Transcript SEP (Opher) - Solar Physics and Space Weather

Heliosphere - Lecture 8
November 08, 2005 Space Weather Course
Electromagnetic Radiation in the Heliosphere
Radio Emission
Numerical studies of CME
Acceleration and Transport of Particles
SEP in Shocks
Chapter 7 - Kallenrode (Energetic Particles in the
Heliosphere)
What we saw:
-Corotating interaction regions
(what are they? How do they form?)
-CMEs in the interplanetary space (magnetic clouds),
(How CMEs propagate in the heliosphere)
-Interplanetary shocks
(CMEs pile up material forming shocks-how those shocks propagate in
space)
-Shock Physics
(what happens at a shock?)
Today:
•
Electromagnetic Radiation in the Heliosphere:
Page 131-134 (new edition) of Kallenrode
•
Coronal Mass Ejections (numerical studies)
•
Energetic Particles in the Heliosphere (Kallenrode
Chapter 7 - new edition & some material from
conference) [Galactic Cosmic Rays, Solar Energetic
Particles (SEPs), Energetic Storm Particles (ESPs)]
•
Transport of Particles (Kallenrode)
•
Diffusive Shock Acceleration (Kallenrode)
Electromagnetic Radiation in the Heliosphere
Figure 6.21 Kallenrode
Impulsive and Gradual Events
• Electromagnetic
Radiation in different
Frequency ranges shows
typical time profiles.
Impulsive phase is related to an impulsive energy release,
probably reconnection, inside a closed magnetic field loop.
• Soft X-Rays and H:
In solar flare most of the electromagnetic radiation is emited as soft X-rays with
wavelength between 0.1 and 10nm
(Soft X-Rays originate as thermal emission in hot plasmas with T~107K.
Most of radiation is continuum emission. (lines of highly ionized O, Ca, Fe are
also present)
H emission is also a thermal emission.
• Hard X-Rays:
Hard X-Rays are photons with energies between a few tens of keV and a few
hundred keV generated as bremsstrahlung of electrons with slightly higher
energies. Only a very small amount of the total electron energy is converted
into hard X-Rays
• Gamma-Rays:
Gamma-ray emission indicated the presence of energetic particles. The spectrum
can be divided into three pars: (a) Bremsstrahlung of relativistic electrons; (b)
Nuclear radiation of excited CNO nuclei leads to a gamma-ray spectrum in the
range of 4 to 7MeV; c ) Decaying pions lead to gamma-ray continuum
emission above 25MeV.
• Radio Emission:
Electrons streaming through the coronal plasma excite Langmuir oscillations.
Near the sun the wavelength are in the meter range. In the interplanetary
space the radio burst are kilometric bursts. The bursts are classified
depending on their frequency drift. The type I radio burst is a continuous
radio emission from the Sun, basically the normal solar radio noise but
enhanced during the late phase of the flare. The other type of bursts can
be divided in fast and slow drifting bursts or continua:
Type III radio burst starts early in the impulsive phase and shows a fast drift
towards lower frequencies. Since the frequency of the langmuir
oscillation depends on the density of the plasma (  pe 0.564 n e rad /s)
The radial speed of the radio source can be determined from this frequency
drift using a density model of the corona.
The speed of type III is about c/3 it is interpreted
as stream of electrons

propagating along open field lines into interplanetary space. Occasionally
the type III burst is suddenly reversed, indicating electrons captured in a
closed magnetic field loop: as the electrons propagate upward, the burst
shows the normal frequency drift which is reversed as the electrons
propagate downward on the other leg of the loop.
• Type II burst
The frequency drift is much slower indicating a radial propagation speed
of its source of about 1000km/s. It is interpreted as evidence of a shock
propagating through the corona. It its not the shock itself that
generated the type II burst but the shock accelerated electrons, As these
electrons stream away from the shock, they generates small type III
structures, giving the burst the appearance of a herringbone in
frequency time diagram with the type II as the backbone and the type
III structures as fish-bones. The type II burst is split into two parallel
frequency bands interpreted as forward and reverse shocks.
Plot showing showing the frequency range of the
metric-DH-kilometric (Nov 04, 1997 event 6-8hrs
taken from the Coordinate Data Analysis CDA)
taken from RAD1 and RAD2, and ground base
observatories. Note the frequency decreases with time
as the shock propagates
outward and the ambient density decreases.
• Another example: Halloween events (WIND data)
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Coronal Mass Ejection-numerical studies (Manchester et al. )
Halloween-inserting magnetograms
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Compare with
ACE data
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Close-up of the flux
Rope inserted
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The field lines are colored
by the velocity-the flux rope added
is shown with white field lines
CME 2 hours after the eruption (the
Purple lines emanate from the AR)
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TIFF (LZW) decompressor
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After 65 hours of simulation. CME is shown as a white isosurface
of density enhancement of a factor 1.8 relative to the original steady
state solution. The magnetic field lines are shown in magenta.
The CME is about to reach the Earth which is at the center of the
orange sphere on the right.
Energetic Particles in the Heliosphere
• Galactic Cosmic Rays (GCR), Anomalous Cosmic
Rays (ACR), Solar Energetic Particles (SEPs),
Energetic Storm Particles (ESPs)
Energies ranges from supra-thermal to 1020 eV
• Galactic Cosmic Rays (GCR)
Energies extending to 1020 eV. The are incident upon the heliosphere uniformly
and isotropically. In the inner heliosphere, the galactic cosmic rays are
modulated by solar activity: the intensity of GCRs is highest during solar
minimum and reduced under solar minimum conditions.
• Anomalous Cosmic Rays (ACR)
Energetically connected to the lower end of the GCRs but differ from them with
respect to composition, charge states, spectrum, and variation with the solar
cycle. As neutrals particles of the interstellar medium travel through the
interplanetary space towards the Sun, they become ionized. These charged
particles then are convected outward with the solar wind and are accelerated at
the Termination Shock. Then they propagate towards the inner heliosphere
where they are detected as anomalous component.
• Solar Energetic Particles (SEPs)
They are accelerated in flares, CMES (?). The injection of these particles into the
heliosphere is point-like in space in time.
• SEP energies extend up to tens-GeV. The ones with GeV can be
observed in neutron monitors on the ground, and the event is
called ground-level event (GLE). Owing to interplanetary
scattering the particle events last between some hours and a
few days. SEP events show different properties, depending on
whether the parent flare is gradual or impulsive. In gradual
events the SEP mix with particles accelerated at the shock.
• Energetic Storm Particles (ESPs)
Originally ESPs were though to be particle enhancements
related to a passage of an interplanetary shock. ESPs are
particles accelerated at interplanetary shocks.
Energy spectra of different ions species in the heliosphere
Transport of Particles
• Spatial Diffusion: consequence of frequent, stochastically
distributed collisions. Instead of individual particles we
will consider an assembly of particles, described by the
distribution function.
• Diffusion is not only spatial diffusion. It can be diffusion
in momentum space (e.g. enhance of temperature,
energy…)
Spatial Diffusion (Drunkyards):
(steps of length )
The average spatial displacement is
x
2
 N
2
• If the particle as a speed v, the total distance s traveled during a time t
is s=vt=N and
x
2
 N  vt  2Dt
2
where D is the diffusion coefficient (1D)
1
D  v
2

In a medium at rest the Diffusion Equation: (it can be shownKallenrode “Interplanetary Transport” chapter) that


 D  Q(r,t)
t
Q is the source

• Diffusion-Convection Equation:
If the particles are scattered in a medium that is moving..in our case the
convection is due to the solar wind: the particles are scattered at
inhomogeneities frozen in the solar wind and propagating with the
solar wind. In this case the streaming of particles is
S  u  D
Where u is the velocity of the convective flow. So the continuity equation reads:


 (u)  (D)
t
Pitch Angle Diffusion: In a plasma, fast particles are more likely
to encounter small-angle interactions. Thus to turn a particle around, a large number
of interactions is required.
In space plasmas small-angle interactions are not due to Coulomb-scattering but due

to scattering a the plasma-waves.
Let assume a magnetized plasma and regards the energetic particles as test particles.
The particles gyrate around the lines of force and a pitch angle can be assigned to each
particle: =cos.
• Each interaction leads to a small change in ->diffusion in pitch angle
space. So now the spatial diffusion is written as:
 
f 
 () 
 
 
• Where  is the pitch angle diffusion coefficient. The scattering can be
different for different pitch angles (different waves available for waveparticle interaction). The transport equation can be written as:

f
f  
f 
 v   () 
t
s  
 
• Where f/s is the derivative along the magnetic field line.
• We also have to include diffusion in momentum space: collisions can
change not only
 the particle direction but also its energy.
f dp
S p  Dpp 
f
p dt
Where Dpp is the diffusion coefficient in momentum space. (the second term
describes ionization-non-diffusive changes in momentum)
(the physics of 
the scattering process is hidden in Dpp).
• Wave-particle interactions: non-liner theory-no general algorithms exist.
•
•
Quasi-linear Theory: its based on perturbation theory; interactions between waves
and particles are considered to first order only. All the terms in second order in the
disturbance are ignored. So only weakly turbulent wave-particle interactions can be
treated this way. We assume that the plasma to be a self-stabilizing system: neither
indefinite wave growth happens nor are the particles trapped in a wave well.
The basic equation that describes the evolution of a distribution particles is the
Vlasov equation:
f
q 
v  B  f
 v  f  E 
  0
t
m 
c  v
•
If you split the quantities in a slowly evolving average part f0,E0,B0 and a fluctuating
part f1,E1, and B1 where the long term averages of the fluctuating quantities vanish
we 
get:
f 0
q
F
q
f1
 v  f 0  v  B0  0  
E

v

B

 1
1
t
m
v
m
v
•

Where the term on the right-hand side describes the interaction between the
fluctuating fields and the fluctuating part of the particle distribution. This term has a
nature of a Boltzman collision term. These collisions result from the non-linear
coupling between particles and wave fields.
Particle Acceleration at Shocks
•
There are different physical mechanisms involved in the particle acceleration in
interplanetary shocks:
• The shock drift acceleration (SDA) in the electric induction field in the shock front
• The diffusive shock acceleration due to repeated reflections in the plasmas converging
at the shock front;
• The stochastic acceleration in the turbulence behind the shock front.
The relative contribution of these mechanisms depends on the properties of the shock:
SDA is important for perpendicular shocks where the electric induction field is
maximal; but vanishes in parallel shocks. Stochastic acceleration requires a strong
enhancements in downstream turbulence to be effective; while diffusive acceleration
requires a sufficient amount of scattering in both upstream and downstream media. In
addition shock parameters such as compression ratio; speed; determine the efficiency
of the acceleration mechanism.
Usually the particles are treated as test particles: they do not affect the shock; and effects
due to the curvature of the shock are neglected.
• Shock Drift Acceleration (SDA)
•
Scattering is assumed to be negligible, to allow for a reasonable long drift
path. Its necessary though that the particles are feed back into the shock for
further acceleration. In shock drift acceleration, a charge particle drift in the
electric field induced in the shock front (in the shock rest frame):
E  uu  Bu  ud  Bd
•
This field is directed along the shock front and perpendicular to both magnetic
field and bulk flow. In addition the shock is a discontinuity in magnetic field
strength (BxB) The direction of the drift depends on the charge of the
particle
 and is always such that the particle gains energy.
The abscissa shows the distance from the shock in gyro-radii. In the left panel the
particle is reflected back into the upstream medium. The other two shos particles
transmitted through the shock. The energy gain of a particle is largest if the particle
can interact with the shock front for a long time. This time depends on the particle’s
speed perpendicular to the shock.
•
•
•
The particle speed relative to the shock is determined by the particle speed, shock
speed, pitch angle and the angle of the shock.
The average energy gain is a factor 1.5-5.
Energy gain then to high energies will require repeated interactions between particles
and shock->scattering in turbulence.
• Diffusive Shock Acceleration
• This is the dominant mechanism at quasi-parallel shocks. Here the electric
induction field in the shock front is small and shock drift acceleration becomes
negligible. In diffusive shock acceleration, the particle scattering in both sides
of the shock is crucial.
• The magnetic fields on both sides of the shock are turbulent. The diffusion
coefficients upstream and downstream are Du and Dd..Where in SDA the
location of the acceleration is well defined, in diffusive shock acceleration, the
acceleration is given by the sum of all pitch angle scatters.
• Example: In the upstream medium the particle gains energy due to a
head-on collision with a scatter center; in the downstream it loses energy
because the scatter center moves in the same direction as the particle.
Since the flow speed (and therefore the velocity of the scattering center)
is larger upstream than downstream a net gain of energy results.
• The energy gain will depend on the velocity parallel to the magnetic field
and on the pitch angle. The equation describing the “statistical”
acceleration is:
f
  U f
f
1   dp  
 Uf    (D  f ) 
p   2 p 2 f  Q( p,r,t)
t
3
p T p p  dt  
From left to right: convection of particles with the plasma flow; spatial

diffusion; diffusion in momentum space; losses due to particle escape
from the acceleration region; and convection in momentum space due to
ionization or Couloumb losses. The term on the right is a source term
describing the injection of particles in the acceleration process.
•
In steady state f/t =0. If we neglect also (in first order the losses and convection in
momentum) we get
f
  U f
 Uf    (D f ) 
p  Q( p,r,t)
t
3
p
•
That the time required to accelerate particles from momentum p0 to p is:

•
3
t
uu  ud
p

po
dp Du Dd 
 

p uu ud 
If we assume that the diffusion coefficient is independent of momentum, then we can
get a characteristic acceleration time

p
3 Du Dd 


 

dp /dt uu  ud uu ud 
In p(t)=p0exp(t/a). We can re-write this as:
•


3r Du
r 1 uu2
Where r=uu/ud the ratio of flow speeds in the shock rest frame. Here Dd/ud is assumed
to be small compared to Du/uu.

•
The energy spectrum expected from diffusive shock acceleration is a power
law:
J(E)  J 0 E 
1 r2

2 r 1 (in the non-relativistic case)
•
With
•
Why do we 
get a power law? The energy gain for each particle is determined
by its pitch angle and the number of shock crossings
(that
 is stochastic). For high energy gains the particle must be “lucky” to be
scattered back towards the shock again and again. Most particles make a few
shock crossings and then escape into the upstream medium. The stochastic
nature of diffusion allows high gains for a few particles, while most particles
make only small gains.
• Self-Generated Turbulence:
Whenever energetic particles stream faster than the Alfven speed, the generate and
amplify MHD waves with wavelengths in resonance with the field parallel
motion of the particles. These waves grow in response to the intensity gradient
of the energetic particles.
• M. Lee developed a theory that suggest that: first the accelerated
particles stream away from the shock. As they propagate upstream, the
particles amplify low-frequency MHD waves in resonance with them.
Particles escaping from the shock at a later time are scattered by these
waves and are partly reflected back towards the shock. These latter
particles again interact with the shock, gaining additional energy. The
net effect is an equilibrium between particles and waves which in time
shifts to higher energies and larger wavelengths.
• In resume: a shock is a highly non-linear system. Either
approximations are used to solve it analytically or studied by means of
numerical simulations.
•
•
•
The rather smooth transition between the maxwellian and the power law is in
agreement with the assumption that the particles are accelerated out of the
solar wind plasma
Low-energy particles:
The three types of acceleration mechanism can be distinguished
•
At High-energy particles (MeV): the different spectra do not reflect the local
acceleration mechanism but the location of the observer relative to the shock.
This is a consequence of the higher speeds of the MeV particles that allows
them to escape from the shock front. An observer in the interplanetary space
samples all the particles that the shock has accelerated on the observer’s
magnetic field line while its propagates outward.
Evidence of shock acceleration
• Indirect evidence:
– Energetic particles in space share one common
characteristic:
• energy spectra are often Power Laws
• Diffusive shock acceleration theory naturally
explains this
• spectral exponents should vary little from one event
to the next.
• Direct evidence:
– Numerous observations of energetic particles
associated with shocks
• Observations of shocks with no accelerated particles
too. This is not well understood.
Observed Power-law spectra
Other power laws here
Mason et al., 1999
• Anomalous Cosmic Rays and the Termination Shock
– Accelerated interstellar pickup ions
– Low charge states (+1) imply that they are accelerated rapidly (about 1 year).
– The best explanation for this is acceleration by a termination shock that is nearly
perpendicular over most of its surface (Jokipii, 1992)
Decker et al., Science, 2005
Large CME-related SEP events
Reames.SSR, 1999
Particle Acceleration at the Earth’s bow shock
(recent Cluster observations)
Kis et al. (2004)
Corotating Interaction Regions
Ulysses data
Compression of the
magnetic field within CIR.
Slow, intermediate, and fast
wind and both a Forward (F)
and Reverse (R) shock.
Energetic Particles peaking at
The F/R shocks, with a larger
intensity at the reverse shock.
HISCALE data courtesy Tom Armstrong
A simple interpretation of the higher intensities at the
reverse shock of a CIR 2-shock pair
• Forward shock – pickup
ions are from slow solar
wind
• Reverse shock – pickup ions
are from the fast wind
– Sart with higher energy
– More efficient acceleration
• This is relevant to our
understanding of SEP
events also.
Giacalone and Jokipii, GRL, 1997
Most IP shocks do not accelerate particles -how well is this really understood?
Slide Courtesy of Glenn Mason
Effect of Large-Scale Turbulent
Interplanetary Magnetic Field
Self-consistent
plasma simulation
Where do shocks exist?
• Direct observations of
collisionless shocks have been
made since the first observations
of the solar wind by Mariner 2.
• The Earth’s bow shock has been
crossed thousands of times
• Theoretically, we expect shocks
to form quite easily.
– In the solar corona, shocks can
form even when the driver gas is
moving slower than the
characteristic wave speed.
(Raymond et al., GRL, 27, 1493, 2000)
Magnetic Reconnection
Tanuma and Shibata, ApJ, 628, L77, 2005
Acceleration by Gradual Compressions
(no shocks)
Gradual Compression
Not a shock !
What is the Acceleration Mechanism?
Diffusive Shock Acceleration
• Discovered by four independent
teams:
– Bell (1978), Krymsky (1977),
Axford et al (1977),
Blandford & Ostriker (1978)
• Requires that particles diffuse across
a diverging flow (a shock)
• Also requires some form of trapping
near the shock
Actual Particle Orbits
Decker, 1988
Parker’s energetic-particle transport equation
advection
diffusion
drift
energy change
Diffusive Shock Acceleration
• Solve Parker’s
transport equation
for the following
geometry
• The steady-state solution for
, for an infinite system, is given by
Kennel et al, 1986
The downstream distribution is power law
with a spectral index that depends only on
the shock compression ratio!
Note that the dependence on compression
ratio is not that strong
J ~ E-2
(r = 2)
J ~ E-1.25 (r = 3)
J ~ E-1 (r = 4) – hardest
Reames.SSR, 1999
Electrons
• In principal, there is no difference between
electrons and ions in the basic picture of DSA
– What scatters the electrons?
• Importance of large-scale fluctuations
– Electrons move rapidly nearly along magnetic lines of
force that can intersect the shock in multiple locations
Heavy Ions
• Heavy ions can also be accelerated efficiently by shocks.
• Particles of a given species with a higher charge state are accelerated faster,
and hence, can reach a higher total energy.
Tylka et al 2005
Mason et al., 2004
The “injection problem”
• What is the particle source?
– Solar wind ions can be
accelerated by shocks
• However, composition of
SEPs are NOT consistend t
with solar wincomposition.
– A simple interpretation is given
at the right
2 related questions:
What is the maximum energy ?
How rapidly can the particles be
accelerated?
Spectral cutoffs and rollovers
• Finite acceleration time
Parallel shocks  slow
Perpendicular shocks  fast
• Free-escape losses
• Limits imposed by the size of the
system
All lead to spectral variations that depend on
the transport parameters (e.g. species,
magnetic turbulence, etc.)
will cause abundance variations that
depend on species, and vary with energy
Acceleration Time in Diffusive Shock Acceleration
• The acceleration rate is given by:
Hence, the maximum energy depends strongly
on both the shock speed and on the level of
magnetic turbulence (which is not well known
near the Sun)
Acceleration time
(Brms/B)2
Particle source
Characteristic
Energy
Termination
shock
(100 AU)
~ year
~0.3-1
IS pickup ions
H, He, N, O, Fe (mostly)
~ 200 MeV
(total energy)
CIRs
(2-5 AU)
~ months
~0.5
Pickup ions, solar wind,
enhanced C/O
~ 1-10 MeV/nuc
Earth’s bow
shock
(1 AU)
~tens of minutes
~1
Pickup ions, solar wind,
magnetosphere ions
~ 100-200
keV/nuc.
Large SEPs
(r > 0.01 AU)
Minutes or less
??
Suprathermals *
H (mostly), He, and
heavy ions, even M > 50
~1 MeV/nuc,
sometimes up to
~20 GeV
Transient IP
shocks
days
~0.3
Suprathermals
Less than ~1
MeV
* Suprathermals pervade the heliosphere – their origin is not well understood
Perpendicular vs. Parallel Shocks
• The acceleration time depends on the diffusion
coefficient
• because
, the acceleration rate is higher for
perpendicular shocks
– For a given time interval, a perpendicular shock
will yield a larger maximum energy than a parallel
shock.
• Perpendicular Shocks:
t = 6 minutes at 7 solar radii
(B = 0.003 Gauss)
– The time scale for
acceleration at a
perpendicular shock is
1-2 orders of magnitude
shorter (or possibly
much more) than that at
a parallel shock.
Test-particle simulations of particles
encountering shocks moving in weak large-scale
magnetic-field turbulence (Giacalone, 2005)
SEPs from CME-Driven Shocks
In the corona
In interplanetary space
How are the particles transported to an
observer?
Interplanetary transport of SEP events
ACE/ULEIS observations
Impulsive-flare-related event
showing intensity variations
Gradual-flare-related event
showing no intensity variations
Numerical Simulations and
simple interpretation of SEP
transport
How do particles escape from
closed-field regions?
• Not well understood.
• Observations indicate that
energetic electrons
(producing radio bursts) are
probably on open field lines
• Reconnection with open
fields?
• Cross-field diffusion?
Important Questions
• What is the temporal evolution of the shock-accelerated
intensity and spectra ?
– Observations made at 1AU are an “integral
• What are the sources ?
– Probably the most important question with regards to Space-Weather
forecasting
• What is the shock geometry (especially back near the Sun)
?
– Parallel and perpendicular shocks have different shock-acceleration
physics
• What is nature of the particle transport ?
– Need to know the form of the magnetic-field power spectrum,
especially near the acceleration site
Combined CME/MHD + Particle
Transport/Acceleration Modeling
Schematic view of CME &
Magnetic Field
Courtesy J. Kota
Time-variation of SEP fluxes
Conclusions
• Shocks provide a natural explanation for most cosmic rays
(including SEPs).
• The rate of acceleration (especially by perpendicular shocks) is
sufficiently high to explain the existence of > GeV/nuc SEP
events.
• Shocks are common in space plasmas. They have been observed
to form very close to the Sun and are expected to form very
easily.