arXiv subjects

M. van Noort

Publications and source records attributed to M. van Noort.

At least 19 recordsLinked to original sources

arXiv2026

Wave excitation by a collapsing granule: insights from IFU observations and high-resolution RMHD simulations

Context. Granular collapse is an ubiquitous process of granular evolution on the solar surface, but it is hard to analyze in sufficient spatial, temporal, and spectral detail. Aims. We analyze the change in physical conditions in the photosphere during a specific granular collapse event and the subsequent atmospheric response. Methods. We contrast a high-resolution radiative magneto-hydrodynamic simulation of a granular collapse performed using the CO5BOLD code with the recent integral field unit observations carried out using the MiHI instrument at the Swedish 1-m Solar Telescope. Results. Our analysis shows that the observed and simulated granular collapse show remarkable similarity. Specifically, they both exhibit the signature of a wave pulse excited in the deep photosphere and visible up to the temperature minimum. This wave is detectable through a blue-wing emission in the observed and synthetic Na i D1 line. We also estimate the acoustic energy flux carried by the wave and analyze its initiation. Conclusions. Combining high-resolution IFU spectropolarimetry and state-of-the-art simulations of the solar lower atmosphere, this study showcases our current capabilities in identifying specific physical processes taking place during the granular collapse and their impact on the atmosphere above.

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arXiv2026

Inspectorch: Efficient rare event exploration in solar observations

The Sun is observed in unprecedented detail, enabling studies of its activity on very small spatiotemporal scales. However, the large volume of data collected by our telescopes cannot be fully analyzed with conventional methods. Popular machine learning methods identify general trends from observations, but tend to overlook unusual events due to their low frequency of occurrence. We study the applicability of unsupervised probabilistic methods to efficiently identify rare events in multidimensional solar observations and optimize our computational resources to the study of these extreme phenomena. We introduce Inspectorch, an open-source framework that utilizes flow-based models: flexible density estimators capable of learning the multidimensional distribution of solar observations. Once optimized, it assigns a probability to each sample, allowing us to identify unusual events. We apply this approach by applying it to observations from the Hinode Spectro-Polarimeter, the Interface Region Imaging Spectrograph, the Microlensed Hyperspectral Imager at Swedish 1-m Solar Telescope, the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory and the Extreme Ultraviolet Imager on board Solar Orbiter. We find that the algorithm assigns consistently lower probabilities to spectra that exhibit unusual features. For example, it identifies profiles with very strong Doppler shifts, uncommon broadening, and temporal dynamics associated with small-scale reconnection events, among others. As a result, Inspectorch demonstrates that density estimation using flow-based models offers a powerful approach to identifying rare events in large solar datasets. The resulting probabilistic anomaly scores allow computational resources to be focused on the most informative and physically relevant events. We make our Python package publicly available at https://github.com/cdiazbas/inspectorch.

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arXiv2026

Morphological variations of solar granules in the presence of magnetic fields

Solar granulation consists of dynamic convective plasma cells that rise from the solar interior to the surface. The interaction between these plasma cells and the Sun's magnetic field provides valuable insights into plasma dynamics near the solar surface and how they evolve in the presence of magnetic fields. This study analyses the morphological characteristics of solar convective cells, investigating the relationship between magnetic field properties and granule dynamics - specifically how granule area, shape, and brightness vary under different magnetic field conditions. Observations of the active region NOAA 11768 were taken with the Swedish 1-m Solar Telescope (SST). A segmentation algorithm was applied to continuum intensity images to identify individual granules and determine their sizes, shapes, and mean brightness. The magnetic field vector and line-of-sight velocity were derived from CRISP spectropolarimetric data to investigate their role in shaping granule properties. We find that granular area decreases systematically with increasing magnetic field strength, with the largest granules occurring in non-magnetic regions and a mean granule area of approximately 1.58 arcsec$^2$ (effective diameter of 1.42 arcseconds). Both mean continuum intensity and granule size decrease with stronger fields, confirming the suppression of convective energy transport in magnetised regions. No correlation was found between mean granule brightness and mean up-flow velocity. Highly elongated granules appear in both magnetic and non-magnetic regions, while near-circular granules are exclusive to non-magnetic areas. An alignment between granule major axes and magnetic field azimuth is observed where the horizontal field component is strong, confirming that granules are highly sensitive to magnetic fields, which inhibit the lateral expansion of convective cells.

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arXiv2025

Thermodynamic and magnetic evolution of an eruptive C-class solar flare observed with SST/TRIPPEL-SP

Solar flares are complex phenomena driven by the release of magnetic energy, but a large energy reservoir is not sufficient to determine their eruptive potential; the magnetic topology and plasma dynamics play a key role. We investigate the thermodynamic and magnetic properties of the solar atmosphere during the rise, peak, and decay phases of a C5.1-class flare and filament eruption in active region NOAA 12561 on 2016 July 7, to understand the origin and atmospheric response of this event. High spatial and spectral resolution spectropolarimetric observations of the chromospheric Ca II 8542A line and nearby photospheric lines were obtained with the TRIPPEL-SP spectropolarimeter at the Swedish 1-m Solar Telescope. Using non-local thermodynamic equilibrium (NLTE) inversions and non-force-free field (NFFF) magnetic extrapolations, we followed the event's evolution from its precursor to its decay. Before the flare, our analysis reveals a complex, sheared magnetic topology with a high free energy content ($\sim2\times10^{30}$ erg). In this precursor phase, we detected persistent, localized heating (temperature increase of $\sim$2000 K) with strong downflows ($\sim$10-20 km/s) deep in the atmosphere. This heating was co-spatial with a bald-patch region, suggesting that low-altitude magnetic reconnection could destabilize the filament of the region. The flare's rise phase was marked by the filament's eruption, with a total speed larger than $\sim$70 km/s, when combining inversions and plane-of-sky motions. Following the eruption, the free energy decreased by $\sim$30$\%$ as post-flare loops formed, connecting the flare ribbons and channeling the released energy into the lower atmosphere. The flare ribbons exhibited significant heating to $\sim$8500 K and downflows up to $\sim$10 km/s, consistent with energy deposition along reconnected loops.

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arXiv2025

Magnetic properties of orphan penumbrae

Orphan penumbrae (OPU) are features resembling sunspot penumbrae, but are not connected to an umbra. Here we compare OPUs and sunspot penumbrae, including their filaments. We also identify and describe the main mechanisms for the formation of OPUs and we characterise their decay process. Our study is based on spectropolarimetric inversions of active regions observed with the Hinode spectropolarimeter. We manually identified 80 individual OPUs, allowing us to study them statistically. In addition, we analysed the time-evolution of selected OPUs using data provided by the Helioseismic and Magnetic Imager. Orphan penumbrae display a broad range of shapes, associated with typically $Ω$-shaped magnetic field configurations, where opposite polarity fields predominate at the two ends of the OPU. In addition, the properties of the OPU filaments are remarkably uniform between different OPUs, resembling the ones in sunspot penumbrae. Most OPUs form by either a patch of a penumbra separating from a sunspot, or by new magnetic flux emerging close to the polarity inversion line of an active region. We observe chromospheric fibrils above almost all OPUs in Hinode H$α$ images, indicating that a part of the magnetic field of the OPUs extends to the chromosphere. Our results show that OPU filaments can form given a broad range of boundary conditions for the magnetic field.

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arXiv2025

The role of the Lorentz force in sunspot equilibrium

Sunspots survive on the solar surface for time-scales ranging from days to months. This requires them to be in an equilibrium involving magnetic fields and hydrodynamic forces. Unfortunately, theoretical models of sunspot equilibrium are very simplified as they assume that spots are static and possess a self-similar and axially symmetric magnetic field. These assumptions neglect the role of small scale variations of the magnetic field along the azimuthal direction produced by umbral dots, light bridges, penumbral filaments, and so forth. We aim at studying whether sunspot equilibrium is maintained once azimuthal fluctuations in the magnetic field, produced by the sunspot fine structure, are taken into account. To this end we apply the FIRTEZ Stokes inversion code to spectropolarimetric observations to infer the magnetic and thermodynamic parameters in two sunspots located at disk center and observed with two different instruments: one observed from the ground with the 1.5-meter German GREGOR Telescope and another with the Japanese spacecraft Hinode. We compare our results with three dimensional radiative magnetohydrodynamic simulations of a sunspot carried out with the MuRAM code. We infer clear variations in the gas pressure and density of the plasma directly related to fluctuations in the Lorentz force and associated with the filamentary structure in the penumbra. Similar results are obtained in the umbra despite its lack of observed filamentary structure. Results from the two observed sunspots are in excellent qualitative and quantitative agreement with the numerical simulations. Our results indicate that the magnetic topology of sunspots along the azimuthal direction is very close to magnetohydrostatic equilibrium, thereby helping to explain why sunspots are such long-lived structures capable of surviving on the solar surface for days or even full solar rotations.

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arXiv2025

Fine-scale opposite-polarity magnetic fields in a solar plage revealed by integral field spectropolarimetry

Plages are small concentrations of strong, nearly vertical magnetic fields in the solar photosphere that expand with height. A high spatial and spectral resolution that can resolve their fine structure is required to characterize them, and spectropolarimetric capabilities are needed to infer their magnetic fields. We constrain the 3D fine structure of the magnetic field in the photosphere of a solar plage from a unique spectropolarimetric dataset with a very high spatial and spectral resolution and a fast temporal cadence. We analyzed spectropolarimetric observations of a solar plage in the two magnetically sensitive spectral lines of neutral iron around 630 nm. The observations were obtained with MiHI, which is an integral field unit attached to the Swedish Solar Telescope. MiHI obtained diffraction-limited, high-cadence observations with high spectral fidelity. These observations were interpreted using the spectropolarimetric inversion with magnetohydrostatic constraints, which allowed us to recover the magnetic and thermodynamic structure of the plage on a geometrical scale. The inversion results reveal that the magnetic field can reach up to 2 kG and that it expands significantly from the deep to the mid-photosphere. Weaker (200 G), and very small (subarcsecond) vertical magnetic loops lie beneath this canopy, rooted in the photosphere. This novel picture of a solar plage, in which weak opposite-polarity field patches surround the main polarity, provides new insight into convection in strongly magnetized plasma.

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arXiv2025

Transverse waves observed in a fibril with the MiHI prototype

Context. Fine-scale structures of the solar chromosphere, particularly fibrils, are known to host various types of magnetohydrodynamic (MHD) waves that can transport energy to the corona. In particular, absorption features observed in the Hα channel have been widely detected that exhibit transverse oscillations. Aims. We aimed to detect a high-frequency transverse oscillation in fibrils. Methods. We conducted a case study on a high-frequency transverse oscillation in a chromospheric fibril. A chromospheric fibril was observed on 24 August 2018, in the Hα spectral line, with the prototype Microlensed Hyperspectral Imager (MiHI) at the Swedish 1- meter Solar Telescope. The MiHI instrument is an integral field spectrograph capable of achieving ultra-high resolution simultaneously in the spatial, temporal, and spectral domains. Results. The detected oscillation characteristics include a period of 15 s and a displacement amplitude of 42 km. Using the bisector method, we derived Doppler velocities and determined that the polarisation of the oscillation was elliptical. Conclusions. The energy contained in the oscillation ranges from 390 to 2300 W/m2, which is not sufficient to balance radiative losses of the chromosphere.

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arXiv2025

High flow speeds and transition-region like temperatures in the solar chromosphere during flux emergence

Context: Flux emergence in the solar atmosphere is a complex process that causes a release of magnetic energy as heat and acceleration of solar plasma at a variety of spatial scales. Methods: We analysed imaging spectropolarimetric data taken in the He 1083 nm line. This line is sensitive to temperatures larger than 15 kK, unlike diagnostics such as \MgIIhk, \CaIIHK, and \Halpha, which lose sensitivity already at 15 kK. The He I data is complemented by imaging spectropolarimetry in the \CaIIK, \Feline, and \Caline\ lines. We employed inversions to determine the magnetic field and vertical velocity in the solar atmosphere. We computed He 1083 nm profiles from a radiation-MHD simulation of the solar atmosphere to help interpretation of the observations. Results: We find fast-evolving blob-like emission features in the He 1083 nm triplet at locations where the magnetic field is rapidly changing direction, and these are likely sites of magnetic reconnection. We fit the line with a model consisting of an emitting layer located below a cold layer representing the fibril canopy. The modelling provides evidence that this model, while simple, catches the essential characteristics of the line formation. The morphology of the emission in the He 1083 nm line is localized and blob-like, unlike the emission in the \CaIIK\ line, which is more filamentary. Conclusions: The modelling shows that the \Heline\ emission features and their Doppler shifts can be caused by opposite-polarity reconnection and/or horizontal current sheets below the canopy layer in the chromosphere. Based on the high observed Doppler width and the blob-like appearance of the emission features, we conjecture that at least a fraction of them are produced by plasmoids. We conclude that transition-region-like temperatures in the deeper layers of the active region chromosphere are more common than previously thought.

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arXiv2025

Superstrong magnetic fields in sunspot bipolar light bridges

Recent solar observations of bipolar light bridges (BLBs) in sunspots have, in a few individual cases, revealed magnetic fields up to 8.2 kG, which is at least twice as strong as typical values measured in sunspot umbrae. However, the small number of such observations hinted that such strong fields in these bright photospheric features that separate two opposite-polarity umbrae, are a rare phenomenon. We determine the field strength in a large sample of BLBs with the aim of establishing how prevalent such strong fields are in BLBs. We apply a state-of-the-art inversion technique that accounts for the degradation of the data by the intrinsic point spread function of the telescope, to the so far largest set of spectropolarimetric observations, by Hinode/Solar Optical Telescope spectropolarimeter, of sunspots containing BLBs. We identified 98 individual BLBs within 51 distinct sunspot groups. Since 66.3% of the BLBs were observed multiple times, a total of 630 spectropolarimetric scans of these 98 BLBs were analysed. All analysed BLBs contain magnetic fields stronger than 4.5 kG at unit optical depth. The field strengths decrease faster with height than the fields in umbrae and penumbrae. BLBs display a unique continuum intensity and field strength combination, forming a population well separated from umbrae and the penumbrae. The high brightness of BLBs in spite of their very strong magnetic fields points to the presence of a so far largely unexplored regime of magnetoconvection.

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arXiv2024

Photospheric Hot Spots at Solar Coronal Loop Footpoints Revealed by Hyperspectral Imaging Observations

Poynting flux generated by random shuffling of photospheric magnetic footpoints is transferred through the upper atmosphere of the Sun where the plasma is heated to over 1 MK in the corona. High spatiotemporal resolution observations of the lower atmosphere at the base of coronal magnetic loops are crucial to better understand the nature of the footpoint dynamics and the details of magnetic processes that eventually channel energy into the corona. Here we report high spatial resolution ($\sim$0.1\arcsec) and cadence (1.33 s) hyperspectral imaging of the solar H$α$ line, acquired by the Microlensed Hyperspectral Imager prototype installed at the Swedish 1-m Solar Telescope, that reveal photospheric hot spots at the base of solar coronal loops. These hot spots manifest themselves as H$α$ wing enhancements, occurring on small spatial scales of $\sim$0.2\arcsec, and timescales of less than 100 s. By assuming that the H$α$ wings and the continuum form under the local thermodynamic equilibrium condition, we inverted the H$α$ line profiles and found that the hot spots are compatible with a temperature increase of about 1000 K above the ambient quiet-Sun temperature. The H$α$ wing integrated Stokes $V/I$ maps indicate that hot spots are related to magnetic patches with field strengths comparable to or even stronger than the surrounding network elements. But they do not show the presence of parasitic polarity magnetic field that would support the interpretation that these hot spots are reconnection-driven Ellerman bombs. Therefore, we interpret these features as proxies of locations where convection-driven magnetic field intensification in the photosphere can lead to energy transfer into higher layers. We suggest that such hot spots at coronal loop footpoints may be indicative of the specific locations and onset of energy flux injection into the upper atmosphere.

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arXiv2024

$\texttt{globin}$: A spectropolarimetric inversion code for the coupled inference of atomic line parameters

For many transitions, atomic data, such as the oscillator strength (log(gf)) and the central wavelength of the line, are poorly constrained or even unknown. We present and test a new inversion method that infers atomic line parameters and the height stratification of the atmospheric parameters from spatially resolved spectropolarimetric observations of the Sun. This method is implemented in the new inversion code $\texttt{globin}$. The new method imposes a spatial coupling in inversion parameters common to all pixels, such as the atomic parameters of the observed spectral lines, and infers atmospheric parameters for each spatial pixel individually. The uniqueness of this method lies in its ability to retrieve reliable atomic parameters even for heavily blended spectral lines. We tested the method by applying it to a set of 18 spectral lines between 4015 Å and 4017 Å, synthesized from a 3D magnetohydrodynamic simulation containing a sunspot and the quiet Sun region around it. The results were then compared with a previously used inversion method where atomic parameters were determined for every pixel independently (pixel-by-pixel method). The new method was able to retrieve the log(gf) values of all lines to an accuracy of 0.004 dex, while the pixel-by-pixel method retrieved the same parameter to an accuracy of only 0.025 dex. The largest differences between the two methods are evident for the heavily blended lines, with the former method performing better than the latter. In addition, the new method is also able to infer reliable atmospheric parameters in all the inverted pixels by successfully disentangling the degeneracies between the atomic and atmospheric parameters. The new method is well suited for the reliable determination of both atomic and atmospheric parameters and works well on all spectral lines, including those that are weak and/or severely blended.

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arXiv2024

The MODEST catalog of depth-dependent spatially coupled inversions of sunspots observed by Hinode/SOT-SP

We present a catalog that we named MODEST containing depth-dependent information on the atmospheric conditions inside sunspot groups of all types. The catalog is currently composed of 942 observations of 117 individual active regions with sunspots that cover all types of features observed in the solar photosphere. We use the SPINOR-2D code to perform spatially coupled inversions of the Stokes profiles observed by Hinode/SOT-SP at high spatial resolution. SPINOR-2D accounts for the unavoidable degradation of the spatial information due to the point spread function of the telescope. The sunspot sample focuses on complex sunspot groups, but simple sunspots are also part of the catalog for completeness. Sunspots were observed from 2006 to 2019, covering parts of solar cycles 23 and 24. The catalog is a living resource, as with time, more sunspot groups will be included.

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arXiv2023

Ultra-high resolution observations of plasmoid-mediated magnetic reconnection in the deep solar atmosphere

Magnetic reconnection in the deep solar atmosphere can give rise to enhanced emission in the Balmer hydrogen lines, a phenomenon referred to as Ellerman bombs. To effectively trace magnetic reconnection below the canopy of chromospheric fibrils, we analyzed unique spectroscopic observations of Ellerman bombs in the H-alpha line. We analyzed a 10 min dataset of a young emerging active region observed with the prototype of the Microlensed Hyperspectral Imager (MiHI) at the Swedish 1-m Solar Telescope (SST). The MiHI instrument is an integral field spectrograph that is capable of achieving simultaneous ultra-high resolution in the spatial, temporal and spectral domains. With the combination of the SST adaptive optics system and image restoration techniques, MiHI can deliver diffraction limited observations if the atmospheric seeing conditions allow. The dataset samples the H-alpha line over 4.5 A with 10 mA/pix, with 0.065"/pix over a field of view of 8.6" x 7.7", and at a temporal cadence of 1.33s. This constitutes a hyperspectral data cube that measures 132 x 118 spatial pixels, 456 spectral pixels, and 455 time steps. There were multiple sites with Ellerman bomb activity associated with strong magnetic flux emergence. The Ellerman bomb activity is very dynamic, showing rapid variability and small-scale substructure. We found a number of plasmoid-like blobs with full-width-half-maximum sizes between 0.1" - 0.4" and moving with apparent velocities between 14 and 77 km/s. Some of these blobs have Ellerman bomb spectral profiles with a single peak at a Doppler offset between 47 and 57 km/s. Our observations support the idea that fast magnetic reconnection in Ellerman bombs is mediated by the formation of plasmoids. These MiHI observations demonstrate that a micro-lens based integral field spectrograph is capable of probing fundamental physical processes in the solar atmosphere.

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arXiv2022

The non-LTE formation of the Fe I 6173 A line in the solar atmosphere

The current analysis is dedicated to a detailed investigation of the non-Local Thermodynamic Equilibrium (NLTE) effects influencing the formation of the Fe I 6173 A line, which is widely used by many instruments including the Helioseismic and Magnetic Imager (HMI) on-board the Solar Dynamics Observatory (SDO) and the Polarimetric and Helioseismic Imager on board the Solar Orbiter. We synthesize the Stokes profiles in a snapshot of a three dimensional magnetohydrodynamic simulation of the solar photosphere under both LTE and NLTE conditions. The simulation cube contains a sunspot and a plage region around it. The LTE and NLTE Stokes profiles formed in different features are compared and analysed. NLTE effects are evident in both intensity and polarization profiles. For the 6173 A line, UV overionization is the dominant NLTE mechanism, and scattering effects are much less important. In addition to Fe, an NLTE treatment of Si, Mg and Al is necessary to set the right photon density in the UV. This is found to further enhance the LTE departures compared to the case where Fe alone is treated in NLTE. These effects in the Stokes profiles survive even when the profiles are averaged spatially or sampled on a coarse wavelength grid such as that used by the SDO/HMI and other magnetographs. The deviations from the LTE profiles are stronger in the Fe I 6173 A compared to the 6301 A - 6302 A lines because in case of the latter, line scattering compensates the effect of UV overionization. Based on the nature of departures from LTE, treating the 6173 A line in LTE will likely result in an over-estimation of temperature and an under-estimation of the magnetic field strength.

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arXiv2021

Similarities of magnetoconvection in the umbra and in the penumbra of sunspots

Context. It is unclear why there is a rather sharp boundary in sunspots between the umbra and the penumbra. Both regions exhibit magnetoconvection, manifesting in penumbral filaments in the penumbra and in umbral dots in the umbra. Aims. Here we compare the physical properties of umbral dots and penumbral filaments. Our goal is to understand how the properties of these convective features change across the boundary between the umbra and the penumbra and how this is related to the rapid increase in brightness at the umbra-penumbra boundary. Methods. We derived ensemble averages of the physical properties of different types of convective features based on observations of two sunspots with Hinode. Results. There are strong similarities between the convective features in the outer parts of the umbra and the ones in the penumbra, with most physical parameters being smooth and continuous functions of the length of the features. Conclusions. Our results indicate that the transition in brightness from the umbra to the penumbra is solely caused by an increased effectiveness of magnetoconvection within individual convective cells. There is no significant difference in the number density of convective elements between the outer umbra and the inner penumbra. Penumbral filaments exhibit a larger area and a higher brightness compared to umbral dots. It is still unclear, how exactly the underlying magnetic field causes the increase in size and brightness of convective features in the penumbra.

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arXiv2021

Non-equilibrium Equation of State in stellar atmospheres

In the stellar chromospheres, radiative energy transport is dominated by only the strongest spectral lines. For these lines, the approximation of local thermodynamic equilibrium (LTE) is known to be very inaccurate, and a state of equilibrium cannot be assumed in general. To calculate the radiative energy transport under these conditions, the population evolution equation must be evaluated explicitly, including all time-dependent terms. We develop a numerical method to solve the evolution equation for the atomic-level populations in a time-implicit way, keeping all time-dependent terms to first order. We show that the linear approximation of the time dependence of the populations can handle very large time steps without losing the accuracy. We reproduce the benchmark solutions from earlier, well-established works in terms of non-LTE kinetic equilibrium solution and typical ionization/recombination time-scales in the solar chromosphere.

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arXiv2021

Influence of NLTE effects in Fe I lines on inverted atmosphere II. 6301 A and 6302 A lines formed in 3DNLTE

This paper forms the second part of our study on how the neglect of NLTE conditions in the formation of Fe I 6301.5 A and the 6302.5 A lines influences the atmosphere obtained by inverting their profiles in LTE. The main cause of NLTE effects is the line opacity deficit due to the excess ionization of the Fe I atoms by the UV photons in the Sun. In the first paper, the above photospheric lines were assumed to have formed in 1DNLTE and the effects of horizontal radiation transfer (RT) were neglected. In the present paper, the iron lines are computed in 3DNLTE. We investigate the influence of horizontal RT on the inverted atmosphere and how it can enhance or reduce the errors due to the neglect of 1DNLTE effects. The iron lines are computed in LTE, 1DNLTE and 3DNLTE. They all are inverted using an LTE inversion code. The atmosphere from the inversion of LTE profiles is taken as the reference model. The test atmospheres from the inversion of 1DNLTE and 3DNLTE profiles are compared with it. The differences between models are analysed and correspondingly attributed to NLTE and 3D effects. The effects of horizontal RT are evident in regions surrounded by strong horizontal gradients in temperature. In some regions, the 3D effects enhance the 1DNLTE effects while in some, they weaken. The errors due to neglecting the 3D effects are less than 5% in temperature while the errors are mostly less than 20% in both velocity and magnetic field strength. These errors are found to survive spatial and spectral degradation. The neglect of horizontal RT is found to introduce errors in the derived atmosphere. How large the errors are depends on how strong the local horizontal gradients are in temperature. Compared to the 1DNLTE effect, the 3D effects are more localised to specific regions in the atmosphere and overall less dominant.

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