Direct Non-Parametric Determination of Characteristics of Acceleration...
Transcript of Direct Non-Parametric Determination of Characteristics of Acceleration...
FelixFest Nov. 2012
Direct Non-Parametric Determination of Characteristics of Acceleration Mechanisms
From Observations Solar Flares and Supernova Remnants
Vahe Petrosian
Stanford UniversityWith
Qingrong Chen
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I. A Brief Review of Acceleration Mechanisms
Basic Equation and Important Coefficients II. Direct-Nonparametric Determination of Acceleration
Coefficients From Observations
Inversion of the Equations
III. Application to Supernova Remnants
IV. Application to Solar Flare
Outline
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I. Acceleration Model and Turbulence 1st and 2nd Order Fermi Basic Equation and CoefficientsBasic Equation and Coefficients
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Fermi Acceleration Mechanisms General Remarks
1. Stochastic Acceleration (Fermi 1949)
Second order Fermi: Scattering by TURBULENCE
Energy Gain rate:
2. Acceleration in converging flows; Shocks
Momentum Change First Order
But need repeated passages across the shock
Most likely scattering agent is TURBULENCE
Energy Gain rate:
FelixFest Nov. 2012
Fermi Acceleration Mechanisms General Remarks
1. Stochastic Acceleration (Fermi 1949)
Second order Fermi: Scattering by TURBULENCE
Energy Gain rate:
2. Acceleration in converging flows; Shocks
Momentum Change First Order
But need repeated passages across the shock
Most likely scattering agent is TURBULENCE
Energy Gain rate:
These rates are obtained from wave-particle interaction
Depend on turbulence spectrum and intensity
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Rate Ratio
Where
At relativistic energies so that
But at Low energies and
Comparison of Stochastic and Shock Acceleration Rates
(Pryadko and Petrosian 1997)
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Rate Ratio
Where
At relativistic energies so that
But at Low energies and
Comparison of Stochastic and Shock Acceleration Rates
(Pryadko and Petrosian 1997)
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Rate Ratio
Where
At relativistic energies so that
But at Low energies and
Hybrid Fermi Mechanism
Comparison of Stochastic and Shock Acceleration Rates
(Pryadko and Petrosian 1997)
(Petrosian 2012)
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Complicated But If Isotropic and Homogeneous (pitch angle and spatially averaged equation)
Diffusion Accel. Loss Escape Source
Particle Acceleration and TransportKinetic Equation
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Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)
Loss Source
Need n, T, B (+soft photon)
We will assume we know these
Energy Loss and Source TermsThe Better Known Coefficients
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Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)
Diffusion Accel. Escape
Diffusion and Acceleration CoefficientsThe Unknowns
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Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)
Diffusion Accel. Escape
Diffusion and Acceleration CoefficientsThe Unknowns
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Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)
Escape
Diffusion and Acceleration CoefficientsThe Last Unknown
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Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)
Escape
Diffusion and Acceleration CoefficientsThe Last Unknown: Tesc
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Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)
Diffusion Accel. Loss Escape Source
Thus, all unknowns depend on
two diffusion coefficients
Particle Acceleration and Transport
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II. DirectNonparametric II. DirectNonparametric Determination of Acceleration Model Determination of Acceleration Model Parameters From Observations Parameters From Observations
Inversion of the EquationsInversion of the Equations
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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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Back to the Leaky Box Model (Steady State)
Two unknowns (or )
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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Observing the Spectrum of Escaping Particles An Important Special Case
Escaping particles during their transport in an outside medium lose energy and emit radiation. The case when they
lose all their energy is referred to as The Thick Target or Complete Cooling
transport model.The transport can be treated by the Leaky Box Model but
now without the acceleration and escape terms.When we observe these particles or their radiation we do not observe the above escaping flux but an effective spectrum
given as follows again for the steady state case.
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Observing the Spectrum of Escaping Particles An Important Special Case
From this now we get
From which again we get
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Observing the Spectrum of Escaping Particles An Important Special Case
From this now we get
From which again we get
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Observing the Spectrum of Escaping Particles An Important Special Case
From this now we get
From which again we get
Another way of writing this we get
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Testing the Acceleration ModelUsing Radio, Xray Gammaray
and Cosmic Ray Data
III. Application to Acceleration of Electrons in Supernova
Remnants
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Supernova Remnant and Cosmic Ray ObservationsA. Toy Model
Sun
Background Galactic Radio, X-ray, Gamma-ray radiation
Cosmic-rays Observed near Earth
This givesNeff (E)
SNR radiation Observed near Earth
From this get Nacc (E)
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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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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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Acceleration Rates and TimesNearby Pulsar Case
Eo depends on many factors: Volume filled with CR electrons SNR rate and active duty cycle
etc.
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Testing the Acceleration ModelUsing RHESSI Images
IV. Application to Acceleration of Electrons in Solar Flares
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Distinct Looptop and Footpoint Sources YOHKOH
RHESSI
Hard X-ray Observations and Basic ModelBremsstrahlung by Electrons
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Connected by Escaping Process
See Petrosian & Chen (2010)ApJ Letters, 2010, 712, 131
The Basic Model: Relating Electrons and Photons
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Bremstrahlung Hard X-ray Emission
Applying our inversion relations we get
and
in terms of observables on the right hand side
Petrosian & Chen (2012) In preparation
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 get
Regularized inversion produced smoothed electron flux visibility spectrum
Fourier Transform Gives
Piana et al. 2007
Regularized Inversion of Photon Images to Electron Images and
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2003 Nov 3 Flare(X3.9 class)
LT source detected up to 100-150 keV (Chen & Petrosian, in preparation)
HXR images by MEM_NJIT
Electron flux images by MEM_NJIT
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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
More Accurate Wave-Particle Model
e.g. Oblique Waves of Kinetic Effects
Influence of a Possible Standing Shock
Energy Dependence not too different
Transport Effects
e.g. Converging Field Lines at the Looptop
Escape time (determined by collisions into the loss cone) will increase with energy
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So How Do We Fix ItPossible Solutions
More Accurate Wave-Particle Model
e.g. Oblique Waves of Kinetic Effects
Influence of a Possible Standing Shock
Energy Dependence not too different
Transport Effects
e.g. Converging Field Lines at the Looptop
Escape time (determined by collisions into the loss cone) will increase with energy
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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 characteristicsusing the newly developed regularized inversion techniques.
2. This is demonstrated by application to RHESSI Imaging spectroscopic data showing some puzzling results.
3. The results from application to supernova remnants and cosmic ray observations are very promising.
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Turbulence and Acceleration A. Wave Particle Interactions
Resonance Condition
Dispersion Relatione.g. parallel propagating waves
Plasma parameters density and B fieldPlasma and gyro-frequencies or
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Turbulence parametersa. Injection and damping wave numbersb. Inertial range spectral index:
c. Turbulence Energy Density
Characteristic Timescale
Turbulence and Acceleration B. Spectral Parameters