Preliminary results from the High Energy Gas Cerenkov Spectrometer indicate that the sub-iron to iron ratio increases beyond 100 GeV/nucleon. This surprising finding is examined in light of various models for the origin and propagation of galactic cosmic rays

Balasubrahmanyan, V. K.

Ormes, J. F.

Streitmatter, R. E.

English

NASA Technical Reports Server

OG 4.1-12
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COSMIC RAY NUCLEI OF ENERGY > 50 GeV/NUC
V. K. Balasubrahmanyan,R. E. Streitmatter,and J. F. Ormes
NASA/Goddard Space Flight Center, Greenbelt, MD 20771
ABSTRACT
Preliminary results from the High Energy Gas Cherenkov
Spectrometer indicate that the sub,iron to iron ratio
increases beyond 100 GeV/nucleon. This surprising finding
is examined in light of various models for the origin and
propagation of galactic cosmic rays.
I. Introduction. The study of the composition of cosmic radiation and
energy distribution has resulted in the development of several
models of cosmic ray propagation and information about sources and
acceleration phenomena (Cesarsky, 1980) [1]. The results from several
balloon experiments and the good statistics data from the HEAO-C
measurement (Englemannet al., 1985) [2] indicate that the matter
traversed by cosmic rays decreases with energy. In the energy range 1-
25 GeV/nuc, this depende_c_ of matter traversed by cosmic rays is
expressed as (rigidity)-u'°. This trend, if continued beyond 50
GeV/nuc, would result in matter traversed decreasing below 1 g/cmL. As
the amount of matter becomes small, the effects of nuclear interaction
in the InterstellarMedium (ISM) become difficult to detect if the
nuclear mean free path^(_) in the ISM is much larger than 1 g/cm2. For
Fe nuclei L = 2.8 g/cmZ and so relatively Fe becomes a more suitable
nucleus to study compared to C, O. The widely differing consequences
predicted by the leaky box, nested leaky box, and the closed galaxy
models could be tested by studying the relative amounts of primary Fe
nuclei and the secondaries from the breakup process.
In addition to these theoretical models, the results from the
experiments on the detection of antiprotons (Golden et al., 1979, [3]
Bogomolov et al., 1979, [4] Buffington et al., 1981) [5] suggest that
the matter traversed by cosmic ray protons may not be consistent with
cosmic ray propagationmodels derived from the study of heavy nuclei.
In this, we discuss some of the suggestive trends seen in the
preliminary data of the High Energy Gas Cherenkov Spectrometer (HEGCS)
and see what we can learn about the conflicting requirement of these
phenomena. Details regardingthe HEGCS experiment and data analysis are
reported in the proceedings of the Conference (paper OG 4.1-11,
Streitmatteret al., 1985) [6].
2. Data in Fe and Sub-Fe Region. In the lower energy region up to 25
GeV/nuc, the HEAO-C (Englemann et al., 1985) [2] with its excellent
charge resolution and statistics gives a reliable data base. Beyond 25
GeV/nuc, several balloon experiments (Simon et al., 1980, [7] and
references therein, and Streitmatter et al., 1985) [6] provide data.
The very low flux of the particles to be detected is the most serious
problem for statistical reliability. Beyond a few hundred GeV/nuc, the
situation is even more murky. JACEE's (Burnettet al., 1983) [8]
finding that the highest energy particle was not an Fe but a Ca and the
absence of Fe nuclei up to a total energy of 1014 eV is in contrast with
 12 
4 
C      NUC 
. . al subrahmanyan. . . tr itm tter.  J. . r es 
SA/ oddard Space Flight enter. reenbelt. MD 20771 
RACT 
reliminary res lts from t e igh ergy as erenkov 
e tro t r i i te t t th  s -iron t  iron r tio 
i reases ond  e /nucl on. is s r rising finding 
is exa ined in light of various odels for the origin and 
propagation of galactic cos ic rays. 
1. I troduction. he study f t e c position f c s ic ra iation a  
~en rgy istribution has resulted in the development of several 
odels of cos ic ray propagation and information about sources and 
acceleration phenomena ( esarsky. 1980) [1]. The results from several 
lloon im ts  t  d istics t  rom t  -C 
easurement ( nglemann et al •• 1985) [2] indicate that the atter 
traversed by cos ic rays decreases ith energy. In the energy range 1-
25 GeV/nuc. this dependeBc~ of atter traversed by cos ic rays is 
expressed as (rigidity)- •• This trend, if continued beyond 50 
e /nuc, ould result in atter traversed decreasing below 1 g/cm2• s, 
t  t f att r o s s all, th  ff ts f l r i t ra tion 
in the Interstellar edium (ISM) become difficult to detect if the 
nuclear mean free path (A) in the ISM is much larger than 1 g/cm2• For 
Fe nuclei A  2.8 g/cm2 and so relatively Fe becomes a ore s itable 
nucleus to study co pared to , . The idely differing consequences 
re icted by t e leaky . ested leaky . and t e cl sed alaxy 
odels could be tested by studying the relative a ounts of primary Fe 
clei and t e sec aries from t e reakup r cess. 
In ition t  t s  t r tical odels, t  r s lts from t  
experiments on the detection of antiprotons ( olden et al •• 1979. [3] 
Bogomolov et al., 1979, [4] Buffington et al., 1981) [5] suggest that 
the atter traversed by cos ic r~y protons ay not be consistent ith 
cos ic ray propagation odels derived from the study of heavy nuclei. 
In t is, we discuss so e of the suggestive trends seen in the 
preliminary data of the igh nergy as herenkov Spectro eter (HEGCS) 
and see hat e can learn about the conflicting requirement of these 
pheno ena. etails regarding the HEGCS experiment and data analysis are 
reported in the proceedings of the onference (paper OG 4.1-11, 
Streitmatter et al., 1985) [6]. 
2. ata in Fe and Sub-Fe egion. In the lower energy region up to 25 
GeV/nuc. the HEAO-C (Englemann et al., 1985) [2] with its excellent 
charge resolution and statistics gives a reliable data base. Beyond 25 
e /nuc, several balloon experiments (Si on et l., 1980, [7] and 
references therein, and Streitmatter et al., 1985) [6] provide data. 
The very low flux of the particles to be detected is the ost serious 
problem for statistical reliability. Beyond a few hundred GeV/nuc, the 
situation is even more murky. JACEE's (Burnett et al., 1983) [8] 
finding that the highest energy particle was not an Fe but a Ca and the 
absence of Fe nuclei up to a total energy of 1014 eV is in contrast with 
https://ntrs.nasa.gov/search.jsp?R=19850025705 2020-03-20T18:03:19+00:00Z
OG 4.1-12
45
the delayed particle EAS experiment of the Maryland group (Goodman et
al., 1982) [9]. The Maryland group concludes that their results are
consistent with a Fe spectrum with a power law exponent -2.39 ± .09. It
is to be remembered, however, that EAS experiments have no charge
resolution to discriminate between Fe primaries and secondaries of Fe.
In Figure (1) we show the preliminary results from HEGCSin the Fe
and sub Fe group. The secondaries of Fe seem to cluster at either the
low or high Cherenkov signal, with a paucity of points in between. Fe,
however, seems to be distributed more uniformly throughout, with the
number of points tapering off at the high signal limit.
Maximum likelihood estimates of the power law exponent for iron
give -2.77 ± 0.12, in good agreement with the energy spectrum of protons
and He nuclei, as obtained by Ryan et al., 1972 [I0] and the JACEE group[9].
3. Double Diffusive Galaxy Model. We have considered a model which has
characteristics of both the two component models previously discussed,
the nested leaky box model (Cowsik and Wilson, 1973) [ii] and the closed
galaxy model (Peters and Westergaard, 1977) [12]. The model is
characterized by two leaky boxes one inside the other as in the nested
leaky box model. The observer is inside the inner box as in the closed
galaxy model. Particles are held in both boxes by diffusive scattering
and so both boxes would act like leaky boxes. The inner box represents
the local interstellar region and the local sources. The lifetime of
particles within this source region would be given by the lOBe
observations and the mean matter traversed would be that given by the
HEAO-3 observations of B and C, N, 0 elements. The nuclei observed from
a local source region would be relatively young. The composition
consists of heavy nuclei.
The outer box would be the galaxy and its halo. This outer box
would contain "old" particles, including protons and their secondary
antiprotons. Particles would propagate therein under the control of a
diffusion coefficient which has the same rigidity dependence as in the
inner box, namely, scattering controlled by magnetic inhomogenieties.
This would be required by the observation that the proton spectrum is
assymptotically the same as those of the heavier nuclei, i.e.,
y : 2.75. The matter traversed by particles in this outer box would
have to be about three times that of the inner box. Since the mean
density is much lower, the lifetime in the outer box would have to be
50-200 time longer than in the inner box.
The source spectra would be given by shock acceleration and the
equilibrium spectra observed would be steepened by the energy dependent
" diffusion in both boxes. This model would remove any conflict between
the low energy composition data and the high energy isotropy, which is
determined by the conditions in the outer box. The I GeV/amu particles
. observed at Earth contain "young" heavy nuclei from nearby sources
(_ 0.5 kpc) and "old" protons and helium nuclei from the galaxy as a
whole.
We may be effectively outside the source of the very lowest energy
particles (~ i00 MeV/amu) because, at this low energy, the diffusion
G -12 
 
t e l ed article AS riment f t e ar land r  ( an t 
l., ) [ ]. e ar land r  ludes t at t eir r sults r  
consistent ith a Fe spectru  ith a po er la  exponent -2.39 ± .09. It 
is t  be re e ere , e er, t at EAS e eriments a e no c ar e 
solution t  iscriminate t   imaries  daries  . 
I  igure  e o  t e eliminary sults fr  GCS i  t e  
a  s  e r . e s ndaries f e seem t  luster t ither t e 
lo  or high herenkov signal, ith a paucity of points in bet een. Fe, 
ho ever, seems to be distributed ore uniformly throughout, ith the 
nu ber f Oints ta ering ff at t e i  si nal limit. 
axi um likelihood stimates f t e r la  t f r iron 
give -2.77 ± 0.12, in good agree ent ith the energy spectru  of protons 
and He nuclei, as obtained by Ryan et al., 1972 [10] and the JACEE group 
]. 
3. ouble iffusive alaxy odel. We have considered a odel hich has 
aracteristics f t  t e t  t ls reviously iscussed, 
the nested leaky box odel ( o sik and ilson, 1973) [11] and the closed 
laxy l ( eters  esterg ard, ) [ 2].  l is 
aracterized  t  le y   inside t e ther  i  t e ted 
leaky  el.  server s i side t e inner   i  t e losed 
galaxy odel. Particles are held in both boxes by diffusive scattering 
and so both boxes ould act like leaky boxes. The inner box represents 
t e l cal interstellar re ion a  t e l cal s rces. he lifetime f 
particles ithin this source region ould be given by the l Be 
observations and the ean atter traversed ould be that given by the 
-3 servations  a  , ,  le ents.  clei s rved  
a local source region ould be relatively young. The compo~ition 
consists of heavy nuclei. 
e ter  l  e t e l y a  its lo. is ter  
ould contain "old" particles, including protons and their secondary 
antiprotons. articles ould propagate therein under the control of a 
diffusion coefficient hich has the sa e rigidity dependence as in the 
inner box, na ely, scattering controlled by agnetic inhomogenieties. 
This would be required by the observation that the proton spectru  is 
assymptotically the sa e as those of the heavier uclei, i.e., 
y ~ 2.75. The atter traversed by particles in this outer box ould 
   t hr e i es hat f e nner . ce e n 
sity is ch lower, t e lifetime i  the uter  l   t   
- 00 ti e longer t an in t e inner . 
The source spectra ould be given by shock acceleration and the 
equilibrium spectra observed would be steepened by the energy dependent 
diffusion in both boxes. This odel ould re ove any conflict bet een 
the low energy co position data and the high energy isotropy, which is 
determined by the conditions in the outer box. The 1 GeV/amu particles 
observed at Earth contain "young" heavy nucl ei from nearby sources 
(~ 0.5 kpc) and "old" protons and helium nuclei fro  the galaxy as a 
hole. 
We may be effectively outside the source of the very lowest energy 
particles (~ 100 eV/amu) because, at this low energy, the diffusion 
OG 4.1-12
46
coefficient will be very small. This could explain the increasing
truncation of the path length distribution below I GeV/amu (Wefel et
al .).
4. Discussion. Remembering that these results are preliminary, one can
note that if iron secondaries do increase at high energies, the
conventional leaky box with a monotonic decrease of matter with energy
will need modification to account for the ratio of Fe secondaries/Fe at
high energies. The antiprotons detected (Golden et al., 1979) [3] do
need more matter traversal than the leaky box model would allow. Cowsik
and Gaisser 1982, [13] postulate separate sources for antiprotons and
heavy nuclei. The normalization of the strengths of these sources would
depend on the relative amounts of antiprotons, secondary, and primary
heavy nuclei. Various considerations of the nature suggest a two
component model for the propagation of cosmic rays.
A leaky box like the outer box with a mean matter traversed would
produRe an iron secondary to iron ratio approximately twice that of a
7g/cm _ inner box, but both boxes produce a ratio which falls with
increasing energy due to the energy dependence of the diffusion
coefficient. It, therefore, seems to be difficult to find an admixture
of the relative abundances of iron from the two components that could
produce a sub-iron to iron ratio which would increase with energy unless
the outer box contributes only at higher energy. This could be the case
probably only if the relative size of the diffusion coefficient were
contrived in the same manner.
In conclusion, it seems difficult to match the increase in the sub-
iron to iron ratio with a shock accelerationmodel including a local
source on a general galactic background without introducing a new
parameter, namely, the variation of diffusion coefficient with position
in the galaxy. Of course, the closed galaxy model itself requires
source spectra which are as steep as proton spectrum. One variant of
this model might be that high energy particles can penetrate into
regions of dense matter. This is the functional equivalent of having a
diffusion coefficient which is contrived in a manner which allows higher
energy particles to pass through more matter.
References
I. Cesarsky, C. J., 1980, Ann. Revs. Astron. Astrophys., I_88,289.
2. Engelmann, J. et al., 1985, to be published in Astron. and
Astrophys.
3. Golden, R. et al., 1979, Phys. Rev. Letters, 43, 1179.
4. Bogomolov, E. A. et al., 1979, Proc. 16th Intl,-.Cosmic Ray Conf.
(Kyoto),__l,330.
5. Buffington, A. et al., 1981, Ap. J., 248, 1179.
6. Streitmatter, R. et al., 1985, paper OG 4.1-11, this Conference.
7. Simon, M. et al., 1980, Ap. J., 239, 712.
8. Burnett, T. H. et al., 1983, Proc. 18th Intl. Cosmic Ray Conf.
(Bangalore),2, 105.
9. Goodman, J. et al-Z,1982, Phys. Rev. D26, 1043.
10. Ryan, M. J., et al., 1982, Phys. Rev. Letters, 28, 985.
OG 4.1-12 
46 
coefficient will be very small. This could explain the increasing 
truncation of the path length distribution below 1 GeV/amu (Wefel et 
a 1.). 
4. Discussion. Remembering that these results are preliminary, one can 
note that if iron secondaries do increase at high energies, the 
conventional leaky box with a monotonic decrease of matter with energy 
will need modification to account for the ratio of Fe secondaries/Fe at 
high energies. The antiprotons detected (Golden et al., 1979) [3J do 
need more matter traversal than the leaky box model would allow. Cowsik 
and Gaisser 1982, [13J postulate separate sources for antiprotons and 
heavy nuclei. The normalization of the strengths of these sources would 
depend on the relative amounts of antiprotons, secondary, and primary 
heavy nuclei. Various considerations of the nature suggest a two 
component model for the propagation of cosmic rays. 
A leaky box like the outer box with a mean matter traversed would 
produ~e an iron secondary to iron ratio approximately twice that of a 
7g/cm inner box, but both boxes produce a ratio which falls with 
increasing energy due to the energy dependence of the diffusion 
coefficient. It, therefore, seems to be difficult to find an admixture 
of the relative abundances of iron from the two components that could 
produce a sub-iron to iron ratio which would increase with energy unless 
the outer box contributes only at higher energy. This could be the case 
probably only if the relative size of the diffusion coefficient were 
contrived in the same manner. 
In conclusion, it seems difficult to match the increase in the sub-
iron to iron ratio with a shock acceleration model including a local 
source on a general galactic background without introducing a new 
parameter, namely, the variation of diffusion coefficient with position 
in the galaxy. Of course, the closed galaxy model 'itself requires 
source spectra which are as steep as proton spectrum. One variant of 
this model might be that high energy particles can penetrate into 
regions of dense matter. This is the functional equivalent of having a 
diffusion coefficient which is contrived in a manner which allows higher 
energy particles to pass through more matter. 
References 
1. Cesarsky, C. J., 1980, Ann. Revs. Astron. Astrophys., 18, 289. 
2. Engelmann, J. et al., 1985, to be published in Astron.and 
Astrophys. 
3. Golden, R. et al., 1979, Phys. Rev. Letters, 43, 1179. 
4. Bogomolov, E. A. et al., 1979, Proc. 16th Inti. Cosmic Ray Conf. 
(Kyoto), 1,330. 
5. Buffington, A-: et al., 1981, Ap. J., 248, 1179. 
6. Streitmatter, R. et al., 1985, paper OG4.1-11, this Conference. 
7. Simon, M. et al., 1980, Ap. J., 239, 712. 
8. Burnett, T. H. et al., 1983, Proc.--18th Intl. Cosmic Ray Conf. 
(Bangalore), 2, 105. 
9. Goodman, J. et a 1-:-, 1982, Phys. Rev. 026, 1043. 
10. Ryan, M. J., et al., 1982, Phys. Rev.Tehers,~, 985. 
OG 4.1-12
47
II. Cowslk, R. and Wilson, L. W., 1973, Proc. 13th Intl. Cosmic Ray
Conf. (Denver), 5, 500.
12. Peters, B. and West_gaard, N. J., 1977, Astrophys. and Space Sci.,
48, 21.
13. Cows'fE, R. and Gaisser, T. K., 1981, Proc. 17th Intl. Cosmic Ray
Conf. (Paris), 2_._218.
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11. o s1k, R. and ilson, l. ., 1973, Proc. 13th Intl. os ic Ray 
onf. ( enver), 5, 500. 
12. Peters, B. and estergaard, N. J., 1977, strophys. and Space Sci., 
, . 
13. Cowsll(, R. and aisser, T. ., 1981, Proc. 17th Intl. Cosmic Ray 
onf. (Paris), b 218. 
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Cosmic ray nuclei of energy 50 GeV/NUC

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