Author name code: milic ADS astronomy entries on 2022-09-14 author:"Milic, Ivan" ------------------------------------------------------------------------ Title: Investigating magnetic field inference from the spectral region around the Mg I b2 line using the weak-field approximation Authors: Vukadinović, D.; Milić, I.; Atanacković, O. Bibcode: 2022A&A...664A.182V Altcode: 2022arXiv220504236V Context. The understanding of the magnetic field structure in the solar atmosphere is important in assessing both the dynamics and the energy balance of the solar atmosphere. Our knowledge about these magnetic fields comes predominantly from the interpretation of spectropolarimetric observations. Simpler approaches based on approximations such as the weak-field approximation (WFA) deserve special attention as key methods in the interpretation of large, high-resolution datasets.
Aims: We investigate the applicability of the WFA for retrieving the depth-dependent line-of-sight (LOS) magnetic field from the spectral region containing the Mg I b2 spectral line and two photospheric Ti I and Fe I lines in its wings.
Methods: We constructed and applied a 12-level model for Mg I atom that realistically reproduces the b2 line profile of the mean quiet Sun. We tested the applicability of the WFA to the spectra computed from the FAL C atmospheric model with different magnetic and velocity fields added on an ad hoc basis . Then we extended the analysis to the spectra computed from two 3D magneto-hydrodynamic (MHD) MURaM simulations of the solar atmosphere. The first MHD cube was used to estimate the Stokes V formation heights of each spectral line. These heights correspond to optical depths at which the standard deviation of the difference between the WFA-inferred magnetic field and the magnetic field in the MHD cube is minimal. The estimated formation heights were verified using the second MHD cube.
Results: The LOS magnetic field retrieved by the WFA is reliable for the magnetic field strength up to 1.4 kG even when moderate velocity gradients are present. The exception is the Fe I line, for which we found a strong discrepancy in the WFA-inferred magnetic fields because of the line blend. We estimated the Stokes V formation heights of each spectral line to be: logτFe = −2.6, logτMg = −3.3, and logτTi = −1.8. We were able to estimate the LOS magnetic field from the MURaM cube at these heights with the uncertainty of 150 G for the Fe I and Ti I lines and only 40 G for the Mg I b2 line.
Conclusions: Using the WFA, we can quickly get a reliable estimate of the structure of the LOS magnetic field in the observed region. This offers a significant advantage in comparison with otherwise time-consuming classical spectropolarimetric inversions. We find that the Mg I b2 line profile calculated from the quiet Sun MURaM simulation agrees very well with the observed mean spectrum of the quiet Sun. Title: Observational Approach to Computing the Poynting Flux in the Quiet Sun Photosphere Authors: Tilipman, Dennis; Martínez Pillet, Valentin; Tremblay, Benoit; Kazachenko, Maria; Milic, Ivan; Yadav, Rahul Bibcode: 2022cosp...44.2516T Altcode: Understanding magnetically-driven processes in the quiet Sun is crucial for understanding chromospheric and coronal heating. The main goal of our study is to quantify the energy output of the quiet Sun photosphere. The amount of magnetic energy being transported upwards from the photosphere can be expressed in terms of the vertical component of Poynting flux, which is a cross-product of magnetic and electric fields. While magnetic fields and energy fluxes within active regions and plage have been evaluated before, quiet Sun magnetograms have only recently become available with the launch of missions such as Hinode and Sunrise and the Daniel K. Inouye Solar Telescope (DKIST) coming online early this year. In this presentation, we present estimates of Poynting flux using IMaX data. As the electric field E is one of the two principal quantities required to compute Poynting flux, we use two distinct approaches to infer E. In the first approach, we derive the electric field using ideal plasma assumption with horizontal velocities obtained from the convolutional neural network (DeepVel, Asensio Ramos et al. 2017). In the second approach, we derive E using the PDFI-SS approach uncurling Faraday's law (Fisher et al. 2020). We discuss the distribution of Poynting flux and whether it is sufficient to explain chromospheric and coronal heating. Title: Evaluating Non-LTE Spectral Inversions with ALMA and IBIS Authors: Hofmann, Ryan A.; Reardon, Kevin P.; Milic, Ivan; Molnar, Momchil E.; Chai, Yi; Uitenbroek, Han Bibcode: 2022ApJ...933..244H Altcode: 2022arXiv220508760H We present observations of a solar magnetic network region in the millimeter continuum with the Atacama Large Millimeter/submillimeter Array (ALMA) and in the Ca 8542 and Na 5896 Å spectral lines with the Interferometric Bidimensional Spectrometer (IBIS). Our goal is to compare the measurement of local gas temperatures provided by ALMA with the temperature diagnostics provided by non-LTE inversions using the STockholm inversion Code (STiC). In performing these inversions, we find that using column mass as the reference height scale, rather than optical depth, provides more reliable atmospheric profiles above the temperature minimum and that the treatment of non-LTE hydrogen ionization brings the inferred chromospheric temperatures into better agreement with the ALMA measurements. The Band 3 brightness temperatures are higher but well correlated spatially with the inversion-derived temperatures at the height of formation of the Ca 8542 line core. The Band 6 temperatures instead do not show good correlations with the temperatures at any specific layer in the inverted atmospheres. We then performed inversions that included the millimeter-continuum intensities as an additional constraint. Incorporating Band 3 generally resulted in atmospheres showing a strong temperature rise in the upper atmosphere, while including Band 6 led to significant regions of anomalously low temperatures at chromospheric heights. This is consistent with the idea that the Band 6 emission can come from a combination of heights ranging from the temperature minimum to upper chromosphere. The poor constraints on the chromospheric electron density with existing inversion codes introduces difficulties in determining the height(s) of formation of the millimeter continuum as well as uncertainties in the temperatures derived from the spectral lines. Title: Quantifying Magnetic Energy Flux in the Quiet Sun Photosphere using Sunrise/IMaX Observations Authors: Tilipman, Dennis; Kazachenko, Maria; Tremblay, Benoit; Martinez-Pillet, Valentin; Milic, Ivan Bibcode: 2021AGUFMSH42B..04T Altcode: Understanding magnetically-driven processes in the quiet Sun is crucial for understanding chromospheric and coronal heating. The main goal of our study is to quantify the energy output of the quiet Sun photosphere. The amount of magnetic energy can be expressed in terms of the Poynting flux, which is a cross-product of magnetic and electric fields. Poynting flux has been computed for active regions and plage, but the weakness of polarimetric signal in the quiet Sun presents a bigger challenge. Quiet Sun magnetic fields have only recently become observable with the launch of missions such as Hinode and Sunrise. The Daniel K. Inouye Solar Telescope (DKIST) is expected to further improve the quality of these observations -- both spatial and temporal resolutions, as well as polarimetric signal, are expected to improve significantly, allowing us to perform reliable inversions of magnetic, electric, and velocity fields, all of which are required to compute the Poynting flux. We test different inversion methods on Sunrise/IMaX data in order to streamline this process once DKIST becomes operational and to understand the limitations of these inversion techniques. In this work, we present our results obtained from velocity and electric field inversions of photospheric images, magnetograms and Doppler velocities from Sunrise/IMaX, the challenges associated with these inversions, and implications for future DKIST observations. We also discuss approaches to extend this analysis from photosphere to overlying layers of the atmosphere, which would allow us to study how these layers respond to magnetic energy injections from below. Title: Limitations of the Ca II 8542 Å Line for the Determination of Magnetic Field Oscillations Authors: Felipe, Tobias; Socas Navarro, Hector; Sangeetha, C. R.; Milic, Ivan Bibcode: 2021ApJ...918...47F Altcode: 2021arXiv210702160F Chromospheric umbral oscillations produce periodic brightenings in the core of some spectral lines, known as umbral flashes. They are also accompanied by fluctuations in velocity, temperature, and, according to several recent works, magnetic field. In this study, we aim to ascertain the accuracy of the magnetic field determined from inversions of the Ca II 8542 Å line. We have developed numerical simulations of wave propagation in a sunspot umbra. Synthetic Stokes profiles emerging from the simulated atmosphere were computed and then inverted using the NICOLE code. The atmospheres inferred from the inversions have been compared with the original parameters from the simulations. Our results show that the inferred chromospheric fluctuations in velocity and temperature match the known oscillations from the numerical simulation. In contrast, the vertical magnetic field obtained from the inversions exhibits an oscillatory pattern with a ~300 G peak-to-peak amplitude, which is absent in the simulation. We have assessed the error in the inferred parameters by performing numerous inversions with slightly different configurations of the same Stokes profiles. We find that when the atmosphere is approximately at rest, the inversion tends to favor solutions that underestimate the vertical magnetic field strength. On the contrary, during umbral flashes, the values inferred from most of the inversions are concentrated at stronger fields than those from the simulation. Our analysis provides a quantification of the errors associated with the inversions of the Ca II 8542 Å line and suggests caution with the interpretation of the inferred magnetic field fluctuations. Title: The Lightweaver Framework for Nonlocal Thermal Equilibrium Radiative Transfer in Python Authors: Osborne, Christopher M. J.; Milić, Ivan Bibcode: 2021ApJ...917...14O Altcode: 2021arXiv210700475O Tools for computing detailed optically thick spectral line profiles out of local thermodynamic equilibrium have always been focused on speed, due to the large computational effort involved. With the Lightweaver framework, we have produced a more flexible, modular toolkit for building custom tools in a high-level language, Python, without sacrificing speed against the current state of the art. The goal of providing a more flexible method for constructing these complex simulations is to decrease the barrier to entry and allow more rapid exploration of the field. In this paper we present an overview of the theory of optically thick nonlocal thermodynamic equilibrium radiative transfer, the numerical methods implemented in Lightweaver including the problems of time-dependent populations and charge-conservation, as well as an overview of the components most users will interact with, to demonstrate their flexibility. Title: Machine learning initialization to accelerate Stokes profile inversions Authors: Gafeira, R.; Orozco Suárez, D.; Milić, I.; Quintero Noda, C.; Ruiz Cobo, B.; Uitenbroek, H. Bibcode: 2021A&A...651A..31G Altcode: 2021arXiv210309651G Context. At present, an exponential growth in scientific data from current and upcoming solar observatories is expected. Most of the data consist of high spatial and temporal resolution cubes of Stokes profiles taken in both local thermodynamic equilibrium (LTE) and non-LTE spectral lines. The analysis of such solar observations requires complex inversion codes. Hence, it is necessary to develop new tools to boost the speed and efficiency of inversions and reduce computation times and costs.
Aims: In this work we discuss the application of convolutional neural networks (CNNs) as a tool to advantageously initialize Stokes profile inversions.
Methods: To demonstrate the usefulness of CNNs, we concentrate in this paper on the inversion of LTE Stokes profiles. We use observations taken with the spectropolarimeter on board the Hinode spacecraft as a test bench mark. First, we carefully analyse the data with the SIR inversion code using a given initial atmospheric model. The code provides a set of atmospheric models that reproduce the observations well. These models are then used to train a CNN. Afterwards, the same data are again inverted with SIR but using the trained CNN to provide the initial guess atmospheric models for SIR.
Results: The CNNs allow us to significantly reduce the number of inversion cycles when used to compute initial guess model atmospheres (`assisted inversions'), therefore decreasing the computational time for LTE inversions by a factor of two to four. CNNs alone are much faster than assisted inversions, but the latter are more robust and accurate. CNNs also help to automatically cluster pixels with similar physical properties, allowing the association with different solar features on the solar surface, which is useful when inverting huge datasets where completely different regimes are present. The advantages and limitations of machine learning techniques for estimating optimum initial atmospheric models for spectral line inversions are discussed. Finally, we describe a python wrapper for the SIR and DeSIRe codes that allows for the easy setup of parallel inversions. The tool implements the assisted inversion method described in this paper. The parallel wrapper can also be used to synthesize Stokes profiles with the RH code.
Conclusions: The assisted inversions can speed up the inversion process, but the efficiency and accuracy of the inversion results depend strongly on the solar scene and the data used for the CNN training. This method (assisted inversions) will not obviate the need for analysing individual events with the utmost care but will provide solar scientists with a much better opportunity to sample large amounts of inverted data, which will undoubtedly broaden the physical discovery space. Title: Sparse Representation of HINODE/SOT/SP Spectra Using Convolutional Neural Networks Authors: Flint, S.; Milic, I. Bibcode: 2021AAS...23821304F Altcode: A fundamental problem in solar spectropolarimetry is relating observed spectra and their polarization to the physical parameters of the underlying atmosphere. One of the difficulties in this process is the fact that the spectra usually can be represented with a much smaller number of hyperparameters than what is suggested by the number of wavelength points used for sampling. Said differently, spectra can usually be compressed or described in a sparser basis. In this work, we use the neural networks to investigate the dimensionality of photospheric spectra, and to compare the compressed spectra with the maps of physical parameters used to generate the said spectra. Title: ALMA and IRIS Observations Highlighting the Dynamics and Structure of Chromospheric Plage Authors: Hofmann, R. A.; Reardon, K.; Milic, I. Bibcode: 2021AAS...23820505H Altcode: Studies of the thermal structure of the solar chromosphere are typically hampered by the complexities of non-LTE radiative transfer. This issue can be addressed using observations of the millimeter continuum, which directly probes the electron temperatures in the chromosphere. In recent years, the Atacama Large Millimeter/submillimeter Array (ALMA) has made it possible, for the first time, to obtain millimeter observations of sufficient spatial resolution to supplement spectral line observations and inversions. Here, we present observations of a plage in the 3.0 mm and 1.2 mm continua with ~2 arcsecond resolution, combined with simultaneous imaging spectroscopy observations from the Interferometric Bidimensional Spectrometer (IBIS) at the Dunn Solar Telescope. We compare the observed ALMA brightness temperatures with temperatures inferred from spectral inversions using the Na D1 5896 Å and Ca II 8542 Å lines, and investigate the wide range of physical heights probed by the millimeter continuum. We find that the millimeter emission arises from a range of heights both above and below the chromospheric calcium line, depending on the local temperature profile and electron densities. Title: Are the Magnetic Fields Radial in the Solar Polar Region? Authors: Sun, Xudong; Liu, Yang; Milić, Ivan; Griñón-Marín, Ana Belén Bibcode: 2021RNAAS...5..134S Altcode: 2021arXiv210601461S We investigate the orientation of the photospheric magnetic fields in the solar polar region using observations from the Helioseismic and Magnetic Imager (HMI). Inside small patches of significant polarization, the inferred magnetic field vectors at 1″ scale appear to systematically deviate from the radial direction. Most tilt toward the pole; all are more inclined toward the plane of sky compared to the radial vector. These results, however, depend on the "filling factor" f that characterizes the unresolved magnetic structures. The default, uninformative f ≡ 1 for HMI will incur larger inclination and less radial fields than f < 1. The observed trend may be a systematic bias inherent to the limited resolution. Title: Sparse Representation of HINODE/SOT/SP Spectra Using Convolutional Neural Networks Authors: Flint, Serena; Milic, Ivan Bibcode: 2021csss.confE.189F Altcode: A fundamental problem in solar spectropolarimetry is relating observed spectra and their polarization to the physical parameters of the underlying atmosphere. One of the difficulties in this process is the fact that the spectra usually can be represented with a much smaller number of hyperparameters than what is suggested by the number of wavelength points used for sampling. Said differently, spectra can usually be compressed or described in a sparser basis. In this work, we use the neural networks to investigate the dimensionality of photospheric spectra, and to compare the compressed spectra with the maps of physical parameters used to generate the said spectra. Title: Looking for Changes in Photospheric Temperature Gradients over Solar Cycle 24 Using Hinode/SP Authors: Crowley, James; Milic, Ivan Bibcode: 2021csss.confE.206C Altcode: <strong>The intent of this project is to study the effects of the solar magnetic cycle on the thermal structure of the solar atmosphere in the quiet Sun. Using data from the spectropolarimeter onboard the Hinode satellite, four datasets were selected from throughout Solar Cycle 24; all datasets selected were near the disk center and without any obvious magnetic signatures. Using an inversion based on the Milne-Eddington model, a quarter-million pixels were inverted from each dataset, using two different inversion schemes. By inverting the data and analyzing the differences in the inverted parameters between the datasets, we attempt to see if the resolution of the Hinode data combined with a Milne-Eddington approach is able to detect meaningful differences in photospheric structure throughout the solar cycle, primarily the source function and its gradient. Our results so far suggest that more detailed inversion and /or data preprocessing is needed to detect eventual presence of the changes. </strong> Title: ALMA observations and spectral inversions - what can we learn about the Sun and our techniques? Authors: Hofmann, R.; Reardon, K.; Milic, I. Bibcode: 2020AGUFMSH0010002H Altcode: Studies of the thermal structure of the solar chromosphere are typically hampered by the complexities of non-LTE radiative transfer. This issue can be addressed using observations of the millimeter continuum, which directly probes the electron temperatures in the chromosphere. In recent years, the Atacama Large Millimeter/submillimeter Array (ALMA) has made it possible, for the first time, to obtain millimeter observations of sufficient spatial resolution to supplement spectral line observations and inversions. Here, we present observations of a plage in the 3.0 mm and 1.2 mm continua with ~2 arcsecond resolution, combined with simultaneous imaging spectroscopy observations from the Interferometric Bidimensional Spectrometer (IBIS) at the Dunn Solar Telescope. We compare the observed ALMA brightness temperatures with temperatures inferred from spectral inversions using the Na D1 5896 Å and Ca II 8542 Å lines, and investigate the wide range of physical heights probed by the millimeter continuum. We find that the millimeter emission arises from a range of heights both above and below the chromospheric calcium line, depending on the local temperature profile and electron densities. Title: Mimicking spectropolarimetric inversions using convolutional neural networks Authors: Milić, I.; Gafeira, R. Bibcode: 2020A&A...644A.129M Altcode: 2020arXiv200602005M Context. Interpreting spectropolarimetric observations of the solar atmosphere takes much longer than the acquiring the data. The most important reason for this is that the model fitting, or "inversion", used to infer physical quantities from the observations is extremely slow, because the underlying models are numerically demanding.
Aims: We aim to improve the speed of the inference by using a neural network that relates input polarized spectra to the output physical parameters.
Methods: We first select a subset of the data to be interpreted and infer physical quantities from corresponding spectra using a standard minimization-based inversion code. Taking these results as reliable and representative of the whole data set, we train a convolutional neural network to connect the input polarized spectra to the output physical parameters (nodes, in context of spectropolarimetric inversion). We then apply the neural network to the various other data, previously unseen to the network. As a check, we apply the referent inversion code to the unseen data and compare the fit quality and the maps of the inferred parameters between the two inversions.
Results: The physical parameters inferred by the neural network show excellent agreement with the results from the inversion, and are obtained in a factor of 105 less time. Additionally, substituting the results of the neural network back in the forward model, shows excellent agreement between inferred and original spectra.
Conclusions: The method we present here is very simple for implementation and extremely fast. It only requires a training data set, which can be obtained by inverting a representative subset of the observed data. Applying these (and similar) machine learning techniques will yield orders of magnitude acceleration in the routine interpretation of spectropolarimetric data. Title: Chromospheric Resonances above Sunspots and Potential Seismological Applications Authors: Felipe, Tobias; Kuckein, Christoph; González Manrique, Sergio Javier; Milic, Ivan; Sangeetha, C. R. Bibcode: 2020ApJ...900L..29F Altcode: 2020arXiv200810623F Oscillations in sunspot umbrae exhibit remarkable differences between the photosphere and chromosphere. We evaluate two competing scenarios proposed for explaining those observations: a chromospheric resonant cavity and waves traveling from the photosphere to upper atmospheric layers. We have employed numerical simulations to analyze the oscillations in both models. They have been compared with observations in the low (Na I D2) and high (He I 10830 Å) chromosphere. The nodes of the resonant cavity can be detected as phase jumps or power dips, although the identification of the latter is not sufficient to claim the existence of resonances. In contrast, phase differences between velocity and temperature fluctuations reveal standing waves and unequivocally prove the presence of an acoustic resonator above umbrae. Our findings offer a new seismic method to probe active region chromospheres through the detection of resonant nodes. Title: Chromospheric resonant cavities in umbrae: unequivocal detection and seismic applications Authors: Felipe, T.; Kuckein, C.; González Manrique, S. J.; Milic, I.; Sangeetha, C. R. Bibcode: 2020sea..confE.196F Altcode: Umbral chromospheric oscillations exhibit significant differences compared to their photospheric counterparts. We evaluate two competing scenarios proposed for explaining those observations: a chromospheric resonant cavity and waves traveling from the photosphere to upper atmospheric layers. The oscillatory signatures of both models have been determined from numerical simulations, and they have been compared to observations. We find that a high-frequency peak in the He I 10830 Å power spectra cannot discriminate between both theories, contrary to the claims of Jess et al. (2019). In contrast, phase differences between velocity and temperature fluctuations reveal a standing pattern and unequivocally prove the presence of an acoustic cavity above umbrae. Our findings offer a new seismic method to probe sunspot chromospheres through the identification of resonant nodes in phase spectra. Title: Spectral deconvolution with deep learning: removing the effects of spectral PSF broadening Authors: Molnar, Momchil; Reardon, Kevin P.; Osborne, Christopher; Milić, Ivan Bibcode: 2020FrASS...7...29M Altcode: 2020arXiv200505529M We explore novel methods of recovering the original spectral line profiles from data obtained by instruments that sample those profiles with an extended or multipeaked spectral transmission profile. The techniques are tested on data obtained at high spatial resolution from the Fast Imaging Solar Spectrograph (FISS) grating spectrograph at the Big Bear Solar Observatory and from the Interferometric Bidimensional Spectrometer (IBIS) instrument at the Dunn Solar Telescope. The method robustly deconvolves wide spectral transmission profiles for fields of view sampling a variety of solar structures (granulation, plage and pores) with a photometrical precision of less than 1%. The results and fidelity of the method are tested on data from IBIS obtained using several different spectral resolution modes. The method, based on convolutional neural networks (CNN), is extremely fast, performing about 10^5 deconvolutions per second on a single CPU for a spectrum with 40 wavelength samples. This approach is applicable for deconvolving large amounts of data from instruments with wide spectral profiles, such as the Visible Tunable Filter (VTF) on the DKI Solar Telescope (DKIST). We also investigate the application to future instruments by recovering spectral line profiles obtained with a theoretical multi-peaked spectral transmission profile. We further discuss the limitations of this deconvolutional approach through the analysis of the dimensionality of the original and multiplexed data. Title: Sun-as-a-star observations of the 2017 August 21 solar eclipse Authors: Dineva, Ekaterina; Denker, Carsten; Verma, Meetu; Strassmeier, Klaus G.; Ilyin, Ilya; Milic, Ivan Bibcode: 2020IAUS..354..473D Altcode: The Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) is a state-of-the-art, thermally stabilized, fiber-fed, high-resolution spectrograph for the Large Binocular Telescope (LBT) at Mt. Graham, Arizona. During daytime the instrument is fed with sunlight from the 10-millimeter aperture, fully automated, binocular Solar Disk-Integrated (SDI) telescope. The observed Sun-as-a-star spectra contain a multitude of photospheric and chromospheric spectral lines in the wavelength ranges 4200-4800 Å and 5300-6300 Å. One of the advantages of PEPSI is that solar spectra are recorded in the exactly same manner as nighttime targets. Thus, solar and stellar spectra can be directly compared. PEPSI/SDI recorded 116 Sun-as-a-star spectra during the 2017 August 21 solar eclipse. The observed maximum obscuration was 61.6%. The spectra were taken with a spectral resolution of ≈ 250000 and an exposure time of 0.3 s. The high-spectral resolution facilitates detecting subtle changes in the spectra while the Moon passes the solar disk. Sun-as-a-star spectra are affected by changing contributions due to limb darkening and solar differential rotation, and to a lesser extend by supergranular velocity pattern and the presence of active regions on the solar surface. The goal of this study is to investigate the temporal evolution of the chromospheric Na D doublet during the eclipse and to compare observations with synthetic line profiles computed with the state-of-the-art Bifrost code. Title: Using the infrared iron lines to probe solar subsurface convection Authors: Milić, I.; Smitha, H. N.; Lagg, A. Bibcode: 2019A&A...630A.133M Altcode: 2019arXiv190407306M Context. Studying the properties of solar convection using high-resolution spectropolarimetry began in the early 1990s with the focus on observations in the visible wavelength regions. Its extension to the infrared (IR) remains largely unexplored.
Aims: The IR iron lines around 15 600 Å, most commonly known for their high magnetic sensitivity, also have a non-zero response to line-of-sight (LOS) velocity below log(τ) = 0.0. In this paper we explore the possibility of using these lines to measure subsurface convective velocities.
Methods: By assuming a snapshot of a three-dimensional magnetohydrodynamic simulation to represent the quiet Sun, we investigate how well the iron IR lines can reproduce the LOS velocity in the cube and to what depth. We use the recently developed spectropolarimetric inversion code SNAPI and discuss the optimal node placements for the retrieval of reliable results from these spectral lines.
Results: We find that the IR iron lines can measure the convective velocities down to log(τ) = 0.5, below the photosphere, not only at the original resolution of the cube, but also when degraded with a reasonable spectral and spatial PSF and stray light. Instead, the commonly used Fe I 6300 Å line pair performs significantly worse.
Conclusions: Our investigation reveals that the IR iron lines can probe the subsurface convection in the solar photosphere. This paper is a first step towards exploiting this diagnostic potential. Title: The specific property of motion of resonant asteroids with very slow Yarkovsky drift speeds Authors: Milić; Žitnik, Ivana Bibcode: 2019MNRAS.486.2435M Altcode: This work examines the specific characteristics of the motion of asteroids with very slow Yarkovsky drift speeds (da/dt) across the two-body mean-motion resonances (MMRs) with Jupiter, whose strengths cover a wide range. Only asteroids that crossed a resonance completely were observed. The investigation was carried out using numerical integrations performed with the public-domain integrator ORBIT9. It was found that the test asteroids with very small Yarkovsky drift speeds moved extremely rapidly across MMRs (order of magnitude 10-5 au Myr-1 or less). This result may indicate that, below a certain boundary value of da/dt, asteroids typically move quickly across MMRs. From the obtained results, it is concluded that the boundary value of the Yarkovsky drift speed is 7 × 10-5 au Myr-1. Title: Mimicking spectropolarimetric inversion using convolutional neural networks Authors: Milic, Ivan; Gafeira, Ricardo Bibcode: 2019AAS...23422605M Altcode: State of the art approach for the interpretation of spectropolarimetric observations of the solar atmosphere are the so called spectropolarimetric inversions. These methods fit a model atmosphere to the observed polarized spectrum and provide us with the maximum-likelyhood solution for the parameters of the underlying atmosphere. Inversions are extremely numerically demanding, because they fully take into account all the physical processes involved in the spectral line formation. This is especially pronounced in the case of spectral lines formed in the solar chromosphere. With the advent of next generation telescopes, such as DKIST, standard, minimization-based, inversions will simply be too slow. In this contribution we propose a way to accelerate the inversions by means of convolutional neural networks. We invert a small sub-set of the data using standard inversion approach and then train a convolutional neural network to generalize the results to the full data set. We analyze this method on different synthetic and observed data sets and compare the results with the results obtained by applying standard inversion methods. We find that, given an extensive enough data set, convolutional neural networks provide results that are very close to the ones obtained by standard inversion methods, in a fraction of time. Title: Center-to-Limb Continuum Polarization in Solar and Stellar Atmospheres Authors: Kostogryz, N. M.; Berdyugina, S. V.; Yakobchuk, T. M.; Milić, I. Bibcode: 2019ASPC..526..139K Altcode: The center-to-limb variation of the intensity (CLVI) and of the linear polarization (CLVP) of stellar radiation arise when the scattering and absorption processes are important in the stellar atmosphere. We model the CLVI and CLVP of continuum radiation, taking into account different contributions of scattering and absorption opacity for a variety of spectral type stars with plane-parallel and spherical PHOENIX atmosphere models. We show how the polarization depends on the effective temperature and surface gravity of a star and how the considered geometry of the stellar atmosphere affects the polarization signal. For the Sun, we compare existing measurements with our theoretical predictions for different solar models (FALA, FALC, FALP, HSRA, and Phoenix). The CLVI and CLVP of stellar atmospheres are also needed to interpret the light curves of transiting exoplanets. Here we present the variation of the polarization in exoplanetary systems caused by transits and grazing transits and discuss how the considered geometry of stellar atmosphere models affect the transit curves of exoplanets. Title: Response Functions for NLTE Lines Authors: Milić, I.; van Noort, M. Bibcode: 2019ASPC..526..179M Altcode: Response functions quantify the sensitivity of the emergent polarized spectrum to perturbations in the atmospheric quantities. They are an important diagnostics tool and an essential ingredient of the so-called inversion codes, widely used in solar spectropolarimetry. The computation of response functions for spectral lines formed out of local thermodynamic equilibrium is complicated because of strong spatial and non-linear couplings of the atomic populations. We have recently proposed a novel, analytic approach for the computation of NLTE response functions, and in this short contribution we discuss the possibilities of computing response functions for scattering polarization. We explicitly show the procedure for a two level atom line (normal Zeeman triplet), and discuss the "formation heights" of intensity and scattering polarization for a prototype line. Title: Department of astronomy at Petnica science center: 2013-2017 Authors: Boskovic, M.; Obuljen, A.; Vukadinovic, D.; Milosevic, S.; Milic, I.; Bozic, N. Bibcode: 2018POBeo..98..101B Altcode: No abstract at ADS Title: Department of astronomy at Petnica science center: 2013-2017 Authors: Boskovic, M.; Obuljen, A.; Vukadinovic, D.; Milosevic, S.; Milic, I.; Bozic, N. Bibcode: 2018POBeo..98...101 Altcode: No abstract at ADS Title: Spectropolarimetric NLTE inversion code SNAPI Authors: Milić, I.; van Noort, M. Bibcode: 2018A&A...617A..24M Altcode: 2018arXiv180608134M Context. Inversion codes are computer programs that fit a model atmosphere to the observed Stokes spectra, thus retrieving the relevant atmospheric parameters. The rising interest in the solar chromosphere, where spectral lines are formed by scattering, requires developing, testing, and comparing new non-local thermal equilibrium (NLTE) inversion codes.
Aims: We present a new NLTE inversion code that is based on the analytical computation of the response functions. We named the code SNAPI, which is short for spectropolarimetic NLTE analytically powered inversion.
Methods: SNAPI inverts full Stokes spectrum in order to obtain a depth-dependent stratification of the temperature, velocity, and the magnetic field vector. It is based on the so-called node approach, where atmospheric parameters are free to vary in several fixed points in the atmosphere, and are assumed to behave as splines in between. We describe the inversion approach in general and the specific choices we have made in the implementation.
Results: We test the performance on one academic problem and on two interesting NLTE examples, the Ca II 8542 and Na I D spectral lines. The code is found to have excellent convergence properties and outperforms a finite-difference based code in this specific implementation by at least a factor of three. We invert synthetic observations of Na lines from a small part of a simulated solar atmosphere and conclude that the Na lines reliably retrieve the magnetic field and velocity in the range -3 < logτ < -0.5. Title: Sweep-by-sweep implicit Lambda iteration for non-LTE radiative transfer in 2D Cartesian coordinates Authors: Milic, I.; Atanackovic, O. Bibcode: 2017POBeo..96..147M Altcode: No abstract at ADS Title: Polarimetry of transiting planets: Differences between plane-parallel and spherical host star atmosphere models Authors: Kostogryz, N. M.; Yakobchuk, T. M.; Berdyugina, S. V.; Milic, I. Bibcode: 2017A&A...601A...6K Altcode: Context. To properly interpret photometric and polarimetric observations of exoplanetary transits, accurate calculations of center-to-limb variations of intensity and linear polarization of the host star are needed. These variations, in turn, depend on the choice of geometry of stellar atmosphere.
Aims: We want to understand the dependence of the flux and the polarization curves during a transit on the choice of the applied approximation for the stellar atmosphere: spherical and plane-parallel. We examine whether simpler plane-parallel models of stellar atmospheres are good enough to interpret the flux and the polarization light curves during planetary transits, or whether more complicated spherical models should be used.
Methods: Linear polarization during a transit appears because a planet eclipses a stellar disk and thus breaks left-right symmetry. We calculate the flux and the polarization variations during a transit with given center-to-limb variations of intensity and polarization.
Results: We calculate the flux and the polarization variations during transit for a sample of 405 extrasolar systems. Most of them show higher transit polarization for the spherical stellar atmosphere. Our calculations reveal a group of exoplanetary systems that demonstrates lower maximum polarization during the transits with spherical model atmospheres of host stars with effective temperatures of Teff = 4400-5400 K and surface gravity of log g = 4.45-4.65 than that obtained with plane-parallel atmospheres. Moreover, we have found two trends of the transit polarization. The first trend is a decrease in the polarization calculated with spherical model atmosphere of host stars with effective temperatures Teff = 3500-5100 K, and the second shows an increase in the polarization for host stars with Teff = 5100-7000 K. These trends can be explained by the relative variation of temperature and pressure dependences in the plane-parallel and spherical model atmospheres.
Conclusions: For most cases of known transiting systems the plane-parallel approximation of stellar model atmospheres may be safely used for calculation of the flux and the polarization curves because the difference between two models is tiny. However, there are some examples where the spherical model atmospheres are necessary to get proper results, such as the systems with grazing transits, with Earth-size planets, or for the hot host stars with effective temperatures higher than 6000 K. Title: Line response functions in nonlocal thermodynamic equilibrium. Isotropic case Authors: Milić, I.; van Noort, M. Bibcode: 2017A&A...601A.100M Altcode: Context. Response functions provide us with a quantitative measure of sensitivity of the emergent spectrum to perturbations in the solar atmosphere and are thus the method of choice for interpreting spectropolarimetric observations. For the lines formed in the solar chromosphere, it is necessary to compute these responses taking into account nonlocal thermodynamic equilibrium (NLTE) effects.
Aims: We show how to analytically compute the response of the level populations in NLTE to a change of a given physical quantity at a given depth in the atmosphere. These responses are then used to compute opacity and emissivity responses, which are then propagated to obtain the response of the emergent intensity.
Methods: Our method is based on the derivative of the rate equations, where we explicitly incorporate spatial coupling in the radiative rate terms. After considering and collecting all interdependencies, the problem reduces to a linear system of equations with a dimension equal to the product of the number of spatial points and the number of energy levels.
Results: We compare analytically computed response functions with those obtained using a finite difference approach and find very good agreement. In addition, a more accurate way of propagating opacity and emissivity perturbations through the numerical solution of the radiative transfer equation was developed.
Conclusions: This method allows for the fast evaluation of the response of the emergent spectrum to perturbations of a given quantity at a given depth, and thus is a significant step towards more efficient NLTE inversions. Title: Inference of magnetic fields in inhomogeneous prominences Authors: Milić, I.; Faurobert, M.; Atanacković, O. Bibcode: 2017A&A...597A..31M Altcode: 2016A&A...597A..31M; 2016arXiv160904954M Context. Most of the quantitative information about the magnetic field vector in solar prominences comes from the analysis of the Hanle effect acting on lines formed by scattering. As these lines can be of non-negligible optical thickness, it is of interest to study the line formation process further.
Aims: We investigate the multidimensional effects on the interpretation of spectropolarimetric observations, particularly on the inference of the magnetic field vector. We do this by analyzing the differences between multidimensional models, which involve fully self-consistent radiative transfer computations in the presence of spatial inhomogeneities and velocity fields, and those which rely on simple one-dimensional geometry.
Methods: We study the formation of a prototype line in ad hoc inhomogeneous, isothermal 2D prominence models. We solve the NLTE polarized line formation problem in the presence of a large-scale oriented magnetic field. The resulting polarized line profiles are then interpreted (I.e. inverted) assuming a simple 1D slab model.
Results: We find that differences between input and the inferred magnetic field vector are non-negligible. Namely, we almost universally find that the inferred field is weaker and more horizontal than the input field.
Conclusions: Spatial inhomogeneities and radiative transfer have a strong effect on scattering line polarization in the optically thick lines. In real-life situations, ignoring these effects could lead to a serious misinterpretation of spectropolarimetric observations of chromospheric objects such as prominences. Title: Response functions for NLTE lines Authors: Milic, Ivan Bibcode: 2017psio.confE..22M Altcode: No abstract at ADS Title: Center-to-limb variation of intensity and polarization in continuum spectra of FGK stars for spherical atmospheres Authors: Kostogryz, N. M.; Milic, I.; Berdyugina, S. V.; Hauschildt, P. H. Bibcode: 2016A&A...586A..87K Altcode: 2015arXiv151107213K
Aims: One of the necessary parameters needed for the interpretation of the light curves of transiting exoplanets or eclipsing binary stars (as well as interferometric measurements of a star or microlensing events) is how the intensity and polarization of light changes from the center to the limb of a star. Scattering and absorption processes in the stellar atmosphere affect both the center-to-limb variation of intensity (CLVI) and polarization (CLVP). In this paper, we present a study of the CLVI and CLVP in continuum spectra, taking into consideration the different contributions of scattering and absorption opacity for a variety of spectral type stars with spherical atmospheres.
Methods: We solve the radiative transfer equation for polarized light in the presence of a continuum scattering, taking into consideration the spherical model of a stellar atmosphere. To cross-check our results, we developed two independent codes that are based on Feautrier and short characteristics methods, respectively,
Results: We calculate the center-to-limb variation of intensity (CLVI) and polarization (CLVP) in continuum for the Phoenix grid of spherical stellar model atmospheres for a range of effective temperatures (4000-7000 K), gravities (log g = 1.0-5.5), and wavelengths (4000-7000 Å), which are tabulated and available at the CDS. In addition, we present several tests of our codes and compare our calculations for the solar atmosphere with published photometric and polarimetric measurements. We also show that our two codes provide similar results in all considered cases.
Conclusions: For sub-giant and dwarf stars (log g = 3.0-4.5), the lower gravity and lower effective temperature of a star lead to higher limb polarization of the star. For giant and supergiant stars (log g = 1.0-2.5), the highest effective temperature yields the largest polarization. By decreasing the effective temperature of a star down to 4500-5500 K (depending on log g), the limb polarization decreases and reaches a local minimum. It increases again with a corresponding decrease in temperature down to 4000 K. For the most compact dwarf stars (log g = 5.0-5.5), the limb polarization degree shows a maximum for models with effective temperatures in the range 4200-4600 K (depending on log g) and decreases toward higher and lower temperatures.

The intensity and polarization profiles are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/586/A87 Title: VizieR Online Data Catalog: Center-to-limb polarization of FGK stars (Kostogryz+, 2016) Authors: Kostogryz, N. M.; Milic, I.; Berdyugina, S. V.; Hauschildt, P. H. Bibcode: 2016yCat..35860087K Altcode: Calculated center-to-limb variations of intensity (limb darkening) for different stellar parameters with spherical atmosphere model approximation. All intensities are normalized to the intensity in the center of stellar disks, therefore, in the centre of the disks (mu=1.0), I(mu)/I(1.0)=1.0. The parameters of spherical Phoenix stellar model atmospheres we considered here are the following: effective temperature is in the range of 4000K-7000K with the step of 100K and for logg=1.0-5.5 with the step of 0.5. All calculations are made for such wavelengths: 4000Å, 4500Å, 5000Å, 6000Å, 7000Å. We also present the position of the stellar limb and calculated stellar radius.

Calculated center-to-limb variations of polarization (CLVP) for different stellar parameters with spherical atmosphere model approximation. All intensities are normalized to the intensity in the center of stellar disks, therefore, in the centre of the disks (mu=1.0), I(mu)/I(1.0)=1.0. The parameters of spherical Phoenix model atmosphere we considered here are the following: effective temperature is in the range of 4000K-7000 K with the step of 100K and for logg=1.0-5.5 with the step of 0.5. All calculations are made for such wavelengths: 4000Å, 4500Å, 5000Å, 6000Å, 7000Å. We also present the position of the stellar limb.

(2 data files). Title: Inhomogeneity and velocity fields effects on scattering polarization in solar prominences Authors: Milić, I.; Faurobert, M. Bibcode: 2015IAUS..305..238M Altcode: One of the methods for diagnosing vector magnetic fields in solar prominences is the so called "inversion" of observed polarized spectral lines. This inversion usually assumes a fairly simple generative model and in this contribution we aim to study the possible systematic errors that are introduced by this assumption. On two-dimensional toy model of a prominence, we first demonstrate importance of multidimensional radiative transfer and horizontal inhomogeneities. These are able to induce a significant level of polarization in Stokes U, without the need for the magnetic field. We then compute emergent Stokes spectrum from a prominence which is pervaded by the vector magnetic field and use a simple, one-dimensional model to interpret these synthetic observations. We find that inferred values for the magnetic field vector generally differ from the original ones. Most importantly, the magnetic field might seem more inclined than it really is. Title: Scattering line polarization in rotating, optically thick disks Authors: Milić, I.; Faurobert, M. Bibcode: 2014A&A...571A..79M Altcode: 2014arXiv1409.2654M Context. To interpret observations of astrophysical disks, it is essential to understand the formation process of the emitted light. If the disk is optically thick, scattering dominated and permeated by a Keplerian velocity field, non-local thermodynamic equilibrium (NLTE) radiative transfer modeling must be done to compute the emergent spectrum from a given disk model.
Aims: We investigate NLTE polarized line formation in different simple disk models and aim to demonstrate the importance of both radiative transfer effects and scattering, as well as the effects of velocity fields.
Methods: We self-consistently solve the coupled equations of radiative transfer and statistical equilibrium for a two-level atom model by means of Jacobi iteration. We use the short characteristics method of formal solution in two-dimensional axisymmetric media and compute scattering polarization, that is Q/I and U/I line profiles, using the reduced intensity formalism. We account for the presence of Keplerian velocity fields by casting the radiative transfer equation in the observer's frame.
Results: Relatively simple (homogeneous and isothermal) disk models show complex intensity profiles that owe their shape to the interplay of multidimensional NLTE radiative transfer and the presence of rotation. The degree of scattering polarization is significantly influenced not only by the inclination of the disk with respect to observer, but also by the optical thickness of the disk and the presence of rotation. Stokes U/I shows double-lobed profiles with amplitude that increases with the disk rotation.
Conclusions: Our results suggest that the line profiles, especially the polarized ones, emerging from gaseous disks differ significantly from the profiles predicted by simple approximations. Even in the case of the simple two-level atom model, we obtain line profiles that are diverse in shape, but typically symmetric in Stokes Q and antisymmetric in Stokes U. A clear indicator of disk rotation is the presence of Stokes U, which might prove to be a useful diagnostic tool. We also demonstrate that, for moderate rotational velocities, an approximate treatment can be used, where NLTE radiative transfer is done in the velocity field-free approximation, and Doppler shift is applied in the process of spatial integration over the whole emitting surface. Title: Inferring Depth-Dependent Quiet Sun Magnetic Fields Authors: Milić, I.; Faurober, M., Bibcode: 2014ASPC..489..157M Altcode: Hanle effect has an invaluable diagnostic value, allowing us to diagnose weak solar magnetic fields from the measure of the depolarization of lines formed in scattering processes. Here we consider two molecular lines which have been studied in the last decade: MgH and C2 lines. Different studies invoke different strengths of the magnetic fields, ranging from ≍ 10 to ≍ 100 Gauss. We try to simultaneously explain all this results with the assumption of depth-dependent magnetic field with large depth gradient. Our inversion method, which relies on the inversion of the center-to-limb variation (CLV) of line-center polarization, can simultaneously explain observed CLV in MgH and C2 lines, but yields very strong gradient of the magnetic field strength. We conclude that a possible way to make this kind of diagnostics more reliable is to combine it with multidimensional modeling of Hanle effect in molecular and atomic lines. Title: Accelerating NLTE radiative transfer by means of the Forth-and-Back Implicit Lambda Iteration: A two-level atom line formation in 2D Cartesian coordinates Authors: Milić, Ivan; Atanacković, Olga Bibcode: 2014AdSpR..54.1297M Altcode: 2014arXiv1401.4562M State-of-the-art methods in multidimensional NLTE radiative transfer are based on the use of local approximate lambda operator within either Jacobi or Gauss-Seidel iterative schemes. Here we propose another approach to the solution of 2D NLTE RT problems, Forth-and-Back Implicit Lambda Iteration (FBILI), developed earlier for 1D geometry. In order to present the method and examine its convergence properties we use the well-known instance of the two-level atom line formation with complete frequency redistribution. In the formal solution of the RT equation we employ short characteristics with two-point algorithm. Using an implicit representation of the source function in the computation of the specific intensities, we compute and store the coefficients of the linear relations J=a+bS between the mean intensity J and the corresponding source function S. The use of iteration factors in the ‘local’ coefficients of these implicit relations in two ‘inward’ sweeps of 2D grid, along with the update of the source function in other two ‘outward’ sweeps leads to four times faster solution than the Jacobi’s one. Moreover, the update made in all four consecutive sweeps of the grid leads to an acceleration by a factor of 6-7 compared to the Jacobi iterative scheme. Title: On some dynamical properties of Phocaea asteroids Authors: Milić, I. S.; Novaković, B. Bibcode: 2014acm..conf..358M Altcode: The Phocaea group is located in the inner asteroid belt, and consists of asteroids having orbital inclination higher than about 20 degrees, and eccentricity ranging between 0.15 and 0.3. This region is known to have dynamical boundaries which completely surround it and produce a confinement of objects inside it [1,2]. An inner boundary in semi-major axis, often related to the 7/2 mean-motion resonance (MMR) with Jupiter, is located at about 2.25 au. However, a non-negligible number of asteroids is still present beyond this limit. The outer boundary, at around 2.5 au, is set by the powerful 3/1 MMR with Jupiter. Moreover, the region is delimited by important secular resonances (SRs): the ν_{6}=g-g_{6} at low inclination, and the ν_{5}=g-g_{5} and ν_{16}=s-s_{6} at high inclination. Also, the asteroids from the region interact with many mean-motion and secular resonances. The most relevant SRs are g-g_{6} - s + s_{6}, g - g_{5} + s - s_{6} and g - g_{6} - 2s + 2s_{6}, as can be recognized by the alignments of objects associated with these resonances (see Figure).

The aim of this work is twofold. First, to investigate the possible relevance of secular resonances with the inner planets for the Phocaea asteroids. Second, to check weather or not the inner boundary of the region in terms of semi-major axis, i.e. 7/2 resonance with Jupiter, could be crossed under the influence of gravitational and/or non-gravitational forces.

Our results confirm the non-negligible importance of secular resonances involving inner planets for the dynamics over long time scales of the asteroids in the Phocaea region. The most obvious interaction is found with the s - s_{4} + g_{3} - g_{7} resonance. The results for the 7/2 resonance show that a significant fraction of the bodies larger than about 600 m, and most of the bodies smaller than the above limit, can transit across the resonance without being removed from the Phocaea region. This means that, despite being effective in pumping up asteroid eccentricities in this region, the 7/2 resonance is not an absolute dynamical boundary for sufficiently small objects, below some hundred meters in diameter. Title: Ubrzanje metoda za rešavanje problema prenosa polarizovanog zračenja u više dimenzija i njihova primena Title: Ubrzanje metoda za rešavanje problema prenosa polarizovanog zračenja u više dimenzija i njihova primena Title: Acceleration of methods for multidimensional polarized radiative transfer and their application; Authors: Milic, Ivan Bibcode: 2014PhDT.......574M Altcode: No abstract at ADS Title: Multidimensional and inhomogeneity effects on scattering polarization in solar prominences Authors: Milić, Ivan; Faurobert, Marianne Bibcode: 2014IAUS..300..453M Altcode: Measurements of magnetic fields in solar prominences via Hanle effect usually assume either single scattering approximation or simple, one-dimensional, slab model in order to perform an inversion and find the unknown magnitude and the orientation of the magnetic field from spectropolarimetric observations. Here we perform self-consistent NLTE modeling of scattering polarization in inhomogeneous 2D slab, illuminated from its sides by the solar continuum radiation. We show that even in the absence of a magnetic field, in the non-optically thin regime, significant non-zero Stokes U is to be expected. Neglecting these effects, in principle, could cause systematic errors in spectropolarimetric inversions, in the case when the prominence is optically thick. Title: Boundary conditions for polarized radiative transfer with incident radiation Authors: Faurobert, M.; Milić, I.; Atanacković, O. Bibcode: 2013A&A...559A..68F Altcode: 2013arXiv1309.4160F Context. Polarized radiative transfer in the presence of scattering in spectral lines and/or in continua may be cast in a reduced form for six reduced components of the radiation field. In this formalism, the six components of the reduced source function are angle-independent quantities. It thus drastically reduces the storage requirement of numerical codes and it is very well suited to solving polarized non-local thermodynamic equilibrium radiative transfer problems in 3D media.
Aims: This approach encounters a fundamental problem when the medium is illuminated by a polarized incident radiation, because there is a priori no way of relating the known (and measurable) Stokes parameters of the incident radiation to boundary conditions for the reduced equations. The origin of this problem is that there is no unique way of deriving the radiation-reduced components from its Stokes parameters (only the inverse operation is clearly defined). The method proposed here aims at enabling to work with arbitrary incident radiation field (polarized or unpolarized).
Methods: In previous studies, an ad-hoc treatment of the boundary conditions, applied to cases where the incident radiation is unpolarized, has been used. In this paper, we show that it is possible to account for the incident radiation in a rigorous way without any assumption on its properties by expressing the radiation field as the sum of a directly transmitted radiation and of a diffuse radiation. This approach was first used by Chandrasekhar to solve the problem of diffuse reflection by planetary atmospheres illuminated by their host star.
Results: The diffuse radiation field obeys a transfer equation with no incident radiation that may be solved in the reduced form. The first scattering of the incident radiation introduces primary creation terms in the six components of the reduced source function. Once the reduced polarized transfer problem is solved for the diffuse radiation field, its Stokes parameters can be computed. The full radiation field is then obtained by adding the directly transmitted radiation field computed in the Stokes formalism.
Conclusions: In the case of an unpolarized incident radiation, the diffuse field approach allows us to validate the previously introduced ad-hoc expressions. The diffuse field approach however leads to more accurate computation of the source terms in the case where the incident radiation is anisotropic. It is the only possible approach when the incident radiation field is polarized. We perform numerical computations of test cases, showing that the emergent line-polarization may be significantly affected by the polarization of the incident radiation. Title: Transfer of polarized line radiation in 2D cylindrical geometry Authors: Milić, I. Bibcode: 2013A&A...555A.130M Altcode:
Aims: This paper deals with multidimensional NLTE polarized radiative transfer in the case of two level atom in the absence of lower level polarization. We aim to develop an efficient and robust method for 2D cylindrical geometry and to apply it to various axi-symmetrical astrophysical objects such as rings, disks, rotating stars, and solar prominences.
Methods: We review the methods of short characteristics and Jacobi iteration applied to axisymmetric geometry. Then we demonstrate how to use a reduced basis for polarized intensity and polarized source function to self-consistently solve the coupled equations of radiative transfer and statistical equilibrium for linearly polarized radiation. We discuss some peculiarities that do not appear in Cartesian geometry, such as angular interpolation in performing the formal solution. We also show how to account for two different types of illuminating radiation.
Results: The proposed method is tested on homogeneous, self-emitting cylinders to compare the results with those in 1D geometries. We demonstrate a possible astrophysical application on a very simple model of circumstellar ring illuminated by a host star where we show that such a disk can introduce a significant amount of scattering polarization in the system.
Conclusions: This method is found to converge properly and, apparently, to allow for substantial time saving compared to 3D Cartesian geometry. We also discuss the advantages and disadvantages of this approach in multidimensional radiative transfer modeling. Title: CCD Observations of ERS with the 60 cm Telescope at ASV Authors: Damljanovic, G.; Milic, I. S. Bibcode: 2013POBeo..92..161D Altcode: We present the observations of extragalactic radio sources (ERS) which are possible in the optical domain and can be used to establish the link between the ICRF2 and the future Gaia Celestial Reference Frame (GCRF). Our telescope of small aperture size (< 1 m) is located in the south of Serbia, near the town of Prokuplje, at the Astronomical Station Vidojevica (ASV) which belongs to the Astronomical Observatory of Belgrade (AOB). It is a Cassegrain-type optical system (D=60 cm, F=600 cm) of equatorial mount. About 40 ERS, from ICRF2 list, were observed at ASV during 2011 and 2012. These observations are of importance to compare the ERS optical and radio positions (VLBI ones), and to investigate the relation between optical and radio reference frames. Also, they are useful to check the possibilities of the instrument. We observed ERS with the CCD Apogeee Alta U42. The observations, reduction and preliminary results of some ERS are presented here. Title: MONECOM: Physical Characteristics Of Main Belt Comets Authors: Bogdanovic, N.; Smolic, I.; Bogosavljevic, M.; Milic, I. Bibcode: 2013POBeo..92..153B Altcode: The aim of the MONECOM project is to carry out photometric observations of several Main-Belt Comets (MBCs). Observations and data reduction were performed by high-school students from three countries (Croatia, Greece and Serbia), supervised by their teachers and local astronomers. Here we present some results obtained by the Serbian group. Title: Observational Astronomy at Petnica Science Center Authors: Milic, I.; Obuljen, A.; Bozic, N.; Smolic, I.; Boskovic, M. Bibcode: 2013POBeo..92..185M Altcode: During years 2012 and 2013, Petnica Science Center has been undergoing a thorough renovation and expansion. One of the new features will be new observational equipment intended for high-level educational work at the Department of astronomy. In this short paper we sum up main observational activities at Petnica Science Center, and discuss desired observational equipment. Title: Astrometric Positions of ICRF2 Radio Sources with Different Reference Catalogues Authors: Damljanovic, G.; Milic, I. S.; Maigurova, N.; Martynov, M.; Pejovic, N. Bibcode: 2012POBeo..91..191D Altcode: We present the results of an investigation of astrometric positions of a few extragalactic radio sources (ERS) from the ICRF2 list. The reference systems are based on the resolutions of the international scientific unions. The celestial system is based on IAU (International Astronomical Union) Resolution A4 (1991). It was officially initiated and named International Celestial Reference System (ICRS) by IAU Resolution B2 (1997). Its definition was further refined by IAU Resolution B1 (2000) and Resolution B3 (2009). The fundamental celestial reference frame (International Celestial Reference Frame -- ICRF) was adopted by the IAU (1997), with its original list of radio objects and two extensions (ICRF-ext1 and ICRF-ext2); hereafter referred to as ICRF1. Alltogether, there were 717 sources: 212 defining ones, 109 new ones, 294 candidate ones, and 102 additional sources. At the IAU XXVII GA (2009), the second realization of the ICRF (the ICRF2) was adopted with the list of precise positions for 3414 compact radio astronomical sources. It is more then five times the number as in the ICRF1. At that moment there were nearly 30 years of VLBI (Very Long Baseline Interferometry) observations of some radio sources. The ICRF2 has a noise threshold of about 0.04 mas (nearly 6 times better than ICRF1) and an axis stability of about 0.01 mas (nearly twice as stable as ICRF1). Also, a search for a relation between optical and radio reference frames is important. To do that, it is necessary to make the observations of some ICRF2 ERS which are visible in the optical domain, and to compare their optical and radio positions (VLBI ones). The optical positions (α and δ) could be calculated using reference stars from some of nowadays big star catalogues. The XPM, 2MASS (with XC1) and DR7 SDSS ones were used here, and the relative method was applied. We started to do that comparison using our CCD observations of a few ERS made with the 2 m RCC telescope (with the focal length of 16 m) of Rozhen National Astronomical Observatory (Bulgarian Academy of Sciences). About 30 fields around ERS were observed with CCD camera VersArray 1300B (1340x1300 pixels, the pixel size is 20x20 micrometers, one pixel is 0.258 arcsec) in the end of March 2011. The main steps of our reduction and preliminary results are presented here.

Based on observations with the 2 m RCC telescope of the Rozhen National Astronomical Observatory operated by the Institute of Astronomy, Bulgarian Academy of Sciences. Title: Resonance Line Polarization in Moving Optically Thick Structures Authors: Milic, I.; Faurobert, M. Bibcode: 2012POBeo..91...45M Altcode: We compute the scattering polarization of lines formed in moving slabs of moderate optical thickness (τ=1 and τ=10) illuminated by a linearly polarized radiation field showing a broad absorption feature. Slabs are one-dimensional and horizontal, placed at a finite height H above a semi-infinite atmosphere. This model is an academic case which represents the formation of emergent radiation in solar filaments. The slabs have a macroscopic velocity in the radial direction with respect to the atmosphere, and are observed at different angles (i.e. at different locations over the solar disk). We investigate the sensitivity of the outgoing polarization to the slab velocity and observing angle. We show that outgoing polarization profiles are at least as sensitive to macroscopic velocity as are intensity profiles. Title: CCD measurements in optical domain and astrometric positions of ICRF2 radio sources Authors: Damljanovic, G.; Milic, I. S. Bibcode: 2012jsrs.conf...92D Altcode: At the IAU XXIIIth GA in 1997, the International Celestial Reference Frame (ICRF) was adopted; hereafter referred to as ICRF1. After the original list of radio objects there were two extensions, ICRF-ext1 and ICRF-ext2. All together, there were 717 sources: 212 defining ones, 109 new ones, 294 candidate ones, and 102 additional ones. At the IAU XXVIIth GA in 2009, the second realization of the ICRF (the ICRF2) was adopted with the list of precise positions for 3414 compact radio astronomical sources. At that moment there were nearly 30 years of VLBI observations. The ICRF2 has a noise floor of about 0.04 mas (near six times better than ICRF1) and an axis stability of about 0.01 mas (nearly twice as stable as ICRF1). Also, it is of importance to make the observations of some ICRF2 extragalactic radio sources (ERS) which are visible in the optical domain, and to compare their optical (calculated via the reference stars) and radio positions (VLBI ones). We started to do it by using the CCD camera VersArray 1300B and the RCC telescope1 (D/F = 2m/16m) of Rozhen National Astronomical Observatory (Bulgarian Academy of Sciences). About 30 frames were observed at the end of March 2011. The main steps of our calculations and some preliminary results (comparison between the measured optical positions and the radio ones) for a few ERS from ICRF2 list were presented here. Title: Hanle diagnostics of weak solar magnetic fields: . Inversion of scattering polarization in C2 and MgH molecular lines Authors: Milić, I.; Faurobert, M. Bibcode: 2012A&A...547A..38M Altcode: Context. The quiet Sun magnetism has been intensively investigated in recent years by various observational techniques. But several issues, such as the question of the isotropy and of the energy density spectrum of the mixed polarity turbulent magnetic fields, are still under debate.
Aims: Here we present an inversion method that allows us to constrain the depth-dependence of the magnetic field strength. We use the center-to-limb variations of linear scattering polarization measured in molecular lines of C2 and MgH molecules with different sensitivities to the Hanle effect. We consider six C2-triplets and one MgH line in the spectral range between 515.7 nm and 516.1 nm observed with the THEMIS Telescope.
Methods: One of the delicate problems with Hanle diagnostics is to disentangle the effects of elastic depolarizing collisions from the depolarization due to the Hanle effect of the magnetic field. By making use of the different sensitivities of the molecular lines in our spectral range to microturbulent magnetic fields and, by using a non-LTE radiative transfer modeling of the line formation, we are able to determine both the depolarizing collision cross-section and the magnetic strength. We use a standard 1D quiet Sun atmospheric model and we invert the full set of center-to-limb polarization rates measured at line centers, with a depth-dependent magnetic field described by three free parameters. The depolarizing collision cross-section is also treated as a free parameter. A downhill simplex method is used to find the best-fitting values for the collisional and magnetic strength parameters.
Results: For the elastic depolarizing collisions cross-section for the C2 lines we obtain α(2) = 1.6 ± 0.4 × 10-9 cm3 s-1, which is within an order of magnitude of the value previously obtained for MgH lines from a differential Hanle effect analysis. The observational constraints provided by the MgH and C2 line polarization give access to the altitude range between z = 200 km and z = 400 km above the base of the photosphere. We find that the turbulent magnetic field strength decreases from 95 Gauss at the altitude z = 200 km to 5 Gauss at z = 400 km.
Conclusions: The turbulent magnetic field strength that we derive from the Hanle effect shows a strong vertical gradient in the upper photosphere. We point out that this behavior may explain why very different turbulent magnetic field strengths have been inferred from the interpretation of Hanle depolarization when using different lines formed at different altitudes. We notice that the presence of a strong depth gradient is not compatible with the assumption of isotropy of the turbulent field. Title: Numerical modeling of the linear polarization in molecular lines of the solar flash spectrum Authors: Milić, I.; Faurobert, M. Bibcode: 2012EAS....55...65M Altcode: Molecular lines formed in the upper photosphere of the Sun show significant degree of linear scattering polarization, when one observes close to the solar limb. Those lines prove to be important tools for turbulent magnetic field diagnostic via the Hanle effect. In order to correctly model the line formation in regions close to the Solar limb, one has to take into account the sphericity of the atmosphere and to model depolarizing collisions and NLTE line formation in details. We present computations of scattering polarization in C2 lines in a 1D spherically symmetric medium described by FALC and FALX models, and compare those computations to observations of the Solar flash spectrum. Title: Focal Length Determination for the 60 cm Telescope at Astronomical Station Vidojevica Authors: Cvetkovic, Z.; Damljanovic, G.; Pavlovic, R.; Vince, O.; Milic, I. S.; Stojanovic, M. Bibcode: 2012SerAJ.184...97C Altcode: The focal length of a telescope is an important parameter in determining the angular pixel size. This parameter is used for the purpose of determining the relative coordinates (angular separation and positional angle) of double and multiple stars, and the precise coordinates of extragalactic radio sources (ERS) that are visible at optical wavelengths. At the Astronomical Station Vidojevica we have collected observations of these objects using two CCD cameras, Apogee Alta U42 and SBIG ST-10ME, attached to the 60 cm telescope. Its nominal focal length is 600 cm as given by the manufacturer. To determine the telescope focal length more precisely for both attached detectors, we used angular-separation measurements from CCD images taken at Astronomical Station Vidojevica. The obtained focal lengths are: F_{42} = (5989±7) mm using the CCD camera Apogee Alta U42 attached to the telescope, and F_{10} = (5972±4) mm with the CCD camera SBIG ST-10ME attached to the telescope. Title: Modeling scattering polarization in molecular solar lines in spherical geometry Authors: Milić, I.; Faurobert, M. Bibcode: 2012A&A...539A..10M Altcode: Context. The atmosphere of the Sun is permeated by a vast amount of magnetic flux that remains invisible in magnetograms based on the Zeeman effect. A model-independent way of measuring weak hidden magnetic fields makes use of the differential Hanle effect on the scattering polarization of molecular lines with different sensitivities to magnetic fields.
Aims: The observed line scattering polarization steeply increases at the solar limb. Here we are interested in interpreting observations performed at the solar limb, where plane-parallel semi-infinite geometry is not valid. The main reason is that the sphericity of the atmosphere means that the line-of-sight optical path intersects only a finite part of the solar atmosphere. In this paper we revisit the modeling of scattering polarization in two molecular lines of C2 and MgH in the spectral range from 515.60 nm to 516.20 nm, where observations performed both inside and above the solar limb are available.
Methods: The solar atmosphere is described by a one-dimensional, spherically symmetric medium following either the FALC or the FALX quiet Sun model. Both the line and background continuum scattering polarizations are computed by means of the "along-the-ray" approach. We assume a two-level atom formalism for the line source function, and we compute the molecule number densities and line opacities assuming LTE. We estimate the elastic and inelastic collision rates by fitting the line intensity and linear polarization in several couples of lines of the Second Solar Spectrum Atlas.
Results: The limb variations of scattering polarization, both in the lines and in the continuum, are strongly modified when the sphericity of the solar atmosphere is accounted for. We show that the line polarization goes through a maximum at 0.4'' above the limb, for both MgH and C2 lines. The contribution of the line rapidly goes to zero at a larger limb distance, but continuum polarization keeps increasing. The maximum polarization rates have an amplitude of 2% to 2.5% when the FALC model is used, which agrees with previous observations, whereas the FALX model leads to much higher rates. We then investigate the Hanle effect of microturbulent magnetic fields on the C2 line linear polarization. We show that polarization observed close to the limb would provide valuable diagnostics of weak magnetic fields in the region of the temperature minimum. Title: Scattering polarization of molecular lines at the solar limb Authors: Milić, I.; Faurobert, M. Bibcode: 2011sf2a.conf..401M Altcode: Molecular lines formed in the upper photosphere of the Sun show linear scattering polarization, when one observes close to the solar limb. This provides us with a diagnostic tool for measuring weak magnetic fields in the solar photosphere through the differential Hanle effect in these lines. However, in order to interpret polarization ratio measured in different lines of different optical thickness, one has to model accurately enough the line formation processes. Observations performed close to and above the solar limb give access to the still poorly known region of the temperature minimum between the photosphere and the chromosphere. The modeling of such observations requires to account for the spherical geometry of the solar atmosphere. Here we revisit the modeling of molecular solar line scattering polarization in spherical geometry and we investigate its diagnostics potential. Title: VizieR Online Data Catalog: Corrected proper motion for HIP stars (Damljanovic+, 2011) Authors: Damljanovic, G.; Milic, I. S. Bibcode: 2011yCatp042018201D Altcode: During the last century, there were many so-called independent latitude (IL) stations with the observations which were included into data of a few international organizations (like Bureau International de l'Heure - BIH, International Polar Motion Service - IPMS) and the Earth rotation programmes for determining the Earth Orientation Parameters - EOP. Because of this, nowadays, there are numerous astrometric ground-based observations (made over many decades) of some stars included in the Hipparcos Catalogue (ESA 1997, Cat. I/239). We used these latitude data for the inverse investigations - to improve the proper motions in declination μδ of the mentioned Hipparcos stars. We determined the corrections Δμδ and investigated agreement of our μδ and those from the catalogues Hipparcos and new Hipparcos (van Leeuwen 2007, Cat. I/311). To do this we used the latitude variations of 7 stations (Belgrade, Blagoveschtschensk, Irkutsk, Poltava, Pulkovo, Warsaw and Mizusawa), covering different intervals in the period 1904.7-1992.0, obtained with 6 visual and 1 floating zenith telescopes (Mizusawa). On the other hand, with regard that about two decades have elapsed since the Hipparcos ESA mission observations (the epoch of Hipparcos catalogue is 1991.25), the error of apparent places of Hipparcos stars has increased by nearly 20mas because of proper motion errors. Also, the mission lasted less than four years which was not enough for a sufficient accuracy of proper motions of some stars (such as double or multiple ones). Our method of calculation, and the calculated μδ for the common IL/Hipparcos stars are presented here. We constructed an IL catalogue of 1200 stars: there are 707 stars in the first part (with at least 20 years of IL observations) and 493 stars in the second one (less than 20 years). In the case of μδ of IL stars observed at some stations (Blagoveschtschensk, Irkutsk, Mizusawa, Poltava and Pulkovo) we find the formal errors less than the corresponding Hipparcos ones and for some of them (stations Blagoveschtschensk and Irkutsk) even less than the new Hipparcos ones.

(1 data file). Title: Corrected mu_delta for Stars of Hipparcos Catalogue from Independent Latitude Observations over Many Decades Authors: Damljanovic, G.; Milic, I. S. Bibcode: 2011SerAJ.182...35D Altcode: During the last century, there were many so-called independent latitude (IL) stations with the observations which were included into data of a few international organizations (like Bureau International de l'Heure - BIH, International Polar Motion Service - IPMS) and the Earth rotation programmes for determining the Earth Orientation Parameters - EOP. Because of this, nowadays, there are numerous astrometric ground-based observations (made over many decades) of some stars included in the Hipparcos Catalogue (ESA 1997). We used these latitude data for the inverse investigations - to improve the proper motions in declination μ_{δ} of the mentioned Hipparcos stars. We determined the corrections Δμ_{δ} and investigated agreement of our μ_{δ} and those from the catalogues Hipparcos and new Hipparcos (van Leeuwen 2007). To do this we used the latitude variations of 7 stations (Belgrade, Blagoveschtschensk, Irkutsk, Poltava, Pulkovo, Warsaw and Mizusawa), covering different intervals in the period 1904.7 - 1992.0, obtained with 6 visual and 1 floating zenith telescopes (Mizusawa). On the other hand, with regard that about two decades have elapsed since the Hipparcos ESA mission observations (the epoch of Hipparcos catalogue is 1991.25), the error of apparent places of Hipparcos stars has increased by nearly 20 mas because of proper motion errors. Also, the mission lasted less than four years which was not enough for a sufficient accuracy of proper motions of some stars (such as double or multiple ones). Our method of calculation, and the calculated μ_{δ} for the common IL/Hipparcos stars are presented here. We constructed an IL catalogue of 1200 stars: there are 707 stars in the first part (with at least 20 years of IL observations) and 493 stars in the second one (less than 20 years). In the case of μ_{&delta}; of IL stars observed at some stations (Blagoveschtschensk, Irkutsk, Mizusawa, Poltava and Pulkovo) we find the formal errors less than the corresponding Hipparcos ones and for some of them (stations Blagoveschtschensk and Irkutsk) even less than the new Hipparcos ones. Title: Correlations of Orbital Elements for Visual Double Stars Authors: Milic, I. S.; Cvetkovic, Z. Bibcode: 2010SerAJ.181...69M Altcode: In this paper, the authors examine the dependence of correlation coefficients of orbital elements on the length of the orbital arc covered by measurements, on measurements of different accuracies, and on the number of measurements. The obtained correlation coefficients for the orbital elements are found to decrease with the orbital arc length covered by measurements, they are independent of the measurement precision, and they do not depend on the number of measurements for long arcs and they decrease with the number of measurements for short arcs. Title: Comparing Observed Prominence Spectra with Simple Models Computed Using GHV Code Authors: Milic, I.; Kotrc, P. Bibcode: 2010POBeo..90..163M Altcode: Emission spectra in seven lines have been computed for 980 prominence models using code originally developed by Gouttebrose, Heinzel and Vial. Prominence is treated as isothermal, isobaric, 1-D slab, with five input parameters determining outgoing radiation. Computed emission spectra in Hα have been compared with observations from the Ondřejov large solar spectrograph and some of the results are discussed. Title: On Estimation of the Optical Thickness of Solar Prominences Authors: Milic, I.; Dejanic, S.; Kotrc, P. Bibcode: 2009POBeo..86..283M Altcode: A method for rough estimation of the optical thickness of solar prominences in Hα line is presented. The method is based on the fitting of observed profiles with the synthetic ones computed by using the model of an isobaric 1-D slab with constant source function under the assumption of complete redistribution. The method was applied on 52 prominences observed with the Ondřejov HSFA2 spectrograph from April 2007 to March 2008.