Author: Ryan J. Campbell, Mihalis Mathioudakis, Peter H. Keys, Chris J. Nelson, Aaron Reid (Queen’s University Belfast), Manuel Collados, Andrés Asensio Ramos (Instituto de Astrofísica de Canarias) and David Kuridze (Aberystwyth University).
Small-scale magnetism in the photophere
In the quiet solar photosphere, we observe granulation as the dominant pattern. Granulation is generated by convective cells rising from the convection zone and characterized by expansive granules and condensed intergranular lanes (IGLs). Magnetism in this layer of the atmosphere is continuously replenished, with flux balanced by the processes of emergence, fragmentation, coalescence and cancellation . In the network, the magnetic field strength, B, is typically large (B > 1000 G), and the vector highly vertical, with respect to the solar normal, but in the internetwork (IN) it has recently been revealed that the field is much weaker (B < 1000 G) and more inclined [2,3]. Observing the temporal evolution of these dynamic structures has previously been a major challenge, with most studies relying on slit-spectropolarimeters that scan in an X-Y plane to build up an image and which cannot, except in an 1D sit-and-stare configuration, build up a high-cadence time-series.
The diagnostic potential of spectropolarimetry
To observe these weak IN fields, we take advantage of the Zeeman effect, describing how spectral lines become split into several components under the action of a magnetic field. Magnetic fields also cause the white, unpolarized light that would otherwise be emitted from the Sun to become polarized. Measurement of Stokes I gives us the intensity, while Stokes Q and U are two independent states of linear polarization and Stokes V concerns circularly polarized light. At disk-centre, the action of inclined fields will result in linearly polarized light (and thus Stokes Q or U), while vertical fields generate circularly polarized light (and thus Stokes V).
The weak IN magnetic field is hidden to the Zeeman effect at low spatial resolutions, due to cancelling of opposite polarity Stokes signals, and therefore requires very high-resolution observations. As the polarization signals produced by weak fields have such low amplitudes, the Zeeman sensitivity of the employed spectral lines and signal-to-noise (S/N) of the observations is also critical. Information about the strength of the magnetic vector is contained both in the amplitude of the polarization profiles and in the splitting of each of their red and blue lobes, while to constrain the inclination of the vector, γ, we need to measure both linear and circular polarization. To constrain the azimuthal angle, Φ, we need to measure signals in both Stokes Q and U. The large effective Landé g-factor (higher value = more magnetically sensitive) and near infrared wavelength of the Fe I line at 1564.9 nm makes it an effective Zeeman diagnostic. In particular, studies (e.g. ) have shown the unique ability of this line to record linear polarization signals generated by horizontal fields, which are typically weaker than the circular polarization signals.
Observing in the near infrared
The new GRIS-IFU (GREGOR Infrared Spectrograph Integral Field Unit) image-slicer mounted at the 1.5 m GREGOR telescope provides the ideal instrument for this purpose. The GRIS-IFU has a very small (3’’ by 6’’) field of view (FOV) but can build up a larger image by ‘mosaicing’. When designing an observing sequence, one must optimize a number of competing factors. If the exposure time is too high, the target can evolve while collecting photons, resulting in further Zeeman cancelling and thus lower measured amplitude of polarization signals. The choice of FOV in the IN is critical, as it is possible with a small FOV to observe relatively low levels of polarization; previous studies with very large FOVs have shown there are enormous regions of the IN apparently devoid of magnetic flux without sufficient S/N .
We present in Figure 1 observations representing the highest spatial resolution near infrared time-series available to date. We chose a 3 by 3 mosaic resulting in a FOV of 9’’ by 18’’. The datasets additionally have a high spectral dispersion (40 mÅ/pixel) and a 64 second cadence. Figure 1 shows the observables from 40 frames from the two datasets recorded. Readers are directed to  (equations 2, 3) for definitions of the wavelength-integrated linear (LP) and circular (CP) polarizations.
An inverse problem
By employing the Stokes Inversions based on Response functions code (SIR, see ), we are able to infer the local thermodynamic, kinematic and magnetic properties of the atmosphere. We consider two inversion setups: scheme 1 (S1), where a magnetic atmosphere (model 2) is embedded in a field free medium (model 1), and scheme 2 (S2), with two magnetic models and a fixed 30% stray light component. Two-component models must be employed as we are not typically resolving the observed small-scale magnetic structures. We therefore quantify the fraction of the pixel element occupied by a given model using its filling factor, α. Also shown in Figure 1 are the line-of-sight velocities, magnetic flux densities and inclination angles returned by S1 inversions.
We find patches of linear polarization with peak magnetic flux densities of the order of 130−150 G and find that linear polarization appears preferentially at granule-IGL boundaries. It is clear that the evolution and fate of these features are highly dependent on granular motions. The weak magnetic field appears to be organized in terms of complex ‘loop-like’ structures, with transverse fields (γ ~ 90 deg, i.e. in the plane of the solar surface) often flanked by opposite polarity longitudinal fields (γ ~ 0,180 deg, i.e. pointing towards or away from the observer, respectively). How many of these loops can you spot in the video?
We reconstructed our observed profiles by, first, the application of principle component analysis (PCA) to remove noise, in the same manner as implemented by , and second, the application of a relevance vector machine (RVM) to remove fringes and other defects (see details in ). Another reason to reconstruct our profiles in this way is to reduce the influence of noise on our inversion results. Figure 2 shows a sample profile with both S1 and S2 outputs. This sample profile is found in linear polarization located along a polarity inversion line (i.e. between two patches of opposite polarity circular polarization). As the pixel’s polarity was consistent across three frames, we were able to temporally bin this profile to increase our S/N and reveal a 3-lobed Stokes V profile.
The case for DKIST and EST
It is clear that we are able to observe highly complex and dynamic magnetic features, but they appear to be organized on scales smaller than we can observe. Multi-lobed Stokes V profiles can be indicative of the presence of opposite polarities, but we cannot determine whether they are co-existing either vertically (along the LOS) or horizontally within the resolution element. GREGOR is the largest solar telescope in Europe, with a 1.5 m primary mirror. The seeing conditions during observations were excellent. The wavelength of our observations, conducted in the near infrared, is a limiting factor. Observations with GRIS (e.g. ) have estimated the effective spatial resolution in these lines as 0.4-0.45’’. The 4 m Daniel K. Inouye Solar Telescope (DKIST) and 4.2 m European Solar Telescope (EST) are required to push the limits of what we can observe even further.
This research has received financial support from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 824135 (SOLARNET).
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