The structure and dynamics of the most energetic events in the Sun’s outer atmosphere such as flares, eruptions, coronal loops and coronal mass ejections are controlled by the magnetic field. Coronal loops are the fundamental building blocks of the coronal field – these are bright, dense structures that trace field lines that connect photospheric regions. Measurements of the magnetic field in loops is key to our understanding of the corona and is crucial to solve the long-standing problem of coronal heating. Despite developments in observation and analysis, a direct quantitative measurement of the magnetic flux density of coronal loops remains a central problem in solar (and stellar) physics .
Despite its promise, solar coronal polarimetry is extremely difficult due to the inherently low signal-to-noise ratios [2,3]. Current instrumentation can only achieve high-resolution polarimetric measurements during certain favorable conditions. In September 2017, Active Region (AR) 12673 produced the most powerful flares of solar cycle 24 as it was rotating from disk centre to the limb. On September 10 2017, the AR was just behind the west limb when it produced an X8.2-class flare at 16:06 UT. High spatial and temporal resolution observations of the flare were acquired with two instruments – CHROMospheric Imaging Spectrometer (CHROMIS) and CRisp Imaging SPectropolarimeter (CRISP) on the Swedish Solar Telescope (SST) in La Palma, Spain. The dataset consists of spectral imaging in Hβ (4861 Å) and full Stokes spectropolarimetry in the magnetically sensitive infrared Ca II line at 8542 Å (Landé g factor 1.1). These lines are usually formed under chromospheric conditions where the plasma temperature is ~7 000 – 20 000 K. The X8.2 flare led to intense heating and evaporation of dense chromospheric plasma into the loop system. The chromospheric plasma underwent rapid cooling (condensation) and the coronal loops subsequently filled with cool plasma radiating strongly in chromospheric lines including Ca II 8542 Å (Fig.1 & 2). The off-limb location of the AR minimized any contamination caused by line-of-sight effects, providing polarisation data of unprecedented quality.
Magnetic field map
Circular polarisation images (Stokes V) of the observed flaring loops acquired in Ca II 8542 Å reveal strong polarization signals along the loops (Fig. 2). The Stokes V component of the polarized light is related to the first derivative of the intensity profile (Stokes I) and the line-of-sight (LOS) component of magnetic field (BLOS) through the weak-field approximation (WFA) . The WFA is applicable when the Zeeman splitting of a line is much smaller than its Doppler broadening, and the magnetic field and LOS velocity are uniform along the LOS. These requirements are satisfied in the observed flare coronal loops . We use the WFA to produce maps of the LOS magnetic field component (BLOS) for the flare coronal loops (Fig. 2). The histograms in Fig. 2 are the distributions of the magnetic field for 3 different height ranges. BLOS of the loop apex region (layer a, between 18 and 26 Mm above the solar surface) ranges from 50 to 180 G with median 90 G. The corresponding values at mid-heights (layer b, 9 to 18 Mm) is as high as 300 G with median 140 G. The uncertainty of the BLOS in Fig. 2 is less than 20% .
The spectra are fitted to Gaussian functions to determine the bulk plasma LOS velocity (Fig. 3). Mapping this value (Dopplergrams) reveals that the left and right part of the loop structures contain regions of red- and blue-shifted plasma, respectively, with velocities between ~ 10-35 km/s (Fig 3A). Movies of this event and time-distance diagrams show strong downflows of dense plasma from the loop apex toward the footpoints. These velocities are the two orthogonal components of the downflowing plasma motions with respect to the observer – the LOS component (Dopplergrams) and the perpendicular component (apparent) . Since the moving plasma is confined to the loops, the direction of the flow velocity follows the direction of the magnetic loops. The average viewing angle of the magnetic field and velocity calculated from the ratio between the LOS and perpendicular components of the velocity vectors is approximately ~ 60 – 80 degrees (Fig. 3). This yields a median of total magnetic field strength, of around 350 G at the loop system apex (region a in Fig. 2), and 420 G at mid-heights (region b).
This unique observation of flaring coronal loops at the solar limb, using high-resolution imaging spectropolarimetry, has allowed us to determine their magnetic field with unprecedented accuracy due to the vantage point, orientation and nature of the chromospheric material that filled the flare loops. We find coronal magnetic field strengths as high as 350 Gauss at heights up to 25 Mm above the solar limb. These measurements are substantially higher than a number of previous estimates and could have considerable implications for our current understanding of the extended solar atmosphere. This constraint is crucial for physical models of coronal ARs, flares and eruptions, and can be used to provide a validation of widely-used numerical methods for the extrapolation of photospheric magnetic fields in the corona. Furthermore, the result is important for upcoming new-generation ground-based solar telescopes such as the 4 m Daniel K. Inouye Solar Telescope (DKIST) and the European Solar Telescope (EST). These telescopes will have advanced chromospheric polarimetric capabilities, which, as demonstrated here, can provide powerful diagnostics for the coronal magnetic field.
-  Casini, R., White, S. M., & Judge, P. G. 2017, SSRv, 210, 145
-  Lin, H., Kuhn, J. R., & Coulter, R. 2004, ApJL, 613, L177
-  Lin, H., Penn, M. J., & Tomczyk, S. 2000, ApJL, 541, L83
-  Kuridze, D., Mathioudakis, M., Morgan, H., et al. 2019, ApJ, The Astrophysical Journal, 874, 126