We are striving for more accurate coronal magnetography based on changes in radio polarization as microwaves cross magnetic field lines at nearly right angles.
The theory of using quasi-transverse propagation for coronal field measurements includes weak dependence on two parameters: plasma density $N_e$ and the magnetic field divergence $L_d$ (see Alissandrakis and Gary, 2021 for a review). We evaluate coronal plasma density from local differential emission measure computed from the Solar Dynamic Observatory (SDO/AIA) data. Additionally, we compute the scale of field divergence at the coronal points of radio measurements by means of the Potential Field Source Surface (PFSS) model. Thus, we have avoided the assumption of constant $N_e \times L_d$ practiced for elongated in latitude bipolar active regions, as in Ryabov (2004).
Our starting assumption is that the topology of fan-spine configurations (FSCs) could be reproduced with the potential field extrapolation at the time of no flaring.
Example
The FSCs are regarded as locations of possible flaring activity and thus are important targets of investigations. There are two systems of field lines: the lower-lying field lines surrounding the inner spine line and the overlying field lines surrounding the outer spine line. The magnetic fields of an FSC include a magnetic null point, a spine line, and a dome-shaped fan surface.
In contrast to the elongated in latitude bipolar active regions, the FSCs represent a dominant sunspot with circumjacent magnetic flux of opposite polarity. When such active regions are close to the central solar meridian, the region of quasi-transverse propagation is dome-shaped for the lower-lying system. This shape evolves during solar axis rotation in accordance with varying propagation angle.
We note stripes of inverted sign of circular polarization observed with the Siberian Solar Radio Telescope (angular resolution $\theta = 20{”}$ at 5.7 GHz) on October 1 and October 3, 2012 (Figure 1). The coronal locations in the regions of quasi-transverse propagation where circular polarization turns to zero are of particular interest since at such locations the radio measurements are independent of the initially emitted polarization. The black arrow points to the coronal location at the height of 5×109 cm, where microwaves cross the shown field line transversally at $B = 23.4 \ G$, $N_e = 1.74 \times 10^{9} \ cm^{-3}$, and $L_d = 3.7 \times 10^{8} cm$.
On October 5 (not shown in Figure 1), the sign of polarization at 5.7 GHz inverted completely for the sunspot-associated microwave source despite the lack of any considerable changes in the photospheric magnetic field. Such an inversion in a sunspot approaching the solar limb is a clear indication of the effect of quasi-transverse propagation of microwaves, while the stripes of the inverted polarity is an unexpected feature. We attribute these stripes to a fragmentation in the three circumjacent sunspots of opposite magnetic polarity (in black colour).
Figure 1 – AR 11579 in the plane of view. (a-b) Sign inversion observed in circular polarization at 5.7 GHz (red to blue contours) in two days. (c-d) Magnitude of the coronal magnetic field computed with the PFSS model at points of transverse propagation of microwaves. (e) Magnetic field lines of the fan-spine configuration against the surface magnetogram. Red and yellow squares mark several perpendicular crossings by microwaves.
Conclusions
The measured coronal field is consistent with the parameters $N_e$ and $L_d$ in the sense that these independently evaluated parameters provide a value of B consistent with the observed degree of the circular polarization at 5.7 GHz. The main conclusion we draw is the confirmation of the possibility to augment radio measurements with PFSS modelling for FSCs in quiet non-flaring states. A broader range of cases is required to formulate general diagnostics for recognizing quasi-transverse propagation in FSCs.
Based on the recent paper: Ryabov B., Vrublevskis A.: 2023, Latvian Journal of Physics and Technical Sciences, 2, 11 doi: https://doi.org/10.2478/lpts-2023-0011
References
Alissandrakis, C.E. & Gary, D.E.: 2021, Front. Astron. Space Sci., 7, 591075
Ryabov, B.: 2004, Chapter 7 in “Solar and Space Weather Radiophysics”, (Dordrecht: Kluwer Academic Publishers)