutrino(jint) at that energy (which, in turn, arrive at a speciÐed angle to the vertical somewhat below depends on the charged-current cross section) and approx- the horizontal. It is then almost assured that such charged imately directly on the radiation length of the muon (Rk) leptons have been generated by neutrinos that traverse produced in the interaction. (We assume here that the linear some large fraction of the EarthÏs diameter and then subse- dimension of the detector is small on the scale ofRk.) We quently undergo charged-current (CC) interactions with the can make a rough estimate of the e†ect of these factors by water and/or ice at the detector or the rock/water/ice fairly writing down a detection probability multiplier that scales close to it. Exclusive selection for upcoming leptons can be as some power of the energy: achieved through a combination of geometry (simply situ- ating all PMTs so they face downward) and triggering ^ Rk ^ n Pl?k AEl . (which can discern upgoing from downgoing signal on the jint basis of fairly simple timing considerations (Spiering 1999; Halzen gives n \ 0.8 and A \ 10~6 for TeV to PeV ener- Andres et al. 2000; the AMANDA collaboration). Note that gies, with E measured in TeV units (Halzen 1998). the highest energy muons might traverse a distance of 10 Note here that all proposed neutrino detectors will have km water equivalent and still retain sufficient energy to ‹ an overburden depth less than the radiation length of produce a detectableCerenkov signal (Gandhi et al. 1996, muons with energies in the energy range we are considering l 1998). The e†ective volume, therefore, fork detection is (see later). This means that the above method actually over- substantially larger than the ““ instrumented ÏÏ volume. estimates the neutrino detection probability for downward- Of course, such a simple triggering system (and geometry) going neutrinos, because the volume of material above a means that one misses out completely on the signal from detector available for the neutrino to interact within (and downgoing neutrinos (which also generate downgoing subsequently produce a muon that might then travel on to leptons in CC interactions). This may seem like a reason- the detector volume) is substantially less than that for able compromise (the e†ective detector area is greater from upward-going neutrinos. below, after all, because of the greater amount of material Employing the above (generous) parameterization of the below the detector than above), until one considers the fact neutrino detection probability allows us to determine that that for high-energy neutrinos, Earth ““ shadowing ÏÏ or the GC signal does not, in fact, emerge clearly from the opacity becomes a signiÐcant e†ect. A neutrino is shadowed background until well into the upper end of the neutrino when its interaction length becomes smaller than the dis- energy spectrum (even for a detector resolution as low as tance it must travel through the Earth to reach a detector. 0¡.3 and the Ñattest empirically allowable neutrino spec- D 15 At energies of 10 eV, Earth opacity a†ects all neutrinos trum, a \ 2.1). It seems that even granted a detector able to except those that reach a detector from an almost horizon- trigger on neutrino-generated, downgoing leptons, we tal direction. It would seem, therefore, that with the scheme cannot, on the basis of our preliminary calculations, con- described above (reject all downgoing leptons) and the Ðdently conclude that we might see the GC source in such a È unavoidable issue of Earth opacity, ultra high-energy neu- way. We therefore restrict ourselves to consideration of the trino telescopy is impossible, except for a tiny window on Sgr A East signal to be found in upcoming leptons. neutrinos that come from a practically horizontal direction. An immediate consequence of this self-imposed È In order for ultra high-energy neutrino astronomy to restriction is that we are unable to reach many conclusions have a future, detector triggering must be designed that about the usefulness of the (successor to the) AMANDA does something smarter than simply rejecting all down- neutrino telescope in regard to observing the GC. This is going leptons; it must be able to select something of the somewhat unfortunate, because the AMANDA experiment, genuine downgoing signal, at least at higher energies. For of all neutrino telescope projects, is probably the best cur- the moment, let us assume that some more discerning rently placed to realize the desired km3 status and thus trigger can be instantiated. The question now is, does the evolve to IceCube.7 This is because AMANDA/IceCubeÏs GC neutrino source have a large enough Ñux at high ener- South Polar location means that the GC is always overhead gies to be seen against the muon background (for reason- from the detector. A detector-speciÐc Monte Carlo calcu- able values of telescope angular resolution), even in lation will probably be needed to settle whether our particu- principle? lar source can be seen by IceCube. We can predict, however, To make this calculation, we Ðrst adopt values for the high-energy (vertical) Ñuxes of atmospheric muons at sea level given elsewhere (Thunman, Ingelman, & Gondolo 7 The IceCube project, provided that it continues to pass through scien- 1996, Fig. 3) and then convolve these Ñuxes with values for tiÐc review and Ðnd funding, will go into construction in the 2001-2002 Antarctic season and should take 6È7 yr to complete. The detector will be the probabilities for these muons to reach the particular operated as it grows (F. Halzen 2000, private communication). Information water and ice depths of the proposed detectors (Antonioli et about IceCube can be found at the IceCube Project website, http:// al. 1997) Then, to determine event rates in a detector due to pheno.physics.wisc.edu/IceCube/. No. 2, 2000 SGR A EAST NEUTRINOS 345 that IceCube may well be able to detect the distinctive Ñavor type). Charged-current interactions of a muon-type ““ double-bang ÏÏ signature of GClq interactions above the neutrino in or near the detector volume result in a nearly background; see below. pointlike hadronic shower and a high-energy muon (kB) We must therefore look to the northern hemisphere for lk which, we reiterate, might travel up to 10 km and still observing platforms about which we can make more con- possess enough energy to be detected. Certainly in the 100 Ðdent predictions regarding the GC source. There are cur- GeV energy scales of relevance to this paper, muons will be rently four neutrino telescope projects under development ““ uncontained ÏÏ in the sense that they cannot be expected to there. The Lake Baikal project is a mature experiment, be both generated and arrested within the km3 detector having run on and o† since 1993. This collaboration has volumes. Such long tracks mean, of course, very good deter- achieved an e†ective energy-dependent detector area of mination of the muonÏs direction of travel. On the other 1000È5000 m2 and has demonstrated the viability of large- hand, the fact that the muons are necessarily uncontained scale water-basedC‹ erenkov technology. The collaboration leads to uncertainty in energy determination. We now is planning for a neutrino telescope of 5È10 ] 104 m 2 e†ec- discuss, in the context of the observation of neutrino- tive area. This will not be a large enough platform for the generated muons, the general issues of angular and energy relatively high energy (and low Ñux) neutrino signal gener- determination in more detail. ated at Sgr A East (Balkanov et al. 1999). Three other projects, all based in the deep Mediterra- 3.3.1. Energy Determination nean, are currently in the design and prototype stage. These An accurate determination of the energy possessed by a are ANTARES, NESTOR, and NEMO. None of these pro- muon neutrino (which produces a muon observed by a jects is guaranteed of the funds to reach km3 status, detector) is limited by three factors: uncertainty in the frac- although this is the stated goal of all three collaborations. tion of the neutrinoÏs total energy imparted to the muon, Needless to say, these deep-sea environment projects call ignorance of the energy loss by the muon outside the instru- for great ingenuity and considerable technical innovation. mented volume, and, Ðnally, the intrinsic energy resolution The ANTARES collaboration has completed preliminary of the detector apparatus itself (ANATRES Collaboration reconnaissance of its chosen site at a depth of 2400 m below 1999). the sea near Toulon. They are also well into design of elec- Regarding the Ðrst factor, it can be shown that the tronics and mechanics for the detector. The collaborationÏs average energy imparted to the muon is half that of the current midterm goal is to have 13 ““ strings,ÏÏ with D1000 neutrino in the CC interactionl d ] k~u, and three- ] ` k attached PMTs, in place by 2003. Such a conÐguration quarters in the interactionlk u k d (ANATRES Collabo- would have an e†ective area of 0.1 km3 (ANATRES Col- ration 1999). A determination of an individual muonÏs laboration 1999). energy, then, might only give us a minimum energy for the The NESTOR collaboration plans for a deployment at neutrino primary, but this problem is not a limiting factor if D4000 m depth o† the southwest Grecian coast. This col- a signiÐcant number of events can be accumulated and if we laboration is at a similar stage of advancement to the take a statistical view. ANTARES group, having completed reconnaissance of Note that when the muon is uncontained, and hence an their chosen site and preliminary Ðeld testing of crucial accurate determination cannot be achieved by measuring components. NESTOR also aims for a 0.1 km2 e†ective the length of the entire muon track, a rougher muon energy area detector in the near future (Trasatti 1999). determination can be achieved forEk [ 1 TeV by measur- Lastly, the NEMO project is least advanced, being in the ingdE /dx, because at such energies, where energy loss is k P early research and development stage. This collaboration is dominated by radiative processes,(dEk/dx) E. It may also investigating the suitability of a site o† the southern Italian eventually be possible to glean some neutrino energy infor- coast. They have conducted Monte Carlo studies of their mation from the hadronic shower resulting from the Ðrst proposed detector layout (Montaruli 1999). CC interaction, if this happens to be within the detector In conclusion, we do not expect to see a km3 neutrino volume (keeping in mind the difficulty posed by the rela- telescope in the northern hemisphere within a decade, but tively small size of such showers on the scale of a next- within two decades the chances for such would seem to be generation detectorÏs PMT spacing). quite good. That we are dealing with uncontained muon tracks means that one can only arrive at a minimum original 3.2. Neutral-Current Interactions muon energy. That we can make some sort of energy deter- Neutral-current (NC) interactions do not identify the mination fromdEk/dx, however, means that we have a incoming neutrino Ñavor and basically constitute a back- much better idea of the original energy of a totally uncon- ground to the more useful charged-current interactions. tained muon than would be imparted by just assigning it a Energy determination for NC events is poor because of the minimum energy, enough to take it across the detector. missing Ðnal-state neutrino. Angular determination is also Given all the above factors, the ANTARES collaboration poor, because the single hadronic shower produced is has judged on the basis of Monte Carlo simulations of their almost pointlike on the scale of a typical detectorÏs PMT detector array that they can gauge a muon neutrinoÏs spacing. NC interactions are only about one-third as energy to within a factor of 3 forEl [ 1 TeV (ANATRES common as CC interactions. Collaboration 1999).

3.3. Muon Neutrinos 3.3.2. Angular Determination The best prospects for observing any neutrino Ñux from Again, three factors limit the determination of the the GC source are o†ered by muon-type neutrinos:lkÏs and primary neutrinoÏs direction of travel. These are the uncer- lkÏs (we remind the reader that neutrino telescopes cannot tainty in the angle between the incominglk and the distinguish a neutrino from an antineutrino of the same resulting k, the deviation of the k away from its original 346 CROCKER, MELIA, & VOLKAS Vol. 130 direction of travel due to multiple scattering, and, lastly, the for the regeneration e†ect due to NC interactions that detectorÏs intrinsic angular resolution as determined by a†ects all neutrino Ñavors. We expect this e†ect to be small; uncertainties in its exact geometry, etc. (ANATRES Col- see Kwiecinski, Martin, & Stasto 1999.) laboration 1999). Of course, the severity of the Ðrst two Muon Neutrino Background problems decreases with increasing energy, but the relative 3.3.4. severity of the two likely changes with energy. For example, We note, in passing, one unavoidable source oflk back- the ANTARES collaboration has determined from MC ground; CClq interactions can mimic CClk interactions if simulations that below 10 TeV total angular resolution is (1) thelq energy is too low to e†ectively separate the orig- limited by detector e†ects, whereas above 100 TeV it is inal CC interaction vertex and the q decay vertex, and (2) limited by the unavoidable angular distribution of the neu- the q decays muonically (the branching ratio for this decay trino interactions. They claim that an angular resolution of is D17%; Caso et al. 1999). 0¡.3 is achievable (ANATRES Collaboration 1999). With such a resolution, the GC signal is above the atmospheric 3.4. Electron Neutrinos neutrino background for energies greater than a few ] 100 In contrast to the case for muon neutrinos, the prospects B GeV. for identifying electrons (e ) in a detector generated by leÏs The AMANDA project (which it is hoped will evolve into from the direction of the GC seem remote. Quite a few of IceCube) has to contend with the short scattering length of the signiÐcant problems with observing thele signal can be theC‹ erenkov light in ice, 24 m, as compared to seawater at related back to the relatively tiny propagation length greater than 200 m. Despite this, IceCube will achieve an (Dmeter) of high-energy electrons (and positrons) in matter. angular resolution of less than 1¡, and perhaps as low as 0¡.4 Perhaps most signiÐcant is that, as with NC interactions, (F. Halzen 2000, private communication). We note that the hadronic and electromagnetic showers initiated by a le such a resolution will mean that many southern sky sources in a CC interaction have almost pointlike dimension on the (i.e., sources of downgoing neutrinos) will be able to be seen scale of the proposed detectors, and hence provide little by IceCube above the atmospheric muon background. directional information. Thus, even if we grant that an electron signal in the appropriate energy range for the GC 3.3.3. Earth Opacity source might be identiÐed, we cannot actually identify the At D4 ] 1013 eV \ 40 TeV, the interaction lengths of all origin of the primary electron neutrino. neutrino Ñavors become less than the EarthÏs diameter. This A second problem is that electron-neutrinoÈinitiated CC means that, in particular,lkÏs are unlikely to reach a detec- events are very difficult to conclusively identify. In principle, tor from a nadir angle of 0¡ (ANATRES Collaboration a smoking gun for such events is presented by the coin- 1999). (The same is true forleÏs, but not lqÏs; see below.) The cident presence of both a hadronic shower (from the dis- and attenuation of thelk interaction length continues until at turbed nucleus) an electromagnetic shower from the D1015 eV it is less than a very small fraction of the EarthÏs quickly braked eB. It is very difficult, however, for the pro- diameter, so that this Ñavor is attenuated over all nadir posed next-generationC‹ erenkov technology to distinguish angles, even those approaching the horizontal. At such high between the two types of showers. Both showers, we repeat, energies, then, the Earth is said to be ““ opaque ÏÏ tolkÏs (and are essentially pointlike on the scale of the typical detectorÏs leÏs) (Nicolaidis & Taramopoulos 1996). We must take both PMT spacing and, after all, are observed only indirectly this e†ect and our self-imposed requirement that the GC through theC‹ erenkov Ñash they produce. Thus, NC events, neutrino source be below the horizon from the observation which produce a pointlike hadronic shower, are difficult to point (in order to avoid the atmospheric muon background distinguish from CCle-initiated events, and provide a sig- problem) into account to generate a more realistic estimate niÐcant background problem. Furthermore, even imagining of the event rate due to the GC source. that we had some reliable technology to identify the pres- Let us assume the best-case scenario forlk ÑuxesÈ ence of a high-energy electron, the CC interactions of lqÏs detector angular resolution of0¡.3 and a neutrino spectrum can still mimic CCle events if (1) the q energy is not high with a \ 2.1Èto make a determination of the expected enough to ensure that the hadronic shower from the CC event rate in a hypothetical km3 detector located on the interaction of the primarylq and the later decay are e†ec- proposed ANTARES site. Note that with this revised tively separated on the scale of the detector, and (2) the q angular resolution, the GC neutrino Ñux is above atmo- decays electronically (with a branching ratio of D18%; spheric neutrino background at an energy around an order Caso et al. 1999). of magnitude lower than previously: a few 100 GeV. Also A yet further problem is the fact that the short path of the note that the GC is below the horizon about two-thirds of electron in matter means that one can only register con- the time from this latitude (Zombeck 1990), and therefore is tainedle CC events, dramatically reducing the e†ective invisible at least one-third of the time (even if low enough volume monitored by the detector in comparison to lk detector resolution were achieved to unequivocally avoid events. the atmospheric muon background problem, ANTARES is Altogether, one cannot but conclude that the chances for being designed with downward-pointing PMTs). Adopting detecting GCleÏs, at this stage, seem remote. the neutrino penetration coefficients calculated by Naumov & Perrone (1999, Fig. 3), we determine that the expected 3.5. Tauon Neutrinos annual event rate fromlkÏs generated at the GC is D40 for Although the chances for observing GClqÏs seem more the no-oscillation case and D20 if oscillations do occur. For hopeful than those for GCleÏs, there will still be consider- a \ 2.4, but retaining an angular resolution of0¡.3, we able problems with this Ñavor. At least two unique signa- expect D5 events without oscillation and D2 with. Clearly, tures for thelq have been identiÐed in the literature: (1) the then, we approach the lower end of statistical relevance with ““ double-bang ÏÏ and (2) Ñat angular dependence of the signal this value for a. (In these calculations we have not allowed or ““ pile-up ÏÏ (Nicolaidis & Taramopoulos 1996; Learned & No. 2, 2000 SGR A EAST NEUTRINOS 347

Pakvasa 1995; Halzen & Saltzberg 1998; Iyer et al. 2000). interaction length of thelq becomes, as for thele andlk, less These both, however, tend to become signiÐcant on the than the Earth diameter. But whereas eÏs and kÏs resulting higher energy side of the GC neutrino spectrum. from CC interactions are stopped in the Earth, qÏs from CC interactions decay back tolqÏs before being stopped, 3.5.1. Double-Bang producing a neutrino with something around one-quarter In more detail, the ““ double-bang ÏÏ signal requires that a the energy of the original and traveling in much the same lq undergo a CC interaction in the detector volume to direction. This process can occur more than once, each iter- produce a q. If the energy of this q is high enough, then the ation producing a progressively lower energylq, ensuring hadronic shower resulting from the initial interaction of the that whatever the energy of the primarylq, alq signal from neutrino primary and the later hadronic shower resulting a point source should reach a detector on the other side of from the q decay will be resolvable on the scale of the detec- the Earth. This signal will exhibit a ““ pile-up ÏÏ just below the tor. Exactly where the resolvability threshold is can prob- energy at which thelqÏs interaction length becomes greater ably only be determined by detector-speciÐc MC than the fraction of the EarthÏs diameter subtended by a ray simulations. The ANTARES group believes that the signal from the source to the detector. 12 certainly cannot be resolved forElq \ 100 TeV (ANATRES In other words, forle,k energies in excess of D10 eV, as Collaboration 1999). AtEq D PeV, toward the upper limit the angle between a neutrino source and the nadir is of the GC neutrino spectrum, the two bangs should be decreased from 90¡, a critical angle will be reached at which separated by about 100 m and clearly resolvable. thele,k Ñux will begin to be attenuated. This attenuation The usefulness of this signature, then, will depend on increases to reach a maximum at 0¡. Furthermore, as the detector speciÐcs and the question of whether a statistically energy of thele,k signal increases, the Ñux attenuation sets signiÐcant Ñux can be obtained from whatever part of the lq in at increasingly large (i.e., increasingly horizontal) angles. spectrum remains able to produce a signal. On the other hand, thelq Ñux, although shifted down- We also note that Earth opacity will signiÐcantly reduce ward in energy, should still be the same. This results in the the Ñux oflqÏs sufficiently energetic to produce the double- Ñat angular dependence of thelq part of the signal at high bang signal if one is looking for the signal in upcoming energies and, given a signiÐcantlq component of the total neutrinos. It is in searching for the double-bang signature neutrino Ñux, a Ñatter than expected angular dependence of from GClqÏs, then, that we can predict that AMANDA (or, the total neutrino Ñux. more precisely, IceCube, the km3 extension of AMANDA) One way to search for al signal, then, is through the ] q may well Ðnd employment in regard to this source; GC decay chainq lq klk (branching ratio D17%; Caso et al. neutrinos will not be a†ected by Earth opacity when 1999). Given the above considerations, if we assume that a observed by IceCube. (The genuine GClq Ñux is substan- signiÐcant part of a neutrino signal is due tolqÏs, we expect tially above that of the atmosphericlqÏs due to ““ prompt ÏÏ an enhancement of the number of kÏs coming from the and conventional Ñux over an angular resolution even as direction of our source, below certain energies and nadir bad as 2¡ [Pasquali & Reno 1999], and 2¡ is a pessimistic angles, over that expected from the ““ raw ÏÏlk andlq Ñuxes. prediction for the IceCubeÏs angular resolution [F. Halzen In order to see this enhancement, however, we require that 2000, private communication; Halzen 1998]). Assuming a the l energy spectrum not be too steep. Otherwise, the best-case scenario forlq detection, viz., the Ñattest allowable increase of the k Ñux in some particular lower energy bin GC spectrum (a \ 2.1), double-bang resolvability all the will be insigniÐcant on the scale of the number of events ] way down to 100 TeV andlk lq oscillations, and that would be recorded there anyway due to the rawlk and assuming a double-bang detection probability given by 1 lq Ñuxes. kmwe/jint (here 1 kmwe means 1 km water equivalent), we Iyer et al. (2000) have made calculations of the pile-up can arrive at an (optimistic) annual event rate prediction for enhancement for neutrino spectra that scale as di†erent IceCube. negative powers: n \ 1, 2, and 3.6. For n \ 1 the enhance- We derive the double-bang detection probability by ment is a noticeable e†ect, but for n \ 2 and greater the employing similar logic to that which led to thelk detection spectra are too steep for the e†ect to be discernible. For the probability presented previously. The di†erence here is that Sgr A East neutrino Ñux, with a best-case spectrum that has we assume that the q decay length is small on the scale of the n \ 2.1, we must unfortunately conclude that the above linear dimension of the detector (hence the 1 in the diagnostic for the presence of a signiÐcantlq component in numerator), whereas previously we assumed that the k radi- the total neutrino signal will not be useful. ation length is large in comparison to this scale. We employ In summary, for thelq case, we believe that the GC can a parameterization of the neutrino interaction length pre- producelqÏs energetic enough to produce a double-bang sented in graphic form in Gandhi et al. (1996, Fig. 11; 1998). signal, but that the spectrum is too steep to evidence lqÏs Using the detection probability described above, and the with pile-up. A preliminary calculation reveals a double- best-case scenarios for the GC spectrum and double-bang bang signal at the threshold of detectability in IceCube, but resolvability, we determine an event rate of one double- a conÐdent indication that this signal will produce a sta- bang signal per year. This is at the threshold of detect- tistically signiÐcant event rate requires a detector-speciÐc ability. study.

3.5.2. Pile-Up 3.5.3. Tauon Neutrino Background The idea behind the secondlq signatureÈthe Ñat angular As has been mentioned, we expect nolq Ñux from pion dependence that has recently received attention from decay from p-p scattering at the GC in the absence of oscil- Halzen & Saltzberg (1998) and Iyer et al. (2000)Èis to lations, and hence, observation of alq Ñux of the order of actually make positive use of the Earth opacity previously thel orl Ñux constitutes prima facie evidence for exactly ] 13 e k mentioned. WhenElq climbs beyond D4 10 eV, the such neutrino oscillations. One must be concerned, 348 CROCKER, MELIA, & VOLKAS Vol. 130 however, about sources of background to thelq oscillation Note in passing that determination of the Ñavor composi- signal, both genuinelq Ñux from sources that have not been tion of the GC neutrino signal could certainly provide for accounted for and falselq signals in the detector. stringent tests of various alternative, no-oscillation explana- One source oflqÏs that we can anticipate at higher ener- tions of the solar and atmospheric neutrino anomalies if gies at the production site is the decay of charmed mesons these are not ruled out in the near future. For instance, a (principallyDs) produced in p-p scattering through q and lq largelk component in the GC neutrino spectrum would production. It should be noted that the cross sections for c imply a much larger lower limit on the““ lk lifetime ÏÏ (we andc production via p-p scattering are greatly uncertain in should, strictly speaking, consider the lifetimes of the mass the energy range of interest, as are the fractional likelihood eigenstates that make up thelk) than is required to explain ] ] ofc Ds and the branching ratio forDs qlq (Caso et al. the atmospheric neutrino anomaly (see, e.g., Barger et al. 1999; Pasquali & Reno 1999). In comparison, however, 1999). On the other hand, Ñavor-changing neutral currents with pion production processes leading tole,k, such (FCNC), invoked as explanations of the atmospheric charmed meson production is still greatly suppressed. The anomaly (Wolfenstein 1978, 1979; Brooijmans 1998; obs obs Ñux ratio'lq /'lk can still, therefore, be expected to be a Gonzalez-Garcia et al. 1999; Lipari & Lusignoli 1999), small number taking this process into account, although cannot a†ect the Sgr A East signal. This is because the obs theor there might be considerable deviation from 1 in 'lq /'lq column density encountered by neutrinos propagating from (if we assume large statistics) without oscillations necessar- the GC to the Earth is far too small to allow this mechanism ily being implied. to occur. FCNC explanations of the atmospheric anomaly, then, predict a GC neutrino event rate undiminished from 4. OBSERVATIONAL CONSEQUENCES: IN PRACTICE thena• ve expectation, and deviation from this would tell against such explanations. If we grant that the GC source will not produceleÏs in an observational energy range, might producel Ïs in an obser- q 5. GENERAL BACKGROUND PROBLEMS vational range, and certainly will produce observational lkÏs, we are left with only one useful Ñux ratio that is There are a number of sources of background to the GC certainly measurable: neutrino signal. Logically, we can break these down into the two general classes: (1) ““ enshrouded sources ÏÏ and (2) ter- obs 'lk restrial background. By the former, we mean any sources of theor , (14) 'lk genuine neutrino signal from the GC that are ““ hidden ÏÏ in the sense that they are not correlated with the GC c-ray and two that may be measurable: spectrum. By the latter we mean the atmospheric neutrino obs obs and muon backgrounds that are endemic. These two have 'lq ('lq/'lk) obs , theor . (15) already been addressed. 'lk ('lq/'lk) As previously discussed, deviation from 1 in the Ðrst 5.1. Background from Enshrouded Sources ratio, by itself, would provide only weak evidence for oscil- We know of two potential sources of an enshrouded neu- lations unless the empirical values of a and'l(10 GeV) were trino signal from the GC. The Ðrst, neutrino production via further constrained (by future c-ray observations). Even if high-energy cosmic-ray scattering on the ambient material this were achieved, however, given the indirectness of the in the Galactic plane, is virtually assured (Gaisser, Halzen, theor 'lk measurement, there would have to be some doubt & Stanev 1995; Ingelman & Thunman 1996). The other, about whether the presence of oscillations had been conclu- neutrino production via annihilation of WIMPs accumulat- sively demonstrated. With empirical determination of the ed in the gravitational well at the GC, is a possibility values of all three ratios, only scenario 3 emerges with a (Jungman, Kamionkowski, & Griest 1996; Gondolo & Silk unique signature. Otherwise, we can only distinguish the 1999). l ] l scenarios (1 and 4) from thel ] l scenarios (2 and k s k q 5.1.1. Neutrino Production o† the Interstellar Medium 5), without being able to conclude anything about le obs obs Note that the Ðrst background source is, like the Sgr A mixing. Certainly, however,'lq /'lk potentially o†ers very strong evidence of oscillations if it is found to deviate sub- East source, due to decay of pions produced in nucleon- stantially from zero. proton scattering. The density of ambient matter in the Given that the measurement of these ratios lies at least a galaxy is greatest, in general, in the Galactic plane, and decade in the future, it is in fact not unlikely that the uncer- greatest of all at the GC, so we can expect a large background neutrino Ñux from this direction. Of course, the tainty regarding thele andlk oscillation modes will be largely dispelled by the time of such measurement, i.e., other pionic decay also leads to the production of cÏs. That we experiments will determine which of the scenarios 1 to 5 (or consider this neutrino source enshrouded, then, is due to the bimaximal or trimaximal oscillations, or even one of the relatively large angular resolution of the proposed neutrino nonoscillation scenarios; see below) actually occurs in telescopes; the neutrino telescopes see neutrinos from a nature. The most interesting science that might be extracted much larger area of sky than the c-deÐned size of Sgr A from GC neutrino observations, then, may be an empirical East. Detailed estimates have been made of the rate of neutrino determination of a and'l(10 GeV) independent of c-ray observations.8 production by the interaction of cosmic rays with the interstellar medium (Ingelman & Thunman 1996). This neutrino 8 ] Ñux has been shown, however, to be below the atmospheric With the certain knowledge thatlk lx oscillations do take place, and hence the knowledge that'obs/'theor must be 1/2, and from an empiri- neutrino background for much of the energy range under lk lk consideration. Even given that the GC background exceeds cal determination of thelk spectrum, one can work backward to obtain 'theor, and thence a and' (10 GeV). ] 14 lk l the atmospheric one above D5 10 eV, the background No. 2, 2000 SGR A EAST NEUTRINOS 349 from0¡.3 of sky (as relevant for ANTARES) is still consider- tainties in the total expected neutrino Ñux calculated on the ably below the signal. basis of c-ray observations. Certainly, the value of a, the 5.1.2. Neutrino Production from W IMP Annihilation numerical power of the power-law proton spectrum at Sgr A East, would have to be further constrained before the The exact Ñavor composition of the neutrino Ñux gener- above became a useful diagnostic [as would' (10 eV)]. The ated by WIMP annihilation is model-dependent. It is con- l actuall Ñux should be able to be inferred from thel event ceivable, for instance, that a largel component might be k k q rate experienced by a future Mediterranean-based km3 present in this signal, if it exists at all. There is a fairly robust C‹ erenkov neutrino detector. and model-independent upper bound to the WIMP mass of Strong conÐrmation of the oscillation signature will 300 TeV (Jungman et al. 1996). Neutrinos generated in require observation ofl Ñux from the GC to see whether WIMP annihilation processes will have typically between e thel :l ratio varies signiÐcantly from 1/2 (although, as one-half and one-third the WIMP rest-mass energy e k discussed, if the small mixing angle solution to the solar (ANATRES Collaboration 1999). We cannot, therefore, neutrino problem is correct,l Ïs will not oscillate on their strictly rule out the possibility that the Sgr A East neutrino e way from the GC). The energetics of the GC ““ beam,ÏÏ signal is polluted with neutrinos from WIMP annihilation. however, place it below the region where next-generation We do not consider this possibility in any detail, however, techniques and detectors are currently predicted to be able because most reasonable WIMP candidates have maximum to identify al component. Such a conÐrmation, then, must masses some orders of magnitude below this. The neutral- e lie some decades in the future. ino, for instance, cannot be more massive than D3 TeV if it Perhaps the best science that might be extracted from the is to be a WIMP candidate (Jungman et al. 1996). Neutrinos GC neutrino spectrum as observed by a future km3 produced in its decay, therefore, can, at worst, be just below C‹ erenkov neutrino detector, assuming that other experi- the energy cuto† of the part of the GC neutrino signal we ments resolve the electron- and muon-type neutrino oscil- are examining. lation mode questions Ðrst, is an empirical determination of 6. CONCLUSION a. By such a determination, a neutrino telescope would The GC neutrino source should produce an observable realize the aspiration expressed in its very name, that, at oscillation signature. The strongest evidence for such would base, it is a device for investigating the nature of astronomical objects, not merely the radiation they emit.9 take the form of alq Ñux attaining a signiÐcant fraction of thelk Ñux from this source. Such alq Ñux can be inferred from the double-bang signature at IceCube, the km3 suc- R. M. C. gratefully acknowledges useful discussion and cessor to the AMANDA telescope. Detector-speciÐc simu- correspondence with D. Fargion, F. Halzen, A. Oshlack, lations are required for a conÐdent determination of W. Rhodes, and M. Whiting. R. R. V. would like to thank whether the double-bang event rate due to the GC will be V. Barger for a useful discussion; he is supported by the statistically signiÐcant in the event that either of scenarios 2, Australian Research Council. R. M. C. is supported 3, or 5 is correct, but preliminary calculations reveal that by the Commonwealth of Australia. F. M. is partially this event rate may be just at the threshold of detectability. supported by NASA under grant NAGW-2518 at the Such simulations are also required to determine whether University of Arizona. IceCube might see the GClk signal against the atmospheric muon background. A deviation from the expectedlk Ñux determined from c-ray observations of the GC is guaranteed for all neutrino oscillation scenarios identiÐed. Observation of such a deviation would, however, constitute more equivocal evidence 9 for oscillation than a stronglq signal, because of uncer- A similar point is made by Ra†elt (1998).

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