NLTE inversion and modeling workshop in Porto, September, 2023
Workshop about NLTE modeling and inverse problems, organized by Ivan Milic (KIS) and Ricardo Gafeira (IA), took place in Porto from 4th to 6th September, 2023. NLTE (non-local thermodynamic equilibrium) is a state of solar atmosphere in which excitation and ionization state of the gas decouple from the local physical conditions (e.g. temperature). This influences the spectral line formation, and in turn the interpretation of the observed spectral lines and their polarization. It is especially relevant for understanding the solar chromosphere, filaments and prominences.
The aim of the workshop was a comprehensive presentation and comparison of the codes for the interpretation of the spectral lines formed in NLTE. It gathered around 40 researchers from Europe and USA, who presented their work and discussed the state of the art. The workshop will be followed up with a research paper on the code comparison and a short white paper on importance of these methods and their development.
Two KIS scientists (Juan Manuel Borrero and Ivan Milic) presented their work, while four more attended the talks and discussions.
Sunspot observation at a spatial resolution of 0.08 acrsec with GREGOR
The various mechanisms of magneto-convective energy transport determine the structure of sunspots. Using speckle-reconstructed images in the 486 nm band, we characterise the appearance of light bridges.
We find branched dark lanes extending along thin (≈1′′) light bridges in sunspots at various heliocentric angles. In thick (>2′′) light bridges the branches are disconnected from the central lane and have a Y shape with a bright grain toward the umbra. The images reveal that light bridges exist on varying intensity levels and that their small-scale features evolve on timescales of minutes. Faint-light bridges show dark lanes outlined by the surrounding bright features. Dark lanes are very common and are also found in the boundary of pores. They have a characteristic width of 0.1′′ or smaller. Intergranular dark lanes of that width are seen in active region granulation. We interpret our images in the context of magneto-convective simulations and findings: While central dark lanes in thin light bridges are elevated and associated with a density increase above upflows, the dark lane branches correspond to locations of downflows and are depressed relative to the adjacent bright plasma. Thick light bridges with central dark lanes show no projection effect. They have a flat elevated plateau that falls off steeply at the umbral boundary. There, Y-shaped filaments form as they do in the inner penumbra. This indicates the presence of inclined magnetic fields, meaning that the umbral magnetic field is wrapped around the convective light bridge.
KIS operates and maintains along with its German partners (MPS and AIP) the GREGOR Telescope.
Data-constrained 3D Solar Modeling
GX Simulatoris an IDL package that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio–both thermal and nonthermal, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface.
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Studying the Poynting flux in the quiet Sun
One of the conduits for the energy transfer from the lower to the upper solar atmosphere is the Poynting flux, the vector product of the magnetic and electric field. Estimating the Poynting flux in the quiet Sun is a challenging open problem, because of the low polarization signals that make estimations of these fields extremely uncertain. In this work, the authors analyze SUNRISE/IMAX observations and state-of-the-art numerical simulations to try to estimate the amount of this flux in the solar photosphere, but also to characterize the biases our methods are suffering from due to the limitations of our methods. They combine spectropolarimetric inversions, machine learning methods, and state-of-the-art electric field inference, to try and estimate energy transfer due to the Poynting flux. This is one of the first attempts of this kind and the results are encouraging, but also bring a lot of unanswered questions.
KIS contributes to the SUNRISE balloon-borne observatory with the Correlation and Wavefront Sensor (CWS):
Inferring of the electric current vector in the solar photosphere
Electric currents play a very important role in the energy balance and transport within the plasma in the solar atmosphere and in particular in the solar corona. They are also proxies for magnetic reconnection which is considered to be the main driver of explosive and transient evens in the chromoshere and corona. Consequently, one of the main goals for the solar physics community has been to measure these electric currents. Despite their importance, routine and direct measurements of electric currents j in the solar atmosphere have not been generally possible. With our new inversion code FIRTEZ-DZ, developed at our institute, we are capable of accurate inferences of the full electric current vector j. This is possible because FIRTEZ considers magneto-hydrostatic equilibrium (MHS) instead of the widely used hydrostatic equilibrium (HE) employed by other inversion codes.
Reference: Pastor Yabar, A.; Borrero, J.M.; Quintero-Noda, C.; Ruiz Cobo, B. (2021), A&ALetters, 656, L20
Sunspot decay
The stability of sunspots is one of the long-standing unsolved puzzles in the field of solar magnetism and the solar cycle. The thermal and magnetic structure of the sunspot beneath the solar surface is not accessible through observations, thus processes in these regions that contribute to the decay of sunspots can only be studied through theoretical and numerical studies.
New insights were gained taking advantage of a numerical simulation of a sunspot with a lateral extension of more than 98 000 km times 98 000 km extending almost 18 000 km beneath the solar surface. These simulations had been performed by Matthias Rempel at the High Altitude Observatory (HAO). A data set of 30 hours, showing a stable sunspot at the solar surface, was analysed with respect to sunspot decay as a PhD project at KIS, in collaboration with the HAO.
This simulation allows to study the non-local dynamics of fluting instability interacting with stabilising buoyance forces within in the magnetic flux tube that constitutes the spot. The simulation shows that the fluting instability causes a corrugation along the circumference of the flux tube (sunspot) which proceeds fastest at a depth around 7500 km beneath the solar surface. For a long time, the decay of the spot is suppressed by the stabilising effect close to the surface which holds the bundle of magnetic field lines together. Yet, ultimately, large intrusions of field-free plasma below the surface form convective bubbles which might form light-bridges in the spot at the solar surface. This can finally disrupt the spot.
The analysis of the simulation also allow to assess the results of a linear stability analysis developed in the 1970s (Meyer, Schmidt, & Weiss 1977). As predicted back then, the magnetic field configuration of a sunspot in the uppermost few 1000 km is stable, mostly due to buoyancy forces. Deeper layers in the spot are unstable to fluting (interchange) instability as it was predicted.
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Microwave imaging spectroscopy
Broadband microwave imaging spectroscopyoffers an entirely new perspective for inferring the evolving coronal parameters of solar flares from microwave observations. These data are becoming increasingly accessible as a routine diagnostics method due to recent technological advances that facilitated the design and development of a new generation of radio instruments, out of which Expanded Owens Valley Solar Array (EOVSA) currently stands out as a world-leading solar dedicated broadband microwave interferometry array. EOVSA features simultaneous imaging at 451 science channels from 1–18GHz, with 1 s cadence. This technique provides a detailed microwave spectrum to be derived at any location of a snapshot image (see Figure on the right). The shape and brightness values of such spectra contain unique fingerprints of the underlying source parameters, such as the magnetic field strength B and the power-law slope $\delta$ of the energetic electron distribution displayed in the spectral plot insets. To facilitate the analysis of the broadband microwave imaging spectroscopy data that led to these breakthrough scientific results, the Dr. Fleishman’s team developed the core methodology, as well as user-friendly analysis (GSFIT) and visualization (GSFITVIEW) tools, which were employed to derive evolving physical parameters in the flare volume.
Polar Magnetic Fields
Polar magnetic fields play a key role in the solar cycle and are a main driver of the solar wind. However, characterizing these fields is extremely difficult due to an array of reasons: projection effects, Zeeman effect biases, noise, and magnetic field disambiguation are just some of the problems. To address these biases, a team consisting of Xudong Sun (University of Hawai’i), Rebecca Centeno (HAO), and Ivan Milic (KIS), is conducting a series of end-to-end studies to identify and characterize the biases encountered in the magnetic field estimation process (i.e. the inversion). In the first paper in the series, the authors explore the limits of standard Milne-Eddington inversion and particularly the usage of the filling factor as a free parameter. The results are illuminating, but also bleak: even inference of the “apparent” magnetic field quantities at the poles suffers from large systematic uncertainties. In the upcoming publications, authors are studying individual biases and ways to mitigate them.
Signatures of Retraction and Reconnection in realistic MHD simulations
Magnetic flux emergence and cancelling in the quiet Sun is a frequently observed phenomena. The two possible physical flux removal mechanisms involved in its disappearance are retraction and reconnection. In order to find distinct observational signatures characterising retraction and reconnection we carry out three dimensional nongrey radiative magnetohydrodynamic simulations of convection near the solar surface and the solar photosphere using the STAGGER code, and employing different initial conditions: 1) mixed polarity simulations with alternating horizontal stripes of opposite vertical magnetic field and separated by a zero field stripe, and 2) flux emergence simulations with continuous injection of magnetic flux from the lower boundary. These initial conditions are meant to represent two different situations in the solar photosphere: magnetic flux cancelling in the absence or presence of magnetic flux emergence, respectively. We analyse the observational signatures of magnetic flux removal processes for flux emergence as well as for mixed polarity magnetohydrodynamic simulations. In the flux emergence simulation we are able to identify ubiquitous reconnection events anywhere from the solar surface to the upper photosphere. For a few of those reconnection events we can identify supersonic upflow velocities in the upper photosphere as well as strong temperature enhancements. Very close to the locations where reconnection takes place we also see strong electric currents, as well as supersonic horizontal velocities leading to sideways plasma compression. In the mixed-polarity simulations we only detect observational signatures of magnetic field retraction, related to large downflow velocities that appear in between regions where opposing horizontal velocities converge. These horizontal velocities are oftentimes supersonic, leading to heating due to shock dissipation. We do not see clear signatures of magnetic reconnection in these mixed polarity simulations. An example of retraction of magnetic field lines and its associated is presented on the right. We suggest that in the quiet Sun emerging flux regions the main flux removal process is reconnection, while in non flux emerging regions, retraction is the the dominant flux removal process.
Reference: Thaler, I. & Borrero, J.M. (2023), A&A, 673, A163
The magnetic field at the boundary between umbra and penumbra
Sunspots are the longest-known manifestation of solar activity and their magnetic nature has been known for more than a century. Despite this, the boundary between umbrae and penumbrae, the two fundamental sunspot regions, has hitherto been solely defined by an intensity threshold.
Using Hinode satellite data, we can give statistical proof of an empirical law governing the boundary between umbra and penumbra in stable sunspots: The vertical component of the magnetic field, Bver, is invariant.
Contours of intensity at 50% of the granular quiet-sun value and contours of Bver=1867 G match. This is illustrated in the Fig. 1, in which contours for intensity (white) and Bver (red) are displayed for some of the spots that where included in the sample. Deviations were studied and shown to be non-significant (Jurcak et al. 2018).
This empirical law applies for all sunspots of the sample with different sizes, morphologies, evolutionary stages, and phases of the solar cycle. Thereby we have unveiled the magnetic property that discriminates between the umbral and penumbral modes of magneto-convection. This discovery carries strong consequences for the understanding of the fundamental processes of energy transport occurring in the magnetic Sun.
The validity of this empirical law and the value of this new constant is now being examined for different wavelengths and data sources. Figure 2 shows intensity images of sunspots observed with the GRIS@GREGOR spectograph. The value of Bver=1843 Gauss is consistent with the results from Jurcak et al 2018 with Hinode data.
We also studied the temporal evolution of Bver at the umbral boundary, in this case using HMI/SDO data. During the first disc passage, NOAA AR 11591, Bver remains constant at 1693 G with a root-mean-square deviation of 15 G, whereas the magnetic field strength varies substantially (mean 2171 G, rms of 48 G) and shows a long-term variation as shown in the residual in Fig. 3 after daily variations due to the satellite orbit are corrected. Hence, during the disc passage of a stable sunspot its umbral boundary can equivalently be defined by using the continuum intensity Ic or the vertical magnetic field component Bver. Contours of fixed magnetic field strength fail to outline the umbral boundary (Schmassmann et al. 2018).
Now, since observations have shown that in stable sunspots the umbral boundary is outlined by a critical value of the vertical magnetic field component, the key question is: What is the nature of the distinct magnetoconvection regimes in the umbra and penumbra? This is still unclear. To follow up on this, we analysed a sunspot simulation in an effort to understand the origin of the convective instabilities giving rise to the penumbral and umbral distinct regimes. We applied the criterion from Gough & Tayler (1966, MNRAS, 133, 85), accounting for the stabilising effect of the vertical magnetic field to investigate the convective instabilities in a MURaM sunspot simulation. The result is shown in Fig. 4: The deep subphotospheric sunspot trunk is magneto-convectivly stable. Upwards from some -5 Mm, columns of instabilty characterise the umbra of the sunspot. The subsphotospheric penumbra exhibits filamentary instabilities that are almost parallel to the solar surface. Hence, the Gough and Tayler criterion as a diagnostic tool reveals the tripartite nature of sunspot structure with distinct regimes of magneto-convection in the umbra, penumbra, and granulation operating in realistic MHD simulations. (Schmassmann et al. 2021)
References:
- Jurčák, J., Rezaei, R., Bello González, N. Schlichenmaier, R., Vomlel, J., 2018, Astronomy & Astrophysics, Volume 611, L4
- Schmassmann, M., Schlichenmaier, R., Bello González, N. 2018, Astronomy & Astrophysics, Volume 620, A104
- Lindner, P., Schlichenmaier, R., Bello González N., 2020, Astronomy & Astrophysics, Volume 638, A25
- Schmassmann, M., Rempel, M., Bello González, N., Schlichenmaier, R., Jurčák, J., 2021, Astronomy & Astrophysics, Volume 656, A92
Data-constrained 3D modeling of a solar flare evolution
Solar flares are driven by release of the free magnetic energy and its conversion to other forms of energy–kinetic, thermal, and nonthermal. Quantification of partitions between these energy components and their evolution is needed to understand the solar flare phenomenon including nonthermal particle acceleration, transport, and escape and the thermal plasma heating and cooling. The challenge of remote sensing diagnostics is that the data are taken with finite spatial resolution and suffer from line-of-sight (LOS) ambiguity including cases when different flaring loops overlap and project one over the other. We address this challenge, for the first time, by devising a data-constrained evolving 3D model of a moderate solar flare. We developed a 3D magnetic model consistent with available imaging data and constrained by the underlying photospheric magnetic field. Then, for each time frame, we adjusted the distributions of the thermal plasma and nonthermal electrons in the model, such that the observables synthesized from the model matched the observations (see figure/animation). This approach removes the LOS ambiguity and permits to disentangle contributions from the overlapping loops. It reveals new facets of electron acceleration and transport, as well as heating and cooling the flare plasma in 3D. We find signatures of substantial direct heating of the flare plasma not associated with the energy loss of nonthermal electrons.
Reference: Fleishman, G.D., Nita, G.M., Motorina, G.G. "Data-constrained 3D modeling of a solar flare evolution: acceleration, transport, heating, and energy budget", ApJ; (in press)