We present high-resolution and multiline observations of a C2-class solar flare (SOL2019-05-06T08:47), which occurred in NOAA AR 12740 on May 6, 2019. The rise, peak, and decay phases of the flare ...were recorded continuously and quasi-simultaneously in the Ca
II
K line with the CHROMIS instrument and in the Ca
II
8542 Å and Fe
I
6173 Å lines with the CRISP instrument at the Swedish 1 m Solar Telescope. The observations in the chromospheric Ca
II
lines exhibit intense brightening near the flare footpoints. At these locations, a nonlocal thermodynamic equilibrium inversion code was employed to infer the temperature, magnetic field, line-of-sight (LOS) velocity, and microturbulent velocity stratification in the flaring atmosphere. The temporal analysis of the inferred temperature at the flare footpoints shows that the flaring atmosphere from log
τ
500
∼ −2.5 to −3.5 is heated up to 7 kK, whereas from log
τ
500
∼ −3.5 to −5 the inferred temperature ranges between ∼7.5 kK and ∼11 kK. During the flare peak time, the LOS velocity shows both upflows and downflows around the flare footpoints in the upper chromosphere and lower chromosphere, respectively. Moreover, the temporal analysis of the LOS magnetic field at the flare points exhibits a maximum change of ∼600 G. After the flare, the LOS magnetic field decreases to the non-flaring value, exhibiting no permanent or step-wise change. The analysis of response functions to the temperature, LOS magnetic field, and velocity shows that the Ca
II
lines exhibit enhanced sensitivity to the deeper layers (i.e., log
τ
500
∼ −3) of the flaring atmosphere, whereas for the non-flaring atmosphere they are mainly sensitive around log
τ
500
∼ −4. We suggest that a fraction of the apparent increase in the LOS magnetic field at the flare footpoints may be due to the increase in the sensitivity of the Ca
II
8542 Å line in the deeper layers, where the field strength is relatively strong. The rest may be due to magnetic field reconfiguration during the flare. In the photosphere, we do not notice significant changes in the physical parameters during the flare or non-flare times. Our observations illustrate that even a less intense C-class flare can heat the deeper layers of the solar chromosphere, mainly at the flare footpoints, without affecting the photosphere.
Context. Spectropolarimetric inversions are routinely used in the field of solar physics for the extraction of physical information from observations. The application to two-dimensional fields of ...view often requires the use of supercomputers with parallelized inversion codes. Even in this case, the computing time spent on the process is still very large. Aims. Our aim is to develop a new inversion code based on the application of convolutional neural networks that can quickly provide a three-dimensional cube of thermodynamical and magnetic properties from the interpreation of two-dimensional maps of Stokes profiles. Methods. We trained two different architectures of fully convolutional neural networks. To this end, we used the synthetic Stokes profiles obtained from two snapshots of three-dimensional magneto-hydrodynamic numerical simulations of different structures of the solar atmosphere. Results. We provide an extensive analysis of the new inversion technique, showing that it infers the thermodynamical and magnetic properties with a precision comparable to that of standard inversion techniques. However, it provides several key improvements: our method is around one million times faster, it returns a three-dimensional view of the physical properties of the region of interest in geometrical height, it provides quantities that cannot be obtained otherwise (pressure and Wilson depression) and the inferred properties are decontaminated from the blurring effect of instrumental point spread functions for free. The code, models, and data are all open source and available for free, to allow both evaluation and training.
Context. Solar flares release an enormous amount of energy (~10(exp 32) erg) into the corona. A substantial fraction of this energy is transported to the lower atmosphere, which results in ...chromospheric heating. The mechanisms that transport energy to the lower solar atmosphere during a flare are still not fully understood.
Aims. We aim to estimate the temporal evolution of the radiative losses in the chromosphere at the footpoints of a C-class flare, in order to set observational constraints on the electron beam parameters of a RADYN flare simulation.
Methods. We estimated the radiative losses from hydrogen, and singly ionized Ca and Mg using semiempirical model atmospheres, which were inferred from a multiline inversion of observed Stokes profiles obtained with the CRISP and CHROMIS instruments on the Swedish 1-m Solar Telescope. The radiative losses were computed taking into account the effect of partial redistribution and non-local thermodynamic equilibrium. To estimate the integrated radiative losses in the chromosphere, the net cooling rates were integrated between the temperature minimum and the height where the temperature reaches 10 kK. We also compared our time series of radiative losses with those from the RADYN flare simulations.
Results. We obtained a high spatial-resolution map of integrated radiative losses around the flare peak time. The stratification of the net cooling rate suggests that the Ca IR triplet lines are responsible for most of the radiative losses in the flaring atmosphere. During the flare peak time, the contribution from Ca II H and K and Mgii h and k lines are strong and comparable to the Ca IR triplet (~32kW m(exp -2)). Since our flare is a relatively weak event, the chromosphere is not heated above 11 kK, which in turn yields a subdued Lyα contribution (~7kW m(exp -2)) in the selected limits of the chromosphere. The temporal evolution of total integrated radiative losses exhibits sharply rising losses (0.4kW m(exp -2) (s(exp -1)) and a relatively slow decay (0.23kW m(exp -2) s(exp -1)). The maximum value of total radiative losses is reached around the flare peak time and can go up to 175kWm2 for a single pixel located at footpoint. After a small parameter study, we find the best model-data consistency in terms of the amplitude of radiative losses and the overall atmospheric structure with a RADYN flare simulation in the injected energy flux of 5 × 10(exp 10) erg s(exp -1) cm(exp -2).
Context.
It has so far proven impossible to reproduce all aspects of the solar plage chromosphere in quasi-realistic numerical models. The magnetic field configuration in the lower atmosphere is one ...of the few free parameters in such simulations. The literature only offers proxy-based estimates of the field strength, as it is difficult to obtain observational constraints in this region. Sufficiently sensitive spectro-polarimetric measurements require a high signal-to-noise ratio, spectral resolution, and cadence, which are at the limit of current capabilities.
Aims.
We use critically sampled spectro-polarimetric observations of the Ca
II
8542 Å line obtained with the CRISP instrument of the Swedish 1-m Solar Telescope to study the strength and inclination of the chromospheric magnetic field of a plage region. This will provide direct physics-based estimates of these values, which could aid modelers to put constraints on plage models.
Methods.
We increased the signal-to-noise ratio of the data by applying several methods including deep learning and PCA. We estimated the noise level to be 1 × 10
−3
I
c
. We then used STiC, a non-local thermodynamic equilibrium inversion code to infer the atmospheric structure and magnetic field pixel by pixel.
Results.
We are able to infer the magnetic field strength and inclination for a plage region and for fibrils in the surrounding canopy. In the plage we report an absolute field strength of |
B
| = 440 ± 90 G, with an inclination of 10° ±16° with respect to the local vertical. This value for |
B
| is roughly double of what was reported previously, while the inclination matches previous studies done in the photosphere. In the fibrillar region we found |
B
| = 300 ± 50 G, with an inclination of 50° ±13°.
Context. The Helioseismic and Magnetic Imager (HMI) provides continuum images and magnetograms with a cadence better than one per minute. It has been continuously observing the Sun 24 h a day for the ...past 7 yr. The trade-off between full disk observations and spatial resolution means that HMI is not adequate for analyzing the smallest-scale events in the solar atmosphere. Aims. Our aim is to develop a new method to enhance HMI data, simultaneously deconvolving and super-resolving images and magnetograms. The resulting images will mimic observations with a diffraction-limited telescope twice the diameter of HMI. Methods. Our method, which we call Enhance, is based on two deep, fully convolutional neural networks that input patches of HMI observations and output deconvolved and super-resolved data. The neural networks are trained on synthetic data obtained from simulations of the emergence of solar active regions. Results. We have obtained deconvolved and super-resolved HMI images. To solve this ill-defined problem with infinite solutions we have used a neural network approach to add prior information from the simulations. We test Enhance against Hinode data that has been degraded to a 28 cm diameter telescope showing very good consistency. The code is open source.
Context.
Our knowledge of the heating mechanisms that are at work in the chromosphere of plage regions remains highly unconstrained from observational studies. While many heating candidates have been ...proposed in theoretical studies, the exact contribution from each of them is still unknown. The problem is rather difficult because there is no direct way of estimating the heating terms from chromospheric observations.
Aims.
The purpose of our study is to estimate the chromospheric heating terms from a multi-line high-spatial-resolution plage dataset, characterize their spatio-temporal distribution and set constraints on the heating processes that are at work in the chromosphere.
Methods.
We used nonlocal thermodynamical equilibrium inversions in order to infer a model of the photosphere and chromosphere of a plage dataset acquired with the Swedish 1-m Solar Telescope (SST). We used this model atmosphere to calculate the chromospheric radiative losses from the main chromospheric cooler from H
I
, Ca
II
, and Mg
II
atoms. In this study, we approximate the chromospheric heating terms by the net radiative losses predicted by the inverted model. In order to make the analysis of time-series over a large field of view computationally tractable, we made use of a neural network which is trained from the inverted models of two non-consecutive time-steps. We have divided the chromosphere in three regions (lower, middle, and upper) and analyzed how the distribution of the radiative losses is correlated with the physical parameters of the model.
Results.
In the lower chromosphere, the contribution from the Ca
II
lines is dominant and predominantly located in the surroundings of the photospheric footpoints. In the upper chromosphere, the H
I
contribution is dominant. Radiative losses in the upper chromosphere form a relatively homogeneous patch that covers the entire plage region. The Mg
II
also peaks in the upper chromosphere. Our time analysis shows that in all pixels, the net radiative losses can be split in a periodic component with an average amplitude of
amp̅
Q
= 7.6 kW m
−2
and a static (or very slowly evolving) component with a mean value of −26.1 kW m
−2
. The period of the modulation present in the net radiative losses matches that of the line-of-sight velocity of the model.
Conclusions.
Our interpretation is that in the lower chromosphere, the radiative losses are tracing the sharp lower edge of the hot magnetic canopy that is formed above the photosphere, where the electric current is expected to be large. Therefore, Ohmic current dissipation could explain the observed distribution. In the upper chromosphere, both the magnetic field and the distribution of net radiative losses are room-filling and relatively smooth, whereas the amplitude of the periodic component is largest. Our results suggest that acoustic wave heating may be responsible for one-third of the energy deposition in the upper chromosphere, whereas other heating mechanisms must be responsible for the rest: turbulent Alfvén wave dissipation or ambipolar diffusion could be among them. Given the smooth nature of the magnetic field in the upper chromosphere, we are inclined to rule out Ohmic dissipation of current sheets in the upper chromosphere.
Aims.
The non-uniform surface temperature distribution of rotating active stars is routinely mapped with the Doppler imaging technique. Inhomogeneities in the surface produce features in ...high-resolution spectroscopic observations that shift in wavelength because of the Doppler effect, depending on their position on the visible hemisphere. The inversion problem has been systematically solved using maximum a posteriori regularized methods assuming smoothness or maximum entropy. Our aim in this work is to solve the full Bayesian inference problem by providing access to the posterior distribution of the surface temperature in the star compatible with the observations.
Methods.
We use amortized neural posterior estimation to produce a model that approximates the high-dimensional posterior distribution for spectroscopic observations of selected spectral ranges sampled at arbitrary rotation phases. The posterior distribution is approximated with conditional normalizing flows, which are flexible, tractable, and easy-to-sample approximations to arbitrary distributions. When conditioned on the spectroscopic observations, these normalizing flows provide a very efficient way of obtaining samples from the posterior distribution. The conditioning on observations is achieved through the use of Transformer encoders, which can deal with arbitrary wavelength sampling and rotation phases.
Results.
Our model can produce thousands of posterior samples per second, each one accompanied by an estimation of the log-probability. Our exhaustive validation of the model for very high-signal-to-noise observations shows that it correctly approximates the posterior, albeit with some overestimation of the broadening. We apply the model to the moderately fast rotator II Peg, producing the first Bayesian map of its temperature inhomogenities. We conclude that conditional normalizing flows are a very promising tool for carrying out approximate Bayesian inference in more complex problems in stellar physics, such as constraining the magnetic properties using polarimetry.
Stokes inversion techniques are very powerful methods for obtaining information on the thermodynamic and magnetic properties of solar and stellar atmospheres. In recent years, highly sophisticated ...inversion codes have been developed that are now routinely applied to spectro-polarimetric observations. Most of these inversion codes are designed to find an optimum solution to the nonlinear inverse problem. However, to obtain the location of potentially multimodal cases (ambiguities), the degeneracies and the uncertainties of each parameter inferred from the inversions algorithms – such as Markov chain Monte Carlo (MCMC) – require evaluation of the likelihood of the model thousand of times and are computationally costly. Variational methods are a quick alternative to Monte Carlo methods, and approximate the posterior distribution by a parametrized distribution. In this study, we introduce a highly flexible variational inference method to perform fast Bayesian inference, known as normalizing flows. Normalizing flows are a set of invertible, differentiable, and parametric transformations that convert a simple distribution into an approximation of any other complex distribution. If the transformations are conditioned on observations, the normalizing flows can be trained to return Bayesian posterior probability estimates for any observation. We illustrate the ability of the method using a simple Milne-Eddington model and a complex non-local thermodynamic equilibrium (NLTE) inversion. The method is extremely general and other more complex forward models can be applied. The training procedure need only be performed once for a given prior parameter space and the resulting network can then generate samples describing the posterior distribution several orders of magnitude faster than existing techniques.
The topology and dynamics of the solar chromosphere are greatly affected by the presence of magnetic fields. The magnetic field can be inferred by analyzing polarimetric observations of spectral ...lines. Polarimetric signals induced by chromospheric magnetic fields are, however, particularly weak, and in most cases very close to the detection limit of current instrumentation. Because of this, there are only few observational studies that have successfully reconstructed the three components of the magnetic field vector in the chromosphere. Traditionally, the signal-to-noise ratio of observations has been improved by performing time-averages or spatial averages, but in both cases, some information is lost. More advanced techniques, like principal-component analysis, have also been employed to take advantage of the sparsity of the observations in the spectral direction. In the present study, we use the spatial coherence of the observations to reduce the noise using deep-learning techniques. We designed a neural network that is capable of recovering weak signals under a complex noise corruption (including instrumental artifacts and non-linear post-processing). The training of the network is carried out without a priori knowledge of the clean signals, or an explicit statistical characterization of the noise or other corruption. We only use the same observations as our generative model. The performance of this method is demonstrated on both synthetic experiments and real data. We show examples of the improvement in typical signals obtained in current telescopes such as the Swedish 1 m Solar Telescope. The presented method can recover weak signals equally well no matter what spectral line or spectral sampling is used. It is especially suitable for cases when the wavelength sampling is scarce.
Context.
The evolution of the photospheric magnetic field plays a key role in the energy transport into the chromosphere and the corona. In active regions, newly emerging magnetic flux interacts with ...the pre-existent magnetic field, which can lead to reconnection events that convert magnetic energy into thermal energy.
Aims.
We aim to study the heating caused by a strong reconnection event that was triggered by magnetic flux cancelation.
Methods.
We use imaging and spectropolarimetric data in the Fe
I
6301& 6302 Å, Ca
II
8542 Å, and Ca
II
K spectral lines obtained with the CRISP and CHROMIS instruments at the Swedish 1-m Solar Telescope. These data were inverted with the STiC code by performing multi-atom, multi-line, non-local thermodynamic equilibrium inversions. These inversions yielded a three-dimensional model of the reconnection event and surrounding atmosphere, including temperature, velocity, microturbulence, magnetic field, and radiative loss rate.
Results.
The model atmosphere shows the emergence of magnetic loops with a size of several arcseconds into a pre-existing predominantly unipolar field. Where the reconnection region is expected to be, we see an increase in the chromospheric temperature of roughly 2000 K as well as bidirectional flows of the order of 10 km s
−1
emanating from there. We see bright blobs of roughly 0.2 arcsec in diameter in the Ca
II
K, moving at a plane-of-the-sky velocity of the order of 100 km s
−1
and a blueshift of 100 km s
−1
, which we interpret as ejected plasmoids from the same region. This scenario is consistent with theoretical reconnection models, and therefore provides evidence of a reconnection event taking place. The chromospheric radiative losses at the reconnection site are as high as 160 kW m
−2
, providing a quantitative constraint on theoretical models that aim to simulate reconnection caused by flux emergence in the chromosphere.
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