GoKawiilObservations and data reduction
In this work we present observations acquired on 14 April 2025 between 21:38 ut and 21:41 ut using the world’s largest telescope for optical and infrared observations of the Sun, DKIST21. During the data acquisition, the atmospheric conditions were variable, with Fried parameter values during the best periods measured around \({r}_{0}\approx 12\,\mathrm{cm}\). The DKIST wavefront correction system was operating in diffraction-limited mode at the time of the observations, as it was measuring and correcting all optical modes that it is capable of detecting. In this work, we focus on the first target of the day, a region containing pores near an active region (NOAA 14060) close to the disk centre with helioprojective Cartesian coordinates (X = −162 arcsec, Y = 168 arcsec), corresponding to \(\mu \approx 0.97\) (Fig. 1).
A dataset was acquired with a diagnostic (FastCam) set-up at DKIST, which was built as a collaborative effort between the National Solar Observatory and the Max Planck Institute for Solar System Research. The set-up was installed in front of the spectrograph entry slit of the visible spectro-polarimeter and removed at the end of the data acquisition for the diagnostic test. The optical set-up enhanced the operation of the feed telescope of the visible spectro-polarimeter, which did not have any other powered optics, resulting—with the pixel cell size of 5.5 μm for the Max Planck Institute camera—in a pixel size of ∆s ≈ 0.00825 arcsec px−1, corresponding to approximately 6 km px−1 on the solar surface. The wavelength chosen for the observation was 416 nm, and we used a narrow band-pass with a full-width at half-maximum of 0.5 nm. The region of interest read out by the camera was set to 2K × 1K px2, which meant that the sensor could be read out at a rate of 740 frames per second while maintaining an exposure time of 100 μs. The camera was equipped with a phase-diversity beam-splitter assembly, which imaged two fields, one in-focus and the other with a de-focus of approximately 0.4 waves root mean square. The two fields were imaged side-by-side onto the sensor in a phase-diversity set-up38,39, which allowed us to determine the residual wavefront aberrations that remained after the correction by the adaptive optics system40. The solar FoV visible in both the focused and the de-focused images corresponds to approximately 5,800 × 4,350 km2 on the Sun (8 × 6 arcsec2). The time span covered by the dataset analysed in this work is about 3 min. The frames observed with this camera were image-reconstructed using multi-frame blind deconvolution41, a technique that can be used to numerically model and remove residual atmospheric aberrations from the data. The algorithm used 2,000 dark- and gain-calibrated camera frames to compute one reconstructed science frame. After image reconstruction, the effective cadence of the imaging data was 2.7 s. We estimated that most frames achieved a spatial resolution of 19 km, the Rayleigh diffraction limit at 416 nm, as inferred from the full-width at half-maximum of the finest structures in the data.
Context imaging was provided by the visible broadband imager (VBI)42, an imaging instrument capable of acquiring large-FoV short-exposure data sequences at a single wavelength within 3 s. In this experiment, the VBI was configured to acquire sequences of 80 frames alternating in wavelength between the red continuum (668.4 nm) and the Hα line (656.3 nm; not shown), with sampling in the images corresponding to 12.3 km px−1 (0.017 arcsec px−1). The frames of each consecutive sequence were image-reconstructed using speckle reconstruction algorithms43 to remove residual seeing effects over the large FoV of approximately 50 × 50 Mm2 (69 × 69 arcsec2). Even though the VBI red channel was started with a 3-min delay with respect to the FastCam data that are presented here, the FoV clearly still contains the (evolved) structure of the higher spatial resolution dataset (Fig. 1).
Full disk observations were provided by the helioseismic and magnetic imager onboard the Solar Dynamics Observatory (SDO/HMI)44. Figure 1a shows a photospheric continuum image from the HMI at 21:40 ut. The HMI image was coaligned with DKIST/VBI/FastCam data using the SolarSoft auto_align_images function through a cross-correlation (Fig. 1).
Numerical simulations and spectral synthesis
Here we compare the observations with MHD simulations performed with the MURaM code22. So that we could perform the simulations at a very high spatial resolution, we focused on a small domain of extent 6.144 × 6.144 × 2.048 Mm3 (with the third dimension, z, being vertical), which is comparable with the high-resolution FastCam FoV. In the vertical direction, the domain extended approximately 1.367 Mm below z = 0 Mm and 0.681 Mm into the overlying atmosphere. A solar-like configuration with granulation driven by radiative losses could not be achieved in the numerical simulation without the overlying stable atmosphere. A realistic photosphere was essential for making the connection between numerical models and observations. We started from a relaxed hydrodynamic simulation to which we added the vertical magnetic field component extracted from the corresponding HMI magnetogram for the observed region (Supplementary Fig. 1). We initialized the domain with a strictly vertical magnetic field of the form \(n{B}_{z}-(n-1)\langle {B}_{z}\rangle \), where \({B}_{z}\) was taken from an HMI magnetogram and was enhanced to compensate for the field dispersal that occurred due to granular motions when the simulation was further relaxed for about 1.8 h (n is the enhancement factor). After the relaxation, the individual flux concentrations were no longer impacted by the initial state. To achieve a realistic simulation of magneto-convection, the critical parameter is the net flux imbalance, which was unchanged by the enhancement. Therefore, the enhanced HMI magnetogram was used solely to create a set-up that looks more closely like the observed distribution, and it was not needed for the development and study of KHIs. We found that a choice of \(n=2.5\) led to a large-scale magnetic field distribution comparable with the HMI magnetogram and the formation of pores that resemble those observed (Supplementary Fig. 1). After initialization with the enhanced magnetogram, the simulation ran for 4,980 s with 12.8-km grid spacing, followed by 1,200 s with 6.4 km and then another 1,200 s with 3.2-km grid spacing. The sequence we analysed also covers 480–720 s in the 3.2-km sequence or 5,460–5,700 s since the initialization with the HMI magnetogram. The simulation was computed with 12 opacity bins and used the Asplund 2009 opacities45.
The grid scale of 3.2 km was greater than the diffusive length scale expected in the photosphere of approximately 1.4 km based on a Spitzer diffusivity \(\eta \) = 2 × 108 cm2 s−1 (ref. 46) and a timescale \(\tau \) = 100 s using \(l\approx \sqrt{\eta \tau }\). The use of the numerical diffusivity22 is, thus, justified for the simulations presented here. However, a spatially dependent Spitzer diffusivity would need to be used for higher resolution simulations.
Developed snapshots of the simulation were used to generate the synthetic spectrum for a wavelength interval between 415.32 nm and 416.7 nm, using 500 spectral points with the one-dimensional version of the Rybicki–Hummer radiative transfer code47 in local thermodynamic equilibrium (Extended Data Fig. 4c). The syntheses included molecular (CH and CN) and atomic lines and the continuum within the band-pass. Intensities were also synthesized at a single continuum wavelength of 500 nm. To save computational time, the vertical grid space was reduced to 9.6 km by using only every third grid point along the vertical axes. We synthesized spectra at disk centre and towards the solar limb at \(\mu =1\) and \(\mu =0.97\), respectively. To synthesize 416 nm intensities at \(\mu =0.97\), the MURaM cube was modified by shifting each horizontal layer relative to the layer below by \(\Delta z\,\tan (\theta )\), where \(\Delta z\) represents the vertical grid spacing and θ is the heliocentric angle, defined as the angle between the line of sight and the solar surface normal. This adjustment aligned the slanted line-of-sight direction vertically. Pixel sampling was foreshortened along the y direction by a factor of \(\mu \) and increased along the z direction by a factor of \(1/\mu \) for the \(\mu =0.97\) data. To closely replicate the DKIST 416-nm filtergrams, the synthetic data were multiplied by the transmission profile of the interference filter employed in the diagnostic set-up (Extended Data Fig. 4c) and integrated over the wavelength range covered by the filter.
Extended Data Fig. 4a,b demonstrates that all common features observed in the 416-nm filtergrams were reproduced in the synthetic images, including KHI vortices and striations. Extended Data Fig. 4c shows the synthetic spectrum averaged over the full FoV of the simulation, overplotted with a solar atlas48 with the same wavelength range as observed by a Fourier transform spectrometer. The two spectra agree to a high level of detail, demonstrating that the simulation accurately reproduced the observed spectral features. The close agreement between the synthetic and observed spectra and images confirms that the simulated data serve as a powerful diagnostic tool for interpreting 416-nm intensity observations.
... continue reading