Physical Review Letters, Jun.29.02
Cosmic Ray Diffusion from the Galactic Spiral Arms, Iron Meteorites, and a Possible Climatic Connection
Nir J. Shaviv
1Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 3H8, Canada
and Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel
(Received 15 August 2001; published 16 July 2002)
We construct a Galactic cosmic ray (CR) diffusion model. The CR flux reaching the Solar System
should periodically increase each crossing of a Galactic spiral arm. We confirm this prediction in the CR
exposure age record of iron meteorites. We find that although the geological evidence for the occurrence
of iceage epochs in the past eon is not unequivocal, it appears to have a nontrivial correlation with the
spiral arm crossings—agreeing in period and phase.
DOI: 10.1103/PhysRevLett.89.051102 PACS numbers: 98.35.Hj, 92.40.Cy, 92.70.Gt, 98.70.Sa
With the possible exception of those at extremely high
energies, cosmic rays (CRs) are believed to originate from
supernova (SN) remnants [1,2]. Moreover, most SNe in
spiral galaxies like our own are those which originate from
massive stars; thus, they predominantly reside in the spiral
arms, where most massive stars are born and shortly thereafter
explode as SNe [3].
Thus, while the Sun is crossing the Galactic spiral arms,
the cosmic ray flux (CRF) is expected to be higher. To
estimate the CRF variation, we construct a simple diffusion
model which considers that the CR sources reside in the
Galactic spiral arms. We expand the basic CR diffusion
models (e.g., Ref. [2]) to include a source distribution
located in the Galactic spiral arms. Namely, we replace a
homogeneous disk with an arm geometry as given by
Taylor and Cordes [4], and solve the time dependent
diffusion problem. To take into account the ‘‘Orion spur’’
[5], in which the Sun currently resides, we add an arm
‘‘segment’’ at our present location. Since the density of HII
regions in this spur is roughly half of the density in the real
nearby arms [5], we assume it to have half the typical CR
sources as the main arms. We integrate the CR sources
assuming a diffusion coefficient of D 1028 cm2= sec,
which is a typical value obtained in diffusion models for
the CRs [2,6,7].We also assume a halo half-width of 2 kpc,
which again is a typical value obtained in diffusion models
[2], but, more importantly, we reproduce with it the 10Be
survival fraction [8]. Thus, the only free parameter in the
model is the angular velocity
p around the
Galaxy of the Solar System relative to the spiral arm
pattern speed, which is later adopted using observations.
Results of the model are depicted in Fig. 1. For the nominal
values chosen in our diffusion model and the particular
pattern speed which will soon be shown to fit various data,
the expected CRF changes from about 25% of the current
day CRF to about 135%. Moreover, the average CRF
obtained in units of today’s CRF is 76%. This is consistent
with measurements showing that the average CRF over the
period 150–700 Myr before present (BP), was about 28%
lower than the current day CRF [12].
Interestingly, the temporal behavior is both skewed and
lagging after the spiral arm passages. The lag arises because
the CRs are emitted from SNe which on average
occur roughly 15 Myr after the average ionizing photons
are emitted. The skewness arises because it takes time for
the CRs to diffuse after they are emitted, thereby forming a
wake after them. This typically introduces a 10 Myr lag in
the flux, totaling about 25 Myr with the SN delay. This lag
is actually observed in the synchrotron emission from
M51, which shows a peaked emission trailing the spiral
arms [1].
The spiral pattern speed of the Milky Way has not
yet been reasonably determined through astronomical observations.
Nevertheless, a survey of the literature reveals
that almost all observational determinations cluster either
around
9 to 13 km s1=kpc [13] or around
2 to 5 km s1=kpc [15]. In fact, one analysis
[14] revealed that both
5 or 11:5 km s1=kpc fit
the data. However, if the spiral arms are a density wave
[16], as is commonly believed [17], then the observations
of the four-arm spiral structure in HI outside the Galactic
solar orbit [18] severely constrain the pattern speed to
* 9:1 2:4 km s1=kpc, since the four-arm density
wave spiral cannot extend beyond the outer four to one
Lindblad resonance [11]. We therefore expect the spiral
pattern speed obtained to coincide with one of the two
aforementioned ranges, with a strong theoretical argumentation
favoring the first range.
To validate the above prediction that the CRF varied
periodically, we require a direct ‘‘historic’’ record from
which the actual time dependence of the CRF can be
extracted. To find this record, we take a compilation of
74 iron meteorites which were 41K=40K exposure dated
[19]. CRF exposure dating (which measures the duration a
given meteorite was exposed to CRs) assumes that the CRF
history was constant, such that a linear change in the
integrated flux corresponds to a linear change in age.
However, if the CRF is variable, the apparent exposure
age will be distorted. Long periods during which the CRF
is low would correspond to slow increases in the exposure
age. Consequently, Fe meteorites with real ages within this
low CRF period would cluster together since they will not
have significantly different integrated exposures. Periods
with higher CRFs will have the opposite effect and spread
apart the exposure ages of meteorites. To avoid real clustering
in the data (due to one parent body generating many
meteorites), we remove all occurrences of Fe meteorites of
the same classification that are separated by less than
100 Myr and replace them by the average. This leaves us
with 42 meteorites.
From inspection of Fig. 1, it appears that the meteorites
cluster with a period of 143 10 Myr or, equivalently,
j
j 11:0 0:8 km s1=kpc, which falls within the
preferred range for the spiral arm pattern speed. If we fold
the CR exposure ages over this period, we obtain the
histogram in Fig. 2. A Kolmogorov-Smirnov (K-S) test
yields a probability of 1.2% for generating this nonuniform
signal from a uniform distribution. Moreover, Fig. 2 also
describes the prediction from the CR diffusion model. We
see that the clustering is not in phase with the spiral arm
crossing, but is with the correct phase and shape predicted
by the CR model using the above pattern speed. A K-S test
yields a 90% probability for generating it from the CR
model distribution. Thus, we safely conclude that spiral
arm passages modulate the CRF with a
143 Myr period.
In 1959, Ney [20] suggested that the Galactic CRF
reaching Earth could be affecting the climate since the
CRF governs the ionization of the lower atmosphere, to
which the climate may in principle be sensitive to. If this
hypothesis is correct, we may be able to see a correlation
between the observed long term CRF variability and the
climate record on Earth.
Interestingly, the CRF reaching Earth is also variable
because of its interaction with the variable solar wind.
Thus, solar activity variations will also have climatic
effects if the CRF affects the climate (e.g., [21]). Under
the assumption that it does affect climate, we can estimate
how large an effect can a possible CRF-temperature relation
be. This can be derived from the fact that the best fit to
the global warming in the past 120 years is obtained if
somewhat less than half is attributed to anthropogenic
greenhouse gases and somewhat more than half to the
increased activity of the Sun [22,23]. Thus, between
about 1940 and 1970, the global temperature, which decreased
by 0.15 K, is best explained as 0:2 K attributed
to the reduced solar activity and
0:05 K to greenhouse
gases [22,23]. A global CRF climate effect is presumably
more likely to arise from CRs that can reach the troposphere
and equatorial latitudes. Thus, it is reasonable to
assume that a possible effect would arise from CRs that
have high rigidities ( * 10–15 GeV=nucleon). We therefore
normalize the low geomagnetic data from Haleakala,
Hawaii, and Huancayo, Peru, to the higher geomagnetic
data of Climax, Colorado [24] that were measured over a
longer period (e.g., [25]). We find that the 0:2 K cooling
correlated with a 1.5% increase in the high rigidity CRF.
Thus, changing the CRF by 1% would correspond to a
global change of 0:13 K, on the condition that CRs are
indeed the link relating solar activity to the climate.
For the nominal values chosen in our diffusion model,
the expected CRF changes from about 25% of the current
day CRF to about 135%. This corresponds to a temperature
change of about
10 to 5 K, relative to today’s temperature.
This range is sufficient to markably help or hinder
Earth from entering an ice-age epoch (IAE).
Extensive summaries of IAEs on Earth can be found in
Crowell [9] and Frakes et al. [10]. Those of the past eon are
summarized in Fig. 1. The nature of some of the IAEs is
well understood, while others are sketchy in detail. The
main uncertainties are noted in Fig. 1. For example, it is
unclear to what extent the milder mid-Mesozoic glaciations
can be placed on the same footing as other IAEs,
nor is it clear to what extent the period around 700 Myr BP
can be called a warm period since glaciations were present,
though probably not to the same extent as the periods
before or after. Thus, Crowell [9] concludes that the evidence
is insufficient to claim a periodicity. On the other
hand, Williams [26] claimed that a periodicity may be
present. This was elaborated upon by Frakes et al. [10].
Comparison between the CRF and the glaciations in the
past 1 Gyr shows a compelling correlation (Fig. 1). To
quantify this correlation, we perform a 2 analysis. To be
conservative, we do so with the Crowell data which are less
regular. Also, we do not consider the possible IAE around
900 Myr, though it does correlate with a spiral arm crossing.
For a given pattern speed, we predict the location
of the spiral arms using the model. We find that a minimum
is obtained for
10:9 0:25 km s1=kpc,
with 2
min 1:1 per degree of freedom (of which there
are 5 6 1). We also repeat the analysis when we
neglect the lag and again when we assume that the spiral
arms are separated by 90
(as opposed to the somewhat
asymmetric location obtained by Taylor and Cordes [4]).
Both assumptions degrade the fit (2
min 2:9 with no lag,
and 2
min 2:1 with a symmetric arm location). Thus, the
latter analysis assures that IAEs are more likely to be related
to the spiral arms and not a more periodic phenomena,
while the former helps assure that the CRs are more likely
to be the cause, since they are predicted (and observed) to
be lagged.
The previous analysis shows that to within the limitation
of the uncertainties in the IAEs, the predictions of the CR
diffusion model and the actual occurrences of IAE are
consistent. To understand the significance of the result,
we should also ask what the probability is that a random
distribution of IAEs could generate a 2 result which is as
small as previously obtained. To do so, glaciation epochs
were randomly chosen. To mimic the effect that nearby
glaciations might appear as one epoch, we bunch together
glaciations that are separated by less than 60 Myrs (which
is roughly the smallest separation between observed glaciations
epochs). The fraction of random configurations that
surpass the 2 obtained for the best fit found before is of
order 0.1% for any pattern speed. (If glaciations are not
bunched, the fraction is about 100 times smaller, while it is
about 5 times larger if the criterion for bunching is a separation
of 100 Myrs or less). The fraction becomes roughly
6 105 (or a 4 fluctuation), to coincidentally fit the
actual period seen in the iron meteorites.
Last, before 1 Gyr BP, there are no indications for any
IAEs, except for periods around 2–2.5 Gyr BP (Huronian)
and 3 Gyr BP (late-Archean) [9]. This too has a good
explanation within the picture presented. Different estimates
to the star formation rate (SFR) in the Milky Way
(and therefore also to the CR production) point to a peak
around 300 Myr BP, a significant dip between 1 and 2 Gyr
BP (about a third of today’s SFR) and a most significant
peak at 2–3 Gyr BP (about twice today’s SFR) [27,28].
This would imply that at 300 Myr BP, a more prominent
IAE should have occurred—explaining the large extent of
the Carboniferous-Permian IAE. Between 1 and 2 Gyr BP,
there should have been no glaciations, and indeed none
were seen. Last, IAEs should have also occurred 2 to 3 Gyr
BP, which explains the Huronian and late-Archean IAEs.
To conclude, by considering that most CR sources reside
in the Galactic spiral arms, we predict a variable CRF.
A record of this signal was indeed found in iron meteorites,
and it nicely agrees with the observations of the
Galactic spiral arm pattern speed. Next, if the apparent
solar activity climate correlation is real and arises from
modulation of the Galactic CRF reaching Earth, then
typical variations of up to O10 K could be expected
from the variable CRF. For each spiral arm crossing, the
average global temperature should reduce enough to trigger
an IAE. The record of IAEs on Earth is fully consistent
with the predicted and observed CRF variation—both in
period and in phase. Moreover, the fit improves when the
predicted lag in the IAEs after each crossing is included
and when the actual asymmetric location of the arms is
considered. Moreover, a random mechanism to generate
the IAEs is excluded. Nevertheless, one should bear in
mind that the weakest link still remains the glaciological
record with its uncertainties. That is, more research on the
timing and extent of glaciations is required.
The last agreement is between the eon time scale star
formation activity of the Milky Way and the presence or
complete absence of IAEs. Here a more detailed research
on the SFR activity would be useful to strengthen (or
perhaps refute) the long term correlation.
If the apparent correlation between observed CRF variations
and climate on Earth is not simply a remarkable
coincidence, an unavoidable question is what is the physical
mechanism behind the CRF-temperature relation?
Currently, there is no single undisputed mechanism
through which cosmic rays can affect the climate. There
are, however, several observational indications that such a
relation could exist. For example, Forbush events during
which the CRF suddenly drops on a time scale of days were
found to correlate with the amount of ‘‘storminess’’ as
encapsulated by the vorticity area index [29], or a concurrent
drop in the cloud cover [30]. There were also
claims that the Galactic CRF, which is modulated by the
solar cycle and slightly lags behind it, correlates with the
low altitude cloud cover variations [25,31]. Clearly, an indepth
study on the possible climatic effects of cosmic rays
is imperative.
The author is particularly grateful to Peter Ulmschneider
for the stimulating discussions which led to the development
of this idea. The author also thanks Norm Murray,
Chris Thompson, and Joe Weingartner for their very helpful
comments and suggestions.
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