Matthias Rempel

Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D): II. A Physics-Informed Machine Learning Method for 3D Solar Photosphere Reconstruction

whawkins — Tue, 23 Dec 2025 16:21:35 +0000

Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D): II. A Physics-Informed Machine Learning Method for 3D Solar Photosphere Reconstruction whawkins Tue, 12/23/2025 - 09:21

Author:

whawkins

Dec 23, 2025

Astrophysical Journal: Inferring the three-dimensional (3D) solar atmospheric structures from observations is a critical task for advancing our understanding of the magnetic fields and electric currents that drive solar activity. In this work, we introduce a novel, Physics-Informed Machine Learning method to reconstruct the 3D structure of the lower solar atmosphere based on the output of optical depth sampled spectropolarimetric inversions, wherein both the fully disambiguated vector magnetic fields and the geometric height associated with each optical depth are returned simultaneously. Traditional techniques typically resolve the 180-degree azimuthal ambiguity assuming a single layer, either ignoring the intrinsic non-planar physical geometry of constant optical-depth surfaces (e.g., the Wilson depression in sunspots), or correcting the effect as a post-processing step. In contrast, our approach simultaneously maps the optical depths to physical heights, and enforces the divergence-free condition for magnetic fields fully in 3D. Tests on magnetohydrodynamic simulations of quiet Sun, plage, and a sunspot demonstrate that our method reliably recovers the horizontal magnetic field orientation in locations with appreciable magnetic field strength. By coupling the resolutions of the azimuthal ambiguity and the geometric heights problems, we achieve a self-consistent reconstruction of the 3D vector magnetic fields and, by extension, the electric current density and Lorentz force. This physics-constrained, label-free training paradigm is a generalizable, physics-anchored framework that extends across solar magnetic environments while improving the understanding of various solar puzzles.

Panel (a) shows the flowchart for training the model. The inputs are the 3D magnetic vector fields with azimuthal ambiguity, and an initial guess of the geometric heights associated with each optical-depth layer. The UNet3DB network predicts 3D vector magnetic field, and the UNet3DZ network provides the geometric heights. They are combined to compute a custom loss function that also considers physical constraints (divergence free magnetic field). Panel (b) shows the post-processing step that assembles the outputs from the neural networks (prediction) and the original input magnetic fields into the final output. Panel (c) shows an example of the 3D data, split with overlaps between nearby subfields. These individual subfields are used as the input for training. Panel (d) presents the UNet3D structure, reproduced from Figure 2 in Cicek et al. (2016).

Using the Hanle Effect in Mg II k to Quantify the Open Flux above the Solar Poles

whawkins — Tue, 16 Sep 2025 20:00:52 +0000

Using the Hanle Effect in Mg II k to Quantify the Open Flux above the Solar Poles whawkins Tue, 09/16/2025 - 14:00

Author:

whawkins

Sep 16, 2025

The Astrophysical Journal: We test the use of the Mg II resonant lines for measurement of the magnetic field at the top of the chromosphere of polar coronal holes (CHs). The Hanle effect in the core of Mg II k enables access to a regime of field strengths where the Zeeman effect has little diagnostic value (especially at the solar poles, where most of the field is transverse to the line of sight). Synthetic Stokes spectra computed from a radiation magnetohydrodynamic simulation of a CH emulating a high viewing angle are inverted with the HanleRT Tenerife Inversion Code, which accounts for the physical processes that lead to scattering-induced polarization and its modification due to the magnetic field and other symmetry-breaking mechanisms. We find that, while degeneracies in the atmospheric model lead to poor inferences of the thermodynamical properties, the magnetic inferences are highly consistent with the model values. The mean magnetic field strength in the simulation cube is typically retrieved with a relative error of δB ∼ 20% and an absolute error of ΔB ∼ 2 G at the top of the chromosphere. This opens up an avenue for promising chromospheric constraints for magnetic extrapolation models that ingest photospheric magnetograms, whose biases and uncertainties are troublesome to the reconstruction of the heliospheric magnetic field.

Inversion of an average synthetic Mg II k spectrum averaged over a 5"x5" area of a quiet Sun coronal hole simulation. The inversion strategy optimizes the fit of the spectral line core to extract the magnetic information at the top of the chromosphere. The synthetic observations are represented by black dots and the best-fit spectrum achieved by the HanleRT-TIC inversion is shown with red lines in the top four panels; additionally, the top-left panel shows the contribution function of the spectral line in blue. The bottom row shows the retrieved magnetic field stratification (red line) and the formal error bars at the inversion nodes derived by HanleRT-TIC. The inversion results are compared to the ensemble of values from the MURaM model atmospheres (gray histogram) used to create the synthetic observation. The height range of formation of the line core is indicated by the vertical blue stripes. The inversion inferences of the magnetic field are compatible with the average values of the simulation within the blue stripes.

The Striated Solar Photosphere Observed at 0.″03 Resolution

whawkins — Wed, 13 Aug 2025 20:28:21 +0000

The Striated Solar Photosphere Observed at 0.″03 Resolution whawkins Wed, 08/13/2025 - 14:28

Author:

whawkins

Aug 13, 2025

Left: G-band intensity image observed with DKIST VBI showing striations with widths of approximately 20‑50 km. Right: Synthetic G-band intensity image computed from a MURaM simulation for an inclination of μ = 0.85, matching the observed inclination. The numerical simulation shows intensity striations on a comparable scale and confirms their association with photospheric magnetic flux concentrations that modulate the geometrical height where the emergent intensity forms.

The Astrophysical Journal Letters: Striated granular edges observed in the solar photosphere represent one of the smallest-scale phenomena on the Sun. They arise from the interaction of strongly coupled hydrodynamic, magnetic, and radiative properties of the plasma. In particular, modulations in the photospheric magnetic field strength cause variations in density and opacity along the line of sight, leading to their formation. Therefore, the striation patterns can be used as valuable diagnostics for studying the finest-scale structure of the photospheric magnetic field. The Daniel K. Inouye Solar Telescope (DKIST) allows observations of the solar atmosphere with a spatial resolution of better than 0 .″ 03 with its current instrumentation. We analyze images acquired with the Visible Broadband Imager using the G-band channel to investigate the characteristics of fine-scale striations in the photosphere and compare them with state-of-the-art radiation-MHD simulations at similar spatial resolution. Both observed and synthetic images reveal photospheric striae with widths of approximately 20‑50 km, suggesting that at least 4 m class solar telescopes are necessary to resolve this ultrafine structure. Analysis of the numerical simulations confirms that the striation observed in the filtergrams is associated with spatial variations in photospheric magnetic flux concentrations, which cause shifts in the geometrical height where the emergent intensity forms. Some fine-scale striations in the synthetic images originate from magnetic field variations of approximately 100 G, resulting in Wilson depressions as narrow as 10 km. This suggests that DKIST G-band images can trace the footprints of magnetic field variations and Wilson depressions at a similar scale.

The role of the Lorentz force in sunspot equilibrium

whawkins — Wed, 13 Aug 2025 19:50:25 +0000

The role of the Lorentz force in sunspot equilibrium whawkins Wed, 08/13/2025 - 13:50

Author:

whawkins

Aug 13, 2025

Scatter plots of the physical quantities in penumbra (extracted along an azimuthal arc) for GREGOR data (red squares), Hinode data (blue circles), and the MHD simulation (black triangles). Pearson correlations coefficients, c, for each of these pieces of data are provided in the legend. Linear fits to the data are shown with thick solid color lines. Upper left: γ − ∥B∥. Upper right: γ − Pg. Lower left: γ − ρ. Lower right: Lϕ − r−1∂Pg/∂ϕ. Each panel also includes three smaller subpanels in which the variations in the physical quantities along ϕ are displayed in purple and green colors. These subpanels are ordered as: GREGOR (left), Hinode (middle), and MHD simulations (right). This is also indicated by the arrows under the correlation coefficients for each data source. We note that the values of the ϕ components of the Lorentz force and of the gas pressure gradient in the simulations have been divided by five. The results demonstrate that, in the azimuthal ϕ direction, penumbral spines and intraspines are in almost perfect magnetohydrostatic equilibrium between the azimuthal components of Lorentz and pressure forces.

Astronomy & Astrophysics: Sunspots survive on the solar surface for timescales 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. Aims. We aim to study whether sunspot equilibrium is maintained once azimuthal fluctuations in the magnetic field, produced by the sunspot fine structure, are taken into account. Methods. We apply the FIRTEZ Stokes inversion code to spectropolarimetric observations to infer the magnetic and thermodynamic parameters in two sunspots located at the 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. Results. 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 an observed filamentary structure. Results from the two observed sunspots are in excellent qualitative and quantitative agreement with the numerical simulations. Conclusions. 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.

International & European news agencies feature Sunspot research

whawkins — Wed, 13 Aug 2025 17:54:48 +0000

International & European news agencies feature Sunspot research whawkins Wed, 08/13/2025 - 11:54

Author:

whawkins

Aug 13, 2025

A recently published paper made quite a splash in the International and European news. Dr. Juan Borrero, of the Institute of Solar Physics (KIS) in Freiburg, led a team of scientists that included HAO's Matthias Rempel. The international team developed a new method for analyzing the stability of sunspots.

International:

Spain:

Mexico:

Meteored

Germany:

Cutting-edge SPIn4D project combines AI and Astronomy

whawkins — Tue, 26 Nov 2024 23:52:25 +0000

Cutting-edge SPIn4D project combines AI and Astronomy whawkins Tue, 11/26/2024 - 16:52

Author:

whawkins

Nov 26, 2024

Astrophysical Journal: The National Science Foundation's Daniel K. Inouye Solar Telescope (DKIST) will provide high-resolution, multiline spectropolarimetric observations that are poised to revolutionize our understanding of the Sun. Given the massive data volume, novel inference techniques are required to unlock its full potential. Here, we provide an overview of our "SPIn4D" project, which aims to develop deep convolutional neural networks (CNNs) for estimating the physical properties of the solar photosphere from DKIST spectropolarimetric observations. We describe the magnetohydrodynamic (MHD) modeling and the Stokes profile synthesis pipeline that produce the simulated output and input data, respectively. These data will be used to train a set of CNNs that can rapidly infer the four-dimensional MHD state vectors by exploiting the spatiotemporally coherent patterns in the Stokes profile time series. Specifically, our radiative MHD model simulates the small-scale dynamo actions that are prevalent in quiet-Sun and plage regions. Six cases with different mean magnetic fields have been explored; each case covers six solar-hours, totaling 109 TB in data volume. The simulation domain covers at least 25 × 25 × 8 Mm, with 16 × 16 × 12 km spatial resolution, extending from the upper convection zone up to the temperature minimum region. The outputs are stored at a 40 s cadence. We forward model the Stokes profile of two sets of Fe i lines at 630 and 1565 nm, which will be simultaneously observed by DKIST and can better constrain the parameter variations along the line of sight. The MHD model output and the synthetic Stokes profiles are publicly available, with 13.7 TB in the initial release.

Schematic representation of the SPIn4D model workflow. The core of the model is the DL neural network, highlighted in blue in the middle of the diagram. The network training step is outlined by the broken green line and uses data derived from the MURaM simulations, both the MHD variables themselves and the Stokes profiles (I, Q, U, V) synthesized from the MHD data cubes (green lines). Once trained on the simulated data, observed Stokes data can be input into the network (red arrow) to produce the most likely 3D MHD state as output (labeled "Predicted MHD Variables"). The network may be trained to receive single-time input Stokes data to produce a reduced dimensional output MHD state ( B , vz , P, T) or to receive multitime input Stokes data to produce a full-dimensional MHD output, including additional derived outputs, such as vector velocities, Poynting flux, and so on. The network may also be trained to produce the derived outputs directly.

Magnetic Field Evolution of the Solar Active Region 13664

whawkins — Thu, 07 Nov 2024 17:46:10 +0000

Magnetic Field Evolution of the Solar Active Region 13664 whawkins Thu, 11/07/2024 - 10:46

Author:

whawkins

Nov 7, 2024

ApJL (Astrophysical Journal Letters): In May 2024, the strongest geomagnetic storm since 2003 hit Earth, peaking with a disturbance index of -412 nT. This storm was triggered by solar activity from solar Active Region (AR) 13664, which produced numerous powerful bursts of energy, including 12 X-class solar flares. Starting around May 7, AR 13664 rapidly grew in size and magnetic energy, sparking intense flare activity.

To better understand how this active region evolved and what led to these major solar eruptions, we used advanced 3D models to analyze the Sun’s magnetic fields. Specifically, we applied the NF2 model, which uses Artificial Intelligence (AI) to integrate physical equations with observational data from the Solar Dynamics Observatory (SDO). This approach allowed us to follow the active region’s magnetic changes in real time, from May 5 through May 11.

Our results show that drops in free magnetic energy coincide with large solar flares, and that all modeled X-class flares were associated with a sudden decrease in magnetic energy. A detailed look at the largest flare on May 10, an X3.9-class event, suggests that the flare resulted from the interaction between separated magnetic domains.

This study provides a detailed record of the magnetic field evolution of AR 13664, now publicly available for further research.

Magnetic field configuration and parameters prior to the X3.9 solar flare and associated filament eruption, as derived from a pre-flare non-linear force-free coronal magnetic field extrapolation on 2024 May 10-05:58:43 UT. Selected magnetic field structures, showing the filament channel colored by the local current density, a fan-spine structure in green, and overlying fields connecting both ribbons in gray.

Annular Eclipse Expedition at Hovenweep

whawkins — Fri, 03 Nov 2023 21:53:04 +0000

Annular Eclipse Expedition at Hovenweep whawkins Fri, 11/03/2023 - 15:53

Author:

whawkins

Nov 3, 2023

The logo that represents all the institutions that made the annular eclipse expedition possible superimposed over the eclipse maxima image.

On 14 October 2023, a captivating annular eclipse graced the skies from Oregon to Texas in the U.S. It was a privilege to not only witness this celestial spectacle but also engage with a curious audience that included a team of solar physicists from both the High Altitude Observatory at NCAR and the National Solar Observatory. Visiting students and/or voluntary collaborators were also among the spectators.

Sunrise and over-imposed eclipse evolution at Hovenweep National Monument in Utah.

Han Uitenbroek

An annular solar eclipse occurs when the Moon passes directly between the Earth and the Sun, but the Moon is too far from Earth to block out the Sun entirely. Instead of a total eclipse, a ring of sunlight is illuminated around the Moon, creating the infamous "Ring of Fire".

Our expedition led us to the historic Hovenweep National Monument in Utah, where, around well-preserved Ancestral Puebloan ruins, we had the opportunity of sharing insights about the Sun! The NPS estimated that over 600 visitors were on site. Favorable weather allowed attendees to experience this remarkable event through an array of telescopes, binoculars, and eclipse glasses.

Photo of the annular eclipse maxima from the eclipse expedition, Hovenweep National Monument.

Han Uitenbroek

Using a colander to create pinhole projections onto paper.

With materials provided by the NASA PUNCH outreach team for the Small Explorer mission, we engaged the public with various activities touching not only on the eclipse science, but also on relevant cultural and historical aspects related to how humans have perceived solar eclipses and other Solar phenomena throughout the centuries, as depicted in paintings, drawings, and petroglyphs.

Some of the images below offer a glimpse into the fascinating natural optical phenomenon of pinhole projection. They illustrate how differently-shaped holes on objects produce shadows that mirror the contour of the light source. This effect becomes especially apparent during an eclipse, resulting in crescents or rings forming within the shadowed area.

Photo collage of observation deck visitors at the annular eclipse expedition, Hovenweep National Monument, UT.

Additionally, our team offered evening astronomy sessions that allowed attendees to explore the beautiful dark skies of Hovenweep. They had the chance to marvel at Saturn's rings, observe the distinctive cloud patterns and moons of Jupiter, witness the splendour of the Andromeda Galaxy, and an array of distant globular clusters and nebulae, providing a rich experience of the wonders above.

Photo collage of outreach table activities at the annular eclipse expedition, Hovenweep National Monument, Utah.

This annular solar eclipse was truly a sight to see, and yet 2024 will provide an even more rare opportunity of a total solar eclipse over the U.S./Canada on April 8th.

We express our gratitude to all attendees for their active participation, to the dedicated team for their unwavering commitment, to the National Parks Service team and to the supporting institutions.

An abundance of stars at Hovenweep National Monument taken during the annular eclipse expedition.

Teams included:

NSO: Alin Paraschiv, Han Uitenbroek
NCAR HAO: Matthias Rempel, Daniela Lacatus, Maurice Wilson, Benoit Tremblay
Students and/or collaborators: Aatiya Ali, Kalista Tyson, Vanessa Mercea, Aidan Halpin

Comprehensive Radiative MHD Simulations of Eruptive Flares above Collisional Polarity Inversion Lines

whawkins — Tue, 31 Oct 2023 15:34:23 +0000

Comprehensive Radiative MHD Simulations of Eruptive Flares above Collisional Polarity Inversion Lines whawkins Tue, 10/31/2023 - 09:34

Author:

whawkins

Oct 31, 2023

Simulation snapshot showing the magnetic field configuration 14 seconds before the peak of the flare.

The Astrophysical Journal: This publication presents a new simulation setup using the MURaM radiative MHD code that allows the study of the formation of collisional polarity inversion lines (cPILs) in the photosphere and the coronal response including flares. In this scheme, we start with a bipolar sunspot configuration and set the spots on collision course by imposing the appropriate velocity field at the footpoints in the subphotospheric boundary. We produce different setups with the same initial spot separation by varying physical parameters such as the collision speed and minimum collision distance. While all setups lead to the formation of an EUV and X-ray sigmoid structure, only the cases with a close passing of the spots cause flares and mass eruptions. The energy release is in the 1–2 erg range, putting the simulated flares into the upper C-class to lower M-class range of GOES X-ray 1–8 Å flux. While the setup with the more distant passing of the spots does not lead to a flare, the corona is nonetheless substantially heated, suggesting noneruptive energy-release mechanisms. We focus our discussion on two particular setups that differ in spot coherence and resulting cPIL length persistence. We find different timings in the transition from a sheared magnetic arcade to magnetic flux rope (MFR); the setup with a large length but shorter duration cPIL produces a MFR during the eruption, while the MFR is preexisting in the setup with a large length and longer duration cPIL. While both result in flares of comparable strength and the eruption of a coronal mass ejection, the setup with preexisting MFR (and embedded filament) leads to an MFR eruption with a larger mass content.

See NOVA highlight

Citation

“Comprehensive Radiative MHD Simulations of Eruptive Flares Above Collisional Polarity Inversion Lines,” Matthias Rempel et al 2023 ApJ 955 105. doi:10.3847/1538-4357/aced4d

Comprehensive Radiative MHD Simulations of Eruptive Flares above Collisional Polarity Inversion Lines

whawkins — Thu, 22 Jun 2023 22:56:57 +0000

Comprehensive Radiative MHD Simulations of Eruptive Flares above Collisional Polarity Inversion Lines whawkins Thu, 06/22/2023 - 16:56

Author:

whawkins

Jun 22, 2023

ApJ: Matthias Rempel et al. present a new simulation setup using the MURaM radiative Magnetohydrodynamic (MHD) code that allows to study the formation of collisional polarity inversion lines (cPILs) in the photosphere and the coronal response including flares. In this scheme we start with a bipolar sunspot configuration and set the spots on collision course by imposing the appropriate velocity field at the footpoints in the subphotospheric boundary. We produce different setups with the same initial spot separation by varying physical parameters such as the collision speed and minimum collision distance. While all setups lead to the formation of an EUV and X-ray sigmoid structure, only the cases with a close passing of the spots cause flares and mass eruptions. The energy release is in the 1 − 2 × 10^31 ergs range, putting the simulated flares into the upper C-class to lower M-class range of GOES X- ray 1-8 ̊A flux. While the setup with the more distant passing of the spots does not lead to a flare, the corona is nonetheless substantially heated, suggesting non-eruptive energy release mechanisms. We focus our discussion on two particular setups that differ in spot coherence and resulting cPIL length persistence. We find different timings in the transition from a sheared magnetic arcade (SMA) to magnetic flux rope (MFR); the setup with a large length but shorter duration cPIL produces a MFR during the eruption, while the MFR is pre-existing in the setup with a large length and longer duration cPIL. While both result in flares of comparable strength and the eruption of a CME, the setup with pre-existing MFR (and embedded filament) leads to an MFR eruption with a larger mass content. Was published in October 2023.

Erupting magnetic flux rope. Field lines are color-coded by twist number. In addition we show a second set of field lines which are selected based on their connectivity to the reconnection region, these field lines are color-coded by temperature. We find tether-cutting reconnection underneath the ejected flux-rope. We show a cross-section through the erupting flux-ropes that display the mass density.

Matthias Rempel

Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D): II. A Physics-Informed Machine Learning Method for 3D Solar Photosphere Reconstruction

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Using the Hanle Effect in Mg II k to Quantify the Open Flux above the Solar Poles

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The Striated Solar Photosphere Observed at 0.″03 Resolution

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The role of the Lorentz force in sunspot equilibrium

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International & European news agencies feature Sunspot research

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Cutting-edge SPIn4D project combines AI and Astronomy

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Magnetic Field Evolution of the Solar Active Region 13664

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Annular Eclipse Expedition at Hovenweep

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Comprehensive Radiative MHD Simulations of Eruptive Flares above Collisional Polarity Inversion Lines

Citation

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Comprehensive Radiative MHD Simulations of Eruptive Flares above Collisional Polarity Inversion Lines

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