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Particle Acceleration in Astrophysics 2. What can we learn from
observations
Vahe Petrosian
Stanford University
Work based on several PhD theses and collaborations with post
doctoral fellows and colleagues
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Plasma properties
Turbulence spectrum
wave-particle interactions
Shock
Background density
Radiating electron spectrum
Acceleration Radiation Observation
The Problem
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Plasma properties
Turbulence spectrum
wave-particle interactions
Shock
Background density
Radiating electron spectrum
Acceleration Radiation Observation
The Forward Fitting Method
Forward Fitting
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Plasma properties
Turbulence spectrum
wave-particle interactions
Shock
Background density
Radiating electron spectrum
Acceleration Radiation Observation
The Inversion Method
Inverse process
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I. Description of a nonparametric inversion methodII.
Applications of the Inversion Method A. Cosmic Rays and Supernova
Remnant Spectra B. Solar Flare Hard X-ray emissions III. Some
Interesting Puzzles of Ion acceleration A. Extreme enhancement of
3He and Heavy ions B. Electron spectra at Flare sites and observed
at Earth
Outline
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Back to the Leaky Box Model (Steady State)
Two unknowns Therefore we need two spectral information
1. Accelerated Particle Flux 2. Escaping Particle Flux These
Give the escape time
If there is no B convergence from this we can get
Then integration of the kinetic equation over E gives
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Back to the Leaky Box Model (Steady State)
Two unknowns Therefore we need two spectral information
1. Accelerated Particle Flux 2. Escaping Particle Flux These
Give the escape time
from which we get Then integration of the kinetic equation over
E gives
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Transport and Spectrum of Escaping Particles An Important
Special Case
If particles lose all their energy in the transport region
then
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Transport and Spectrum of Escaping Particles An Important
Special Case
RecallRecall that
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Transport and Spectrum of Escaping Particles An Important
Special Case
RecallRecall that
From These we can get the effective acceleration rate
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Plasma properties
Turbulence spectrum
wave-particle interactions
Shock
Background density
Radiating electron spectrum
Acceleration Radiation Observation
The Inversion MethodFor radiating sources the first step is to
obtain particle
spectrum fromphoton spectrum
Inverse process
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We need to invert this to obtain
There are two methods that work well when the cross section is a
simple function of photon and particle energies like bremsstrahlung
and synchrotron. IC more complex but approximation can be used
satisfying this requirements.
1. Generalized Inversion method by Piana et al.
2. The Johns-Lin method of matrix inversion
The Inversion MethodFor radiating sources the first step is to
obtain particle
spectrum fromphoton spectrum
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Using Observed Radiation and Cosmic Ray Spectra
II-A. Application to Acceleration of Electrons in Supernova
Remnants
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Supernova Remnant and Cosmic Ray ObservationsA. Toy Model
Sun
Cosmic-rays Observed near Earth This gives SNR radiation
Observed near Earth gives
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Supernova Remnant and Cosmic Ray ObservationsA. Toy Model
Sun
Cosmic-rays Observed near Earth This gives SNR radiation
Observed near Earth gives
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Spectra of Accelerated ElectronsFrom Radio and X-ray (and
gamma-ray?) Observations
Hui, Li et al. 2010
Lazendic et al. 2004
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Effective Spectra of Escaping ElectronsTwo Interpretation of the
Bump
Klein-Nishina Effect in IC Losses Nearby Pulsar Stawarz,
Petrosian & Blandford Fermi Collabor. Abdo et al.
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Effective Spectra of Escaping ElectronsTwo Interpretation of the
Bump
Klein-Nishina Effect in IC Losses Nearby Pulsar Stawarz,
Petrosian & Blandford Fermi Collabor. Abdo et al.
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Escape Time: Two Methods
A.
B.
Injected Q obtained using e.g. GalpropFitting to the obseved CR
spectrum
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RESULTS From Two Methods
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RESULTS: Scatering Time
Two methods of determining the coefficient or the scattering
time
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Solid Curves from Escape timeDashed (SA) and Dotted (Shock) from
Acceleration times
RESULTS: Scattering Time
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Scattering And Acceleration Times Interaction with Parallel
Waves
Pryadko and Petrosian 1997
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Using Observed hard X-ray Spectra from Loop top and Foot points
of
Flare Loops
II-B. Application to Acceleration of Electrons in Solar
Flares
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Cartoon and Observation of a Flare Loop
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HXR:
Connected by Escaping Process
See Petrosian & Chen (2010)ApJ Letters, 2010, 712, 131
The Basic Solar Flare Model Relating Electrons and Photons
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Results From Inversion of the Kinetic Equation
(Petrosian & Chen, 2010 ApJ L, 712, 131)
From these we derive Energy Dependence of the diffusion
rates
Both Coefficients Depend only on Observables
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Bremsstrahlung Hard X-ray Emission
Applying our inversion relations we get
and
or
Petrosian & Chen (2013) See recent astro-ph posting
The Basic Model: Relating Electrons and Photons
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RHESSI produces count visibility, Fourier component of the
source
Defining electron flux visibility spectrum and count cross
section
We getRegularized inversion produced smoothed electron flux
visibility spectrum
Fourier Transform GivesPiana et al. 2007
Regularized Inversion of Photon Images to Electron Images
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2003 Nov 3 Flare(X3.9 class)
LT source detected up to 100-150 keV (Chen & Petrosian
2013)
HXR images by MEM_NJIT
Electron flux images by MEM_NJIT
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2003 November 3 Flare X3.9
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2005 September 8 Flare M2.1
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Escape and Scattering Times Theory and Empirical Determinations
Effenberger and VP 2017 Chen & VP 2013
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Scattering And Acceleration Times Interaction with Parallel
Waves
Pryadko and Petrosian 1997
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So How Do We Fix ItPossible Solutions
Weak Diffusion andConverging Field Lines at the Loop topEscape
time (determined by scatterings into the loss cone) will increase
with energy
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Trapped by a Magnetic Bottle
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Scattering And Acceleration Times Interaction with Parallel
Waves
Pryadko and Petrosian 1997
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SUMMARY and CONCLUSIONS
1. For sources where observations give the Accelerated and
Escaping Particle Spectra we can determine the basic acceleration
parameters given the plasma characteristics using the newly
developed inversion technique.2. The results from application to
supernova remnants and cosmic ray observations are very
promising.3. Application to RHESSI Imaging spectroscopic data show
some new results.
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Extreme enhancement of 3He and heavy ions
III. Some Interesting Puzzle on Acceleration of Ions
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●2. SEP-Ion Spectra and 3He Enrichment “Impulsive” Events Mason
et al. 2016 “Gradual” Events Desi t al. 2015
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●2. SEP ION Enrichments “Impulsive” Events Mason et al. 2016
Reames et al.
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He3, He4 Fluence RatiosNot bimodal: gradual variation with
acceleration rate
Observations
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Resonant Wave-Particle Interactions4He and 3He
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B. He3, He4 Abundances and Spectra
(Liu, Petrosian and Mason, 2004 ApJ)
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He3, He4 Fluence RatiosNot bimodal: gradual variation with
acceleration rate
Observations Model Results
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Flare accelerated He4 SpectraDo not agree with observed gradual
events
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Diffusion Accel. Loss Escape Source by Turbulence by Shock and
Turbulence
Observed SEPs
● Kinetic Equation The Leaky Box Model● Re-Acceleration at the
CME Shock
Flare Accelerated Particles
Gradual or Delayed EventsRe-acceleration at the CME shock
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Solution with Source term flare accelerated electrons
Gradual or Delayed EventsRe-acceleration at the CME shock
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BUT Flare accelerated He4 Spectraafter re-acceleration at the
CME-shock agree
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Numerical treatment of re-Acceleration
Re-acceleration timescales
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RHESSI 2019
A. Electrons
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RHESSI 2019
● 1. SEP and HXR Electron Spectra
“Impulsive; Prompt” “Gradual; Delayed” Events
Krucker et al. 2007
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● 1. SEP and HXR Electron Spectra Distributions of “Impulsive;
Prompt” and “Gradual; Delayed”
VP 2016
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● 1. SEP and HXR Electron Numbers Correlations of “Impulsive;
Prompt” Events only
Krucker et al. 2007
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● Escape up: SEPs ●
● Escape down: HXRs●
●
●
● Impulsive or Prompt Events● Acceleration by Turbulence at the
Flare Site
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New Direction: Motivated by two new results
Krucker et al. 2007
Strong diffusion
● Impulsive or Prompt Events● Acceleration by Turbulence only at
the Flare Site
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New Direction: Motivated by two new results
Krucker et al. 2007
Weak diffusion
● Impulsive or Prompt Events● Acceleration by Turbulence only at
the Flare Site
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New Direction: Motivated by two new results
Krucker et al. 2007
Relative numbers of RPP and SEP (electrons)
● Impulsive or Prompt Events● Acceleration by Turbulence only at
the Flare Site
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Solution with Source term flare accelerated electrons
●Gradual or Delayed Events● Re-acceleration at the CME shock
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1. Inversion methods can determine the Fokker-Planck
Coefficients directly and non parametrically from observed
spectra.2. Both Shock and Stochastic Acceleration Driven by
Turbulence Can Account For Many High Energy Astrophysical
Phenomena.
SUMMARY and CONCLUSIONS 2
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EnrichmentSlide 41Slide 42Resonant Wave-Particle Interactions 4He
and 3HeSlide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide
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