Upper Limits on Fluxes of Low Energy Interstellar Cosmic Rays and Nuclear Gamma Rays

M. YOSHIMORI Deprirtnlent oj'Physic.r, Rikkyo Unil,ersity, Toshimrt-ku, Tokyo, Japrrrl

Received September 5, 1974

The upper limits on an interstellar flux of low energy cosmic rays are derived from interpre- tations of the y ray spectral feature at 473 + 30 keV, the enhancement in the flux of galactic diffuse y rays, the ionization rate of interstellar hydrogen, and the abundance ratios of stellar light elements. The derived upper limits are compared with the observed flux and the demodu- lated flux. Nuclear y rays are emitted from excited nuclei which are produced by inelastic collisions between low energy cosmic rays and the interstellar gas. Fluxes of nuclear y rays emitted from ,7Li*, l;C*, l;N*, and 'go* are evaluated and found to be of the order of to photons s-l .

On a calcule des limites supkrieures au flux interstellaire de rayons cosmiques de basse energie, a partir d'interpretation des caracteristiques du spectre de rayons y a 473 _+ 30 keV, du renforcement du flux galactique de rayons y diffus, du taux d'ionisation de I'hydrogene interstellaire et des rapports d'abondance des elements legers dans les etoiles. Les limites superieures calculCes sont comparees avec le flux observe et le flux demodule. Des rayons y nucleaires sont Cmis par des noyaux excites produits par les collisions inClastiques entre les rayons cosmiques de basse Cnergie et le gaz interstellaire. On a calcule les flux de rayons y nucleaires Cmis par :Li*, '2,C*, l;N*, IgO*, et on a trouve qu'ils Ctaient de I'ordre de a photons cm-Z s-'. [Traduit par le journal]

Can. J. Phys., 53,917(1975)

1. Introduction

An investigation of low energy interstellar cosmic rays offers information on a mechanism of solar modulation and a heating of the inter- stellar gas. The spectrum of low energy cosmic rays observed in the vicinity of the Earth is different from the interstellar spectrum because low energy cosmic rays in the vicinity of the Earth are much modulated by the solar wind. The mechanism of solar modulation which in- cludes diffusion, convection, and adiabatic energy loss in the solar wind has been investigat- ed by Urch and Gleeson (1972a,b, 1973). The demodulated spectrum above 100 MeV. is in agreement with the observed spectrum but a discrepancy between the above two spectra appears below 100 MeV. Since a correction for demodulation is uncertain below 100 MeV, it is difficult to calculate the precise interstellar spectrum below 100 MeV on the basis of the theory of solar modulation.

In this paper, in order to derive upper limits of the interstellar proton flux below 100 MeV, the observed results of the y ray spectral feature at 473 + 30 keV, the enhancement in the diffuse y ray flux in the 0.5 MeV to 10 MeV energy range, the ionization rate of interstellar hydro-

gen, and the abundance ratios of stellar light elements are used. The derived upper limits are compared with the observed flux and the de- modulated flux. The fluxes of galactic nuclear y rays are evaluated from the derived inter- stellar flux. The evaluated fluxes of nuclear y rays, especially 478 keV y rays emitted from ZLi*, are compared with the observed flux at 473 ) 30 keV.

2. Upper Limits on the Interstellar Flux of Low Energy Protons

Since cosmic rays observed in the vicinity of the Earth are modulated by the solar wind, it is necessary to demodulate the observed spectrum in order to derive the interstellar spectrum. Low energy cosmic rays are more modulated by the solar wind than high energy ones. The theory on solar modulation has been extensively in- vestigated and the interstellar spectrum above a few hundred MeV has been calculated from the Fokker-Planck equation which includes three terms of diffusion, convection, and adiabatic energy loss in the solar wind. However, solar modulation effects on low energy cosmic rays below 100 MeV have not been understood sufficiently. Therefore, the interstellar spectrum

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918 CAN. 1. PHYS. VOL. 53, 1975

of low energy cosmic rays must be derived from other viewpoints.

The upper limits on the interstellar flux of low energy protons can be derived from the follow- ing observed results.

2.1. Deviation from the Flux of the y Ray Line Feature at 473 f 30 k e V

The y ray line feature at 473 A. 30 keV from the direction of the galactic center was observed by Johnson et al. (1972) and Johnson and Haymes (1973). The observed y ray flux within the line feature was (1.8 f 0.3) x photons cm-2 s-'. Many investigators who were in- terested in y ray astronomy were surprised by the observed result and a few interpretations have been proposed to explain the observed result. Fishman and Clayton (1972) interpreted the observed y ray line feature as the 478 keV nuclear line y rays emitted from ZLi* which are produced by inelastic collisions of low energy ZLi with interstellar hydrogen. In order to ex- plain the observed line flux at 473 keV, the re- quired interstellar flux of ZLi in the 2 MeV/nucl. to 10 MeV/nucl. range must be about 48 nuclei cm-2 s-'. If it is assumed that the ratio of pro- ton to Li in low energy cosmic rays is 8 x lo3, which is the same ratio as that observed in high energy cosmic rays, the proton flux in the 2 MeV to 10 MeV range becomes 6 x lo4 nuclei cm-2 s-I. It is considered to be the upper limit on the interstellar proton flux.

There is a possible objection to the above derived proton flux. The above proton flux represents an energy density of 120 eV cm-3 which, if maintained over a large fraction of the galactic volume, would create dynamic instabili- ties. Therefore, it is not likely that the derived proton flux exists uniformly throughout the galaxy. However, it could be in existence in active regions such as supernova remnants and the galactic center. As an example, this situation probably exists within the Gum Nebula (Ramaty et al. 1971). It has the pulsating radio source in the center and the vast ionized sphere which may be the result of ionization by low energy cosmic rays.

2.2. Deoiation from the Difuse y Ray Flux in the 0.5 M e V to I0 M e V Range

Galactic diffuse y rays in the 0.3 MeV to 27 MeV range were observed by Trombka et al. (1973). The observed result shows that the flux in the 0.5 MeV to 10 MeV range is about three

times as large as the extrapolated flux of hard X rays. If it is assumed that the enhancement in the y ray flux is due to nuclear y rays emitted from 'EC*, ':N*, and ';0*, it is possible to set an upper limit on the interstellar flux of low energy C, N, and 0 . The observed result shows that the enhancement flux in diffuse y rays is about photons cm-2 s-I sr-'. The above result leads to the upper limit on the inter- stellar flux of C, N, and 0 of 10 nuclei cmW2 s-' in the 5 MeV/nucl. t o 30 MeV/nucl. If it is assumed that the ratio of proton to C, N, and 0 is 2 x lo2, which is the same ratio as that ob- served in high energy cosmic rays, the upper limit on the interstellar proton flux becomes 2 x lo3 nuclei cm-2 s-'.

2.3. Deviation from the Ionization Rate o f Interstellar Hydrogen

A part of the interstellar gas is ionized by low energy cosmic rays. Recently, the state of ioniza- tion of trace elements in the interstellar gas is observed by OAO-3 Copernicus (MCszAros 1973, 1974). The observed result shows that the upper limit on the ionization rate of interstellar hydrogen is 4 x lo-'' s-' per hydrogen. The above result leads to the upper limit on the differential proton flux of 5 x nuclei cm-2 s- ' sr-' MeV-' at 1 MeV.

2.4. Deviation from the Abundance Ratios of Stellar Light Elements

The hypothesis that most of the stellar Li, Be, and B (light elements) are generated by the action of galactic cosmic rays on the interstellar gas was presented by Reeves et al. (1970) and Fowler et al. (1970). In order to explain the Li abundance in a young star, the proton flux in- tegrated over the life of the galaxy above 30 MeV must be about 12 nuclei cm-2 s-' for a galactic age of 12 x lo9 y. To explain the meteoritic B isotopic ratio and the upper limit on the solar B/Be ratio, the upper limit on proton flux of 5 nuclei cm-2 s-' in the 5 MeV to 30 MeV range is required.

The upper limits on interstellar fluxes of low energy protons derived from the above con- siderations are shown in Fig. 1. In Fig. 1, diffuse y rays, ionization rate, and L elements stand for the upper limits derived from subsects. 2.2, 2.3, and 2.4 respectively. The upper limit derived from subsect. 2.1 is too large to be shown in Fig. 1. The observed, demodulated, w-2.6 , and E - ~ . ~ lines shown in Fig. 1 represent

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YOSHIMORI: UPPER LIMITS OF FLUXES 919

deduced from the above derived upper limits and the energy density of cosmic rays in the galaxy. The deduced spectrum is represented by the dotted curve in Fig. 1.

FIG. 1. Estimated upper limits on the flux of low energy interstellar protons.

the proton spectrum observed in the vicinity of the Earth, the proton spectrum demodulated on the basis of the theory of solar modulation, a power law spectrum in total energy, and a power law spectrum in kinetic energy respec- tively. The interstellar proton spectrum can be

3. Upper Limits on Nuclear 7 Ray Fluxes

Upper limits on fluxes of nuclear y rays emitted from :Li*, '$*, ';N*, and ':0* can be evaluated from the above derived spectrum. These excited nuclei are produced by two pro- cesses. One is that C, N, and 0 in the interstellar gas are excited by inelastic collisions with low energy protons, and the other is that low energy Li, C, N, and 0 are excited by inelastic collisions with interstellar hydrogen. In the first process, nuclear y rays are emitted from excited nuclei at rest, but in the second process, nuclear y rays are emitted from excited nuclei in motion. Therefore, the first process forms line y ray spectra and the second one forms broad y ray spectra due to the Doppler broadening. The line width due to the Doppler broadening depends on a velocity of the excited nucleus. If the energy of nuclear y rays emitted from the excited nucleus at rest is Eo, the observed energy becomes Eo ((1 + p)/(1 - p))'I2 when the excited nucleus comes on at the velocity of v = cp (c is the light velocity) and Eo ((1 - P)/(1 + p))'I2 when the ex- cited nucleus goes away at the velocity of v = cp.

The flux of nuclear y rays observed at the Earth per unit area per unit time due to ith type excited nuclei is represented by

+ 1/4n Jv np/r2 d V JE:h Oi(E)oi(E) dE photons cm-2 s-'

where ni is the number density of ith type nuclei in the interstellar gas, r is the distance to the emitting volume, +i(E) dE is the omnidirectional flux of cosmic ray ith type nuclei between E and E + dE, oi(E) is the cross section for production of ith type excited nuclei from the inelastic collision of (p,pt), and E,, is the threshold energy for the production of excited nuclei. The first term in the right-hand side of [ l ] corresponds to the first process and the second term to the second process. For the purpose of calculation, the proton spectrum deduced in a previous section is applied, +,(E)/47r, in the above equation. It is assumed that spectral shapes of C, N, and 0 are the same shape as the proton spectrum, and their abundance ratios are p: Li : C : N : 0 = 1 : 2.76 x : 1.72 x 10-3:4.66 x 1.48 x The above ratios are those observed in high energy cosmic rays (Shapiro 1971). Cross sections for production of excited nuclei are obtained from a search of pub- lished cross section data (Gleyvod et al. 1965; Locard et al. 1967; Ramaty and Lingenfelter 1973). Furthermore, it is assumed that the number density of interstellar hydrogen is 1 cm-3 and the abundance ratios in the interstellar gas are p :C:N:O = 1:5.3 x 10-4:9.5 x 10-':9.2 x (Cameron 1968). Broadening y ray spectra are obtained from the second term, as mentioned above.

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CAN. J. PHYS. VOL. 53, 1975

TABLE 1 . Calculated fluxes of galactic nuclear gamma rays s-')

Nucleus Energy(MeV) 1 st Process 2nd Process

In order to simplify the calculation, it is assumed that the energy of the nucleus does not change throughout the inelastic collision. That is, if energy per nucleon of the excited nucleus is E, observed y ray energy distributes from

(M is the proton rest mass). The fluxes of nuclear y rays evaluated from the two processes are shown in Table 1. It is found that y ray fluxes from the second process are higher than those from the first process. It is due to the relative abundances of heavy nuclei in cosmic rays being higher than those in the interstellar gas. The predicted nuclear y ray spectrum for viewing the galactic center with a half angle of 10" is shown in Fig. 2. As shown in Fig. 2, line y rays are superposed on broadening ones. Here, it is assumed that the FWHM of observed line y rays is 50 keV. Since 478 keV line y rays are emitted from :Li* below a few MeV/nucl., the spectrum becomes sharper than other spectra. In Fig. 2 the energy spectrum of galactic diffuse y rays observed by Trombka et al. (1973) and the extrapolated spectrum of hard X rays, E-2.1 , are shown for comparison.

4. Discussion

The diffuse y ray flux observed by Trombka et al. (1973) is two orders of magnitude larger than the nuclear y ray fluxes evaluated in a pre- vious section. The y ray flux at 473 f 30 keV observed by Johnson et al. (1972) is four orders of magnitude larger than that evaluated from the de-excitation of :Li*. If y rays observed at 473 f 30 keV are due to the de-excitation of :Li*, which are produced by the reaction of :Li(p,pl):Li*, it implies that the proton flux below 10 MeV in the galactic disk is four orders of magnitude larger than the derived upper limit

on the proton flux. If it is true, fluxes of nuclear y rays emitted from 'gC*, ';N*, and 'go* will exceed the diffuse y ray flux. Therefore, they will be easily observed.

It is not likely from the viewpoint of the energy density of cosmic rays that the low energy proton flux in the galactic disk is four orders of magnitude larger than the derived upper limit on the proton flux. In order to lower the proton flux in the galactic disk, any nuclear reaction other than :Li(p,pr):Li* must be taken into consideration. One interesting reaction which can produce :Li* is ;He- ($He,p):Li*. This reaction was pointed out by Kozlovsky and Ramaty (1974). Since the cosmic ray abundance of $He is many orders of magni- tude larger than :Li, the above reaction will contribute more to the 478 keV y ray flux. In addition to :Li*, :Be* is produced by the nuclear reaction of iHe($He,n):Be* and :Be* emits 431 keV nuclear y rays. It is predicted that the cross section for $He(iHe,n):Be* is nearly equal to that for $~e($He,p):Li*. The y ray peak observed at 473 f 30 keV may con- sist of 478 and 431 keV nuclear y rays, but the observation of Johnson et al. (1972) did not show the presence of the 431 keV line. It is probably due to low energy resolution and low statistical accuracy.

Ramaty et al. (1973) suggested that the y ray peak observed at 473 f 30 keV is due to gravi- tationally redshifted positron annihilation radia- tion produced at the neutron star surface. In the

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YOSHIMORI: UPPER LIMITS OF FLUXES 921

RG. 2. Calculated energy spectrum of nucIear gamma rays for viewing the galactic center with a half angIe 10".

above suggestion, it is assumed that positrons are emitted from 'AC, ';N, and ' iO which are produced by nuclear reactions of accelerated protons with ';C, ':N, and '20 nuclei on the surface of the neutron star. Gurthrie and Tademaru (1973) suggested that electron-posi- tron pairs are produced by high energy y rays emitted in the vicinity of the neutron star which is rapidly rotating and has a very large magnetic field of the order of 1012 G. If the electrons and

observation of Johnson et al. (1972) seems to imply an increased neutron star density in the galactic center.

Though some ideas have been suggested to explain the y ray peak observed at 473 + 30 keV, it is difficult to determine which ideas are most satisfactory. In order to do so, the y ray energy spectrum must be accurately observed with a Ge(Li) detector. The Ge(Li) detector is superior in energy resolution. The Rikkyo University Gamma Ray Astronomy Group is scheduled to observe galactic line y rays with a Ge(Li) detector surrounded by a well-type plastic scintillator.

Acknowledgments

The author would like to thank Drs. K. Okudaira and Y. Hirasima for valuable discus- sion during the work.

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