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

FelixFest Nov. 2012

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

FelixFest Nov. 2012

I.  Acceleration Model and                     Turbulence           1st and 2nd  Order Fermi Basic Equation and CoefficientsBasic Equation and Coefficients

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:

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

FelixFest Nov. 2012

Rate Ratio

Where

At relativistic energies so that

But at Low energies and

Comparison of Stochastic and Shock Acceleration Rates

(Pryadko and Petrosian 1997)

FelixFest Nov. 2012

Rate Ratio

Where

At relativistic energies so that

But at Low energies and

Comparison of Stochastic and Shock Acceleration Rates

(Pryadko and Petrosian 1997)

FelixFest Nov. 2012

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)

FelixFest Nov. 2012

Complicated But If Isotropic and Homogeneous (pitch angle and spatially averaged equation)

Diffusion Accel. Loss Escape Source

Particle Acceleration and TransportKinetic Equation

FelixFest Nov. 2012

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

FelixFest Nov. 2012

Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)

Diffusion Accel. Escape

Diffusion and Acceleration CoefficientsThe Unknowns

FelixFest Nov. 2012

Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)

Diffusion Accel. Escape

Diffusion and Acceleration CoefficientsThe Unknowns

FelixFest Nov. 2012

Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)

Escape

Diffusion and Acceleration CoefficientsThe Last Unknown

FelixFest Nov. 2012

Complicated But If Isotropic and Homogeneous (or pitch angle and spatially averaged equation)

Escape

Diffusion and Acceleration CoefficientsThe Last Unknown: Tesc

FelixFest Nov. 2012

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

FelixFest Nov. 2012

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

FelixFest Nov. 2012

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

FelixFest Nov. 2012

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

FelixFest Nov. 2012

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.

FelixFest Nov. 2012

Observing the Spectrum of Escaping Particles An Important Special Case

From this now we get

From which again we get

FelixFest Nov. 2012

Observing the Spectrum of Escaping Particles An Important Special Case

From this now we get

From which again we get

FelixFest Nov. 2012

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

FelixFest Nov. 2012

Testing the Acceleration ModelUsing Radio, X­ray Gamma­ray 

and Cosmic Ray Data

III. Application to  Acceleration of Electrons in Supernova 

Remnants  

FelixFest Nov. 2012

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

FelixFest Nov. 2012

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.

FelixFest Nov. 2012

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.

FelixFest Nov. 2012

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.

FelixFest Nov. 2012

Acceleration Rates and TimesNearby Pulsar Case

Eo depends on many factors: Volume filled with CR electrons SNR rate and active duty cycle

etc.

FelixFest Nov. 2012

Results For Supernova Remnants With Klein-Nishina Effect Nearby Pulsar

Eo

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Testing the Acceleration ModelUsing RHESSI Images

IV. Application to  Acceleration of Electrons in Solar Flares 

FelixFest Nov. 2012

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

FelixFest Nov. 2012

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

FelixFest Nov. 2012

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

FelixFest Nov. 2012

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

FelixFest Nov. 2012

2003 Nov 3 Flare: Model Parameters

Electron Spectra Time Scales

40 40

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Scattering And Acceleration Times Interaction with Parallel Waves

Pryadko and Petrosian 1997

FelixFest Nov. 2012

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

FelixFest Nov. 2012

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

FelixFest Nov. 2012

Comparison of Model with Observations

40 40

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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.

FelixFest Nov. 2012

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

FelixFest Nov. 2012

Turbulence parametersa. Injection and damping wave numbersb. Inertial range spectral index:

c. Turbulence Energy Density

Characteristic Timescale

From these we get the diffusion coefficients and all timescales

Turbulence and Acceleration B. Spectral Parameters