Diagnosing kappa distribution in the solar corona with

Diagnosing kappa distribution in the solar corona with the polarized microwave gyroresonance radiation Alexey A. Kuznetsov 1, Gregory D. Fleishman 2 1 Institute of Solar-Terrestrial Physics (Irkutsk, Russia ) 2 New Jersey Institute of Technology (Newark, USA)

Gyroresonance radiation Ø Produced by thermal electrons in strong magnetic fields above sunspots. Ø “Slowly varying component” of the solar radio emission. Ø Typical frequencies: 1 – 10 GHz. ~ Ø Demonstrates a high correlation with the sunspot number. SDO HMI magnetogram SDO AIA 171 Å SSRT 5. 7 GHz I SSRT 5. 7 GHz V Images of the Sun at different wavelengths, observed on 2011 -08 -01, 03: 13 → 2

Gyroresonance radiation Equation of radiation transfer: For thermal electrons (β << 1), gyroemission (and absorption) is significant only in narrow layers with f ≈ sf. B, s = 1, 2, 3, . . . For Maxwellian distribution (e. g. , Zheleznyakov 1970): Under the typical coronal conditions, gyrolayers with s ≤ 3 are optically thick (τ >> 1) and gyrolayers with s > 3 are transparent (τ << 1) the observed emission is produced at the 3 rd gyrolayer. 3

Gyroresonance radiation from kappa-distributions Gyroresonance radiation theory was extended to kappa-distributions (Fleishman & Kuznetsov 2014). Optical depth of the s-th gyrolayer: Emission intensity from the s-th gyrolayer: Relative optical depths for the kappa-distribution. The factor R describes deviation from the Kirchhoff’s law. Ø For s > 2, optical depth for the kappadistribution is larger than for Maxwellian one (and increases with decreasing κ). Ø In the optically thick regime (τ >> 1), the brightness temperature still increases with increasing optical depth. Brightness temperature vs. optical depth. 4

Gyroresonance radiation from kappa-distributions Polarization degree Brightness temperature For the 3 rd gyrolayer and viewing angle θ = 60°, the ratio of optical depths is τO / τX ≈ 0. 04. Maxwellian distribution κ = 10 5

Gyroresonance radiation from kappa-distributions Simulated gyroresonance emission spectra (for a typical magnetic field and plasma profile): Emission intensity Polarization degree 6

Diagnosing kappa-distributions in the solar active regions Indicators of kappa-distribution: Ø Qualitative effect: optically thick gyroresonance emission has a significant polarization (detection requires high spatial resolution). Ø Quantitative effect: polarization of low-resolution microwave images is higher than predicted by the Maxwellian model (detection requires to know the magnetic field structure and plasma distribution). Selection criteria of the active region: Ø Simultaneous observations with SDO and SSRT. Ø Observation time near local noon and near the summer solstice at the SSRT location. Ø Large area / simple structure. Siberian Solar Radio Telescope (SSRT). Ø Working frequency: 5. 7 GHz. Ø Spatial resolution: up to 21’’. Selected active region: AR 11476 (observed in May 2012). 2012 -05 -08 2012 -05 -09 2012 -05 -10 2012 -05 -11 2012 -05 -12 2012 -05 -13 2012 -05 -14 2012 -05 -15 7

Simulations of gyroresonance radiation with GX Simulator Magnetic field structure. 2012 -05 -11 02: 44 Plasma density distribution. GX Simulator (Nita et al. 2015, 2017). Magnetic field extrapolation: Weighted Optimization Nonlinear Force-Free Field reconstruction (Wiegelmann 2004), implementation by A. S. Stupishin (Fleishman et al. 2017); based on vector SDO magnetograms. Plasma code: Enthalpy-Based Thermal Evolution of Loops (EBTEL, Klimchuk et al. 2008; Bradshaw & Cargill 2010, Cargill et al. 2012 a, b). Heating rate: Top view of the active region. 8

Simulation results: high-resolution images Stokes I, 5. 7 GHz Brightness temperature Stokes V, 5. 7 GHz Polarization degree 9

Fitting algorithm Before comparison with the observations, the simulated images must be convolved with the instrument response function. For a known magnetic field structure, the simulated microwave emission depends on two parameters: base heating rate Q 0 and kappa-distribution index κ. 1) For each observation time and the value of κ, find the parameter Q 0 that provides the best agreement of the observed and simulated intensity (Stokes I) maps: 2) For each observation time, find the value of κ that provides the best agreement of the observed and simulated polarization (Stokes V) maps: 10

Simulations vs. observations: 2012 -05 -11 Model parameters: Stokes I, 5. 7 GHz ηmax = -5. 9% Stokes V, 5. 7 GHz Observed images Stokes I, 5. 7 GHz § Maxwellian distribution; § Q 0 = 5500. ηmax = -0. 8% Stokes V, 5. 7 GHz Simulated images 11

Simulations vs. observations: 2012 -05 -11 Model parameters: § κ = 10; Stokes I, 5. 7 GHz ηmax = -5. 9% Stokes V, 5. 7 GHz Observed images Stokes I, 5. 7 GHz § Q 0 = 1500. ηmax = -2. 3% Stokes V, 5. 7 GHz Simulated images 12

Simulations vs. observations: 2012 -05 -11 Agreement between the simulations and observations vs. κ: 13

Simulations vs. observations: 2012 -05 -08 Model parameters: Stokes I, 5. 7 GHz ηmax = -7. 8% Stokes V, 5. 7 GHz Observed images Stokes I, 5. 7 GHz § Maxwellian distribution; § Q 0 = 21000. ηmax = -0. 6% Stokes V, 5. 7 GHz Simulated images 14

Simulations vs. observations: 2012 -05 -08 Model parameters: § κ = 14; Stokes I, 5. 7 GHz ηmax = -7. 8% Stokes V, 5. 7 GHz Observed images Stokes I, 5. 7 GHz § Q 0 = 10000. ηmax = -7. 1% Stokes V, 5. 7 GHz Simulated images 15

Simulations vs. observations: 2012 -05 -08 Agreement between the simulations and observations vs. κ: 16

Simulations vs. observations: 2012 -05 -14 Model parameters: Stokes I, 5. 7 GHz ηmax = -33. 3% Stokes V, 5. 7 GHz Observed images Stokes I, 5. 7 GHz § Maxwellian distribution; § Q 0 = 50000. ηmax = 6. 2% Stokes V, 5. 7 GHz Simulated images 17

Simulations vs. observations: 2012 -05 -14 Model parameters: § κ = 7; Stokes I, 5. 7 GHz ηmax = -33. 3% Stokes V, 5. 7 GHz Observed images Stokes I, 5. 7 GHz § Q 0 = 9500. ηmax = 25. 1% Stokes V, 5. 7 GHz Simulated images 18

Escape of radiation If the magnetic field is nearly perpendicular to the line-of-sight, even small variations of the field direction can affect the observed polarization sign. R L R R L L 19

Simulations vs. observations: 2012 -05 -14 Agreement between the simulations and observations vs. κ: 20

Simulations vs. observations: AR 11476 Best agreement is achieved: Ø for Stokes I maps: for the Maxwellian distribution; Ø for Stokes V maps: § in the eastern hemisphere: for the Maxwellian distribution; § in the western hemisphere: for κ ≈ 7 – 20; Ø for ηmax: for κ ≈ 7 – 20 (except of two cases near the disk center). 21

Conclusions Ø Gyroresonance microwave emission is a powerful diagnosing tool for kappa-distributions in the solar corona; polarization of the emission is especially sensitive to the distribution type; however, it is also sensitive to other minor details of the model, such as the magnetic structure and the heating law. Ø We have computed the gyroresonance emission for the solar active region AR 11476 for different κ indices with the GX Simulator code and compared the results with the observations of the Siberian Solar Radio Telescope. Ø The best agreement of the simulated and observed intensity maps is achieved for the Maxwellian distribution (or for κ well above 20). Ø Comparison of the simulated and observed polarization maps are not yet conclusive in terms of the favorable kappa-index: § Sometimes, the simulations/observations favor the presence of kappa-distribution (with κ ≈ 7 – 20). § Different comparison criteria favor different indices. § The simulations are not yet perfect enough to reproduce the structure of the polarization maps in detail. Ø Ways to improve the diagnostic capability of the microwave observations: § Using more accurate models of the magnetic field and plasma in the active regions. § Improving spatial resolution of the radio telescopes. § Using multi-wavelength microwave observations (SRH, EOVSA, MUSER). 22