Observing Solar Flare X-ray Polarization with Prospective CubeSat Missions

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Nugget
Number: 398
1st Author: Natasha JEFFREY
2nd Author:
Published: 4 January 2021
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Contents

Introduction

X-ray observations show us that solar flares are extremely efficient particle accelerators, but the method of acceleration (e.g., turbulence, shock acceleration) is debated. Many of the essential diagnostics of acceleration remain ill-determined: the directivity (the electron velocity angle relative to the guiding magnetic field); the magnetic field itself; the high-energy cutoff, if any; the low-energy cutoff, if any; the spatial extent of the acceleration region; the time profile.

We already do have observations of the bremsstrahlung and gyrosynchrotron emission spectra, of course. But since the birth of X-ray solar physics, X-ray polarization has been under-studied compared to other X-ray observables. Observations and studies exist, but many results have large uncertainties (Ref. [1]). However, the X-ray polarization spectrum is an observable that can provide a direct link to several key properties of energetic electrons, including the directivity and high energy cutoff, properties that are difficult to obtain from the observation of the X-ray flux spectrum from a single viewing angle.

Past studies, as listed in our present work (Ref. [2]), have extensively dealt with theories and model calculations. See also past Nuggets 119, 130, and 165. We have now used new electron and X-ray transport simulations that account for collisions, turbulent scattering and X-ray albedo (Compton backscattering of X-rays in the photosphere). We have shown that X-ray polarization, specifically the degree of polarization (DOP, %), can be used to constrain the directivity (anisotropy) and high energy cutoff of flare-accelerated electrons together. Our main aim was not to reiterate past studies but to provide results showing how prospective new observations, even with relatively cheap CubeSat missions, can be used to determine these vital acceleration parameters, even without imaging information.

Polarization without imaging information

In Figure 1, we present the new computational results: the DOP as a function of energy for different assumptions about the properties of accelerated electrons and the flaring corona, such as electron directivity (left panel), high-energy cutoff of the electron spectrum (middle panel) and variations in coronal turbulent scattering levels (right panel). The figure presents spatially integrated results, i.e. no imaging information (the Sun as a star) and for a flare located at a heliocentric angle of 60 degrees. The lines at the top show spectral ranges for three proposed new instruments.

Figure 1: The modeled degree of polarization (DOP) as a function of energy for various properties. Left: DOP vs. energy for different electron directivities from beamed (pink) to isotropic (green), middle: DOP vs. energy for different electron high energy cutoffs E_H from 100 keV (pink) to 300 keV (green) and right: DOP vs. energy for different levels of turbulent scattering from some level of scattering (green, blue) to no scattering (pink). The vertical dotted line at 20 keV denotes the chosen low energy cutoff in the simulation.

Directivity: The directivity of bremsstrahlung emission is the traditional property derivable from the X-ray polarization degree with the DOP increasing with increased directivity. Especially with realistic electron and X-ray transport simulations, even spatially integrated DOP observations could provide detailed information about the electron anisotropy, with any directivity clearly observable in the DOP spectrum. This is true even in the presence of X-ray albedo, where some fraction of the X-rays are Compton backscattered in the photosphere. In general, the albedo component acts to decrease the observed directivity of beamed distributions and slightly increase the directivity of isotropic distributions.

High-energy cutoff: The DOP spectrum is not a one-trick pony; it contains abundant information regarding the plasma environment and electron properties. The DOP spectrum is greatly affected by the highest energy electrons in the distribution. If undetected high-energy electrons are present in the distribution then they decrease the DOP at all energies in the spectrum due to the angular dependence of the bremsstrahlung cross section. This effect competes with the directivity measurement.

Coronal turbulent scattering: Ref. [3] described turbulent scattering in a flare using a combination of X-ray and microwave observations. However, the presence or absence of turbulent scattering in the flaring corona is generally difficult to constrain, and unknown from the X-ray flux spectrum alone. The modeling results show that the absence of turbulent scattering can be determined from the DOP spectrum, since even very low levels of turbulent scattering will remove any trace of directivity even if the distribution is initially beamed.

Using spatially integrated X-ray flux and X-ray polarization observations together

A fuller understanding of flare acceleration processes will come from missions capable of both X-ray flux and polarization spectral measurements together. In Figure 2, we present one practical way of determining a range of accelerated electron properties using the X-ray flux and DOP spectra together. The black points represent X-ray flux and DOP data generated from a simulation. Applying the "warm-target" model (see Nugget 264) to the X-ray flux spectrum helps to constrain the coronal plasma properties and the following acceleration parameters: low energy cutoff E_c, the spectral index \delta and the rate of acceleration \dot{N}. Using the constrained X-ray flux parameters, then the resulting X-ray DOP spectra should only be dependent upon the high-energy cutoff E_H, directivity and turbulent scattering (if present, and ignoring any other non-collisional transport mechanisms in this example). In this example, we determine from the DOP spectra that the accelerated electron distribution is close to beamed, has E_H\approx 100 keV, and no turbulent scattering is present in the corona.

Figure 2: One simulation example of how the X-ray flux (left) and DOP (right) spectra can be used together to estimate the properties of the accelerated electron distribution. Applying the warm target function (f_thick_warm in OSPEX) to the X-ray flux spectrum (black points) helps to constrain the coronal plasma properties and the following acceleration parameters: low energy cutoff E_c , the spectral index \delta and the rate of acceleration \dot{N}. Once these parameters are constrained, the high-energy cutoff, directivity and turbulent scattering can be constrained from the DOP spectrum (black points right panel; coloured lines represent different simulation runs/fits).

Summary

X-ray polarimetry is a vital tool for constraining the solar flare acceleration mechanism especially when used alongside the X-ray flux spectrum. However, it has been overlooked as a useful diagnostic and often seen as a one-trick pony for detecting directivity (emission anisotropy). Just like the flux spectrum, the X-ray DOP spectrum is highly sensitive to many, and currently unknown, properties such as the accelerated electron pitch-angle distribution, highest energy accelerated electrons and the presence of (or lack of) turbulence in the corona. We have simulation tools available to analyse the X-ray DOP spectrum in detail, if the observations become available. Although imaging polarimetry is always highly desired, our results show that spectro-polarimeters without imaging capabilities can also provide strong constraints on these unknown properties.


References

[1] "Deducing Electron Properties from Hard X-ray Observations"

[2] "Probing solar flare accelerated electron distributions with prospective X-ray polarimetry missions"

[3] "Diffusive transport of energetic electrons in the solar corona: X-ray and radio diagnostics"

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