Return-current Model Spectra and Enhanced Plasma Resistivity
From RHESSI Wiki
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gradual energy releases may also take place. | gradual energy releases may also take place. | ||
The hard X-rays come from | The hard X-rays come from | ||
- | [bremsstrahlung], | + | [https://en.wikipedia.org/wiki/Bremsstrahlung bremsstrahlung], |
- | a very inefficient emission mechanism, and | + | a very inefficient emission mechanism, and the mere existence of hard X-ray sources |
- | a large amount of energy. | + | implies a large amount of energy in energetic electrons. |
== The "number problem" == | == The "number problem" == | ||
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electrons in the active region corona, where the acceleration would | electrons in the active region corona, where the acceleration would | ||
take place. | take place. | ||
- | This has been referred to as the electron number problem in solar flares: | + | This has been referred to as the ''electron number problem'' in solar flares: |
(1) Where do all the electrons come from that produce the bremsstrahlung | (1) Where do all the electrons come from that produce the bremsstrahlung | ||
emission, which may last from a few seconds to a few minutes? | emission, which may last from a few seconds to a few minutes? | ||
(2) What keeps the electron beam stable to charge separation and | (2) What keeps the electron beam stable to charge separation and | ||
- | magnetic pinching? | + | [http://www.plasma-universe.com/Pinch magnetic pinching]? |
A co-spatial return current has been proposed to answer these questions. | A co-spatial return current has been proposed to answer these questions. | ||
This current would flow in the opposite direction to the direct | This current would flow in the opposite direction to the direct | ||
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acceleration region to the thick target (Ref. [1]), where electrons | acceleration region to the thick target (Ref. [1]), where electrons | ||
are collisionally stopped and generate bremsstrahlung. | are collisionally stopped and generate bremsstrahlung. | ||
- | In the following, we tested whether a return current model | + | In the following, we tested whether a return-current model can provide |
acceptable fits to the RHESSI spectra. | acceptable fits to the RHESSI spectra. | ||
- | We found that spectra with strong breaks can be fitted with | + | |
+ | We have found (Ref. [2]) that spectra with strong breaks can be fitted with | ||
a return current model. | a return current model. | ||
We fitted 206 spatially integrated spectra from 16 RHESSI flares with a | We fitted 206 spatially integrated spectra from 16 RHESSI flares with a | ||
co-spatial return-current model to deduce the potential drop that drives | co-spatial return-current model to deduce the potential drop that drives | ||
- | the return current and causes the spectral flattening | + | the return current and causes the spectral flattening. |
- | index, the electron flux at 50 keV, the low-energy cutoff and any high-energy | + | This fixes the injected spectral index, the electron flux at 50 keV, the low-energy cutoff and any high-energy |
cutoff at injection. | cutoff at injection. | ||
We then deduce plasma parameters such as the resistivity. | We then deduce plasma parameters such as the resistivity. | ||
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obtained from the RHESSI spectral ts! | obtained from the RHESSI spectral ts! | ||
- | == Return current collisional thick-target model: RCCTTM == | + | == Return current collisional thick-target model: the RCCTTM == |
The assumptions of the model are as follows: | The assumptions of the model are as follows: | ||
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<li> | <li> | ||
Injected single power-law | Injected single power-law | ||
- | electron | + | electron flux density distribution with a sharp low-energy cutoff E<sub>c</sub> |
and a high-energy cutoff E<sub>high</sub>. | and a high-energy cutoff E<sub>high</sub>. | ||
<li> | <li> | ||
Steady-state electric-field-driven return | Steady-state electric-field-driven return | ||
current with electrons streaming along the loop, balanced by a | current with electrons streaming along the loop, balanced by a | ||
- | co-spatial return current in the opposite direction | + | co-spatial return current in the opposite direction, for which '''j'''<sub>RC</sub> |
= '''j'''<sub>direct</sub>. | = '''j'''<sub>direct</sub>. | ||
<li> | <li> | ||
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energy by Coulomb collisions. | energy by Coulomb collisions. | ||
<li> | <li> | ||
- | + | The observed hard X-ray spectral flattening at lower energies is due to the return current. | |
- | energies is due to the return current. | + | |
This is achieved by choosing flare spectra with strong enough breaks | This is achieved by choosing flare spectra with strong enough breaks | ||
- | that cannot be explained with non-uniform target ionization and albedo alone. | + | that cannot be explained with non-uniform target ionization and X-ray Compton |
- | + | [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=42 albedo] alone. | |
+ | We first fit the spectra with a spectral model having an insignicant low-energy cutoff (at 2 keV) | ||
to insure that the contribution to the spectral flattening at lower | to insure that the contribution to the spectral flattening at lower | ||
- | energies is due | + | energies is due solely to the potential drop. |
We then fix the potential drop and fit the spectra with the highest | We then fix the potential drop and fit the spectra with the highest | ||
low-energy cutoff that keeps the Χ<sup>2</sup> within one sigma of | low-energy cutoff that keeps the Χ<sup>2</sup> within one sigma of | ||
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Electrons are accelerated near the top of the loop, and lose their | Electrons are accelerated near the top of the loop, and lose their | ||
energy due to the potential drop along the loop before they reach | energy due to the potential drop along the loop before they reach | ||
- | the chromosphere, where the density is high enough for | + | the chromosphere, where the density is high enough for |
- | collisions to dominate. | + | [https://en.wikipedia.org/wiki/Coulomb_collision Coulomb collisions] to dominate. |
]] | ]] | ||
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breaks or flattenings at lower energies. Figure 2 shows fit parameters | breaks or flattenings at lower energies. Figure 2 shows fit parameters | ||
from the flare SOL2002-06-02. | from the flare SOL2002-06-02. | ||
- | The fit parameters of our return current model (currently in OSPEX under | + | The fit parameters of our return current model (currently in RHESSI's |
- | thick2 rc) are the return-current potential drop, the spectral index from | + | [http://hesperia.gsfc.nasa.gov/~dennis/OSPEX/The_Basics/ OSPEX] software under |
+ | "thick2 rc") are the return-current potential drop, the spectral index from | ||
the acceleration region, the electron | the acceleration region, the electron | ||
flux at 50 keV, and the low-energy cutoff. | flux at 50 keV, and the low-energy cutoff. | ||
- | This | + | This was a rare case for which a high-energy |
- | cutoff significantly improved the spectral fits in | + | cutoff significantly improved the spectral fits in four time intervals. |
[[File: 259f2.png|thumb|center|600px|Figure 2: | [[File: 259f2.png|thumb|center|600px|Figure 2: | ||
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An interesting parameter is the resistivity, which we deduce from | An interesting parameter is the resistivity, which we deduce from | ||
- | the potential drop and the electron flux density using Ohm's law, | + | the potential drop and the electron flux density using |
+ | [https://en.wikipedia.org/wiki/Georg_Ohm Ohm's] law, | ||
with the electric field given by the potential drop and the loop | with the electric field given by the potential drop and the loop | ||
half-length, and the current density given by the electron flux density | half-length, and the current density given by the electron flux density | ||
- | (we estimate the source sizes from RHESSI | + | (we estimate the source sizes from RHESSI images of the loop |
and footpoint area). | and footpoint area). | ||
We proceeded then to compare this inferred resistivity with the | We proceeded then to compare this inferred resistivity with the | ||
- | theoretical Spitzer resistivity at the temperature derived from the | + | theoretical |
+ | [http://www.sns.ias.edu/~jnb/Papers/Popular/Spitzer/spitzer.html Spitzer] resistivity at the temperature derived from the | ||
RHESSI spectral fits and at a much lower, chromospheric, temperature. | RHESSI spectral fits and at a much lower, chromospheric, temperature. | ||
The Spitzer resistivity is due to electron-ion collisions and is | The Spitzer resistivity is due to electron-ion collisions and is | ||
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The return-current collisional thick-target model (RCCTTM) | The return-current collisional thick-target model (RCCTTM) | ||
provides acceptable fits to RHESSI data with strong spectral breaks. | provides acceptable fits to RHESSI data with strong spectral breaks. | ||
- | The flattening of the | + | The flattening of the X-ray spectrum is explained by a potential drop |
from the acceleration region to the thick-target. | from the acceleration region to the thick-target. | ||
<li> | <li> | ||
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plasma that electrons encounter along their path to the thick target. | plasma that electrons encounter along their path to the thick target. | ||
We find that these resistivities are typically enhanced by one to eight | We find that these resistivities are typically enhanced by one to eight | ||
- | orders of magnitude compared to the Spitzer values at T | + | orders of magnitude compared to the Spitzer values at T around 20 MK. |
In cases where the resistivity is higher than the Spitzer value at | In cases where the resistivity is higher than the Spitzer value at | ||
T = 10<sup>4</sup> K, which could feasibly be present along the legs | T = 10<sup>4</sup> K, which could feasibly be present along the legs |
Revision as of 16:58, 29 August 2015
Nugget | |
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Number: | 259 |
1st Author: | Meriem Alaoui |
2nd Author: | and Gordon Holman |
Published: | 31 August 2015 |
Next Nugget: | |
Previous Nugget: | A Failed Eruption with a Two-Ribbon Flare |
List all |
Contents |
Introduction
Solar flares involve sudden brightening across the whole range of the electromagnetic spectrum, and in particular the hard X-ray emission has proved to be a crucial factor in deciphering flare physics. The most common hard X-ray emission is an "impulsive" source that seems to define the main energy release of a flare, although other more gradual energy releases may also take place. The hard X-rays come from bremsstrahlung, a very inefficient emission mechanism, and the mere existence of hard X-ray sources implies a large amount of energy in energetic electrons.
The "number problem"
In the late 1970's several authors estimated the number of electrons in the downward-streaming beam thought to be required to explain the observed X-ray bremsstrahlung emission, and concluded that it must be several orders of magnitude higher than the number of electrons in the active region corona, where the acceleration would take place. This has been referred to as the electron number problem in solar flares: (1) Where do all the electrons come from that produce the bremsstrahlung emission, which may last from a few seconds to a few minutes? (2) What keeps the electron beam stable to charge separation and magnetic pinching? A co-spatial return current has been proposed to answer these questions. This current would flow in the opposite direction to the direct current created by the downward-streaming electrons. We consider it here as co-spatial and steady-state, serving to resupply the acceleration region with electrons from the thermal background and also to ensure that the beam is stable. The return current affects the shape of the X-ray spectrum by creating a flattening at lower energies due to a potential drop from the acceleration region to the thick target (Ref. [1]), where electrons are collisionally stopped and generate bremsstrahlung. In the following, we tested whether a return-current model can provide acceptable fits to the RHESSI spectra.
We have found (Ref. [2]) that spectra with strong breaks can be fitted with a return current model. We fitted 206 spatially integrated spectra from 16 RHESSI flares with a co-spatial return-current model to deduce the potential drop that drives the return current and causes the spectral flattening. This fixes the injected spectral index, the electron flux at 50 keV, the low-energy cutoff and any high-energy cutoff at injection. We then deduce plasma parameters such as the resistivity. This resistivity was found to be up to eight orders of magnitude greater than the classical resistivity deduced from temperatures obtained from the RHESSI spectral ts!
Return current collisional thick-target model: the RCCTTM
The assumptions of the model are as follows:
3. Fitted parameters and resistivity in the plasma
We find that the RCCTTM provides good ts to RHESSI spectra with strong breaks or flattenings at lower energies. Figure 2 shows fit parameters from the flare SOL2002-06-02. The fit parameters of our return current model (currently in RHESSI's OSPEX software under "thick2 rc") are the return-current potential drop, the spectral index from the acceleration region, the electron flux at 50 keV, and the low-energy cutoff. This was a rare case for which a high-energy cutoff significantly improved the spectral fits in four time intervals.
An interesting parameter is the resistivity, which we deduce from the potential drop and the electron flux density using Ohm's law, with the electric field given by the potential drop and the loop half-length, and the current density given by the electron flux density (we estimate the source sizes from RHESSI images of the loop and footpoint area). We proceeded then to compare this inferred resistivity with the theoretical Spitzer resistivity at the temperature derived from the RHESSI spectral fits and at a much lower, chromospheric, temperature. The Spitzer resistivity is due to electron-ion collisions and is proportional to T3/2.
Conclusions
In Ref. [2] we describe this project in more detail, and draw the following basic conclusions.
References
[1] "Understanding the Impact of Return-current Losses on the X-Ray Emission from Solar Flares"
[2] Alaoui & Holman, article in preparation
RHESSI Nugget Date | 31 August 2015 + |
RHESSI Nugget First Author | Meriem Alaoui + |
RHESSI Nugget Index | 259 + |
RHESSI Nugget Second Author | and Gordon Holman + |