Galactic cosmic rays (GCR) interact to produce secondary fragments as they pass through the interstellar medium (ISM). Abundances of the long-lived radioactive secondaries ^(10)Be, ^(26)Al, ^(36)Cl, and ^(54)Mn can be used to a derive the confinement time of cosmic rays in the galaxy. Abundances for these species have been measured recently using the Cosmic Ray Isotope Spectrometer (CRIS) aboard the Advanced Composition Explorer (ACE) spacecraft. To interpret this data we have modeled the production and propagation of the radioactive secondaries, taking into account recently published isotopic production cross-sections. Abundances for all species are consistent with a confinement time of π_(esc) ~22 x 10^6 years

Binns, W. R.

Christian, E. R.

Cummings, A. C.

George, J. S.

Hink, P. L.

Klarmann, J.

Leske, R. A.

Lijowski, M.

Mewaldt, R. A.

Stone, E. C.

von Rosenvinge, T. T.

Wiedenbeck, M. E.

Yanasak, N. E.

Caltech Authors - Main

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OG.1.1.03 
Implications for Cosmic Ray Propagation from ACE 
Measurements of Radioactive Clock Isotope Abundances 
N.E. Yanasak1, W.R. Binns3 , A.C. Cummings2 , E.R. Christian4 , J.S. George2 , 
P.L. Hink3 , J. Klarmann3 , R.A. Leske2, M. Lijowski3 , R.A. Mewaldt2 , 
E.C. Stone2 , T.T. von Rosenvinge4, and M.E. Wiedenbeck1 
1 Jet Propulsion Laboratory, Pasadena, CA 91109, USA 
2 California Institute of Technology, Pasadena, CA 91125, USA 
3Washington University and McDonnell Center for the Space Sciences, St. Louis, MO 63130, USA 
4 NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA 
Abstract 
Galactic cosmic rays (GCR) interact to produce secondary fragments as they pass through the interstellar 
medium (ISM). Abundances of the long-lived radioactive secondaries 10Be, 26 Al, 36Cl, and 54Mn can be used 
to a derive the confinement time of cosmic rays in the galaxy. Abundances for these species have been mea-
sured recently using the Cosmic Ray Isotope Spectrometer (CRIS) aboard the Advanced Composition Explorer 
(ACE) spacecraft. To interpret this data we have modeled the production and propagation of the radioactive sec-
ondaries, taking into account recently published isotopic production cross-sections. Abundances for all species 
are consistent with a confinement time of Tesc ""22x 106 years. 
1 Introduction: 
Information about the spallation of galactic cosmic rays into secondary fragments as they propagate through 
the ISM is retained in the abundances of those fragments observed at Earth. Stable secondaries act as a gauge 
for the amount of ISM material the GCRs traverse but offer few if any details about the material distribution or 
propagation history. Abundances of the long-lived secondary radionuclide "clocks" reflect a balance between 
production by spallation in the ISM and decay or escape during the propagation time of cosmic rays, and thus 
probe these details mentioned above. The abundance of the clock isotope10 Be has been measured for about 20 
years, but recent measurements of other species with a variety of halftives such as 26 Al and 36Cl using Voyager, 
Ulysses, and CRIS can present a more comprehensive picture of GCR propagation. 
The decay of these clock isotopes provides the necessary timing to study propagation history, but specific 
interpretation of the clock abundances depends on the type of propagation model used. The so-called "leaky 
box" model (LBM) assumes a homogeneous distribution of ISM matter and predicts a galactic confinement 
time and an average ISM density from clock isotope abundances. Under certain circumstances, the leaky box 
model is a suitable approximation to more realistic models of GCR diffusion, but observable differences arise in 
the shorter halflife clock abundances if one assumes significant inhomogeneities in the local matter distribution. 
Despite the oversimplified nature of the LBM, abundance predictions for a variety of GCR species have been 
fairly consistent with measurements. The galactic geometry for diffusion models is not well-constrained by 
observation, and in general the interpretation of clock abundances is limited to a particular choice of geometry. 
One recent diffusion model uses the fractional abundance of the clock isotopes which survive propagation to 
predict a local galactic diffusion coefficient for various geometries (Ptuskin and Soutoul 1998), which offers a 
straightforward experimental test. 
2 Propagation Model: 
A steady-state LBM was used to calculate the post-propagation GCR abundances observed by CRIS (Binns 
et al. 1999). With the exception of an overabundance of 22Ne, the source abundances were taken to be solar, 
adjusted for a FIP-like fractionation. The source spectra obey a power-law dependence in rigidity. Ionization 
energy loss, spallation, radioactive decay, and single electron attachment and stripping rates in the ISM were in-
corporated in the model. The composition of the ISM was chosen to be 90% H, 10% He. The amount of energy 
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loss was adjusted to reflect a 25% ionized H population in the ISM, consistent with observations (Nordgren et 
al. 1992). 
The GCR pathlength distribution (PLD) for a single leaky box is exponential. The mean ISM pathlength 
was adjusted to match four secondary to primary ratios from CRIS (B/C, F/Ne, PIS, and (Sc+V)/Fe). HEA0-3 
data at the higher energies were used as a consistency check (Englemann et al. 1990). As suggested by previous 
work (e.g., Lukasiak et al. 1994), we assume the following form of the mean pathlength >.: 
Fitting the energy dependence of the secondary to primary ratios is crucial for determining the ISM density and 
confinement time over the energy range of the data. Typically, a value of n=1 has been used in many models. 
Tan et al. (1987) sug-
gest that suppression of 
GCR diffusion can lead 
to higher values of n. 
Previous low energy ex-
periments which have 
measured these ratios at 
multiple energies indicate 
a need for n rv2-4 to fit 
the data (e.g., Krombel 
and Wiedenbeck 1988), 
and this trend is present 
in the CRIS data as well. 
Our model requires 
slightly different mean path-
lengths to fit CRIS low-Z 
ratios and the sub-Fe/Fe 
0.25 
0.5 
______ 1" Ulysses 
0 ISEE-3 --...---
0 Voyage 
<ll O . 3 -;;;;:==:+:!==---! T CRIS 
CJlrrl 0.15 F--_...""""i'<-1----1 ... SIS 
~ O."'T-l-l'l''l"'l;ll.'9'-------i_---='~ 
.s 
"til 0.20 0.4 
"" 
0 rr1 0.10 0.15-.+-.l.-----
.--< 
0.10------
0.12 
.s 0.10 
+' 
ell 
"" 
0.02 
100 1000 
0.08 
0.07 o.5 
0 il 0.06 0.4 
"" 0.05 u 
""- 0.04 
u 
co 0.03 
C"J 
0.02 
0.3 
0.25 
0.2 
0.15 
O.lll-----
0.01 ~-~-------~ 
0.18 
.s 0.16 
+' 
ell 
"" 
0.14 
i 0.12 
';;;' 0.10 
-tj<';;2 0.08 
lD 
0.06 
100 1000 
Kin. Energy (in MeV /nuc) 
0.75 
0.3 
0. 2 5 ---1'="--f:l':-=,._-
0. 2 
0.15--- 1 
0.1 
0.05 -----+---
100 
Kin. Energy (in MeV /nuc) 
1.0 
0.75 
0.5 
0.4 
0.3 
0.25 
0.2 
0.15 
1000 
100 1000 
Kin. Energy (in MeV /nuc) 
ratio. PLDs which are Figure 1: Radioactive clock abundance ratios. Curves show calculated densities of 
truncated at shorter path- ISM hydrogen (atoms/cm 3). A 10Be data point from the SIS instrument on ACE is 
lengths have been sug- shown for comparison. Experiment references can be found in Table 1. 
gested before as a resolu-
tion to this discrepancy (e.g., Garcia-Munoz et al. 1987, Webber 1993), consistent with models including con-
centrations of matter around discrete GCR sources in the galaxy. For this study, we adjusted the mean path-
length for each clock isotope to match the secondary to primary ratio data for the parent nucleus which con-
tributes the most to that clock species. Consequences of this method are addressed later. 
Solar modulation of the cosmic ray spectra was simulated using a spherically symmetric model described 
by Fisk (1971). The diffusion coefficient was calculated using a specified force-field modulation parameter¢ 
(rv 555 MV for CRIS data, adapted from Badhwar and O'Neill 1993). 
3 Discussion: 
The clock isotopic abundances are interpreted within the leaky box framework to specify a galactic confine-
ment time. Given a mean pathlength and a confinement time, one can calculate the mean ISM density through 
which the GCRs propagate, but the clock abundances are sensitive to this time of propagation. The relationship 
between mean pathlength >., density p, and confinement time Tesc can be written as A = p(3cTesc· ISM densi-
ties derived in this framework should not necessarily be consistent between the various clock species. Cosmic 
rays diffuse through the galaxy, and given a similar diffusion rate for each species, each clock will sample a 
volume of the ISM for a time comparable to its decay lifetime. Using the simple relation for diffusion distance 
© University of Utah • Provided by the NASA Astrophysics Data System 
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l = (DTdecay) 112 and a typical diffusion coefficient D r-vl028 cm2 s-1 (Ptuskin and Soutoul 1998), 10Be will 
sample a region within r-v275 pc of the solar system, while 36Cl will sample a smaller region of r-v 120 pc. 
Differences in the average den-
sities derived using each clock 
should be characteristic of these 
different surrounding volumes. 
Figure 1 shows a compari-
son between radioactive clock 
abundances measured by re-
cent experiments and our model 
calculations assuming various 
interstellar H densities. Data 
previous to CRIS were reported 
as one abundance per experi-
ment covering a fairly wide en-
ergy range, owing to the lim-
ited statistical accuracy. Be-
cause of the larger number of 
events, CRIS data can be plot-
ted at multiple energies and 
compared to the predicted en-
ergy dependence. For direct 
comparison, the previously re-
I 
Table 1 : Mean confinement times of the GCR clock nuclei. 
Clock Experiment* I Tesc (in Myr)f I 
lOBe ACE/CRIS(this work) 21.0 ( +2.4, -1.9) 
Ulysses(Connell 1998) 26.0 ( +4.0, -5.0) 
ISEE-3(Wiedenbeck and Greiner 1980) 8.4 ( +4.0, -2.4) 
26Al ACE/CRIS(this work) 22.3 ( + 1.6, -1.5) 
Ulysses(Simpson and Connell 1998) 19.0 ( +3.0, -3.0) 
Voyager(Lukasiak et al. 1997b) 13.5 ( +8.5, -4.5) 
ISEE-3(Wiedenbeck 1983) 9.0 ( +20.0, -6.5) 
36Cl ACE/CRIS(this work) 25.0 ( +4.2, -3.4) 
Ulysses(Connell et al. 1998) 18.0 ( + 10.0, -6.0) 
54Mn ACE/CRIS+(this work) 29.6 ( +2.2, -3.4) 
Ulysses§ (Du Vernois 1997) 14.0 ( +6.0, -4.0) 
*Other Voyager results are reported as surviving fractions. 
t Quoted errors are statistical. 
+Assumes T1; 2=0.63 Myr. (Wuosmaa et al. 
§Assumes T1; 2=1 Myr. 
1998) 
ported abundances have been adjusted to the solar modulation level relevant to CRIS. To within statistical un-
certainties, the CRIS data are consistent with previous experiments, and density predictions from this model 
(p r-v 0.15-0.4 H atoms/cm3) are compara-
ble to results from the Ulysses group (Con-
nell 1998). 
Interpretation is complicated by observed 
inhomogeneities in the local ISM. The pre-
dicted densities are lower than the aver-
age galactic disk density of r-v 1 atom/cm3, 
which may imply significant propagation 
in a galactic halo of lesser density. How-
ever, this could also indicate a substantial 
amount of propagation in a local ISM cav-
ity (Ptuskin and Soutoul 1998). The 36Cl 
abundance is suggestive of a higher local 
ISM density than the longer-lived species 
indicate, but the difference is not significant. 
1.0000 
c 
.S 0.1000 
+.l 
() 
(1j 
~ -Of) 0.0100 
c 
·s;: 
» 
5 0.0010 
[/] 
halflife(in years) 
Figure 2: Surviving fraction of clock isotopes. Curves are model 
The energy dependences of the clock abun- predictions from 10Be abundance. 
dances shown in this propagation model are 
not inconsistent with the data, although they 
are not clearly indicated either. Both the energy dependence and the value of the calculated density are depen-
dent on the chosen mean pathlength parameterization, which is different for the sub-Fe/Fe and lower-Z ratios. 
The confinement time is less reliant on the parameterization of the mean pathlength than the average ISM 
density. Using an ISM density appropriate for each species, the confinement times calculated from the CRIS 
clock abundances are presented in Table 1, along with previous experimental results. Considering the large 
© University of Utah • Provided by the NASA Astrophysics Data System 
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uncertainty in the halflife of 54Mn ("'"' 40%, from Wuosmaa et al. 1998), CRIS predicts a confinement time 
of Tesc rv22x 106 years which is consistent with all species. The confinement times obtained from our model 
calculations are comparable to recent Ulysses results, but they yield somewhat longer times than ISEE-3 results 
and earlier calculations (e.g., Garcia-Munoz et al. 1981). This may be a result of other experimental groups 
using different mean ISM pathlengths to calculate the confinement time, originating from earlier measurements 
of the fragmentation partial cross sections. 
The surviving fraction for each clock is shown in Figure 2. A comparison of these with the predictions of 
Ptuskin and Soutoul's model yields a local diffusion coefficient D ranging from 2 x 1028 - 1029 cm2 s- 1 . 
Assuming a consistent value of D for all clock species, 26 Al and 36Cl abundances do not appear to support 
simple galactic models composed of a single gas layer or a thin layer, but these are not ruled out for higher 
values of D. The surviving fraction of 14C is a discriminating test of these models and the value of D. CRIS 
should record"'"' 30 14C events during a 2 year period, assuming a mean ISM density consistent with other clock 
abundances (Stone et al. 1999). Whether these few events ("'"' 5 x 10-4 % of total carbon) can be distinguished 
from background is under investigation. 
4 Conclusions: 
Within the context of our leaky-box model, we find a confinement time from CRIS data of Tesc "'"'22x 106 
years which is consistent for all species. This time is characteristic of a mean ISM H density between 0.15 and 
0.40 atoms/cm3 , assuming our parameterization of the mean pathlength. The surviving fractions for all clock 
species imply a local diffusion coefficient from Ptuskin and Soutoul's model ranging from 2 x 1028 - 1029 
cm2s- 1 . 
References 
Binns, W.R., et al., 1999, Proc. 26th ICRC, OG.1.1.06 (Salt Lake City) 
Badhwar, G.D., & O'Neill, P.M., 1993, Proc. 23rd ICRC, 3, 535 (Calgary) 
Connell, J.J., 1998, ApJ 501, L59 
Connell, J.J., DuVernois, M.A., & Simpson, J.A., 1998, ApJ 509, L97 
Duvernois, M.A., 1997, ApJ 481, 241 
Englemann, J.J., et al, 1990, A&A 233, 96 
Fisk, L.A., 1971, JGR 76, 221 
Garcia-Munoz, M., et al., 1987, ApJ Supp. 64,269 
Garcia-Munoz, M., et al., 1981, Proc. 17th ICRC, 2, 72 (Paris) 
Krombel, K.E., & Wiedenbeck, M.E., 1988, ApJ 328, 940 
Lukasiak, A., McDonald, F.B., & Webber, W.R., 1994, ApJ 430, L69 
Lukasiak, A., McDonald, F.B., & Webber, W.R., l 997a, Proc. 25th ICRC, 3, 389 (Durban) 
Lukasiak, A., McDonald, F.B., & Webber, W.R., l 997b, ApJ 488, 454 
Nordgren, T., Cordes, J.M., & Terzias, Y., 1992, AstronJ 104, 1465 
Ptuskin, V.S., & Soutoul, A., 1998, A&A 337, 859 
Simpson, J.A., & Connell, J.J., 1998, ApJ 497, L85 
Stone, E.C., et al., 1998, Space Sci Rev 86, 285 
Tan, L.C., et al., 1987, Proc. 20th ICRC, 2, 239 (Moscow) 
Webber, W.R., 1993, ApJ 402, 188 
Webber, W.R., 1998, Space Sci Rev 86, 239 
Wiedenbeck, M.E., & Greiner, D.E., 1980, ApJ 239, LI 39 
Wiedenbeck, M.E., 1983, Proc. 18th ICRC, 9, 147 (Bangalore) 
Wuosmaa, A.H., et al., 1998, Phys. Rev. Lett. 79, 4302 
© University of Utah • Provided by the NASA Astrophysics Data System 


English

Implications for Cosmic Ray Propagation from ACE Measurements of Radioactive Clock Isotope Abundances

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OG.1.1.03 
Implications for Cosmic Ray Propagation from ACE 
Measurements of Radioactive Clock Isotope Abundances 
N.E. Yanasak1, W.R. Binns3 , A.C. Cummings2 , E.R. Christian4 , J.S. George2 , 
P.L. Hink3 , J. Klarmann3 , R.A. Leske2, M. Lijowski3 , R.A. Mewaldt2 , 
E.C. Stone2 , T.T. von Rosenvinge4, and M.E. Wiedenbeck1 
1 Jet Propulsion Laboratory, Pasadena, CA 91109, USA 
2 California Institute of Technology, Pasadena, CA 91125, USA 
3Washington University and McDonnell Center for the Space Sciences, St. Louis, MO 63130, USA 
4 NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA 
Abstract 
Galactic cosmic rays (GCR) interact to produce secondary fragments as they pass through the interstellar 
medium (ISM). Abundances of the long-lived radioactive secondaries 10Be, 26 Al, 36Cl, and 54Mn can be used 
to a derive the confinement time of cosmic rays in the galaxy. Abundances for these species have been mea-
sured recently using the Cosmic Ray Isotope Spectrometer (CRIS) aboard the Advanced Composition Explorer 
(ACE) spacecraft. To interpret this data we have modeled the production and propagation of the radioactive sec-
ondaries, taking into account recently published isotopic production cross-sections. Abundances for all species 
are consistent with a confinement time of Tesc ""22x 106 years. 
1 Introduction: 
Information about the spallation of galactic cosmic rays into secondary fragments as they propagate through 
the ISM is retained in the abundances of those fragments observed at Earth. Stable secondaries act as a gauge 
for the amount of ISM material the GCRs traverse but offer few if any details about the material distribution or 
propagation history. Abundances of the long-lived secondary radionuclide "clocks" reflect a balance between 
production by spallation in the ISM and decay or escape during the propagation time of cosmic rays, and thus 
probe these details mentioned above. The abundance of the clock isotope10 Be has been measured for about 20 
years, but recent measurements of other species with a variety of halftives such as 26 Al and 36Cl using Voyager, 
Ulysses, and CRIS can present a more comprehensive picture of GCR propagation. 
The decay of these clock isotopes provides the necessary timing to study propagation history, but specific 
interpretation of the clock abundances depends on the type of propagation model used. The so-called "leaky 
box" model (LBM) assumes a homogeneous distribution of ISM matter and predicts a galactic confinement 
time and an average ISM density from clock isotope abundances. Under certain circumstances, the leaky box 
model is a suitable approximation to more realistic models of GCR diffusion, but observable differences arise in 
the shorter halflife clock abundances if one assumes significant inhomogeneities in the local matter distribution. 
Despite the oversimplified nature of the LBM, abundance predictions for a variety of GCR species have been 
fairly consistent with measurements. The galactic geometry for diffusion models is not well-constrained by 
observation, and in general the interpretation of clock abundances is limited to a particular choice of geometry. 
One recent diffusion model uses the fractional abundance of the clock isotopes which survive propagation to 
predict a local galactic diffusion coefficient for various geometries (Ptuskin and Soutoul 1998), which offers a 
straightforward experimental test. 
2 Propagation Model: 
A steady-state LBM was used to calculate the post-propagation GCR abundances observed by CRIS (Binns 
et al. 1999). With the exception of an overabundance of 22Ne, the source abundances were taken to be solar, 
adjusted for a FIP-like fractionation. The source spectra obey a power-law dependence in rigidity. Ionization 
energy loss, spallation, radioactive decay, and single electron attachment and stripping rates in the ISM were in-
corporated in the model. The composition of the ISM was chosen to be 90% H, 10% He. The amount of energy 
© University of Utah • Provided by the NASA Astrophysics Data System 
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loss was adjusted to reflect a 25% ionized H population in the ISM, consistent with observations (Nordgren et 
al. 1992). 
The GCR pathlength distribution (PLD) for a single leaky box is exponential. The mean ISM pathlength 
was adjusted to match four secondary to primary ratios from CRIS (B/C, F/Ne, PIS, and (Sc+V)/Fe). HEA0-3 
data at the higher energies were used as a consistency check (Englemann et al. 1990). As suggested by previous 
work (e.g., Lukasiak et al. 1994), we assume the following form of the mean pathlength >.: 
Fitting the energy dependence of the secondary to primary ratios is crucial for determining the ISM density and 
confinement time over the energy range of the data. Typically, a value of n=1 has been used in many models. 
Tan et al. (1987) sug-
gest that suppression of 
GCR diffusion can lead 
to higher values of n. 
Previous low energy ex-
periments which have 
measured these ratios at 
multiple energies indicate 
a need for n rv2-4 to fit 
the data (e.g., Krombel 
and Wiedenbeck 1988), 
and this trend is present 
in the CRIS data as well. 
Our model requires 
slightly different mean path-
lengths to fit CRIS low-Z 
ratios and the sub-Fe/Fe 
0.25 
0.5 
______ 1" Ulysses 
0 ISEE-3 
--...---
0 Voyage 
<ll O . 3 -;;;;:==:+:!==---! T CRIS 
CJlrrl 0.15 F--_...""""i'<-1----1 ... SIS 
~ O."'T-l-l'l''l"'l;ll.'9'-------i_---='~ 
.s 
"til 0.20 0.4 
"" 
0 rr1 0.10 0.15-.+-.l.-----
.--< 
0.10------
0.12 
.s 0.10 
+' 
ell 
"" 
0.02 
100 1000 
0.08 
0.07 o.5 
0 il 0.06 0.4 
"" 0.05 
u 
""- 0.04 
u 
co 0.03 
C"J 
0.02 
0.3 
0.25 
0.2 
0.15 
O.lll-----
0.01 ~-~-------~ 
0.18 
.s 0.16 
+' 
ell 
"" 
0.14 
i 0.12 
';;;' 0.10 
-tj<';;2 0.08 
lD 
0.06 
100 1000 
Kin. Energy (in MeV /nuc) 
0.75 
0.3 0. 2 5 ---1'="--f:l':-=,._-
0. 2 
0.15--- 1 
0.1 
0.05 -----+---
100 
Kin. Energy (in MeV /nuc) 
1.0 
0.75 
0.5 
0.4 
0.3 
0.25 
0.2 
0.15 
1000 
100 1000 
Kin. Energy (in MeV /nuc) 
ratio. PLDs which are Figure 1: Radioactive clock abundance ratios. Curves show calculated densities of 
truncated at shorter path- ISM hydrogen (atoms/cm 3). A 10Be data point from the SIS instrument on ACE is 
lengths have been sug- shown for comparison. Experiment references can be found in Table 1. 
gested before as a resolu-
tion to this discrepancy (e.g., Garcia-Munoz et al. 1987, Webber 1993), consistent with models including con-
centrations of matter around discrete GCR sources in the galaxy. For this study, we adjusted the mean path-
length for each clock isotope to match the secondary to primary ratio data for the parent nucleus which con-
tributes the most to that clock species. Consequences of this method are addressed later. 
Solar modulation of the cosmic ray spectra was simulated using a spherically symmetric model described 
by Fisk (1971). The diffusion coefficient was calculated using a specified force-field modulation parameter¢ 
(rv 555 MV for CRIS data, adapted from Badhwar and O'Neill 1993). 
3 Discussion: 
The clock isotopic abundances are interpreted within the leaky box framework to specify a galactic confine-
ment time. Given a mean pathlength and a confinement time, one can calculate the mean ISM density through 
which the GCRs propagate, but the clock abundances are sensitive to this time of propagation. The relationship 
between mean pathlength >., density p, and confinement time Tesc can be written as A = p(3cTesc· ISM densi-
ties derived in this framework should not necessarily be consistent between the various clock species. Cosmic 
rays diffuse through the galaxy, and given a similar diffusion rate for each species, each clock will sample a 
volume of the ISM for a time comparable to its decay lifetime. Using the simple relation for diffusion distance 
© University of Utah • Provided by the NASA Astrophysics Data System 
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l = (DTdecay) 112 and a typical diffusion coefficient D r-vl028 cm2 s-1 (Ptuskin and Soutoul 1998), 10Be will 
sample a region within r-v275 pc of the solar system, while 36Cl will sample a smaller region of r-v 120 pc. 
Differences in the average den-
sities derived using each clock 
should be characteristic of these 
different surrounding volumes. 
Figure 1 shows a compari-
son between radioactive clock 
abundances measured by re-
cent experiments and our model 
calculations assuming various 
interstellar H densities. Data 
previous to CRIS were reported 
as one abundance per experi-
ment covering a fairly wide en-
ergy range, owing to the lim-
ited statistical accuracy. Be-
cause of the larger number of 
events, CRIS data can be plot-
ted at multiple energies and 
compared to the predicted en-
ergy dependence. For direct 
comparison, the previously re-
I 
Table 1 : Mean confinement times of the GCR clock nuclei. 
Clock Experiment* I Tesc (in Myr)f I 
lOBe ACE/CRIS(this work) 21.0 ( +2.4, -1.9) 
Ulysses(Connell 1998) 26.0 ( +4.0, -5.0) 
ISEE-3(Wiedenbeck and Greiner 1980) 8.4 ( +4.0, -2.4) 
26Al ACE/CRIS(this work) 22.3 ( + 1.6, -1.5) 
Ulysses(Simpson and Connell 1998) 19.0 ( +3.0, -3.0) 
Voyager(Lukasiak et al. 1997b) 13.5 ( +8.5, -4.5) 
ISEE-3(Wiedenbeck 1983) 9.0 ( +20.0, -6.5) 
36Cl ACE/CRIS(this work) 25.0 ( +4.2, -3.4) 
Ulysses(Connell et al. 1998) 18.0 ( + 10.0, -6.0) 
54Mn ACE/CRIS+(this work) 29.6 ( +2.2, -3.4) 
Ulysses§ (Du Vernois 1997) 14.0 ( +6.0, -4.0) 
*Other Voyager results are reported as surviving fractions. 
t Quoted errors are statistical. 
+Assumes T1; 2=0.63 Myr. (Wuosmaa et al. 
§Assumes T1; 2=1 Myr. 
1998) 
ported abundances have been adjusted to the solar modulation level relevant to CRIS. To within statistical un-
certainties, the CRIS data are consistent with previous experiments, and density predictions from this model 
(p r-v 0.15-0.4 H atoms/cm3) are compara-
ble to results from the Ulysses group (Con-
nell 1998). 
Interpretation is complicated by observed 
inhomogeneities in the local ISM. The pre-
dicted densities are lower than the aver-
age galactic disk density of r-v 1 atom/cm3, 
which may imply significant propagation 
in a galactic halo of lesser density. How-
ever, this could also indicate a substantial 
amount of propagation in a local ISM cav-
ity (Ptuskin and Soutoul 1998). The 36Cl 
abundance is suggestive of a higher local 
ISM density than the longer-lived species 
indicate, but the difference is not significant. 
1.0000 
c 
.S 0.1000 
+.l 
() 
(1j 
~ 
-Of) 0.0100 
c 
·s;: 
» 5 0.0010 
[/] 
halflife(in years) 
Figure 2: Surviving fraction of clock isotopes. Curves are model 
The energy dependences of the clock abun- predictions from 10Be abundance. 
dances shown in this propagation model are 
not inconsistent with the data, although they 
are not clearly indicated either. Both the energy dependence and the value of the calculated density are depen-
dent on the chosen mean pathlength parameterization, which is different for the sub-Fe/Fe and lower-Z ratios. 
The confinement time is less reliant on the parameterization of the mean pathlength than the average ISM 
density. Using an ISM density appropriate for each species, the confinement times calculated from the CRIS 
clock abundances are presented in Table 1, along with previous experimental results. Considering the large 
© University of Utah • Provided by the NASA Astrophysics Data System 
19
99
IC
RC
..
..
3.
..
.9
Y
uncertainty in the halflife of 54Mn ("'"' 40%, from Wuosmaa et al. 1998), CRIS predicts a confinement time 
of Tesc rv22x 106 years which is consistent with all species. The confinement times obtained from our model 
calculations are comparable to recent Ulysses results, but they yield somewhat longer times than ISEE-3 results 
and earlier calculations (e.g., Garcia-Munoz et al. 1981). This may be a result of other experimental groups 
using different mean ISM pathlengths to calculate the confinement time, originating from earlier measurements 
of the fragmentation partial cross sections. 
The surviving fraction for each clock is shown in Figure 2. A comparison of these with the predictions of 
Ptuskin and Soutoul's model yields a local diffusion coefficient D ranging from 2 x 1028 - 1029 cm2 s- 1 . 
Assuming a consistent value of D for all clock species, 26 Al and 36Cl abundances do not appear to support 
simple galactic models composed of a single gas layer or a thin layer, but these are not ruled out for higher 
values of D. The surviving fraction of 14C is a discriminating test of these models and the value of D. CRIS 
should record"'"' 30 14C events during a 2 year period, assuming a mean ISM density consistent with other clock 
abundances (Stone et al. 1999). Whether these few events ("'"' 5 x 10-4 % of total carbon) can be distinguished 
from background is under investigation. 
4 Conclusions: 
Within the context of our leaky-box model, we find a confinement time from CRIS data of Tesc "'"'22x 106 
years which is consistent for all species. This time is characteristic of a mean ISM H density between 0.15 and 
0.40 atoms/cm3 , assuming our parameterization of the mean pathlength. The surviving fractions for all clock 
species imply a local diffusion coefficient from Ptuskin and Soutoul's model ranging from 2 x 1028 - 1029 
cm2s- 1 . 
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Implications for Cosmic Ray Propagation from ACE Measurements of Radioactive Clock Isotope Abundances

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