Suprathermal Tails in Coronal
Proton Velocity Distributions
J. L. Kohl, A. Panasyuk, S. Cranmer, S. Fineschi,
L. D. Gardner, D.H. Phillips, J. C. Raymond,
and M. Uzzo
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Theory of shock acceleration of
SEPs
M. A. Lee (1983,
2005) developed a
theory of coupled
turbulent wave
excitation and
proton acceleration
at shocks.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Theory of shock acceleration of
SEPs
 In this theory, in order to produce large SEP events, it is
necessary for a suprathermal seed particle population to exist
after the first encounter of the coronal plasma with a CME
shock. The theory requires that .001 to .01 of this proton
velocity distribution have an injection speed higher than 2
times the difference between the shock speed and the wave
phase speed (~VA in corona).
 Alternatively, there could be a pre-existing suprathermal
population in the corona that would help to satisfy this
requirement. Gopalswamy et al. (2004) found higher SEP
intensities when there was a preceding CME within ~24 hours
that perhaps left behind suprathermals.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Theory of shock acceleration of
SEPs
 The threshold velocity for particle injection is extremely
uncertain. There are several lines of evidence that particles
of 1000 to 2000 km/s (i.e., 5.2 – 20.7 keV) are preferentially
accelerated. From the experimental side, that includes
creation of anomalous cosmic rays from pick-up ions. Theories
such as the transparency function of Gieseler et al. give similar
results.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Density of Suprathermal Seed
Particles
Preshock
fi (v): Resonantly
scattered Ly constrains the
seed particle distribution
fe(v): Thomson-scattered
Ly
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
kappa needed to provide various
population fractions with velocities
above the injection velocity
Injection speeds of 940 –
1460 km/s, are 6.1 to 9.7 in
units of V1/e
A kappa distribution
where .01 - .001 of the
population has speeds
beyond 6.1 to 9.7 V1/e has a
kappa between 4 and 2.
Hence, proton velocity
distributions resembling
kappa distributions with
kappa values in this range
and lower are of interest.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Proton velocity distribution in a
diffuse coronal region
Kappa = 21.8 ± 7.0
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Suprathermal Tails in Coronal
Proton Velocity Distributions
Observation of a proton velocity
distribution with kappa = 3.5
Kappa = 3.5 ± 0.34
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
NESSC
5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Pseudo-kappa function
– Data clearly show asymmetrical
wings.
– Kappa-function cannot model
asymmetrical line profiles.
– Idea is to create a function that
is close to a kappa-function
when the line is symmetrical
but allows for a shift of the
wings relative to the core.
– Some theoreticians use a
power-law, so a sum of
Gaussian and power-law
function seems natural.
– For example the plot on the
right shows that a kappafunction does not fit the
observation.
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5 April 2006
f ( )  (1  x 2 /  )1
G *e
 ( x /  )2
+
A /(1  (( x  ) /  )  )
Suprathermal Tails in Coronal
Proton Velocity Distributions
Pseudo-kappa function
•
•
We empirically determine the
dependency of all parameters
(G,A,δ,ρ and σ) of the kvalue of approximated
function.
The only additional parameter
(vs kappa-function) is the Δ –
shift which allow us to fit
asymmetrical profiles.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Best fit to data
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
Effect of Stray Light
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Suprathermal Tails in Coronal
Proton Velocity Distributions
10 Feb 2006
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Suprathermal Tails in Coronal
Proton Velocity Distributions
10 Feb 2006
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Suprathermal Tails in Coronal
Proton Velocity Distributions
Conclusions
UVCS/SOHO is able to measure proton
velocity distributions including departures
from Maxwellians.
These observations may lead to testing and
refining theories of SEP production.
Work is in progress: line of sight, more
observations and archival data analyses to be
done.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Simulation of observation for
kappa = 4
 Simulation includes coronal
emission assuming kappa = 4,
Poisson noise, Binning to UVCS
sampling, Random flat field
uncertainty, Detector
background, Fitting with and
without error in instrument
profile
 Fit with no profile error yields
kappa = 3.92 +/- 0.66
 Fit with profile error yields
kappa = 3.66 +/- 0.59
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
 Kappa is large
 19 Jan 2005,
22:01 + 2:00
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
 Kappa = 3.43 ± 1.0
 19 Jan 2005,
22:01 + 3:30
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
19 Jan 05, 22:01 + 5:30
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5 April 2006
19 Jan 05, 22:01 + 6:00
Suprathermal Tails in Coronal
Proton Velocity Distributions
Interpretation
 Phil Isenberg suggested that the non-Maxwellian tails
might be associated with heat flux along the magnetic
field.
 He speculates that the appearance and disappearance
of these tails could be due to rotations of the field
direction into and out of the line of sight.
 He points out that this interpretation probably would
not be consistent with a symmetric LOS velocity
distribution.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Interpretation
 Next week Gang Li of UC, Riverside will give an
SSP seminar describing his recent theoretical finding
that a predecessor CME can greatly enhance
turbulence upstream of a second shock. This
decreases the acceleration time scale at the second
shock allowing fast particle acceleration to occur.
 To explain the result of Gopalswamy et al., the
turbulence would need to be present for several hours
after the first shock.
 It is not clear if our observations indicate any increase
in turbulence following a predecessor shock.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
LASCO C2 image of CME
region on 23 & 24 Dec 1996
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Simulation of observation for
kappa = 4
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Suprathermal Tails in Coronal
Proton Velocity Distributions
UVCS Determinations of
Pre-CME Corona
 UVCS routinely obtains the densities, temperatures,
outflow speeds, ionization states and elemental
abundances in the pre-CME corona
 Densities obtained by UVCS can be combined with
Type II radio burst drift rates to obtain shock speeds
 The angle between the shock front and the magnetic
field requires the pre-shock field direction, which can
be determined from the streamer morphology
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Testing and Guiding Theoretical
Models of SEP Acceleration
 The measured and derived parameters allow
shock acceleration and current sheet models to
be tailored to a specific event.
 The theoretical models can then predict SEP
acceleration, transport and energy spectra for
those events.
 In situ measurements of SEP energy spectra
near the Sun (e.g., by Inner Heliospheric
Sentinels) can then be used to test and guide
the theoretical models.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Key Parameters in Theories of
SEP Acceleration by shocks
Pre-shock plasma conditions (including the
supra-thermal seed particle population)
The shock speed
The compression ratio (which yields the
Mach number)
The angle between the magnetic field and
the shock motion
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Proton Velocity Distributions
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Proton Velocity Distributions
20 Jan 2005 Event
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Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
20 Jan 2005 Event
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Suprathermal Tails in Coronal
Proton Velocity Distributions
Density of Suprathermal
Seed Particles
Preshock
fe(v): Thomson-scattered Ly
fi (v): Resonantly scattered Ly
constrains the seed particle
distribution
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
Lin and Forbes Unified Model
of a Flare and CME
In the Lin and Forbes model, a
stressed magnetic arcade begins to
rise. A current sheet develops as
external pressure forces
oppositely directed magnetic field
lines to reconnect. The liberated
energy heats and drives the CME
and drives energetic particles
downward producing the flare.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
SEP source regions
The source regions of solar
energetic particles (SEPs) are not well
established and the physical processes
associated with their acceleration are
not well understood.
Gradual phase SEPs are believed to
be produced by CME shocks, while
impulsive phase SEPs are believed to
be produced in the current sheet or
other sites closely associated with the
solar flare.
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
UVCS observations of CME
shocks
Broad lines appear
when shock forms
Shock speeds can be
determined from
detection of shock
arrival at different
heights
Unshocked foreground/ background
shocked O+5 (T > 108 K)
At onset radius, Mach
number = 1, so Vshock
gives VAlfven .
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5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions
The required insertion speed for
producing observed SEP events
UVCS observations of CME
shocks yielded an upper limit
for the Alfven speed VA = 540
km/s at 2.3 Rsun
Assuming a shock speed of
1000 km/s and 270 < VA < 540
km/s at 3.5 Rsun , we derive an
injection speed of 920 to 1460
km/s (4.4 – 10.1 keV).
Unshocked foreground/ background
shocked O+5 (T > 108 K)
Proton V1/e in a streamer at
3.5 Rsun is 150 km/s.
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Suprathermal Tails in Coronal
Proton Velocity Distributions
UVCS Instrument Profile
Left: UVCS instrument profile. Right: High spectral resolution scan of Ne-Pt
hollow cathode spectrum convolved with UVCS instrument profile (black) and
UVCS scan of lamp spectrum (red).
NESSC
5 April 2006
Suprathermal Tails in Coronal
Proton Velocity Distributions