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The National Science Foundation's Daniel K. Inouye Solar Telescope (DKIST) will provide high-resolution, multi-line 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 conducted; each case covers six solar-hours, totaling 109 TB in data volume. The simulation domain covers at least $25\times25\times8$ Mm with $16\times16\times12$ 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., Comment: Submitted to AAS Journals. Comments welcome

Poor generalization performance caused by distribution shifts in unseen domains often hinders the trustworthy deployment of deep neural networks. Many domain generalization techniques address this problem by adding a domain invariant regularization loss terms during training. However, there is a lack of modular software that allows users to combine the advantages of different methods with minimal effort for reproducibility. DomainLab is a modular Python package for training user specified neural networks with composable regularization loss terms. Its decoupled design allows the separation of neural networks from regularization loss construction. Hierarchical combinations of neural networks, different domain generalization methods, and associated hyperparameters, can all be specified together with other experimental setup in a single configuration file. Hierarchical combinations of neural networks, different domain generalization methods, and associated hyperparameters, can all be specified together with other experimental setup in a single configuration file. In addition, DomainLab offers powerful benchmarking functionality to evaluate the generalization performance of neural networks in out-of-distribution data. The package supports running the specified benchmark on an HPC cluster or on a standalone machine. The package is well tested with over 95 percent coverage and well documented. From the user perspective, it is closed to modification but open to extension. The package is under the MIT license, and its source code, tutorial and documentation can be found at https://github.com/marrlab/DomainLab.

We address the online combinatorial choice of weight multipliers for multi-objective optimization of many loss terms parameterized by neural works via a probabilistic graphical model (PGM) for the joint model parameter and multiplier evolution process, with a hypervolume based likelihood promoting multi-objective descent. The corresponding parameter and multiplier estimation as a sequential decision process is then cast into an optimal control problem, where the multi-objective descent goal is dispatched hierarchically into a series of constraint optimization sub-problems. The subproblem constraint automatically adapts itself according to Pareto dominance and serves as the setpoint for the low level multiplier controller to schedule loss landscapes via output feedback of each loss term. Our method is multiplier-free and operates at the timescale of epochs, thus saves tremendous computational resources compared to full training cycle multiplier tuning. It also circumvents the excessive memory requirements and heavy computational burden of existing multi-objective deep learning methods. We applied it to domain invariant variational auto-encoding with 6 loss terms on the PACS domain generalization task, and observed robust performance across a range of controller hyperparameters, as well as different multiplier initial conditions, outperforming other multiplier scheduling methods. We offered modular implementation of our method, admitting extension to custom definition of many loss terms.

Spectropolarimetric observations used to infer the solar magnetic fields are obtained with a limited spatial resolution. The effects of this limited resolution on the inference of the open flux over the observed region have not been extensively studied. We aim to characterize the biases that arise in the inference of the mean flux density by performing an end-to-end study that involves the generation of synthetic data, its interpretation (inversion), and a comparison of the results with the original model. We synthesized polarized spectra of the two magnetically sensitive lines of neutral iron around 630\,nm from a state-of-the-art numerical simulation of the solar photosphere. We then performed data degradation to simulate the effect of the telescope with a limited angular resolution and interpreted (inverted) the data using a Milne-Eddington spectropolarimetric inversion code. We then studied the dependence of the inferred parameters on the telescope resolution. The results show a significant decrease in the mean magnetic flux density -- related to the open flux observed at the disk center -- with decreasing telescope resolution. The original net magnetic field flux is fully resolved by a 1m telescope, but a 20\,cm aperture telescope yields a 30\% smaller value. Even in the fully resolved case, the result is still biased due to the corrugation of the photospheric surface. Even the spatially averaged quantities, such as the open magnetic flux in the observed region, are underestimated when the magnetic structures are unresolved. The reason for this is the presence of nonlinearities in the magnetic field inference process. This effect might have implications for the modeling of large-scale solar magnetic fields; for example, those corresponding to the coronal holes, or the polar magnetic fields, which are relevant to our understanding of the solar cycle., Comment: To be published in A&A

We identify 182 flares on 158 stars within 100 pc of the Sun in both the near-ultraviolet (NUV: 1750-2750 \r{A}) and far-ultraviolet (FUV: 1350-1750 \r{A}) using high-cadence light curves from the Galaxy Evolution Explorer (GALEX). Ultraviolet (UV) emission from stellar flares plays a crucial role in determining the habitability of exoplanetary systems. However, whether such UV emission promotes or threatens such life depends strongly on the energetics of these flares. Most studies assessing the effect of flares on planetary habitability assume a 9000 K blackbody spectral energy distribution that produces more NUV flux than FUV flux ($R \equiv F_{\rm FUV} / F_{\rm NUV} \approx \frac{1}{6}$). Instead, we observe the opposite with the excess FUV reaching $R \approx \frac{1}{2} - 2$, roughly $3-12$ times the expectation of a 9000 K blackbody. The ratio of FUV to NUV time-integrated flare energies is 3.0 times higher on average than would be predicted by a constant 9000 K blackbody during the flare. Finally, we find that the FUV/NUV ratio at peak tentatively correlates ($\sim 2 \sigma$ significance) both with total UV flare energy and with the G - RP color of the host star. On average, we observe higher FUV/NUV ratios at peak in $E_{\text{UV}}>10^{32}$ erg flares and in flares on fully convective stars., Comment: Submitted to MNRAS, comments welcome

M-dwarf flares observed by the \textit{Transiting Exoplanet Survey Satellite} (\textit{TESS}) sometimes exhibit a "peak-bump" light-curve morphology, characterized by a secondary, gradual peak well after the main, impulsive peak. A similar "late phase" is frequently detected in solar flares observed in the extreme-ultraviolet from longer hot coronal loops distinct from the impulsive flare structures. White-light emission has also been observed in off-limb solar flare loops. Here, we perform a suite of one-dimensional hydrodynamic loop simulations for M-dwarf flares inspired by these solar examples. Our results suggest that coronal plasma condensation following impulsive flare heating can yield high electron number density in the loop, allowing it to contribute significantly to the optical light curves via free-bound and free-free emission mechanisms. Our simulation results qualitatively agree with \textit{TESS} observations: the longer evolutionary time scale of coronal loops produces a distinct, secondary emission peak; its intensity increases with the injected flare energy. We argue that coronal plasma condensation is a possible mechanism for the \textit{TESS} late-phase flares., Comment: 31 pages, 13 figures, accepted for publication in ApJ

Delta ($\delta$) sunspots sometimes host fast photospheric flows along the central magnetic polarity inversion line (PIL). Here we study the strong Doppler shift signature in the central penumbral light bridge of solar active region NOAA 12673. Observations from the Helioseismic and Magnetic Imager (HMI) indicate highly sheared, strong magnetic fields. Large Doppler shifts up to 3.2 km s$^{-1}$ appeared during the formation of the light bridge and persisted for about 16 hours. A new velocity estimator, called DAVE4VMwDV, reveals fast converging and shearing motion along the PIL from HMI vector magnetograms, and recovers the observed Doppler signal much better than an old version of the algorithm. The inferred velocity vectors are largely (anti-)parallel to the inclined magnetic fields, suggesting that the observed Doppler shift contains significant contribution from the projected, field-aligned flows. High-resolution observations from the Hinode/Spectro-Polarimeter (SP) further exhibit a clear correlation between the Doppler velocity and the cosine of the magnetic inclination, which is in agreement with HMI results and consistent with a field-aligned flow of about 9.6 km s$^{-1}$. The complex Stokes profiles suggest significant gradients of physical variables along the line of sight. We discuss the implications on the $\delta$-spot magnetic structure and the flow-driving mechanism., Comment: 17 pages, 14 figures. Accepted for publication in ApJ

We study joint learning of network topology and a mixed opinion dynamics, in which agents may have different update rules. Such a model captures the diversity of real individual interactions. We propose a learning algorithm based on multi-armed bandit algorithms to address the problem. The goal of the algorithm is to find each agent's update rule from several candidate rules and to learn the underlying network. At each iteration, the algorithm assumes that each agent has one of the updated rules and then modifies network estimates to reduce validation error. Numerical experiments show that the proposed algorithm improves initial estimates of the network and update rules, decreases prediction error, and performs better than other methods such as sparse linear regression and Gaussian process regression.

We study the extent to which Milne-Eddington inversions are able to retrieve and characterize the magnetic landscape of the solar poles from observations by the spectropolarimeter onboard Hinode. In particular, we evaluate whether a variable magnetic filling factor is an adequate modeling technique for retrieving the intrinsic magnetic properties from every pixel in the polar field of view. We first generate synthetic spectra emerging from a numerical simulation of a "plage" region at an inclined line of sight of 65$^{\circ}$, and degrade the data to emulate real observations. Then, we invert the synthetic spectra with two Milne-Eddington inversion codes that feature different treatments of the magnetic filling factor, and relate the retrieved magnetic quantities back to their original values in the simulation cube. We find that while the apparent retrieved magnetic properties map well the spatially-degraded simulation, the intrinsic magnetic quantities bear little relation to the magnetic field at the native resolution of the simulation. We discuss the systematic biases caused by line-of-sight foreshortening, spatial degradation, photon noise and modeling assumptions embedded in the inversion algorithm., Comment: Accepted for publication in ApJ

Using time-distance local helioseismology flow maps within 1 Mm of the solar photosphere, we detect inflows toward activity belts that contribute to solar cycle scale variations in near-surface meridional flow. These inflows stretch out as far as 30 degrees away from active region centroids. If active region neighborhoods are excluded, the solar cycle scale variation in background meridional flow diminishes to below 2~m~s$^{-1}$, but still shows systematic variations in the absence of active regions between Sunspot Cycles 24 and 25. We, therefore, propose that the near-surface meridional flow is a three component flow made up of: a constant baseline flow profile that can be derived from quiet Sun regions, variations due to inflows around active regions, and solar cycle scale variation of the order of 2~m~s$^{-1}$. Torsional oscillation, on the other hand, is found to be a global phenomenon i.e. exclusion of active region neighborhoods does not affect its magnitude or phase significantly. This non-variation of torsional oscillation with distance away from active regions and the three-component breakdown of the near-surface meridional flow serve as vital constraints for solar dynamo models and surface flux transport simulations., Comment: 14 pages, 9 figures, accepted for publication in the Astrophysical Journal

Despite investments in multiple space and ground-based solar observatories by the global community, the Sun's polar regions remain unchartered territory - the last great frontier for solar observations. Breaching this frontier is fundamental to understanding the solar cycle - the ultimate driver of short-to-long term solar activity that encompasses space weather and space climate. Magnetohydrodynamic dynamo models and empirically observed relationships have established that the polar field is the primary determinant of the future solar cycle amplitude. Models of solar surface evolution of tilted active regions indicate that the mid to high latitude surges of magnetic flux govern dynamics leading to the reversal and build-up of polar fields. Our theoretical understanding and numerical models of this high latitude magnetic field dynamics and plasma flows - that are a critical component of the sunspot cycle - lack precise observational constraints. This limitation compromises our ability to observe the enigmatic kilo Gauss polar flux patches and constrain the polar field distribution at high latitudes. The lack of these observations handicap our understanding of how high latitude magnetic fields power polar jets, plumes, and the fast solar wind that extend to the boundaries of the heliosphere and modulate solar open flux and cosmic ray flux within the solar system. Accurate observation of the Sun's polar regions, therefore, is the single most outstanding challenge that confronts Heliophysics. This paper argues the scientific case for novel out of ecliptic observations of the Sun's polar regions, in conjunction with existing, or future multi-vantage point heliospheric observatories. Such a mission concept can revolutionize the field of Heliophysics like no other mission concept has - with relevance that transcends spatial regimes from the solar interior to the heliosphere., Comment: This White Paper was submitted in 2022 to the United States National Academies Solar and Space Physics (Heliophysics) Decadal Survey

Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output injection. The observer then estimates the system's state in the original coordinates by inverting the transformation map. However, finding a suitable injective transformation whose inverse can be derived remains a primary challenge for general nonlinear systems. We propose a novel approach that uses supervised physics-informed neural networks to approximate both the transformation and its inverse. Our method exhibits superior generalization capabilities to contemporary methods and demonstrates robustness to both neural network's approximation errors and system uncertainties., Comment: Proceedings of the 2023 American Control Conference (ACC)

Rapid increase of horizontal magnetic field ($B_h$) around the flaring polarity inversion line is the most prominent photospheric field change during flares. It is considered to be caused by the contraction of flare loops, the details behind which is still not fully understood. Here we investigate the $B_h$-increase in 35 major flares using HMI high-cadence vector magnetograms. We find that $B_h$-increase is always accompanied by the increase of field inclination. It usually initiates near the flare ribbons, showing step-like change in between the ribbons. In particular, its evolution in early flare phase shows close spatio-temporal correlation to flare ribbons. We further find that $B_h$-increase tends to have similar intensity in confined and eruptive flares, but larger spatial-extent in eruptive flares in a statistical sense. Its intensity and timescale have inverse and positive correlations to the initial ribbon separations, respectively. The results altogether are well consistent with a recent proposed scenario which suggests that the reconnection-driven contraction of flare loops enhances photospheric $B_h$ according to the ideal induction equation, providing statistical evidence to the reconnection-driven origin for $B_h$-increase for the first time., Comment: 14 pages, 5 figures, 2 tables. Accepted for publication in ApJL

With the aim of investigating how the magnetic field in solar active regions (ARs) controls flare activity, i.e., whether a confined or eruptive flare occurs, we analyze 106 flares of Geostationary Operational Environmental Satellite (GOES) class $\geq$M1.0 during 2010$-$2019. We calculate mean characteristic twist parameters $\alpha$$_{FPIL}$ within the "flaring polarity inversion line" region and $\alpha$$_\mathrm{HFED}$ within the area of high photospheric magnetic free energy density, which both provide measures of the nonpotentiality of AR core region. Magnetic twist is thought to be related to the driving force of electric current-driven instabilities, such as the helical kink instability. We also calculate total unsigned magnetic flux ($\Phi$$_\mathrm{AR}$) of ARs producing the flare, which describes the strength of the background field confinement. By considering both the constraining effect of background magnetic fields and the magnetic non-potentiality of ARs, we propose a new parameter $\alpha$/$\Phi$$_\mathrm{AR}$ to measure the probability for a large flare to be associated with a coronal mass ejection (CME). We find that in about 90\% of eruptive flares, $\alpha$$_\mathrm{FPIL}$/$\Phi$$_\mathrm{AR}$ and $\alpha$$_\mathrm{HFED}$/$\Phi$$_\mathrm{AR}$ are beyond critical values (2.2$\times$$10^{-24}$ and 3.2$\times$$10^{-24}$ Mm$^{-1}$ Mx$^{-1}$), whereas they are less than critical values in $\sim$ 80\% of confined flares. This indicates that the new parameter $\alpha$/$\Phi$$_\mathrm{AR}$ is well able to distinguish eruptive flares from confined flares. Our investigation suggests that the relative measure of magnetic nonpotentiality within the AR core over the restriction of the background field largely controls the capability of ARs to produce eruptive flares., Comment: 7 pages, 4 figures, 1 table and 1 online database

Dark matter can decay via gravity portals and contribute a minor decay (MD) width. This paper proposes that nonminimal coupling between the Higgs field and gravity can lead to additional gravity-Higgs portals for gravitational dark matter to decay and contribute additional decay (AD) width. For scalar dark matter candidates with a mass less than 5 TeV, the decay branching ratios are almost independent of whether dark matter decay through gravity portals or gravity-Higgs portals; therefore, it is almost impossible to distinguish gravity portals from gravity-Higgs portals by observing decay products. For fermionic singlet dark matter candidates, their MD products are diverse, while their AD products are monotonous, only neutrinos and Higgs bosons. As for both dark matter candidates, gravity-Higgs portals prefer to dominate the decay at around several hundred GeV. Besides, for both TeV dark matter candidates, there is still a vast parameter space alive.

Violent solar flares and coronal mass ejections (CMEs) are magnetic phenomena. However, how magnetic fields reconnecting in the flare differ from non-flaring magnetic fields remains unclear owing to the lack of studies of the flare magnetic properties. Here we present a first statistical study of flaring (highlighted by flare-ribbons) vector magnetic fields in the photosphere. Our systematic approach allows us to describe key physical properties of solar flare magnetism, including distributions of magnetic flux, magnetic shear, vertical current and net current over flaring versus non-flaring parts of the active region, and compare these with flare/CME properties. Our analysis suggests that while flares are guided by the physical properties that scale with AR size, like the total amount of magnetic flux that participates in the reconnection process and the total current (extensive properties), CMEs are guided by mean properties, like the fraction of the AR magnetic flux that participates (intensive property), with little dependence on the amount of shear at polarity inversion line (PIL) or the net current. We find that the non-neutralized current is proportional to the amount of shear at PIL, providing direct evidence that net vertical currents are formed as a result of any mechanism that could generate magnetic shear along PIL. We also find that eruptive events tend to have smaller PIL fluxes and larger magnetic shears than confined events. Our analysis provides a reference for more realistic solar and stellar flare models. The database is available online and can be used for future quantitative studies of flare magnetism., Comment: 25 pages, 12 figures, accepted to The Astrophysical Journal (10 November 2021); Link to FlareMagDB dataset: http://solarmuri.ssl.berkeley.edu/~kazachenko/FlareMagDB/

Whilst intense solar flares are almost always accompanied by a coronal mass ejection (CME), reports on stellar CMEs are rare, despite the frequent detection of stellar 'super flares'. The torus instability of magnetic flux ropes is believed to be one of the main driving mechanisms of solar CMEs. Suppression of the torus instability, due to a confining background coronal magnetic field that decreases sufficiently slowly with height, may contribute to the lack of stellar CME detection. Here we use the solar magnetic field as a template to estimate the vertical extent of this 'torus-stable zone' (TSZ) above a stellar active region. For an idealised potential field model comprising the fields of a local bipole (mimicking a pair of starspots) and a global dipole, we show that the upper bound of the TSZ increases with the bipole size, the dipole strength, and the source surface radius where the coronal field becomes radial. The boundaries of the TSZ depend on the interplay between the spots' and the dipole's magnetic fields, which provide the local- and global-scale confinement, respectively. They range from about half the bipole size to a significant fraction of the stellar radius. For smaller spots and an intermediate dipole field, a secondary TSZ arises at a higher altitude, which may increase the likelihood of 'failed eruptions'. Our results suggest that the low apparent CME occurrence rate on cool stars is, at least partially, due to the presence of extended TSZs., Comment: 12 pages, 10 figures. Data and 3 interactive figures available via Zenodo. Accepted to MNRAS

Bald patch (BP) is a magnetic topological feature where U-shaped field lines turn tangent to the photosphere. Field lines threading the BP trace a separatrix surface where reconnection preferentially occurs. Here we study the evolution of multiple, strong-field BPs in active region 12673 during the most intense, X9.3 flare of solar cycle 24. The central BP, located between the initial flare ribbons, largely "disintegrated" within 35 minutes. The more remote, southern BP survived. The disintegration manifested as a 9-degree rotation of the median shear angle; the perpendicular component of the horizontal field (with respect to the polarity inversion line) changed sign. The parallel component exhibited a step-wise, permanent increase of 1 kG, consistent with previous observations of the flare-related "magnetic imprint". The observations suggest that magnetic reconnection during a major eruption may involve entire BP separatrices, leading to a change of magnetic topology from BPs to sheared arcades., Comment: 7 pages, 5 figures, 2 animations via Zenodo. Accepted for publication in ApJL

We present a new data product, called Space-Weather MDI Active Region Patches (SMARPs), derived from maps of the solar surface magnetic field taken by the Michelson Doppler Imager (MDI) aboard the Solar and Heliospheric Observatory (SoHO). Together with the Space-Weather HMI Active Region Patches (SHARPs), derived from similar maps taken by the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory, these data provide a continuous and seamless set of maps and keywords that describe every active region observed over the last two solar cycles, from 1996 to the present day. In this paper, we describe the SMARP data and compare it to the SHARP data., Comment: 11 pages, 3 figures, accepted in ApJS