Radio polarimetric imaging of the solar corona at low frequencies

Abstract

The coronal magnetic field (B) plays an important role in the formation, evolution, and dynamics of the small, as well as large scale structures in the solar corona. Measurements of the coronal magnetic field strengths, particularly in the radial distance range ≈ 1.1 - 3.0 R (R is the radius of photospheric Sun) is presently difficult because of practical reasons. Polarization observations, by measuring the Stokes-V parameter of the received radio signal, are generally used as a tool to measure the magnetic field strength associated with the radio emission; the latter is one of the widely pursued areas of research in the solar coronal physics, in addition to the currently available but limited methods of estimating the magnetic field strength using simultaneous radio imaging and spectral observations. Ground based radio observations provide an excellent tool to observe and study the corona in the aforesaid height range. Therefore, the primary objectives of this thesis are to : 1. design, develop and characterize spectro-polarimeter that can receive the polarized radio emission (at low frequencies) from the Sun with high temporal, spectral resolution, etc.; 2. compare the data obtained using the new instruments with the existing instruments in order to improve the observing capabilities of new instruments; 3. estimate the magnetic field strengths from the observed polarized radio emission associated with various forms of solar coronal activities observed at other wavelength parts of the electromagnetic spectrum. As for the first objective is concerned, I designed and developed two spectropolarimeters : i Near ionospheric cut-off frequency spectro-polarimeter that can operate over 15 - 85 MHz frequency range. ii Wide-band spectro-polarimeter that can operate over 50 - 500 MHz frequency range. For the first spectro-polarimeter system, I designed and characterized a Log-Periodic Dipole Antenna (LPDA) that works in the 15 - 85 MHz range. The VSWR (Voltage Standing Wave Ratio) of the antenna is ≤ 3.0 throughout the band. It has a directional gain of 6 dBi and has an effective collecting area of ≈ 0.3λ 2 . Two identical antennas were fabricated and kept in mutually orthogonal orientations to arrange the frontend. Since the signal strength received by the iii antennas from the background sky were found to vary drastically over the observing bandwidth it was difficult to handle the entire frequency band with a single digital backend system. Therefore, the signal was split into two sub-bands (15 - 25 MHz & 25 - 85 MHz) using appropriate filters designed as part of the thesis work. The signals were then amplified using Low Noise Amplifier (LNA) and were fed to a digital backened receiver. The latter consists of an Analog to Digital Converter (quad ADC) and a Field Programmable Gate Array (FPGA). I have characterized the ADC for its linear range of operation, signal-to-noise ratio (SNR), spurious free dynamic range (SFDR), etc. The FPGA used in the digital receiver is ROACH (Reconfigurable Open Architecture Computing Hardware) designed by CASPER community1 . The spectro-polarimeter was implemented by me on ROACH FPGA to process the signals real time using Fast Fourier transforms (FFT), polyphase filter banks (PFBs), correlators, etc. The data acquisition system consists of a vector accumulator, packetizer, and a 10 Gbe data transfer module and a PC. As a part of calibration, the Galactic Center (GC) was observed with the entire system and the Stokes-I and Stokes-V flux profiles were obtained. MATLAB and Python codes were written to analyze the observed spectro-polarimetric data. The spectra obtained with the FPGA based system and the old Spectrum Analyzer (SA) based spectro-polarimeters were compared to study the performance of the former. The SA is a product of M/s. Agilent Technologies. I have developed the data acquisition program for recording the signal from the antenna system desgined by me. In that study, it was found that the SNR of the FPGA system was 10 times better than the SA system. Also, the new instrument was able to detect weak bursts in the presence of strong bursts as the dynamic range (≈ 48 dB) got improved in addition to sensitivity (≈ 10−6 mW). Comparison for the latter was done by integrating data from both instruments for a time interval of 1 sec and for a bandwidth of 1 MHz. The FPGA system is better than the SA based system because the latter works on sweep mode using the superheterodyne principle. It takes up to 4 ms to sweep through the observing band and takes ≈ 240 ms to write the data; It does not take any observations while writing the data. Whereas the FPGA backend neither sweeps nor has an idle time. So, it fetches more data as compared to SA system during an acquisition period. For the second spectro-polarimeter system, I designed and characterized a 1 https://casper.ssl.berkeley.edu/wiki/ROACH iv compact Cross Polarized Log-Periodic Dipole Antenna (CLPDA) that works in the 50 - 500 MHz range. The VSWR of the antenna is < 2.0 throughout the band. It has a directional gain of about 6.9 dBi, an effective collecting area of ≈ 0.3 λ 2 and a polarization cross-talk of about -30 dB. The outputs of the CLPDA were amplified using LNAs and were given to Quadrature Hybrid (QH). The latter is a device that has two transmission lines pass close enough to each other for coupling the signal travelling on one line with the other line; This splits the input signal into two parts whose amplitude are nearly equal but with 90o phase difference between them. The outputs of the QH were given to two commercial SA to record the Stokes-I and Stokes-V flux of the received radio waves. The entire setup was characterized by feeding known linear and circularly polarized signals; The error in the degree of circular polarization (DCP) was measured to be ≤ 2 %. Since the FPGA was not available in the beginning, SA based system was developed. But, later on it became available and a FPGA based system was also developed with a spectral and temporal resolution of 100 kHz and 100 ms, respectively. Both systems were calibrated by observing the GC. Then both of them were kept for solar observations to compare their performances. It was found that the SNR of the FPGA based system was higher than the SA based system by 18 dB. Also, the new instrument was able to detect weak bursts in the presence of strong bursts as the dynamic range (≈ 48 dB) got improved in addition to sensitivity (≈ 10−6 mW). With the first spectro-polarimeter, a narrow band (24 - 28 MHz) type-II radio burst was observed on July 23, 2016. It is well known that the type II solar radio bursts are considered to originate from plasma waves excited by magnetohydrodynamic (MHD) shocks and converted into radio waves at the local plasma frequency and/or its harmonics. They are the direct diagnostic of MHD shocks in the solar atmosphere. A closer inspection of the above type II burst indicated that it is split, and appears as two bands (upper frequency band [UFB] and lower frequency band [LFB]). The LFB and UFB bands relate to emission from the coronal regions ahead of and behind the associated MHD shock, respectively. The type II burst was found to have temporal association with a white-light Coronal Mass Ejection (CME) observed by the SOHO/LASCO-C2 and STEREO-A/COR1 coronagraphs. The onset of the type-II burst was almost at the peak time of the Hα and X-ray flares occurred around the same time. Using the spherically symmetric inversion technique, the electron density (Ne) of the background solar corona and during the CME as well were determined using the measured polarized brightness from the v coronagraph data. The values are 0.4 × 106 cm−3 and 2.2 × 106 cm−3 (≈ 5 times the background electon density), respectively. Combining the background density estimates of the two coronagraphs a 5th order polynomial was fitted to describe the density over the radial distance range 1.5 - 6.4 R . Also from the observed type-II burst data, the electron density corresponding to the observed frequency was determined. Its value is 2.2 × 106 cm−3 . Using the electron density model and the drift rate measured from the LFB and UFB of the type-II burst, the velocity of the agent responsible for the generation of type-II was calculated to be ≈ 800 km/s. The latter is almost equal to the speed of the associated CME observed with the above mentioned coronagraphs. Since one of the objectives of this thesis work is to estimate the coronal magnetic field strength, using B(G) = 5.1 × 10−5vAfp (vA is the Alf´ven speed and fp is the plasma frequency), the strength of the magnetic field was estimated. The value varies from 0.51 to 0.48 (± 0.02) Gauss in the radial distance range 2.65 - 2.82 R . The white-light data were also used to estimate B, by following shock stand-off distance method. It was found that B = 0.32 G at r = 3.11 R (STEREO-A/COR1) and B = 0.12 G at r = 4.40 R (SOHO/LASCO-C2). By combining the radio and white-light measurements of B, a single power-law for B was obtained. As per that B(r) = 6.7×r −2.6 in the radial distance range 1.8 - 4.6 R . The power-law index is in good agreement with the values published already. With the SA based second spectro-polarimeter, a type-V burst was observed on May 02, 2016. Type-V bursts are the signature of propagating non-thermal electron beams along curved paths in the solar atmosphere. They are due to synchrotron radiation when the electrons moves spirally in the solar magnetic fields with near relativistic speed. The DCP of the burst was found to vary from 1 % to 6 %. Assuming second harmonic plasma emission, the magnetic field strength was estimated using B = fp×DCP 2.8×a(θ) , where θ is the viewing angle. The power-law fit to the data points gave B(r) = 6.3 × r −3.9 in the radial distance range 1.1 - 1.9 R . With the FPGA (ROACH) based second spectro-polarimeter, a high frequency type-II burst (50 - 430 MHz) was observed on November 4, 2015. The bursts were attributed to MHD shocks driven by flare blast waves. GRAPH also imaged the burst at 80 MHz. SOHO/LASCO-C2 running difference image showed the onset of a CME erupted around that time. Wind/WAVES instrument also observed the above burst upto 14 MHz. GOES-15 recorded an M1.9 class soft X-ray flare (and Hα flare as well) from AR 12445 located at N14W64 on the Sun during the vi above time. SDO/AIA showed Extreme Ultra-Violet (EUV) wave associated with the above AR. The empirical relation between the frequency of the type-II burst and its radial height, as given by Gopalswamy, was used to determine the electron density. The height vs time details of the CME leading Edge (LE) using whitelight data, EUV wavefront LE from SDO/AIA data, location of type-II burst using radio observations, showed a close association between type-II burst and CME LE. The superimposition of shock speed at different instant of time and the X-ray light curve showed that the onset time of type-II is close to the time of maximum shock speed. Also, the consistency in the speeds and the initial agreement between their h–t measurements indicate that the type II burst and the EUV wave are both driven by the same CME. The probable location of the type II burst (when the shock speed was at maximum) was estimated based on its deprojected location and the kinematics of the associated MHD shock. Calculations indicate that the burst should have been located at ≤ 1.12 R . This is reasonably consistent with the location of the CME LE in the SDO/AIA 211 ˚A image. There is a good correspondence between the time profile of the type-II burst shock speed and the X-ray light curve of the flare. The cross-correlation coefficient between the shock speed and the X-ray flux is ≈ 0.86. Furthermore, the maximum in both cases occurred at almost the same time. And finally the strength of the magnetic field associated with this event was estimated to be ≈ 3 G at about 1.5 R . Yet another type-II burst was observed on March 16, 2016 with the newly built spectro-polarimeter. The frequency range of the burst is ≈ 50 - 90 MHz. The peak DCP varies in the range ≈ 8 - 11 %. It has a split-band structure. It is associated with a C2.2 class soft X-ray (SXR) flare (observed with GOES-15 satellite) from the NOAA sunspot active region AR12522 located at N12W83. The optical data were obtained in EUV at 211 ˚A with the SDO/AIA, and in whitelight with STEREOA/COR1 and the SOHO/LASCO. COR1 observed a CME around the same time as the type-II burst. SDO/AIA showed a flux rope structure and a diffuse shock ahead of it, beneath the CME location. The radial height of the layers that are responsible for the type-II emission were calculated at 40 and 26.7 MHz; The values are 1.6 and 1.9 R . The corresponding electron densities are 1.98 × 107 cm−3 and 8.8 × 106 cm−3 , respectively. As mentioned earlier, the spherically symmetric inversion technique was used to calculate the electron density from white-light observations. A power-law fit to all the data points gives Ne = 2.3 × 108 r −5.3 in the range r = 1.6 − 2.2 R . The same power-law was used to obtain the electron vii density over the height (1.1 - 1.3 R ) of the flux rope and the values were found to be in good agreement with those published earlier. Combining all the heighttime data, the trajectory of the CME was constructed. From the latter, it was inferred that the CME had undergone a high acceleration during its onset phase whereas it is constant in the coronagraph field of view. From the SDO/AIA data, using shock stand-off distance method, the strength of the magnetic field (B) were determined at different radial heights. And, with the band splitting technique, radio spectro-polarimeter data were used to determine B, again at different radial heights. Finally a common power-law was fitted to arrive at a single coronal magnetic field distribution to cover the height range 1.1 - 2.2 R . The equation of the fit is B(r) = 2.6 × r −2.21 . One of the most common radio signature of any flicker on the Sun is a solar type-III burst. The latter are the fast drifting structures in the solar dynamic spectra, which occur when the electrons get accelerated along the open magnetic filed lines in the solar atmosphere. These radio bursts give information regarding electron acceleration along magnetic field lines in the middle corona as well as nearEarth region, which can not be studied currently in any other wavelengths. High spatio-temporal and spectral observations of these bursts obtained with LOFAR (LOw Frequency ARray) were used to study the structure of the open coronal magnetic field lines in the middle corona. On March 30, 2018, there was a B2.1 X-ray flare at active region (AR) 22703, which was recorded by GOES-2 satellite. The radio signature of that activity was observed with e-CALLISTO (Compound Astronomical Low cost Low frequency Instrument for Spectroscopy and transportable Observatory) and LOFAR spectrometers. The radio bursts were imaged with Low Band Antennas (LBAs) of the LOFAR which operates over 10 - 90 MHz. Interferometric tied-array beam imaging observations were carried out with high dynamic range, high spatial resolution between 80 and 20 MHz. The core LOFAR stations were used with spectral and temporal resolution of ≈ 195 kHz and ≈ 160 ms, respectively. Snapshot synthesis images of five type-III bursts were developed for the analysis. Taurus sky model was used to calibrate the images. The five trails in the spectra seem to follow five different lanes in the solar maps made with the interferometric observations at various times in different frequency channels. The densities at various heliocentric distances for the observed type-III were calculated. The values were comparable to those estimated earlier using white-light and EUV data. Using the observed DCP (25 % – 30 %) and second harmonic approximation, viii B was estimated. The spectral index of B was found to vary between 1.6 and 3.4. The spectro-polarimeter instruments designed in the PhD work may be improved further by increasing the bit resolution of the ADC and increasing the frequency and time resolution. For calibration, a more accurate method can be adopted, for example, circularly polarized emission from the satellites. A realistic approach for real time automatic detection of solar radio bursts can be done onboard. Real time RFI mitigation could be a way to effectively use all the bits in the ADC, to improve the DR of the system further. This would increase the probability of detecting weak bursts. The ROACH based digital spectro-polarimeter backend can serve the first step for developing the new digital backend for polarimetric imaging of the Sun with the augmented-GRAPH. The latter would overcome the limitations such as fixed bandwidth and fixed frequency observations, etc. This FPGA based correlator may be implemented on ROACH-2 board.