Inverse muon charge ratio induced by solar neutrons

Astroparticle Physics ELSEVIER

Astroparticle

Physics

11 ( 1999) 335-346 www.elsevier.nl/locate/astropart

Inverse muon charge ratio induced by solar neutrons J.N. Capdevielle,

Y. Muraki

B C&e,+? de France, Paris 75231. France b STE-lab, Nagoya rmivenity, Nagoyu 464-8601, Japan Received 24 August

1998; revised

12 December

1998; accepted

23 December

1998

Abstract An extensive Monte Carlo calculation has been carried out on the propagation of solar flare particles in the energy range I-100 GeV. The fluxes of neutrons and muons are derived as a function of primary neutron and proton energies. A very interesting result, an inverse muon charge ratio effect, is predicted during solar flare neutron arrivals. This consequence can be applied to high energy neutron emission resulting in the inverse muon charge ratio during bursts of neutron emission by several astronomical objects within a few parsec from Earth.@ 1999 Elsevier Science B.V. All rights reserved.

1. Introduction We have carried out extensive Monte Carlo calculations on secondary particles produced by primary solar flare particles in the Earth’s atmosphere and arriving at the altitudes of Mt. Chacaltaya (5200 m above sea level) and Mt. Norikura (2800 m a.s.1.). We are especially interested in muons induced by solar flare neutrons, arriving at Mt. Chacaltaya and Mt. Norikura. In an earlier experiment at Mt. Chacaltaya, a large area muon detector was installed under the Nagoya-BASJE new scintillation detector, two decades ago. Muons penetrating an absorber of 2.0 m of galena were detected by a 60 m2 scintillator array. Muons with incident energies greater than 600 MeV can penetrate this material [ 11. At Mt. Norikura, an experiment with a different design is being operated, utilizing a 36 m* muon telescope in which muons with incident energy greater than N 100 MeV from different directions can be identified by a pair of scintillators [ 21. Between upper and lower scintillators, a layer of 5 cm thick lead sheet is inserted in. Showers are absorbed by the lead

sheet and the two decks of scintillators are separated by 1.73 m. Our Monte Carlo computation focuses on one question: what is the energy threshold above which the primary neutrons can produce muons which can trigger the detectors? We have found an important fact by present calculation that the muon flux induced by solar neutrons exceed the flux of neutrons approximately beyond 30 GeV of incident neutron energy. We propose here to use the muon signal to elucidate a very important question, i.e., how high ions are accelerated at the solar surface. In performing the Monte Carlo computations, we have pointed out another very interesting feature: the muon charge ratio is inverted, i.e. there is a negatively charged muon excess over the positively charged in contrast with the positive excess observed in cosmic rays. The excess of negatively charged muons is induced by solar neutrons in the Earth’s atmosphere. Namely, in case of one pion production by incident neutrons, the charge of pions must be either neutral or negative. Neutral pions produce electromagnetic

0927-6505/99/s see front matter @ 1999 Elsevier Science B.V. All rights reserved PI1 50927.6505(99)00002-X

336

J.N. Capdevielle, Y: Muraki/Astroparticle Physics I1 (1999) 335-346

showers, while negative pions make negative muons. At least at the high energy region where we can neglect the target charge effect, this feature becomes realistic, We also propose in this paper that this signal can be used for the confirmation of neutron arrivals. In Section 2, we describe the fundamental processes and parameters of the Monte Carlo calculation. Then in Section 3, results of the Monte Carlo calculation are given, i.e. the detection efficiencies of muons, neutrons, and photons induced by solar neutrons and protons as a function of primary neutron or proton energy. One of the most interesting results, the inverse effect of muon charge ratio, is highlighted. Finally, in Section 4, we will discuss the possibility of measuring the inverse muon charge ratio using standard techniques. The electronic antineutrino enhancement correlated with the negative charge excess of the muons is briefly considered in Sections 3 and 4.

2. Method of simulation of propagation and interaction of solar flare particles in Earth’s atmosphere Our simulation was performed using version 5.20 of the programme CORSKA, developed by Capdevielle et al. [ 31. We have adapted this code to the various interactions and specific processes concerning the particle propagation through the atmosphere by dividing the dynamical energy range for the computation into two parts: (a) the lower parts of the high energy domain, at energies lower than the energy attained in CERN ISR and in Fermilab for p-A collisions, i.e., at laboratory energies in the range 50 GeV < Et& < 1000 GeV, (The most energetic particles seen to date from solar flares penetrating the atmosphere have been reported at energies above 500 GeV by the Baksan group [ 41, using the underground scintillation telescope BUST.) (b) the intermediate energy region and the nuclear physics domain, at energies less than 4 I 10 GeV, i.e. at Elab < 50 GeV. Here fi denotes total energy in the CM System of the colliding hadrons. 2.1. Fundamental processes and basic assumptions 2.1.1. High energy part Among the large variety of interaction models and respective Monte Carlo generators, various sets of op-

tions are available in the implementation of CORSIKH. The majority of them are based on GribovRegge arguments. In our calculations, we have limited our choice to the default option of the Hybrid Dual Parton Model (HDPM) to describe the multiple production in the various hadron-air collisions [ 51. This selection was motivated by the comparatively short computer time required for the calculations and the reproduction of the fundamental part of the accelerator data over a wide parametric range. The selection used here, besides being efficient, has sufficient accuracy when compared with more sophisticated models [ 61, at least in this energy range for Elab = 50 GeV1000 GeV Furthermore, taking account of the situation that only a very small proportion of cascades can be initiated in the high energy region in case of solar flares, this high energy region of the Monte Carlo routine has been used only to derive some asymptotic tendencies. The HDPM contains, however, some important features such as diffractive and non-diffractive components, correlation between the average transverse momentum and central rapidity density, charge exchange probabilities, especially for pions and kaons, and cross sections in agreement with the measured values, even for incoming charged mesons with momenta up to 300 GeV/c. This model developed according to the guide lines and arguments based on the dual parton model [7] to reproduce the CERN and Fermilab colliders data, is not perfectly adapted to describe the hadron-nucleus collisions at energies less than 10 GeV. This is a general difficulty for all the models of the Gribov-Regge family when they have to be combined with the Glauber theory [ 81.

2.1.2. Intermediate energy part In consequence, at energies less than 80 GeV (in the Laboratory system), all the hadron multi-production is provided by the program GHEISHA [9], which is included in the CORSIKA package. This program plays an important role in the present work. We underline here how the very detailed processes implemented in GHEISHA have been critical in determining solar flare consequences. The exhaustive character of this code is illustrated by some of the typical features listed below: - elastic and quasi-elastic scattering, - diffractive dissociation,

J.N. Capdevielle. ): Muraki/Astroparticle Physics I I (1999) 335-346

nuclear excitation (when the creation of particles is energetically disallowed), treatment of K+/-, K”‘s, T’S, KNO scaling, nuclear evaporation, Fermi motion, self-absorption in heavy nuclei (Argon, Nitrogen and Oxygen), annihilation channels against neutrons or protons in the nuclear target, and production of As, KS, Cs, %, Rs, and as. 2.2. Multiparticle production at intermediate energies A small part of the fundamental characteristics of those interactions, where the hegemony of pionization appears at energies only above 6 GeV, is reproduced below, with some analytical descriptions following the GHEISHA [9] user’s guide. The total average multiplicity (n) in hadron-hadron collisions is described by (n) = 3.626 + 0.666 ln( E,,) +0.3371n2(E,,)

+0.1181n3(E,,),

(1)

plus some higher terms for E,, > 6 GeV (EaV = & - rni - m, ) , being the available energy, m; and m, corresponding to the mass of the projectile and one of the nucleons in the target, respectively. This multiplicity fluctuates according to the KNO scaling [ IO], (n)P(z)

= z exp( -Tz2/4)

,

with z = n/(n),

(2)

with a conditional probability p (n+, no, n-: n) for the production of positive, neutral and negative pions. In the absence of other particle production, the final states in p-p collisions, for instance, are constrained by the conditions IQ + n, = 2

and

n,, + n+ - n- = 2.

(3)

At the highest energy, this KNO generation in GHEISHA is consistent in continuity with the situation generated by CORSZKA with other models (in the present case, HDPM), using the negative binomial distribution. The elastic and inelastic cross sections are tabulated in GHEISHA as functions of momenta of 7r+, n--, K+, K-, Ki, p and p; all the other cross sections are evaluated in the charge independent approximation for the forward scattering

337

amplitude within the scheme of the naive quark parton model. Strange particle production (kaon and hyperon production) follows respectively the rates (KK) = -0.033

+ 0.085 ln( E,,) ,

(KY) = -0.069

+ 0.085 ln( E,,)

(4)

The branching ratios are l/4 for KfK-, l/8 for KfKf, K+Kz, K,OK-, KtjK-, 1116fortheotherkaon pairs, 0.34 for K’A, 0.17 for KZR, KfA. Final states with two particles, in reactions like n-+11 + +‘p, rr-p + +n, K”p -+ K+n, .. .. Z-p + Zen, An, nA, are treated by tables. Charge, baryon and PZ-7 strangeness numbers are conserved exactly. Intranuclear cascades for hadron-air interactions have been adapted from the energy flux cascade model [ 111 with an average number of particles produced in addition, nad = tu(s)(A1i3

- 1)2&.

Here n,, is the number of backward primary interaction and

15) particles

(Y(S) = 0.312 + 0.2 ln[ In s] + 0.00017~‘~~. 2.3.

in the

(6)

Details of the calculation technique

The treatment of the electromagnetic cascade has been carried out using the programme EGS4 [ 121, adapted to the Earth’s atmosphere simultaneously with the hadron and lepton propagation. Muons are propagated down to mountain levels. In this calculation, we have taken into account the various energy losses, the deviations in the direction of propagation caused by the multiple Coulomb scattering and the Earth’s magnetic field. In order to describe precisely the behaviour of muons and hadrons in the atmosphere at energies above 50 MeV and in parallel the development of y’s and eflabove 10 MeV, we have employed GHEISHA with its lowest energy threshold set at 50 MeV. In the electromagnetic cascades, the selection of threshold for electromagnetic particles has been set to 10 MeV because of the reduced time of computation (when compared to the threshold near 1 MeV) and the investigation of the environment by the detectors registering neutrons above 50 MeV. Our Monte Carlo generator of solar flare events has been adapted from CORSIKA, linked with GHEISHA

338

J.N. Capdevielle, K Muraki/Astroparticle Physics 11 (1999) 335-346

and EGS4, using the HDPM option where necessary. Following the CORSIKA standards, the main data produced in the output is included in one binary data file. Target diagrams at each of the experimental altitudes such as Norikura and Chacaltaya (2800 m and 5200 m a.s.1. respectively) and in some cases also for sea level, Mauna Kea (4200 m) and Tibet (4300 m a.s.1.) or Akeno (900 m a.s.1.) are generated for each event. The target diagram contains the momenta and coordinates of each particle: neutron, proton, positive and negative muons, gamma, electron and positron. One data bank of half a million events induced in atmosphere by solar neutrons or protons with kinetic energies between 1 and 100 GeV has been obtained. Some sets have been sampled, also, following the primary cosmic ray energy spectrum, considered above 10 GeV, as represented by a unique power law (differential energy spectrum with y = -2.7) according to the recent compilations [ 13,14 ] involving minimal and maximal solar activity under 10 GeV.

3. Nucleons, muons, electromagnetic at mountain altitude

components

3.1. Detectiorz ejjiciency The results of the simulations performed with CORSZKA can be compared (for proton primaries) with the measured fluxes of the soft and the hard components. In Fig. 1, the differential and integral spectra for neutrons, differential spectrum for protons at Mt. Norikura [ 151 are presented. As shown in Fig. 1, our Monte Carlo results have reproduced quite well the experimental data at the Norikura for neutrons and protons above 50 MeV. Such an agreement can be further improved, especially for intensities of neutrons and protons around 100 MeV, if we employ a more realistic primary spectrum generating the primary protons. Here a simple power law with an exponent y = -2.7 has been assumed. Such simple approach is a tolerable description of the situation as the major contribution to the nucleon component at this altitude is coming from primaries above 10 GeV. There is a small effect of the primaries with energies lower than 10 GeV that we can estimate, from our calculations at fixed primary energy, to an underestimation by about 20% (when compared to the situation of Fig. 1) for parti-

Kinetic

energy,T(MeV)

Fig. 1. The differential (solid line) and integral (dashed line) spectra of neutrons and protons at Mt. Norikura are shown as a function of the neutron (and proton) energy. The differential spectrum value is shown on the left ordinate, while the integral neutron flux is presented on the right ordinate. Our Monte Carlo results are shown by the histogram for integral and differential neutron fluxes and for differential proton fluxes. It can be seen that Monte Carlo results reproduce quite well the observed data.

cles in the energy intervals [50, 100 MeV]; this is a consequence of the uncertainty of the solar modulation during the period of the experimental run. According to the compilation made by Simpson in 1983 [ 131, the proton integral intensity above 10 GeV was normalized to 140 part./sr/sec./m2. The relative abundance of secondary particles per primary particle (primary neutrons with vertical incidence) at the Norikura level (Fig. 2) is characterized by the dominance of the neutron secondaries (when compared to other particles above 50 MeV) for primary energies less than 45 GeV. Beyond this energy of primary neutrons, the muon component is overcoming the neutral flux. An inclination of 30 deg. of the pri-

J.N. Capdevielle.1 Muraki/AstroparticlePhysics I I (1999) 335-346

339

10

Neutrons and gammas at Chacaltaya (5200m a&I) _ Mt.Norikura (2800m a,s,l) neutrons 1

> 50MeV,30 IO-1

. ,’

I’

deg.,’ #’ >’ ,’

*‘-y > SOMeV,O deg.

I

_-

J 1

10

1 o-2

I

1

102

neutron Ruxes. mary neutron beam with respect to the vertical results in a general decrease by about 25% of all fluxes. In the case of proton primaries, the relative situation regarding the secondaries shown in Fig. 2 is conserved. The cascades are slightly more absorbed than in the case of neutron primaries, the secondary fluxes being most often reduced by about 5%. As expected, the respective fluxes of secondary particles are more abundant at 5200 m altitude than at Mt. Norikura. It can be ascertained (see Figs. 3 and 4) that the secondary neutron dominance is general at primary neutron energies lower than 30 GeV. Similar remarks apply for Norikura concerning events generated by protons giving the same yields of particles with a minor reduction by 3-4%. We define a critical energy EC, tabulated on Table 1,

,“I#_

J 102

Primary neutron energy, E”(G~v)

En (GeV) Fig. 2. The expected neutron, gamma, and muon relative abundances expected at Mt. Norikura per primary neutron incident vertically on the top of atmosphere are given as a function of primary neutron energy. At primary neutron energies less than 45 GeV, the secondary neutron flux is dominant over muon flux; at higher primary energies, muon fluxes are more dominant than secondary

I

10

Fig. 3. Secondary neutron, gamma-ray fluxes at Mt. Chacaltaya for vertical incidence of primary neutrons at various energies E, are shown. For primary neutrons incident at 30 degree zenith angle, the expected secondary neutron fluxes are slightly less than in the case of the vertical incidence. The expected energy spectrum for photons with energy greater than SO MeV is shown for the vertical primary neutron incidence. In comparison with Fig. 2. the secondary neutron flux is higher by a factor 2 than the one expected at the altitude of Mt. Norikura.

as the primary energy at which one secondary particle is obtained for one primary particle. In Table 1, we list the critical energy of primary neutrons for different species of secondaries. 3.2.

Lateral spread and particle

collimation

properties

In the small cascades initiated by solar particles with energies less than 100 GeV, the lateral deviations of the secondaries are very large. For muons, the emission angle of the parent pion or kaon is important and the propagation under the geomagnetic field increases further the lateral spread. The multiple Coulomb scattering plays here a smaller role. For electrons and

J.N. Capdevielle,

340

Table 1 Critical energy for the different components secondary particle per one primary nucleon. angle of 30 deg. Level

Muons (E,

> 100 MeV)

Chacaltaya Norikura

20 GeV (25 GeV) 28 GeV (33 GeV)

Z Muraki/Astroparticle

Physics 11 (1999) 335-346

in case of neutron- induced events. The critical energy is the energy at which there is one The values within the brackets correspond to the incidence of primary neutrons at a zenith

EcL > 600 MeV

En > 50 MeV

E, > 50 MeV

27 GeV (31 GeV) 36 GeV (39 GeV)

6 GeV (8 GeV) 15 GeV (25 GeV)

15 GeV 33 GeV

Table 2 The muon charge ratio produced by very high energy protons and neutrons. The third column denotes the muon production ratio, i.e. number of muons per one incident proton or neutron. For En = 100 TeV, a high muon charge ratio like 2.0 is expected. This arises from a reason that muons with energy > 5 TeV are produced at very forward region. Those tendencies have been derived from samples of 10000 events and the large variations observed are also due to the limited convergence correlated with this relatively small statistics when

compared to the rare decays of pions, kaons, parents above some TeV’s. El) (TeV target)

Ew > TeV

n(/J)ln(p+n)

n(P+ )/tr(p--

)

p or n

10

1

0.225*0.014

1.19 0.69

P n

50

2

0.078f0.006

0.954 0.67

P n

5

0.040*0.003

0.8 0.33

P

I

0.529f0.011

0.98 1.0

P n

0.031*0.004

2.0 0.82

P n

10

0.0075f0.0015

0.9

n

5 10

0.0026f0.005 0.0008f0.00015

1.01 0.91

rl n

100 (a few pc)

5

10L7eV (Cyg. X-3)

gammas, the lateral spread is mainly generated by the multiple Coulomb scattering in the atmosphere. The average distance (R,) from the primary particle axis are - 2 km and - 1 km for the muons with energy greater than 50 MeV induced by primary neutrons with the energy Ee = 10 GeV and 100 GeV respectively at Mt. Chacaltaya and Mt. Norikura. In the first approximation, we can say that the lateral spread of the penetrating component is similar for proton or neutron initiated cascades. A similar circumstance happens for the other secondary particles of these cascades. Inside a 10 GeV cascade, positive electrons above 50 MeV are incident on the average at 1.79 km from the axis (Chacaltaya) and at 0.18 km above 500 MeV (2.06 and 0.16 km respectively for electrons). These values are 0.63 and

n

0.37 m respectively for positrons with E. = 100 GeV, becoming 0.62 and 0.36 km for electrons. Gammas above 50 MeV and 2 GeV present respectively radii of 2.1 and 1.1 km inside one 10 GeV shower, becoming 0.70 and 0.18 km inside a 100 GeV shower. Similarly, neutrons above 50 MeV and 2 GeV are incident at 3 km and 1.05 km from the axis (2 km and 0.52 km for E, = 100 GeV) ; for protons secondaries, those values are 2.28 km and 1.31 km for E, = 10 GeV, 1.33 km and 0.97 km for E, = 100 GeV, respectively. The collimation, i.e. the angular deviation of incoming secondaries relative to the direction of the primary particle is more interesting for the most energetic secondaries, especially muons. The average angle of incidence of the muon (0) referred to the direction of the primary particle is given as follows: for the muons

J.N. Capdevielle.

Y; Muraki/Astroparticle

Physics I1 (I 999) 335-346

341

a k

._6 z

1.5 -

9 4 2 E

1.0

I 0.1

muon energy, E,

I 1.0

10.0

(GeV)

Fig. 5. The muon charge ratio r at sea level is plotted as a function of muon energy. The experimental data show an almost constant value as 1.25 and our Monte Carlo calculations based on CORSXA reproduce those data fairly well at a very low energy region.

3.3. The negative muon excess in neutron-induced events

;’

lo_*

1

,

:

I

I

I

lI111,

10

102

Primary neutron energy, E,(GeV) Fig. 4. The same pIot as Fig. 3 for muons. The muon energy is set at EP > 500 MeV at which muons can penetrate the galena absorber of Chacaltaya. The solid lines are for the vetical incidence of primary neutrons and the dashed lines are for incidence at 30 degrees.

EF > 2 GeV induced by E,J = 10 GeV and 100 GeV neutrons, the values turn out to be 0.14 radians and 0.075 radians, respectively, at Mt. Chacaltaya and Mt. Norikura. Our Monte Carlo calculation shows that the collimation is the same for positively and negatively charged muons with only a small dependence on the depth. At larger depths, the muons with wider angles are eliminated by their decay. The collimation does not depend on the charge of the primary nucleon. Muons above 2 GeV can be seen within an angle of less than 10 degrees with respect to the Sun, and this angle, on the average, can be smaller than 2 degrees for muons above 10 GeV in the most energetic showers. For neutron and gamma secondaries, it is difficult to use the collimation effect which appears only at the highest primary energies, say above 5 GeV, i.e. only in a very small proportion of secondaries. with

3.3.1. The positive muon excess irz proton-induced events The positive excess transmitted from the primary radiation to the charged 7r or K mesons and reflected by their decay products at sea level was pointed out by Puppi and Dallaporta more than half a century ago [ 161. The excess of positive muons over negative muons is one of the most well-known properties of cosmic rays. The muon charge ratio J_L~I,I.- observed at sea level is a function of energy, however, as shown in Fig. 5, the ratio is approximated as to be 1.25 [ 171; such a value is exactly reproduced by CORSXA (Fig. 5) for the most common muon energy of 2 GeV. The altitude dependence of this positive muon excess has been recently measured by the experiments HEAT [ 181 and CAPRICE [ 191. CAPRICE is a balloon borne magnet spectrometer equipped with a ring imaging Cerenkov light detector (RICH), a timeof-flight system and a silicon tungsten calorimeter; HEAT combines similarly a superconducting magnet spectrometer with a drift tube tracking hodoscope, a transition radiation detector and an electromagnetic calorimeter. The results of our first approach by simulation (these experiments deal with muons in the kinetic energy range 200 MeV-3 GeV) are reproduced in Fig. 6

J.N. Capdevielle, Y. Muraki/Astroparticle Physics 11 (1999) 335-346

342

excess, owing to the isospin symmetries for isoscalar targets involved in GHEZSHA. The air target is well known to reduce the positive excess to 1.22, when a value of 1.46 can be expected from an isolated proton target (Frazer et al., 1975). With CORSZKA all the constituents argon, nitrogen, oxygen, are taken into account. For muons of very high energy, r increases with E, (see Fig. 5) for the reason that the more important production of muons takes place via charged kaons (K+ and K- are not isospin multiplets) and the K+, KO’s produced in association with leading A’s or

CORSKA (E,, >2OOMeV )

1.8

1.6

. 0 a

X

0

HEAT95:0.3< 1 R / <0,9GV;R,,<
X’S.

/ /< I R1<

1

10

,

,11111!1 102

I

IIIIII

10’

Atmospheric depth (g/cm’) Fig. 6. Results of our Monte Carlo calculation on cosmic ray muon charge ratio are presented as a function of atmospheric depth by the solid line. The experimental data (various points) are compiled by Tarle et al. [ 18I. Present Monte Carlo calculation has treated muon energy in a very low energy domain such as 200 MeV. A general good agreement between observations and our Monte Carlo result can be seen.

together with the experimental data compiled by Tarle et al. [ 181 in 1997. A general agreement between our calculation and experimental data can be seen except for the data point of CAPRICE. The value measured by CAPRICE at 3.45 g/cm2 (which corresponds to almost 40 km altitude in the residual atmosphere) shows a significant enhancement of the positive muon excess r = 1.64 f 0.08 in the momentum range of 0.2-2.3 GeV/c. This appears too high in comparison with simulation and also disagrees with the measurements of MASS [ 201, giving an approximately constant value r = 1.27 f 0.05 at 5.8 g/cm2, and earlier magnetic spectrometer measurements [ 2 1,221 giving also r = 1.3 f 0.04 at 3 g/cm2 and r = 1.27 f 0.05 at 11 g/cm2, respectively. In order to understand the disagreement result of CAPRICE, we have changed in our simulation the value of the geometric solid angle for the acceptance, as well as the value of the magnetic field components between latitudes of 20 to 40 degrees, without finding any tendency confirming the result of CAPRICE which could have arisen from a contamination of the muons by protons (extremely abundant at this altitude). CORSZKA reproduces quite well the positive

3.3.2. The negative muon excess in neutron induced-events As can be expected by using the same arguments used in the treatment of diffusion equations and replacing the input proton primaries at the top of the atmosphere by neutron primaries, the positive muon excess changes into negative muon excess. This comes naturally under 80 GeV through GHEISHA and the treatments of charge conservation, isospin conservation and charge exchange incorporated inside. We have ascertained this property directly on the charged pions and kaons produced in the earliest interactions. This effect is also reproduced in continuity and in similar proportions at higher primary energy with the option HDPM, where the arguments about isospin and charge are also reversed for a primary neutron. The natural isospin spectroscopy of the atmosphere (nis) is shown on Fig. 7 at the Chacaltaya level for samples of 20000 to 1000 events with primary energies increasing from 5 up to 100 GeV. Positive excess for protons and negative excess for neutrons have quite symmetric behaviour when plotted as a function of muon kinetic energy, especially for muon energies closer to that of the leading cluster. An energy threshold for muons 20 to 10 times lower than the primary energy appears to give the best chances to observe a non-negligible number of muons with a maximal contrast. This effect, present at all the altitudes, combined with the muon collimation properties (Section 3.2) can be used as a new signature of energetic neutrons emitted in solar flares.

J.N. Capdevielle,

L Muraki/Astroparticle

Physics II (1999) 335-346

343

1 proton

primary

5,10,20,50,100

GeV

1.6 y +‘ p &. .E! z I& E U 0” 8

1.4 1.2 1 0.8

-

0.6 -

neutron

primary

GeV

5,10,20,50,100

0.2

neutron

primary

50,500GeV

10 muon energy,

E L1 (GeV)

Fig. 7. Calculated values of atmospheric muon charge ratio produced by proton (solid line) and neutron(dotted lines) primaries of various energies, as a function of muon energy. A clear inverse muon charge ratio is expected.

3.4. The electron antineutrino induced events

excess

for neutron

In relation with neutron induced phenomena, we would like to point out a quite interesting fact on electron antineutrino excess. Namely, another astrophysical effect appears in the case of neutron primaries, correlated with the increase of electron neutrino abundance. We have in atmosphere, when conditions are such that all particles have comparable chances of decay, i.e. at very low energy, vfi N q N (Y, + q), VrIvr N p+/p”- = r. This simplified approximation suggests an 1.25 times enhancement of q will come as well as the negative muon proportion increases during the solar Aares. The decrease of r indicates also an increase of the ratio of electron antineutrino to electron neutrinos. Symmetrically, an excess of electron neutrinos to electron antineutrinos would be expected in proton induced showers. We have then selected the neutrino version of COR-

neutrino energy,

E y WV)

Fig. 8. The ratio of electron neutrino/electron antineutrino is plotted as a function of neutrino energy. Proton and neutron primary energy is taken as 50 GeV and 500 GeV. Again a clear inverse isospin effect of neutrino flux is expected.

to reproduce the behavior of neutrinos in the atmosphere and compare the properties of protons and neutrons induced cascades. The actual conditions of neutrino production and propagation, including exact kinematics of two and three body decays, taking into account the polarization of the muons [ 231 allowing more accurate estimations than the crude hypothesis above-mentioned. The excess of electron antineutrinos is well confirmed by our Monte Carlo simulation in an energy window extended from about 1% up to 10% of the primary neutron energy. A symmetric situation excess of electronic neutrinos is observed in the case of proton-induced showers (as illustrated on Fig. 8 = 500 GeV). The proportion of muonic for E, = E,, neutrinos to muonic antineutrinos remains comparable (for protons and neutrons) and consequently the total ratio of neutrinos to antineutrinos is not very much affected by the contrast neutron/proton primaries. In the case of astrophysical targets where neutral Hydrogen and Helium are the most common constituents, the factor r = ,u+/,ufor proton primaries

SIKH

344

J.N. Capdevielle,

Y. Muraki/Astroparticle

rises up to 1.5, as asymmetries in isospin conservation, charge conservation and exchange become more important. Then, the excess of electronic antineutrinos generated by neutrons in such media can be expected to be more consequential. Here we have just introduced an interesting aspect from a theoretical point of view.

4. Discussions

and summary

Let us consider now how to confirm our predictions by observations. According to the compilation data on muons by Allkofer [24], the cosmic ray muon flux above 3 GeV at production (or 1 GeV at sea level) is N 80/m2/sec. So, in case we employ a muon detector with 1 m* in area, the number of muons expected in the energy range above 1 GeV is approximately 800 per 10 seconds at high latitude (Kiel standard). Those muons are produced by the galactic cosmic rays beyond > 30 GeV and their fhtx is - lOO/m’/sec. Among these 800 cosmic ray produced muons, one expects to see 444 and 356 positively charged and negatively charged muons respectively on the basis of r = 1.25. High energy solar neutrons are thought to be impulsively produced over time spans of ten seconds at the solar surface [25]. In that case the solar neutrons with energy about 30 GeV arrive at the top of the atmosphere with the same intensity as the galactic cosmic ray protons, one can record 450 negative muons and 350 positive muons around 1 GeV produced by solar neutrons using a 1 m* detector over 10 seconds. Here one must recognise the fact that the solar neutrons with energy 30 GeV arrive at the Earth only 0.44 seconds later than the light, while neutrons with kinetic energy 100 MeV arrive at the globe about 11 minutes later than the light. The solar neutron produced muons are in addition to 444 positively charged and 356 negatively charged muons produced by galactic cosmic rays. Then we will observe a total of 794 positively muons and 806 negatively muons during 10 seconds. The charge ratio becomes almost 1.O (794/806 = 0.985 f 0.050), drastically changing from 1.247 (= 4441356) during the brief time interval solar flare (about 10 s) . In addition to such a remarkable feature of inverse charge effect, we will see during a solar flare double number of muons, i.e. 1600f40 instead of 800. This gives us 200- statistical significance.

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Here we have defined our statistical significance by the following equation: the charge ratio (R) = A/B and la is defined by SR = A/B[ 1/A + 1/B]‘12. This number is based on our results of the Monte Carlo calculation presented in Table 1, which describes that the production of one low energy muon is expected for one neutron with an energy - 30 GeV (E,). However, not all solar flares yield neutrons with hard spectra. For examples, the solar neutrons observed on May 24th 1990 had quite a soft spectrum (differential spectral index y = -4.0). At the top of the atmosphere, the flux of neutrons at 1 GeV is estimated as to be 2000/m2/sec/MeV [26], In this flare, a large size neutron ground level enhancement was observed [27]. However, owing to the soft energy spectrum, the integral flux of solar neutrons beyond 30 GeV can be estimated to be 25 neutrons/m*/sec. This then leads to an enhancement of 7.7~ only the muon flux over 10 seconds. In case the high energy ions were accelerated for more than 30 seconds, we will observe 750 neutrons during above period and we might see a 20~ excess. Even in the case in which the acceleration was continued for only 3.4 seconds, we might see a 3~ muon excess at that time. If we use a much larger muon detector like Milagro 5000 m2 [28] instead of the 1 m2 detector described above, a 4 x lo6 muon excess will be observed in the flare for 10 seconds, and they will get a huge statistical significance signal like 440a. For neutrons with a hard spectrum such as the June 3rd 1982 flare [ 291 (differential y = -2.4)) neutrons with primary energy 2 30 GeV can be estimated as to be 1800/m*/sec at the top of the atmosphere. Therefore, the other detectors will see an extreme good statistical signal. For example, by the Akeno 200 m2 detector it is expected a 88a excess and for the Ooty air shower detector (with a muon detector area of 576 m2), one expects a 92-150~ excess. The situation looks quite hopeful, regardless of the spectral exponent of the solar neutron energy spectrum. The authors thank Prof. Ramana Murthy for pointing out this advantage. In the case solar neutrons are produced with a hard spectrum (y = -2.4) like the galactic cosmic ray spectrum, there are several possibilities to see the inverse charge-ratio effect. We have many cosmic ray muon detectors in the world. If we can switch on again all or most of these muon spectrometers, we will have a possibility to observe such a phenomenon. Or one

J.N. Capdevielle, l! Muraki/Astroparticle Physics I I (1999) 335-346

can construct a very simple iron spectrometer, with a total area of 10 m” and with a thickness of 30 cm iron. Then one will obtain a Maximum Detectable Momentum (M.D.M.) of muons as 1 GeV, so we will be able to measure low energy muons in the energy range between 600 MeV and 1000 MeV by this detector. Then you will see the 17a inverse excess. If one can use small superconducting magnet spectrometers used in the accelerator experiments, one can obtain very interesting data on ,u+lpduring the solar flare time. The other idea to confirm the inverse charge-ratio effect is to use scintillators. As negative muons are absorbed in the materials (and form muonic atoms), while positive muons are scattered, therefore, the life time of muons in the material takes different value between positive and negative muons. The experimental data shows that for positive muons the life time was 2.2 psec, while for negative muons it turns out to be 0.88 ,usec. We could identify the charge ratio by this method. In fact, Vulpescu et al. [ 301 have obtained the muon charge ratio as 1.20 f 0.06 by this method. We consider here that this technique could be applied to identify the stop muon charge ratio inside water Cherenkov detectors. We can add another technique to discriminate more clearly the positive muons from negative muons. It can be realized by measurements of the emission angle of electrons by TDC. One of the examples of such experiments of muons can be seen in the bibliography of Mine [ 3 1 J. Since p”+ is produced with the helicity of - 1 and p- with +l, the electron distribution after their decay must be slightly different, following an angular distribution like 1 + ( F)uP, cos( /3), where Pp (polarization factor of muons) is about 0.3. Finally, we will discuss here a possibility of observing the negative muon excess during the phenomena on a much larger scale in the Universe. Recently, the acceleration of electrons up to 200 TeV is confirmed by two experiments, one in the X-ray region [ 321 and the other in the TeV region [33] from SN1006. It would be natural to think that protons are also accelerated in this object by the shock acceleration, although we have not yet obtained any direct evidence. It would be a pity for cosmic ray physicists if we cannot define the place where cosmic rays are accelerated. It might be possible that protons and helium ions are accelerated near Loop I or Geminga. In the case of Loop I, the distance is estimated as to be 130 Z!Z75 pc. (Let

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us take the distance as 50 PC.) Then neutrons at energies of 5 PeV emitted by this object can arrive at the Earth, since the neutron decay length is 1.8 Astronomical Unit in the rest frame of neutron. Observations on high energy electrons (Nishimura et al. [ 341) tell us that electrons are accelerated beyond 10 TeV It would be natural then to think that protons and ions too are accelerated up to a few PeV there. We may see a TeV muon excess in the direction of Loop I. Furthermore, if cosmic rays are accelerated within 1 pc, we will be able to see an inverse muon charge ratio by the observation It would be interesting to search the negative excess in the muon charge ratio with use of a large amount of data set of Super Kamiokande in the RA and declination map. This is another method to locate the site of proton acceleration in our Universe. If we prepare appropriate size detectors, then as in the case of solar flares, we will be able to see this sophisticated cosmic ray phenomena. Here we shall introduce the typical counting rate for such muons produced by galactic originated neutrons in Table 2. From this table, the detection of muon excess appears feasible in case neutron signals exceed the background. It is still a riddle how protons are accelerated in the Universe. As yet, one does not understand fully the acceleration of solar cosmic rays, one may use the characteristic neutron signal to elucidate this problem. We have calculated a Monte Carlo calculation to use muon signals in order to know the acceleration limit of how high particles are accelerated at the solar surface. We have demonstrated here that using muon signals is a powerful method to get a very important knowledge on highest solar cosmic rays. We believe that in the near future some muon detectors in the world will be able to observe this interesting cosmic ray phenomenon. Simultaneously, the analysis of electron antineutrino excess correlated with solar flares and the possible anisotropy of this excess in the galactic plane, in the direction of galactic center or other point sources and other astrophysics targets like AGNs, can provide new and fundamental observations.

Acknowledgement The authors thank Prof. PV. Ramanamurthy for careful reading of the manuscript and valuable comments.

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