Calculations of the propagation of UH-nuclei were improved by extending the number of individual nuclides considered, and by using more recent evaluations of the rigidity dependence of the escape length, the possible source composition, and altered cross sections. The effects of using different expressions for the dependence of abundances on first ionization potentials (FIP) are outlined. The sensitivity of the calculated elemental abundances to the various changes made in the propagation assumptions are discussed

Brewster, N. R.

Kertzman, M. P.

Waddington, C. J.

English

NASA Technical Reports Server

1OG7.1-1
VARIATIONS IN THE PROPAGATION OF UH-NUCLEI
C. J. Waddington, N. R. Brewster, and M. P. Kertzman
School of Physics and Astronomy, University of Minnesota
116 Church St. S.E., Minneapolis, Minnesota 55455, U.S.A.
Abstract. We have investigated the sensitivity of the predictions of a
model of the propagation of UH-nuclei in the interstellar medium on
various assumptions.
i. Introduction. At the Paris Conference we reported, Brewster et al.
(1981) our initial calculations on the propagation of UH-nuclei, using a
leaky box formalism. These results have been discussed in more detail
elsewhere, Brewster et al. (1983a). We have since improved this
calculation by extending the number of individual nuclides considered,
as well as using more recent evaluations of the rigidity dependence of
the escape length, the possible source composition, and altered cross
sections. We have also considered the effects of using different
expressions for the dependence of abundances on first ionization
potentials (FIP). In this paper we discuss the sensitivity of the
calculated elemental abundances to the various changes made in the
propagation assumptions. Details are available in Brewster (1985) and
Brewster et al. (1985).
2. Modifications. The number of nuclides considered has been
essentially doubled from 580 to 1316 and now includes virtually every
one with 26_Z_83 listed in the "Chart of the Nuclides" (as well as the
longest-lived isotopes of Th and U). Those added were all short-lived,
and so their production probabilities were included in the cross
sections for the production of their final decay products. This has the
effect of increasing the partial production cross sections for all the
long-lived nuclides, and thus increasing secondary-to-primary abundance
ratios.
Another change was in the dependence on rigidity, R, of the mean
escape length, % . A recent analysis by Ormes and Protheroe indicatesec
a steeper dependence on rigidity than the R-°'4 we used previously.
This dependence is expressed as:
-3/2
= (26.9)[1 + (1.88/R) 2] R-0"7, R < 11.4 GV
% [g/cm2]
esc = (25.8) R-0"7 R > 11.4 GV
normalized to A = 6.0 g/cm2 at a kinetic energy of T = 5 GeV/nucleon.
esc
The constants mn front allow for propagation in a hypothetical
interstellar medium (ISM) composed of pure hydrogen. As a consequence
of making this change we have also used a different injection spectrum,
dJ/dT _ R-2"° rather than _ R-2"3, as is required for consistency with
the observed rigidity spectra of R-2"7
Another modification introduced is a change in the assumed solar
system source abundances, which is not a change in the propagation model
as such. We now use the Anders and Ebihara (1982) abundances, rather
than the earlier Cameron (1982) compilation.
https://ntrs.nasa.gov/search.jsp?R=19850026550 2020-03-20T17:00:33+00:00Z
2
OG7.1-1
Cosmic ray propagation models generally use the semi-empirical
fnrmulas of Silberberg and Tsao (1973, 1977) to calculate the partial,
do, and total, gT' cross sections needed for the model. These do and OT
values have been adjusted by "scaling" from the measured do values of
Au-nuclei observed at the Bevalac, Brewster et al. (1983b).
3. Effects of the Modifications. The effects of making these
modifications are demonstrated in the Table for the abundances of
various selected elements relative to 106 Fe-nuclei and several
abundance ratios. Column (i) shows the predicted abundances near earth
as calculated by Brewster et al. (1983a), based on the Cameron (1982)
solar system abundances at the source. Column (2) shows the effect of
increasing the number of nuclides while (3) shows the percentage change
due to this modification. As expected, using the larger set of nuclides
increases the abundances of almost all the elements relative to iron,
since all the partial cross sections were increased. The difference is
greatest for the most secondary species like Z = 70. In this table we
have also defined various ratios of groups of elements. It should be
noted that elements with 44_Z_48, 62_Z_69, and 70_Z_74 are presumed to
be predominately, although not purely, secondary in origin, whereas the
others are mostly primary, originating in the source.
Table: Abundances and abundance ratios (see text)
All Exp Step
Original Nuclides % A&E % FIP R-0"7 % FIP % Scaling %
(I)-(2) (2)-(4) (4)-(7) (4)-(9) (7)-(11)
z (i) (2) (3) (4) (5) (6) (7) (8) (9) (10) (ll) (12)
38 27 26 -4% 26 0% 46 46 77% 26 0% 48 4%
46 3.2 4.2 31% 4.0 -5% 4.2 4.1 3% 3.2 -20% 4.9 20%
50 5.5 6.7 22% 6.3 6% 7.1 7.1 13% 5.1 -19% 8.4 18%
52 6.0 6.6 10% 5.2 -21% 4.6 4.6 -12% 2.3 -56% 5.4 17%
56 3.9 4.3 10% 4.0 -7% 7.9 8.0 100% 4.0 0% 9.4 18%
70 .27 .51 89% .57 12% .64 .64 12% .54 5% I.i 72%
78 .90 .95 6% .95 0% .74 .75 -21% .95 0% 1.0 33%
82 1.5 1.5 0% 1.8 20% 2.0 2.1 17% 1.8 0% 2.4 14%
NI/N 2
N (44_8) .56 .59 5% .61 3% .57 .56 -8% .75 23% .56 0%
N (50_Z_58)
N (62_E69) .52 .73 40% .67 -8% .86 .84 25% .68 I% 1.I 31%
N (75_Z_83)
N (70_74) .24 _35 46% .31 -11% ,34 .33 6% .31 0% .45 36%
N (75_Z=83)
N 180_Z_83) .85 .80 -6% .99 24% 1.3 1.3 31% .97 -2% i.i -15%
N (75_Z_79)
The effect of using the Anders and Ebihara (1982) abundances is
shown in Column (4) with the resulting percentage changes shown in (5).
These changes are entirely due to the differences between the two
abundance compilations and while significant are relatively minor.
The application of corrections for the apparent dependence of
source_ abundances on FIP are shown in the next few columns. Column (6)
shows the effect of an exponential FIP dependence of the form f = 9.32
exp (-0.288I), so f = 1.0 for a potential, I, of I = 7.75 eV, while (9)
3
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I i I I I I
I I I I I I
50 40 50 60 70 80.
ATOMIC NUMBER, Z
Fig. I. The ratio of the abundances of a solar system source after
propagation, with and without the application of a FIP correction, as a
function of the atomic number Z.
shows that of a step dependence with f = 1 for I _ 9 eV and f = 0.3 for
I > 9 eV. Column (7) shows the very minor effect of changing the
rigidity dependence. The differences between no FIP correction and
exponential or step FIP dependence are shown in Columns (8) and (i0)
respectively. There is clearly a strong effect, both on FIP and on
which FIP dependence is assumed. This can be more clearly seen in Fig.
i, which shows the Z dependence of the abundance changes and illustrates
the fact that a step FIP dependence, unlike the exponential dependence,
never increases the abundances significantly, but only depletes them.
Figure 1 also shows the effects of a FIP dependence with a step at 10.2
eV, the Lymann H , which while not a good fit to the abundance ratios if
standard solar abundances are assumed, is reasonable if C2 chondritic
meteorite abundances are assumed, Binns et al. (1984). This higher
energy step can be seen to still further reduce the effect of applying a
FIP correction.
The differences between these various FIP dependencies are large
enough that it should be possible to test them by examining data in the
32_-<Z_42 and 50_=Z_60 charge ranges. For example, the large relative
abundances of ^^Sr and 56Ba reported from the HEAO C3 experiment, Binns
et al. (1981,J_1983), Both appear to imply that the exponential FIP
dependence is a better representation than the step dependencies unless
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0G7•1-1
the source abundances are quite anomalous.
The effects on the exponential FIP abundances of adjusting the oT
and do values, by scaling the predicted values on the basis of those
observed for Au-nuclei, Brewster et al. (1983b), are shown in Column
(Ii). The scaling factors used for do are shown in Fig. 2 as a function
I f i I
Fig. 2. The scaling factor
_.o applied to the predicted
cross-sections as a function
of AZ.
0.5 _ _ _B _ '
CHARGECHANGE,_Z
of the charge change, AZ, and can be seen to increase do values for
small AZ and decrease them for large AZ. Column (12) shows the
percentage changes between (7) and (II) and can be seen to be always
positive, reflecting the greater importance of small charge changes in
the propagation process. The recent observations reported elsewhere at
this conference, Kertzman et al. (1985; OG 7.2-21), on the interactions
of other heavy nuclei show that these scaling factors are strongly Z
dependent and hence that the application of the Au-results to other
primary nuclei is probably not justified, see e.g. the recent Pb/Pt
results also reported at this conference, Waddington et al. (1985; OG
4.4-7).
4. Acknowledgements. This work was supported in part by NASA under
grants NGR 24-005-050 and NAG8-500. We are indebted to P. S. Freier for
her comments and interest, and to M. H. Israel and E. C. Stone for
useful comments.
References
Anders, E., and Ebihara, M. (1982), Geochimica et Cosmochimica Acta, 46,
2363.
Binns, W. R., et al. (1981), Ap. J. 247, LII5.
Binns, W. R., et al. (1983), Ap. J. 267, L93.
Binns, W. R., et al. (1984), COSPAR Symposium.
Brewster, N. R. (1985), Ph.D. Thesis, Univ. of Minn.
Brewster, N. R., Freier, P. S., and Waddington, C. J. (1981), 17th ICRC,
Vol. 9, 126.
• (1983a), Ap.J. 264, 324.
• (1985), to be published in Ap.J., July i.
Brewster, N. R•, et. al. (1983b), Proc. 18th ICRC, 9, 259.
Cameron, A. G. W. (1982), Essays in Nuclear Astrophy., ed. C. A. Barnes,
Cambridge U. Press.
Kertzman, M. P., et al. (1985), this conf., Paper OG 7.2-21•
Ormes, J. F., and Protheroe, R. J. (1983), Ap.J. 264, 324•
Silberberg, R., and Tsao, C. H. (1973), Ap. J. Suppl. 25, 335.
• (1977), Proc. 15th ICRC, 2, 84.
Waddington, C. J., et al. (1985), this conf., Paper OG 4•4-7•


Variations in the propagation of UH-nuclei

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