The Rise and Fall of The Low Energy Cut Off

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{{Infobox Nugget
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|name = Nugget
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|title = Nugget Details
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|number = 89
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|first_author = Ewan Dickson
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|second_author = Eduard Kontar
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|publish_date = 17 November 2008
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|next_nugget = [[TBD]]
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|previous_nugget = [[SEPs Link not Confirmed]]
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== Introduction ==
== Introduction ==

Revision as of 16:05, 13 November 2008


Nugget
Number: 89
1st Author: Ewan Dickson
2nd Author: Eduard Kontar
Published: 17 November 2008
Next Nugget: TBD
Previous Nugget: SEPs Link not Confirmed
List all



Contents

Introduction

A typical spatially integrated electron spectrum of a solar flare is often viewed as a combination of thermal and non-thermal components: the former follows Maxwell distribution and the latter is a power-law or broken power-law. As much as the power-law fit is used in solar flare physics a pure power law spectrum diverges for small energies, making the total number of solar flare electrons infinite. To combat this artifact a low energy cut off is often imposed at some (arbitrary) value. As the soft and hard X-ray spectra apparently merge together seamlessly this addition has always been somewhat controversial. The ambient plasma has a finite temperature and the power-law like spectrum should merge with the background Maxwellian at near thermal energies. Therefore the death to the low energy cut off has been declared as the finite temperature limits the total energy.

While the suggested scenario seems like the death to the arbitrary value of low energy cut off, the nails into the coffin of the low energy cut off have been recently unscrewed by RHESSI observations.High resolution RHESSI spectra often require the introduction of a low energy cut off well above the thermal energies to make a power-law fit work. More sophisticated techniques based on the regularization theory have lead to the same puzzling conclusion: the electron spectrum should dip How can the observations of dips in the inverted electron spectra be explained?

Albedo

It is believed that Compton scattering of X-rays in the lower solar atmosphere could distort an observed X-ray spectra detected from solar flares. Compton backscattering is at its highest in the range 30 - 100 keV and for the solar events near the disk centre. The addition of a scattered component causes a flattening of the spectrum at low energies. This effect could then lead to spectra appearing to require a cut off. To determine the electron flux regularised inversion was used, the advantage of this technique being that it is model independent, whereas forward fitting relies on parametrically given functions (usually a thermal component plus a power law) which has the disadvantage that it can easily miss unexpected, but real, features such as a dip.

The technique of applying a correction for albedo and then using inversion to determine the electron spectrum of flares which appeared to require a low energy cut off was first performed in 2005 (see here and here for details). It was found that the correction did remove the dip from the electron spectrum for a few events.

How common is the low energy cut off?

To determine whether the removal of the dip is just an effect which occurs in the particular flares examined or whether it is a more general systematic effect a statistical survey of flares in the RHESSI catalogue has been conducted. Although for most flares the thermal component completely dominates at low energies and so would hide any genuine cut off, there are flares with weak thermal component and these are the flares which suggest a low energy cut off is necessary. This is characterised by the low value γ0, the photon spectral index fitted only in the range 15 to 20 keV.

In total 177 flares have been found (see here for details). For each of these flares the electron spectra has been calculated and examined for unusual features such as dips, and 18 such flares were found with a significant dip. Figure 1 shows an example of such event. An albedo correction has then been applied, after which none of the flares show a dip (Figure 1).

Figure 1: Plot of electron distribution spectrum for the 1 April 2004 23:00 UTC solar flare. The blue line denotes the uncorrected electron spectrum and the green line denotes the electron spectrum after correction for albedo. Both lines are plotted with 1σ error bars. The dip depth, d, is shown as the difference between the minimum and the following maximum.

The dips seem to occur in a fairly narrow energy range with minima of between 13 and 19 keV. As the position of each flare should have a significant effect on the albedo the heliocentric angle of each flare showing a dip has been calculated.

Figure 2a:Histogram of the 18 events with a significant dip as a function of μ, the cosine of the heliocentric angle of the flare.
Figure 2b:Histogram showing the percentage of flares with a dip as a function of spectral index γ
Figure 2

It has been found that the flares showing dips are far more likely to occur near the solar centre (high μ). This is consistent with the theory that the flattened spectra, and hence the dips, are caused by the influence of the albedo .Of the flares found with dips over 70 % occurred at points with a μ>0.5.As justification for the choice of flares studied, the number of flares is calculated as a percentage of total flares studied for given ranges in γ0 (Figure 2). As expected, dips are far more likely to occur for flares with a low value of γ0 (Figure 2).

Conclusions

The small number of flares found with dips (18 out of 177) suggests that the vast majority of flares are not so flat that they require a low energy cut off. Of the flares found with flat spectra and spectral indices between 1.5 and 2 over 60% show a dip (Figure 2). In all of the flares studied the dip appears to be consistent with the albedo model. Observations which had previously required a low energy cut off can be also understood in terms of the spectrum being the result of albedo distortion. Most of the flattened spectra are found in events where the flare occurs close to the disk centre, and therefore where the albedo has the greatest effect. Even in the near solar limb events the correction for albedo still alters the spectrum and can remove the need for a dip in the spatially integrated electron spectrum. The results also suggest that if there is a low energy cut off it is buried deeper in the thermal component and therefore has a value below ~1 keV.

As even isotropic emission correction for albedo can satisfactorily explain the flattening of spectra and dips in the electron spectra it seems possible that this may be the end for the low energy cut off in the mean electron spectrum.

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