Microwave Images of a Single-Loop Flare: Observations and Simulations
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|1st Author:||Alexey Kuznetsov|
|2nd Author:||Eduard Kontar|
|Published:||28 April 2014|
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Solar flares are known to produce intense radio emission that exhibits complicated and diverse temporal and spectral patterns. In the microwave range (at the frequencies above 5 GHz), the emission is formed primarily by the gyrosynchrotron radiation generated by accelerated electrons in coronal magnetic loops. Therefore the microwave observations can be used to study the magnetic field, plasma and accelerated electrons in the flaring loops (cf RHESSI Nugget 198). Since the microwave emission is generated at relatively large heights (in the solar corona), it carries valuable information about the accelerated electrons in those regions of the flaring loops where other diagnostic methods (e.g., based on the hard X-ray observations) often fail.
Direct inversion of the solar radio data is impossible (cf RHESSI Nugget 28). Therefore, to recover the emission source parameters, we have to use a forward-fitting approach, when we create some model of the flaring region, calculate the microwave emission from that region, compare the simulation results with observations, adjust the model parameters as necessary, and this process is repeated until an acceptable agreement between the simulations and observations is achieved. The key step in the above mentioned algorithm is calculation of the microwave emission. The recently developed IDL program GX Simulator (Ref. ) is a powerful, versatile and easy-to-use tool for 3D simulations of gyrosynchrotron emission from the solar flares. We have applied this tool to reconstruct the properties of the accelerated electrons in the 21 May 2004 flare (SOL2004-05-21) that had a relatively simple structure both in X-rays and in radio. We have used the microwave images obtained by the Nobeyama Radioheliograph at the frequencies of 17 and 34 GHz.
This flare occurred in active region AR 10618 at S10E53. The microwave and hard X-ray lightcurves of the flare (obtained by the Nobeyama Radiopolarimeters (NoRP) and RHESSI, respectively) demonstrate a good correlation (see Fig. 1a). In the 34 GHz microwave images (see Fig. 1b), we see a well-defined loop-shaped structure. The same structure is visible in the RHESSI hard X-ray images (see Fig. 1b): at lower energies (12-25 keV), the emission is peaked at the loop top; at 25-50 keV, the entire loop (both the loop top and the footpoints) is visible; finally, at 50-100 keV, only the footpoints are visible. According to the SOHO/MDI magnetogram (see Fig. 1b), the active region under consideration contained two sunspots with strong magnetic fields of opposite polarities, whose locations agree well with the footpoints of the supposed flaring loop. Therefore we conclude that the 21 May 2004 flare had a relatively simple single-loop structure (see the previous Nugget on X-ray loops), which makes it a good candidate for modelling. We note also that neither the RHESSI lightcurves nor the images reveal a noticeable X-ray flux at energies above 100 keV.
GX Simulator is the recently developed interactive IDL tool (e.g., ; see Fig. 2). This tool allows us:
- to create a 3D magnetic field model based on the extrapolation of a photospheric magnetogram (in this study, we have used the linear force-free extrapolation);
- to select a magnetic field line and coronal magnetic flux tube of interest;
- to populate that magnetic tube with thermal and nonthermal electrons with specified parameters;
- to calculate 2D maps of the resulting gyrosynchrotron emission at different frequencies (using the new fast gyrosynchrotron software described in Ref. ).
GX Simulator is currently available as a part of SolarSoft (the package gx_simulator).
The aim of our simulations was to reproduce both the observed microwave spectrum and the spatial distribution in a realistic magnetic field. We considered the 1D profiles of the microwave brightness temperature along the suggested loop axis (that is shown in Fig. 1b) at the frequencies of 17 and 34 GHz. At the first step, we have searched for the magnetic tube with the required shape and size, by comparing the extrapolated magnetic field lines with the microwave images and varying the linear force-free magnetic parameter α.
At the next step, we have searched for the appropriate spatial and energy distribution of the accelerated electrons along the flaring loop. We have found that a simple (e.g., exponential or gaussian) spatial distribution of the accelerated electrons does not allow us to reproduce the observations. Therefore we have chosen a more complicated spatial distribution consisting of four Gaussians. By varying the parameters of that model distribution (currently, this variation should be performed manually), we achieved an agreement between the simulated and observed microwave brightness profiles with an accuracy of about 10% or better. The accelerated electrons had a rather hard spectrum with the spectral index δ of about 2.
The chosen “active” magnetic tube, the inferred spatial distribution of the accelerated electrons along the loop axis, and the calculated microwave image are shown in Fig. 3. This figure also demonstrates the total (spatially integrated) emission spectra. We can see that there is a good agreement between the simulated and observed spectra – at least, at high frequencies. At lower frequencies (4 GHz and below), the observed emission is stronger than the simulated one possibly due to a contribution of either plasma emission or additional gyrosynchrotron sources with weak magnetic field.
The accelerated electrons in this event were strongly concentrated near the loop top (see Fig. 3) – probably, as a result of trapping in the inhomogeneous magnetic field. This feature explains the non-detection of hard X-rays at high energies (>100 keV), because such X-rays are produced mainly in the dense plasma in the loop footpoints, whereas in the considered event the concentration of the high-energy electrons in the loop footpoints was very low.
Spatially-resolved microwave observations together with 3D simulations can be an effective tool for diagnosing the energetic electrons in solar flares. However, this diagnosing method currently requires some additional data – namely, the extrapolated magnetic field. We anticipate that the multiwavelength imaging radio/microwave observations with new instruments might allow us to put observational constraints on the magnetic field as well.
For more details of the study, see the paper .