Statistics of Cosmic-ray Fluctuations for Habitable Planets in
the Interstellar Environment
David S. Smith, Seth Redfield, and John Scalo (UT-Austin, Dept. of Astronomy)
Abstract
Galactic cosmic rays are believed to play a role as contributor to ozone layer chemistry, biological mutation
rates, and climate. The solar wind modulates the low-energy Galactic cosmic-ray flux in our solar system, but this
modulation depends on the size and other properties of the heliosphere and the details of cosmic-ray propagation.
It has been suggested for decades that the cosmic-ray flux on Earth, and presumably other habitable planets,
should be greatly enhanced when the Sun traverses interstellar clouds and reduced when it passes through voids,
but the frequency and duration of such events remains very uncertain. We attempt to quantify the problem by
using simulations of the heliosphere moving through two sets interstellar medium models: (1) 3D MHD
simulations, with temporal resolution spanning ~103-109 years, and (2) new absorption line observations of gas
toward stars within about 500 pc along a narrow cone representing the Sun’s relatively recent historical and future
Galactic trajectories. Using a pressure balance approximation for the heliosphere size dependence, and a
convection-diffusion solution to the cosmic-ray transport, we model the time series of terrestrial cosmic-ray fluxes
and estimate the probability distribution of cosmic-ray fluxes and associated durations. We show that, during an
interstellar cloud passage, cosmic-ray flux enhancements of 10-100, much larger than those implicated in recent
attempts to connect cosmic rays and climate, can occur every ~100,000 yr, depending weakly on cloud properties.
Finally, we outline future observations which will allow us to reconstruct the approximate history and future of the
terrestrial cosmic-ray flux over the past 30 Myr.
Introduction
The interstellar medium (ISM) is a dynamic and complex environment, which ensures the Sun, and our
solar system, have encountered a wide range of conditions. At the top of the poster is a map of the carbon
monoxide structure of the outer Galaxy, as viewed from the Sun, showing the rich detail. As the solar system
traverses the ISM, the heliosphere size fluctuates due to changing interstellar pressures. Since the
heliosphere filters the Galactic cosmic-ray flux incident at the Earth, wide excursions in the terrestrial cosmicray flux should be observed, with low-energy fluxes much larger than the present flux when the solar system
passes through interstellar clouds, and much smaller when it passes through low-density voids. These
fluctuations in cosmic-ray flux may be associated with stochastic changes in stratospheric chemistry, climate,
and variations in the surface mutation rate in organisms throughout the history of life on Earth.
The present work aims to reconstruct the history of the cosmic-ray flux by estimating the historical
interstellar environment along the Sun’s Galactic journey, using approximate models for heliosphere-ISM
dynamics and heliospheric propagation of cosmic rays.
Here we concentrate on two situations that involve relatively small timescales (~103–107 yr): (1) a brief
time in the past when the solar system passed through a relatively compact, dense interstellar cloud, which
may have occurred ~10-100 Myr ago, and (2) a reconstruction of the more recent history of the solar system
environment as it passed through the clouds and voids of the Local Interstellar Bubble. For the latter recent
history, we outline a prototype of the observations, involving interstellar optical and UV lines and reddening
toward local stars, that our reconstruction will require.
Because we know the present trajectory of the Sun, our calculations can in principle be compared with
empirical studies of the history of changes associated with climate proxies (e.g. 18O and 13C isotope
fluctuations, heavy element abundances; Zachos et al. 2001, Science) and records that may directly record
the cosmic-ray history (e.g. 14C, 10Be in ice cores, meteoritic track chronologies). Many of these records could
have other causal agents, such as variations in the carbon cycle or in the Earth’s precession, obliquity and
eccentricity, but by inferring definite timing histories from our models, we hope to disentangle direct cosmic-ray
variations from these other effects.
Passage through an Interstellar Cloud
First we have studied the cosmic-ray variations due to passage of the solar system through
a molecular cloud whose average density is large enough to result in complete demodulation of
cosmic rays by pushing the heliopause inside of 1 AU. The time in the past when such an event
last occurred is very uncertain because the Sun’s present motion is highly inclined to the Galactic
plane (~320). But since the Sun’s vertical oscillation period in the Galaxy is about 60 Myr, it may
have encountered one of the local molecular cloud complexes currently within a few hundred
parsecs.
Figure 1: Map of the interstellar material within
250 pc (from Lallement et al. 2003, Astr.
Astrophys.). Dark shadings indicate high density
material. The Sun is roughly located in the center
of the Local Bubble, a cavity devoid of much
dense material. Dense environments are only
~100 pc distant, which means the Sun has
passed (or will pass) through them in <10 Myr.
The red and blue arrows trace the past and
future solar paths, respectively. The time
required to traverse the length of each arrow is
18.3 Myr, based on the Sun’s present speed of
~13 km s-1 (Dehnen & Binney 1998, MNRAS)
As a model for these cloud complexes we use a 3D, magnetohydrodynamic, numerical
simulation of isothermal, supersonic, turbulent clouds kindly provided by P. Padoan. These models
agree with several observed statistical properties of molecular clouds (see Nordlund & Padoan
2003, Lect. Notes Phys.). We scaled the model cloud to a size of 10 pc and mean total number
density of both 30 (similar to a typical classical diffuse neutral hydrogen cloud) and 300 cm-3
(similar to a typical molecular cloud). The model cloud possesses complex density and velocity
structure spanning several orders of magnitude in density, with spatial scales down to ~0.04 pc
(~3000 yr).
We track the size of the heliosphere in the apex direction by balancing the solar-wind ram
pressure with the fluctuating ram pressure within the cloud (Zank & Frisch 1999, Astrophys. J.),
including a detailed treatment of gravitational focusing which dominates the physics at these
densities (Begelman & Rees 1976, Nature). We include only ram pressure and ignore magnetic
effects for this initial work. We track the cosmic-ray flux using a simplified convection-diffusion
model for heliospheric cosmic-ray propagation assuming a radially constant diffusion coefficient
calibrated to give a factor of 100 reduction in the flux at 10 MeV for the current heliospheric apex
distance of 155 AU (Gurnett et al. 2003, Geophys. Res. Lett.). In order to build up a statistical
sample, we passed the solar system through the simulation cube along random trajectories 105
times.
Figure 2: High-resolution time series of densities and cosmicray fluxes encountered on a sampled trajectory through the
simulated cloud with average density 30 cm-3. The 10-MeV
cosmic-ray flux is presented relative to the present-day level.
The extreme variability of the cosmic-ray flux is evident,
particularly in the lower-density regions. A drop in the density
of roughly three orders of magnitude between 0.2 and 0.5 Myr
becomes a flux reduction of ~106. Note that at densities above
about 10 cm-3, the fluctuations in the cosmic-ray flux are
damped due to the saturation effect of demodulation. The
accretion of dust and gas into the solar system could still vary
significantly, however, as this is a different physical process
than is discussed here.
Figure 3: Probability distribution of durations and
recurrence times for a 10-MeV cosmic-ray flux
enhancement ranging from 10 to 100 above present levels.
Clouds of two different average densities are modeled: 30
and 300 cm-3. The lower density cloud should be
encountered far more frequently, roughly by a factor of 100,
than the higher-density cloud, since the frequency of clouds
at a given density from various cloud catalogues is a strong
inverse power law. Selection effects such as column
density thresholds should hide more low density clouds,
and the highest density clouds tend to have smaller sizes;
both effects imply that the frequency of encounters of
planetary systems with high-density clouds should be even
smaller, although the high densities could still lead to
intense cosmic-ray fluxes. Note that, for example, in the
low-density cloud (30 cm-3), a cosmic-ray flux enhancement
of 10-100 lasting 20,000 yr will occur roughly every 1.4
Myr, while in the high-density cloud, these events occur
every 12.5 Myr. The averages of the histograms give the
overall average durations and recurrence times of 10-100
enhancement events inside of these clouds.
Reconstructing our Historical Local Interstellar Environment
We can reconstruct the volume density our solar system likely encountered over the last 30 Myr years by
measuring the distribution and physical characteristics of the interstellar medium along the direction of the Sun's
historical trajectory. This reconstruction will require new astronomical observations involving interstellar optical and
UV lines and reddening toward local stars. Here we describe an experiment and observing program to compare our
recent interstellar volume density history with existing geological records to directly explore the link between our
astronomical environment and the cosmic-ray flux incident on the Earth's atmosphere.
Figure 4: Using high-resolution spectroscopy, we can
measure the physical characteristics of clouds in the
ISM. Spectral observations of nearby stars contain
information both on the stellar light and absorption from
intervening interstellar material (i.e., clouds). Some
examples of absorption lines are shown. Modeling the
shape of the absorption line provides information on the
physical properties of the cloud, including the quantity of
gas, projected velocity, temperature, internal
turbulence, and depletion onto dust grains. By
combining individual observations of numerous stars at
various distances along a particular direction, we can
reconstruct the line-of-sight density distribution.
Figure 5: Distribution of appropriate background
sources within 500 pc of the Sun, and within 4
degrees of the direction of solar motion. This
demonstrates the feasibility of reconstructing the
interstellar density distribution along these lines of
sight. Only stars with accurate distance
measurements (Hipparcos) are included. This limits
the sample to stars brighter than about 12
magnitudes. There are approximately 100 potential
targets in each direction. The median distance
between targets is ~3 pc, which corresponds to a time
resolution of ~0.2 Myr. We can resolve individual
cloud components with high resolution spectroscopy,
however, so the time resolution may be improved by a
factor of 2-3.
Figure 6: The solid black histogram shows an illustrative density profile
along the historical solar trajectory. The red histogram indicates our
"observed" reconstruction of the density profile given spectroscopic
observations of the 100 stars along the historical solar path shown in
Figure 5. The illustrative density profile was created with a finite number
of discrete clouds of uniform density based on the number density of
clouds in the local ISM (Redfield & Linsky 2004, ApJ) and the
distribution of volume densities of local clouds (Gaustad & Van Buren
1993, PASP). We then convert the variable density profile into a
predicted cosmic-ray flux history. Over relatively modest density
fluctuations of 1-2 orders of magnitude, the cosmic-ray flux varies by 23 orders of magnitude around the present value. Such an astronomical
cosmic ray history could then be compared directly with geological
tracers of cosmic-ray flux (e.g. 10Be) and climate (e.g. 18O, 13C) out to
65 Myr (Zachos et al. 2001, Science; Jokipii & Marti 1986, Gal. & Sol.
Sys.). This comparison may provide much-sought-after evidence of a
physical relationship between the Galactic interstellar environment and
our planet.