# Presentation: 248675

## Nonthermal Hard X-Ray Radiation from Solar Flares: Observations and Models

- Gordon D. Holman
- Laboratory for Solar and Space Physics
- NASA Goddard Space Flight Center

## What do we mean by “hard X-rays and “nonthermal radiation”?

**Hard X-rays**: 10 keV – 300 keV, between soft X-rays and gamma-rays
**Nonthermal radiation**: radiation from an electron distribution that is *not locally Maxwellian*

## First X-ray Observations

- X-rays first observed from the Sun by Friedman (Naval Research Lab.) with Geiger counters on a V-2 rocket in 1949
- First detection of a solar flare in hardX-rays/-rays: 1958 by Peterson & Winckler (Univ. of Minnesota) during a balloon flight from Cuba (1958 *Physical Review Letters*)

## First Image of Hard X-ray Footpoints?

*Solar Maximum Mission* (SMM)Hard X-ray Imaging Spectrometer (HXIS)
- Hoyng et al., *The Astrophysical Journal Letters*, 1981

## Spectra from the Solar Maximum Mission Hard X-Ray Burst Spectrometer

- Dennis, *Solar Physics*, 1985

## Flare Spectra Obtained with Cooled Germanium Detectors - 1980 Balloon Flight

- 34 MK “superhot” plasma
- Lin et al., *The Astrophysical Journal Letters*, 1981
- Double power-law spectra
- Lin & Schwartz, *The Astrophysical Journal*, 1987

## SMM HXRBS Spectra Indicating a Thermal Component at Low Energies

- 3 February 1982

- Kiplinger et al., *The Astrophysical Journal*, 1989

## From Fast Electrons to Bremsstrahlung Photons

- Nv
- photons s-1 ion-1

- Nph = nNv
- photons s-1 cm-3

- Nv
- electrons cm-2 s-1

- Bremsstrahlung
- Cross section (cm2)

- nions cm-3

## From an Electron Distribution Function to a Bremsstrahlung Spectrum

- Nph(ε, E) = nN(E)v(ε, E)

- ε = photon energy
- E = electron energy

- Differential cross section(ε, E) = d(ε, E)/dε

- Electron Flux Distribution Function  F(E) = N(E)v   electrons cm-2 s-1 keV-1

- Nph(ε) = n ε F(E)(ε, E) dE
- photons s-1 cm-3 keV-1

## Photon Flux at Detector& Mean Electron Flux

- I(ε) = (1/4R2) Vn(r)ε F(E,r)(ε, E) dE dV
- photons s-1 cm-2 keV-1

- R = 1 AU

- I(ε) = (1/4R2) ε [Vn(r)F(E,r) dV] (ε, E) dE

- I(ε) = (1/4R2) nV εF(E) (ε, E) dE
- photons s-1 cm-2 keV-1

- Mean Electron Flux: F(E) = (1/nV) Vn(r)F(E,r) dV

## Thick-Target Bremsstrahlung I

- I(ε) = (1/4R2) V ε n(r) F(E,r) (ε, E) dE dV

- I(ε) = (1/4R2) x ε n(x) F(E,x) (ε, E) dE dx

- F(E,x) dE = F(E0) dE0

- F(E,x) (dE/dx) dx= F(E0) dE0

- F(E,x) dx = F(E0) dE0 / (dE/dx)

- I(ε) = (1/4R2) 
-  εF(E0) E0 [ n(x) (ε, E) / (dE/dx) ] dE dE0

- For a steady state and E = E(x), electron flux conservation gives

## Thick-Target Bremsstrahlung II

- I(ε) = (1/4R2) εF(E0) E0ε [ n(x) (ε, E) / (dE/dx) ] dE dE0

- For collisional energy losses in a *fully ionized plasma*,

- dE/dx =  *K* n / E

- I(ε) = (1/*K*4R2) εF(E0) [ εE0 (ε, E) E dE ] dE0

- Independent of plasma density, n(x)!
- Can deduce the injected electron flux distribution,F(E0) electrons s-1 keV-1

## Accelerated ElectronNumber Flux & Energy Flux

- dNel/dt =  F(E0) dE0
- electrons s-1

- dWel/dt =  E F(E0) dE0
- erg s-1

## The Bremsstrahlung Cross Section

- Nonrelativistic approximations
- Kramers:   (ε, E) = 0 /εE
- Bethe-Heitler: (ε, E) = (0 /εE) ln[ (E/ε)1/2 + (E/ε - 1)1/2 ]
- For relativistic, angle dependent, and polarization dependent cross sections, see Koch & Motz, *Reviews of Modern Physics*, 1959, and Haug, *Astronomy & Astro-physics*, 1997.

## Approximate Results for Power-Law Electron Distributions(Brown, Solar Physics, 1971)

- Assume I(E)  E    (photons s-1 cm-2 keV-1)
- Thin target: F(E)  E (  1)          (electrons cm-2 s-1 keV-1)
- Thin target: N(E)  E(  1⁄2)         (electrons cm-3 keV-1)
- Thick target: F(E0)  E0(+1)         (electrons s-1 keV-1)

## Spectra from Electron Distributions with a Low-Energy Cutoff

- Holman, *The Astrophysical Journal*, 2003

- N(E) = KE-3el. cm-3 keV-1

- N(E) = KE-5el. cm-3 keV-1

## Spectra from Electron Distributions with a High-Energy Cutoff

- Holman, *The Astrophysical Journal*, 2003

- N(E) = KE-3el. cm-3 keV-1

- N(E) = KE-5el. cm-3 keV-1

## Forward Fit to a RHESSI Flare Spectrum

- 23 July 200200:30:00 – 00:30:20 UT

- ( Observed Flux – Model Flux ) / 

- Best-Fit Model Mean Electron Flux Electron Distribution

- Holman et al., *The Astrophysical Journal Letters*, 2003

## Spectral Fits to the 15 April 2002 Flare

- Sui et al., ApJ, 2005

## Regularized Inversion of the July 23 Spectrum Compared with the Forward Fit Result

- Piana et al., *The Astrophysical Journal Letters*, 2003

## Photon Spectra from Theoretical Electron Distributions with “Interesting Features”

- Brown et al., *The Astrophysical Journal*, 2006

## Three Inversions and a Forward Fit to the Theoretical Photon Spectra

## Alternative Emission Mechanisms

- Inverse Compton Radiation
- Synchrotron Radiation
- Inverse (proton-electron) bremsstrahlung
- Electron-electron bremsstrahlung – becomes significant at energies above ~100 keV

## Anisotropic Electron Distribution

- photon

- 

- 0

- Massone et al., *The Astrophysical Journal*, 2004

## Compton Backscattered Photons (Albedo)

- Kasparova et al., *Solar Physics*, 2005

## Partially Ionized Thick Target

- Brown, *Solar Physics*, 1973

## Time Delays & Electron Propagation

- Aschwanden et al., *The Astrophysical Journal*, 1995

## Hard X-Ray PolarimetryX4.8 Flare of 23-July-2002

**20 - 40 keV Polarization**

**Mark McConnell, UNH**

## Model Flare Loop with Cusp

## Model Loop in Hard X-Rays

## Change with Plasma Density in Loop

## Computed Spectra

## Energy Deposition

## Presentations at the SPD Meeting

- Oral
- 27.05, Wednesday June 28, 10:50 AM – 12:25 PM: Wei Lu *X-ray Emission from Flaring Loops: Comparison Between RHESSI Observations and Hydrodynamic Simulations*
- 28.05, Wednesday June 28, 1:30 – 3:00 PM:  Linhui Sui *Motion of 3-6 keV Nonthermal Sources Along a Flare Loop*
- Poster
- 13.15: Gordon Holman *Understanding X-Ray Source Motions in a Solar Flare Loop*