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Low-ionisation structures (LISs) are commonly found in planetary nebulae (PNe) but they are still poorly understood. The recent discovery of unforeseen molecular hydrogen gas (H2) has changed what we think we know about these microstructures and PNe. For an overall understanding of LISs, an [Fe II] 1.644$\mu$m imagery survey in PNe with LISs was carried out with the aim to detect the [Fe II] 1.644$\mu$m emission line, a common tracer of shocks. We present the first detection of [Fe II] 1.644$\mu$m line directly associated with the LISs in four out of five PNe. The theoretical H I 12-4 recombination line is also computed either from the Br$\gamma$ or the H$\beta$ line and subtracted from the observed narrowband line fluxes. [Fe II] 1.644$\mu$m flux ranges from 1 to 40x10$^{-15}$ ergs cm$^{-2}$ s$^{-1}$ and the surface brightness from 2 to 90x10$^{-5}$ erg cm$^{-2}$ s$^{-1}$ sr$^{-1}$. The R(Fe)=[Fe II] 1.644$\mu$m/Br$\gamma$ line ratio is also computed and varies between 0.5 and 7. In particular, the [Fe II] 1.644$\mu$m line is detected in NGC 6543 (R(Fe)<0.15), the outer pairs of LISs in NGC 7009 (R(Fe)<0.25), the jet-like LISs in IC 4634 (R(Fe)$\sim$1) and in several LISs in NGC 6571 (2

We report the first spatially resolved detection of the near-infrared [C I] $\lambda$8727 emission from the outer pair of low-ionization structures in the planetary nebula NGC 7009 from data obtained by the Multi Unit Spectroscopic Explorer integral field unit. This atomic carbon emission marks the transition zone between ionized and neutral gas, and for the first time offers direct evidence that LISs are photodominated regions. The outer LIS pair exhibits intense [C I] $\lambda$8727 emission, but He I $\lambda$8733 is absent. Conversely, the inner pair of knots shows both lines, likely due to the host nebula emission. Furthermore, the [C I] $\lambda$8727 line is absent in the host nebula emission, but He I $\lambda$8733 is present. Although the origin of the [C I] $\lambda$8727 line is still debated, its detection supports the scenario of photoevaporated dense molecular clumps., Comment: 9 pages, 5 figures, 3 tables

We consider the {\em correlated knapsack orienteering} (CSKO) problem: we are given a travel budget $B$, processing-time budget $W$, finite metric space $(V,d)$ with root $\rho\in V$, where each vertex is associated with a job with possibly correlated random size and random reward that become known only when the job completes. Random variables are independent across different vertices. The goal is to compute a $\rho$-rooted path of length at most $B$, in a possibly adaptive fashion, that maximizes the reward collected from jobs that processed by time $W$. To our knowledge, CSKO has not been considered before, though prior work has considered the uncorrelated problem, {\em stochastic knapsack orienteering}, and {\em correlated orienteering}, which features only one budget constraint on the {\em sum} of travel-time and processing-times. We show that the {\em adaptivity gap of CSKO is not a constant, and is at least $\Omega\bigl(\max\sqrt{\log{B}},\sqrt{\log\log{W}}\}\bigr)$}. Complementing this, we devise {\em non-adaptive} algorithms that obtain: (a) $O(\log\log W)$-approximation in quasi-polytime; and (b) $O(\log W)$-approximation in polytime. We obtain similar guarantees for CSKO with cancellations, wherein a job can be cancelled before its completion time, foregoing its reward. We also consider the special case of CSKO, wherein job sizes are weighted Bernoulli distributions, and more generally where the distributions are supported on at most two points (2-CSKO). Although weighted Bernoulli distributions suffice to yield an $\Omega(\sqrt{\log\log B})$ adaptivity-gap lower bound for (uncorrelated) {\em stochastic orienteering}, we show that they are easy instances for CSKO. We develop non-adaptive algorithms that achieve $O(1)$-approximation in polytime for weighted Bernoulli distributions, and in $(n+\log B)^{O(\log W)}$-time for the more general case of 2-CSKO., Comment: Full version of APPROX 2024 paper

We have performed wide-field, ultra-low surface brightness H$\alpha$ emission line mapping around NGC 1068 with the newly commissioned Circumgalactic H$\alpha$ Spectrograph (\chas). NGC 1068 is notable for its active galactic nucleus, which globally ionizes gas in the disk and halo. Line-emitting diffuse ionized gas is distributed throughout the galactic disk and large-scale ionized filaments are found well beyond the disk, aligned with the cone angle of the central jet. We report the discovery of a new Ribbon of ionized gas around NGC 1068 beyond even the known outer filamentary structure, located 20 kpc from the galaxy. The H$\alpha$ surface brightness of this Ribbon is on the order of the bright Telluric lines, ranging from $[4-16]$ R with fainter regions on the order of the sky background continuum. Unlike previous extended emission, the Ribbon is not as well aligned with the current axis of the central jet. It is not associated with any galactic structure or known tidal features in the halo of NGC 1068, though it may originate from a larger distribution of unmapped neutral atomic or molecular gas in the halo. The morphology of the Ribbon emission in H$\alpha$ is correlated with extended UV emission around NGC 1068. H$\alpha$ to UV flux ratios in the Ribbon are comparable to extended emission line ratios in the halos of NGC 5128, NGC 253, and M82. The H$\alpha$ excess in the Ribbon gas suggests ionization by slow-shocks or a mixture of in-situ star formation and photoionization and collisional ionization processes., Comment: 18 pages, 5 figures, 4 tables, Accepted for publication in ApJ

We apply the HanleRT Tenerife Inversion Code to the spectro-polarimetric observations obtained by the Chromospheric LAyer SpectroPolarimeter. This suborbital space experiment measured the variation with wavelength of the four Stokes parameters in the near-ultraviolet spectral region of the Mg II h & k lines over a solar disk area containing part of an active region plage and the edge of a sunspot penumbra. We infer the stratification of the temperature, the electron density, the line of-sight velocity, the micro-turbulent velocity, and the longitudinal component of the magnetic field from the observed intensity and circular polarization profiles. The inferred model atmosphere shows larger temperature and electron density in the plage and the superpenumbra regions than in the quiet regions. The shape of the plage region in terms of its brightness is similar to the pattern of the inferred longitudinal component of the magnetic field in the chromosphere, as well as to that of the overlying moss observed by AIA in the 171 A band, which suggests a similar magnetic origin for the heating in both the plage and the moss region. Moreover, this heating is particularly significant in the regions with larger inferred magnetic flux. In contrast, in the superpenumbra, the regions with larger electron density and temperature are usually found in between these regions with larger magnetic flux, suggesting that the details of the heating mechanism in the chromosphere of the superpenumbra may be different to those in the plage, but with the magnetic field still playing a key role., Comment: Accepted for publication in the Astrophysical Journal

In decision-making scenarios, \textit{reasoning} can be viewed as an algorithm $P$ that makes a choice of an action $a^* \in \mathcal{A}$, aiming to optimize some outcome such as maximizing the value function of a Markov decision process (MDP). However, executing $P$ itself may bear some costs (time, energy, limited capacity, etc.) and needs to be considered alongside explicit utility obtained by making the choice in the underlying decision problem. Such costs need to be taken into account in order to accurately model human behavior, as well as optimizing AI planning, as all physical systems are bound to face resource constraints. Finding the right $P$ can itself be framed as an optimization problem over the space of reasoning processes $P$, generally referred to as \textit{metareasoning}. Conventionally, human metareasoning models assume that the agent knows the transition and reward distributions of the underlying MDP. This paper generalizes such models by proposing a meta Bayes-Adaptive MDP (meta-BAMDP) framework to handle metareasoning in environments with unknown reward/transition distributions, which encompasses a far larger and more realistic set of planning problems that humans and AI systems face. As a first step, we apply the framework to two-armed Bernoulli bandit (TABB) tasks, which have often been used to study human decision making. Owing to the meta problem's complexity, our solutions are necessarily approximate, but nevertheless robust within a range of assumptions that are arguably realistic for human decision-making scenarios. These results offer a normative framework for understanding human exploration under cognitive constraints. This integration of Bayesian adaptive strategies with metareasoning enriches both the theoretical landscape of decision-making research and practical applications in designing AI systems that plan under uncertainty and resource constraints.

The Mg II k resonance line is commonly used for diagnosing the solar chromosphere. We theoretically investigated its intensity and polarization in solar prominences, taking 3D radiative transfer and Hanle and Zeeman effects into account. We used an optically thick 3D model representative of a solar prominence and applied several inversion methods to the synthetic Stokes profiles, clarifying their pros and cons for inferring prominence magnetic fields. We conclude that the self-consistent 3D inversion with radiative transfer is necessary to determine the magnetic field vector, although its geometry cannot be inferred with full fidelity. We also demonstrate that more traditional methods, such as those based on the weak field approximation or the constant-property slab assumption, can offer useful information under certain conditions., Comment: 9 pages, 9 figures, accepted for publication in A&A

Handwriting is a complex task that involves the coordination of motor, perceptual and cognitive skills. It is a fundamental skill for the cognitive and academic development of children. However, the technological, and educational changes in recent decades have affected both the teaching and assessment of handwriting. This paper presents a literature review of handwriting analysis in children, including a bibliometric analysis of published articles, the study participants, and the methods of evaluating the graphonometric state of children. The aim is to synthesize the state of the art and provide an overview of the main study trends over the last decade. The review concludes that handwriting remains a fundamental tool for early estimation of cognitive problems and early intervention. The article analyzes graphonometric evaluation tools. Likewise, it reflects on the importance of graphonometric evaluation as a means to detect possible difficulties or disorders in learning to write. The article concludes by highlighting the need to agree on an evaluation methodology and to combine databases.

Optical heterodyne detection is a powerful technique for characterizing a wide range of physical excitations. Here, we use two types of optical heterodyne detection techniques (fundamental and parametric pumping) to microscopically characterize the high-frequency auto-oscillations of single and multiple nano-constriction spin Hall nano-oscillators (SHNOs). To validate the technique and demonstrate its robustness, we study SHNOs made from two different material stacks, NiFe/Pt and W/CoFeB/MgO, and investigate the influence of both the RF injection power and the laser power on the measurements, comparing the optical results to conventional electrical measurements. To demonstrate the key features of direct, non-invasive, submicron, spatial, and phase-resolved characterization of the SHNO magnetodynamics, we map out the auto-oscillation magnitude and phase of two phase-binarized SHNOs used in Ising Machines. This proof-of-concept platform establishes a strong foundation for further extensions, contributing to the ongoing development of crucial characterization techniques for emerging computing technologies based on spintronics devices, Comment: 7 pages

Given the reproducing kernel $k$ of the Hilbert space $\mathcal{H}_k$ we study spaces $\mathcal{H}_k(b)$ whose reproducing kernel has the form $k(1-bb^*)$, where $b$ is a row-contraction on $\mathcal{H}_k$. In terms of reproducing kernels this it the most far-reaching generalization of the classical de Branges-Rovnyaks spaces, as well as their very recent generalization to several variables. This includes the so called sub-Bergman spaces in one or several variables. We study some general properties of $\mathcal{H}_k(b)$ e.g. when the inclusion map into $\mathcal{H}$ is compact. Our main result provides a model for $\mathcal{H}_k(b)$ reminiscent of the Sz.-Nagy-Foia\c{s} model for contractions. As an application we obtain sufficient conditions for the containment and density of the linear span of $\{k_w:w\in\mathcal{X}\}$ in $\mathcal{H}_k(b)$. In the standard cases this reduces to containment and density of polynomials. These methods resolve a very recent conjecture regarding polynomial approximation in spaces with kernel $\frac{(1-b(z)b(w)^*)^m}{(1-z\overline w)^\beta}, 1\leq m<\beta, m\in\mathbb{N}$.

Mid-infrared emission features probe the properties of ionized gas, and hot or warm molecular gas. The Orion Bar is a frequently studied photodissociation region (PDR) containing large amounts of gas under these conditions, and was observed with the MIRI IFU aboard JWST as part of the "PDRs4All" program. The resulting IR spectroscopic images of high angular resolution (0.2") reveal a rich observational inventory of mid-IR emission lines, and spatially resolve the substructure of the PDR, with a mosaic cutting perpendicularly across the ionization front and three dissociation fronts. We extracted five spectra that represent the ionized, atomic, and molecular gas layers, and measured the most prominent gas emission lines. An initial analysis summarizes the physical conditions of the gas and the potential of these data. We identified around 100 lines, report an additional 18 lines that remain unidentified, and measured the line intensities and central wavelengths. The H I recombination lines originating from the ionized gas layer bordering the PDR, have intensity ratios that are well matched by emissivity coefficients from H recombination theory, but deviate up to 10% due contamination by He I lines. We report the observed emission lines of various ionization stages of Ne, P, S, Cl, Ar, Fe, and Ni, and show how certain line ratios vary between the five regions. We observe the pure-rotational H$_2$ lines in the vibrational ground state from 0-0 S(1) to 0-0 S(8), and in the first vibrationally excited state from 1-1 S(5) to 1-1 S(9). We derive H$_2$ excitation diagrams, and approximate the excitation with one thermal (~700 K) component representative of an average gas temperature, and one non-thermal component (~2700 K) probing the effect of UV pumping. We compare these results to an existing model for the Orion Bar PDR and highlight the differences with the observations., Comment: 26 pages, 12 figures, 3 tables. Submitted to A&A, under review (1st revision)

Measurable linear scattering polarization signals have been predicted and detected at the solar disk center in the core of chromospheric lines. These forward-scattering polarization signals, which are of high interest for magnetic field diagnostics, have always been modeled either under the assumption of complete frequency redistribution (CRD), or taking partial frequency redistribution (PRD) effects into account under the angle-averaged (AA) approximation. This work aims at assessing the suitability of the CRD and PRD-AA approximations for modeling the forward-scattering polarization signals produced by the presence of an inclined magnetic field, the so-called forward-scattering Hanle effect, in the chromospheric CaI 4227 A line. Radiative transfer calculations are performed in semi-empirical 1D solar atmospheres, out of local thermodynamic equilibrium (LTE). A two-step solution strategy is applied: the non-LTE RT problem is first solved considering a multilevel atom and neglecting polarization phenomena. The same problem is then solved including polarization, considering a two-level atom and keeping fixed the lower-level population calculated at the previous step. The emergent linear polarization signals calculated under the CRD and PRD-AA approximations are analyzed and compared to those obtained by modeling PRD effects in their general angle-dependent (AD) formulation. With respect to the PRD-AD case, the CRD and PRD-AA calculations significantly underestimate the amplitude of the line-center polarization signals produced by the forward-scattering Hanle effect. The results of this work suggest that a PRD-AD modeling is required in order to develop reliable diagnostic techniques exploiting the forward-scattering polarization signals observed in the CaI 4227 A line. These results need to be confirmed by full 3D calculations including non-magnetic symmetry-breaking effects.

We study the circular polarization of the magnetic field induced transition (MIT) between the $3d^5(^6S)4d\ ^7D_2$ and $3d^5(^6S)4p\ ^7P_4^\circ$ states of \ion{Cr}{1} at 533.03~nm (wavelength in air). The fractional circular polarization $V/I$ of this spectral line resulting from the solution of the radiation transfer problem in a sunspot model permeated by a homogeneous magnetic field of 3~kG shows amplitudes of about $2\%$. Spectro-polarimetric observations of two sunspots were obtained with the Zurich Imaging Polarimeter-3 at the Istituto ricerche solari Aldo e Cele Dacc\`o (IRSOL) observatory observatory in Locarno, Switzerland. The observed $V/I$ profiles show approximately anti-symmetrical shapes with an amplitude of around $0.1\%$ and $0.2\%$ for the two sunspots. The center of this profile coincides with the wavelengths predicted for the above-mentioned MIT. We apply an inversion code to the spectro-polarimetric data of the \ion{Cr}{1} permitted lines at 532.91 and 532.98~nm, as well as to the MIT line at 533.03~nm, to infer a stratification of the emitting atmosphere. We compare the $V/I$ profiles synthesized in the inferred atmosphere models with the observations, showing that the observed signal likely corresponds to the MIT line., Comment: Accepted for publication in the Astrophysical Journal

Most low-mass stars form in stellar clusters that also contain massive stars, which are sources of far-ultraviolet (FUV) radiation. Theoretical models predict that this FUV radiation produces photo-dissociation regions (PDRs) on the surfaces of protoplanetary disks around low-mass stars, impacting planet formation within the disks. We report JWST and Atacama Large Millimetere Array observations of a FUV-irradiated protoplanetary disk in the Orion Nebula. Emission lines are detected from the PDR; modelling their kinematics and excitation allows us to constrain the physical conditions within the gas. We quantify the mass-loss rate induced by the FUV irradiation, finding it is sufficient to remove gas from the disk in less than a million years. This is rapid enough to affect giant planet formation in the disk.

Solar magnetic fields alter scattering polarization in spectral lines like Sr I at 4607 {\AA} via the Hanle effect, making it a potential diagnostic for small-scale mixed-polarity photospheric magnetic fields. Recently, observational evidence for scattering polarization in the Sr I 4607 {\AA} at the solar disk center was found. Here, we investigate the reliability of the reconstruction method making possible this detection. To this end, we apply it to linear polarization profiles of the Sr I 4607 {\AA} line radiation emerging at the disk center obtained from a detailed 3D radiative transfer calculation in a magneto-hydrodynamic simulation snapshot with a small-scale dynamo contribution. The reconstruction method systematically reduces the scattering amplitudes by up to a factor of two, depending on the noise level. We demonstrate that the decrease can be attributed to two systematic errors: first, the physical constraint that underlies our assumptions regarding the dependence of scattering polarization on the quadrupolar moment of the radiation field, and second, the limitations of our method in accurately determining the sign of the radiation field tensor from the observed intensity image. However, consistently applying the reconstruction process and after taking into account image degradation effects due to the temporally variable image quality, such as imposed by seeing, observed and synthesized polarization signals show remarkable agreement. We thus conclude that the observed scattering polarization at solar disk center is consistent with that emerging from magneto-hydrodynamic model of the solar photosphere with an average magnetic field of 170 G at the visible surface., Comment: Accepted for publication in ApJ

Several recent studies have linked the exceptional North Atlantic and Eurasian atmospheric evolution during late February and March 2018 to the Sudden Stratospheric Warming (SSW) that took place a few weeks earlier. February 2018 was characterized by an abrupt transition from the positive to the negative phase of the North Atlantic Oscillation (NAO) and a subsequent persistence of the negative NAO for several weeks. This paper investigates the contribution of atmospheric and oceanic phenomena to both the 2018 event and a set of 19 identified analogues (including the former) for the period 1959-2022. Evidence is given that La Ni\~na conditions in the tropical Pacific and upstream North Atlantic cyclones play an important role as a trigger for these events. Ensuing two-way tropospheric-stratospheric coupling and eddy feedbacks provide extended-range persistence for negative NAO conditions. These results may help improve the prediction of such exceptional events.

We investigate the main physical mechanisms that shape the intensity and polarization of the Ba II D1 line at 4934 angstroms via radiative transfer numerical experiments. We focus especially on the scattering linear polarization arising from the spectral structure of the anisotropic radiation in the wavelength interval spanned by the line's hyperfine structure (HFS) components in the odd isotopes of barium. After verifying that the presence of the low-energy metastable levels only impacts the amplitude, but not the shape, of the D1 linear polarization, we relied on a two-term atomic model that neglects such metastable levels but includes HFS. The D1 fractional linear polarization shows a very small variation with the choice of atmospheric model, enhancing its suitability for solar magnetic field diagnostics. Tangled magnetic fields with strengths of tens of gauss reduce the linear polarization and saturation is reached at roughly 300 G. Deterministic inclined magnetic fields produce a U/I profile and, if they have a significant longitudinal component, a V/I profile, whose modeling requires accounting for HFS and the Paschen-Back effect. Because of the overlap between HFS components, the magnetograph formula cannot be applied to infer the longitudinal magnetic field. Accurately modeling the D1 intensity and polarization requires an atomic system that includes the metastable levels and the HFS, the detailed spectral structure of the radiation field, the incomplete Paschen-Back regime for magnetic fields, and an accurate treatment of collisions., Comment: Accepted for publication in the Astrophysical Journal

Major depressive disorder (MDD) is a complex psychiatric disorder that affects the lives of hundreds of millions of individuals around the globe. Even today, researchers debate if morphological alterations in the brain are linked to MDD, likely due to the heterogeneity of this disorder. The application of deep learning tools to neuroimaging data, capable of capturing complex non-linear patterns, has the potential to provide diagnostic and predictive biomarkers for MDD. However, previous attempts to demarcate MDD patients and healthy controls (HC) based on segmented cortical features via linear machine learning approaches have reported low accuracies. In this study, we used globally representative data from the ENIGMA-MDD working group containing an extensive sample of people with MDD (N=2,772) and HC (N=4,240), which allows a comprehensive analysis with generalizable results. Based on the hypothesis that integration of vertex-wise cortical features can improve classification performance, we evaluated the classification of a DenseNet and a Support Vector Machine (SVM), with the expectation that the former would outperform the latter. As we analyzed a multi-site sample, we additionally applied the ComBat harmonization tool to remove potential nuisance effects of site. We found that both classifiers exhibited close to chance performance (balanced accuracy DenseNet: 51%; SVM: 53%), when estimated on unseen sites. Slightly higher classification performance (balanced accuracy DenseNet: 58%; SVM: 55%) was found when the cross-validation folds contained subjects from all sites, indicating site effect. In conclusion, the integration of vertex-wise morphometric features and the use of the non-linear classifier did not lead to the differentiability between MDD and HC. Our results support the notion that MDD classification on this combination of features and classifiers is unfeasible.

For a fixed analytic function g on the unit disc, we consider the analytic paraproducts induced by g, which are formally defined by $T_gf(z)=\int_0^zf(\zeta)g'(\zeta)d\zeta$, $S_gf(z)=\int_0^zf'(\zeta)g(\zeta)d\zeta$, and $M_gf(z)=g(z)f(z)$. We are concerned with the study of the boundedness of operators in the algebra $\mathcal{A}_g$ generated by the above operators acting on Hardy, or standard weighted Bergman spaces on the disc. The general question is certainly very challenging, since operators in $\mathcal{A}_g$ are finite linear combinations of finite products (words) of $T_g,S_g,M_g$ which may involve a large amount of cancellations to be understood. The results in the paper "Composition of analytic paraproducts, J. Math. Pures Appl. 158 (2022) 293--319" show that boundedness of operators in a fairly large subclass of $\mathcal{A}_g$ can be characterized by one of the conditions $g\in H^\infty$, or $g^n$ belongs to $BMOA$ or the Bloch space, for some integer $n>0$. However, it is also proved that there are many operators, even single words in $\mathcal{A}_g$ whose boundedness cannot be described in terms of these conditions. The present paper provides a considerable progress in this direction. Our main result provides a complete quantitative characterization of the boundedness of an arbitrary word in $\mathcal{A}_g$ in terms of a ``fractional power'' of the symbol $g$, that only depends on the number of appearances of each of the letters $T_g,S_g,M_g$ in the given word.

(Abridged) We investigate the impact of radiative feedback from massive stars on their natal cloud and focus on the transition from the HII region to the atomic PDR (crossing the ionisation front (IF)), and the subsequent transition to the molecular PDR (crossing the dissociation front (DF)). We use high-resolution near-IR integral field spectroscopic data from NIRSpec on JWST to observe the Orion Bar PDR as part of the PDRs4All JWST Early Release Science Program. The NIRSpec data reveal a forest of lines including, but not limited to, HeI, HI, and CI recombination lines, ionic lines, OI and NI fluorescence lines, Aromatic Infrared Bands (AIBs including aromatic CH, aliphatic CH, and their CD counterparts), CO2 ice, pure rotational and ro-vibrational lines from H2, and ro-vibrational lines HD, CO, and CH+, most of them detected for the first time towards a PDR. Their spatial distribution resolves the H and He ionisation structure in the Huygens region, gives insight into the geometry of the Bar, and confirms the large-scale stratification of PDRs. We observe numerous smaller scale structures whose typical size decreases with distance from Ori C and IR lines from CI, if solely arising from radiative recombination and cascade, reveal very high gas temperatures consistent with the hot irradiated surface of small-scale dense clumps deep inside the PDR. The H2 lines reveal multiple, prominent filaments which exhibit different characteristics. This leaves the impression of a "terraced" transition from the predominantly atomic surface region to the CO-rich molecular zone deeper in. This study showcases the discovery space created by JWST to further our understanding of the impact radiation from young stars has on their natal molecular cloud and proto-planetary disk, which touches on star- and planet formation as well as galaxy evolution., Comment: 52 pages, 30 figures, submitted to A&A

The long-standing paradox of the linear polarization signal of the Na i D1 line was recently resolved by accounting for the atom's hyperfine structure and the detailed spectral structure of the incident radiation field. That modeling relied on the simplifying angle-averaged (AA) approximation for partial frequency redistribution (PRD) in scattering, which potentially neglects important angle-frequency couplings. This work aims at evaluating the suitability of a PRD-AA modeling for the D1 and D2 lines through comparisons with general angle-dependent (AD) PRD calculations, both in the absence and presence of magnetic fields. We solved the radiative transfer problem for polarized radiation in a one-dimensional semi-empirical atmospheric model with microturbulent and isotropic magnetic fields, accounting for PRD effects, comparing PRD-AA and PRD-AD modelings. The D1 and D2 lines are modeled separately as two-level atomic system with hyperfine structure. The numerical results confirm that a spectrally structured radiation field induces linear polarization in the D1 line. However, the PRD-AA approximation greatly impacts the Q/I shape, producing an antisymmetric pattern instead of the more symmetric PRD-AD one, while presenting a similar sensitivity to magnetic fields between 10 and 200 G. Under the PRD-AA approximation, the Q/I profile of the D2 line presents an artificial dip in its core, which is not found for the PRD-AD case. We conclude that accounting for PRD-AD effects is essential to suitably model the scattering polarization of the Na i D lines. These results bring us closer to exploiting the full diagnostic potential of these lines for the elusive chromospheric magnetic fields.

In single molecule orientation localization microscopy, valuable information about the orientation and longitudinal position of each molecule is often encoded in the shape of the point spread function (PSF). This shape, though, can be affected significantly by aberrations and other imperfections in the imaging system, leading to erroneous estimation of the measured parameters. A basic solution is to model the aberrations as a scalar mask in the pupil plane that is characterized through phase retrieval algorithms. However, this approach is not suitable for cases involving polarization-dependent aberrations, introduced either through unintentional anisotropy in the elements or by using birefringent masks for PSF shaping. Here, this problem is addressed by introducing a fully vectorial model in which the polarization aberrations are represented via a spatially-dependent Jones matrix, commonly used to describe polarization-dependent elements. It is then shown that these aberrations can be characterized from a set of PSF measurements at varying focal planes and for various polarization projections. This PZ-stack of PSFs, which contains both phase and polarization projection diversity, is used in a phase retrieval algorithm based on nonlinear optimization to determine the aberrations. This methodology is demonstrated with numerical simulations and experimental measurements. The pyPSFstack software developed for the modeling and characterization is made freely available., Comment: 13 pages for main manuscript and 14 pages for the supplemental document

The JWST has captured the most detailed and sharpest infrared images ever taken of the inner region of the Orion Nebula, the nearest massive star formation region, and a prototypical highly irradiated dense photo-dissociation region (PDR). We investigate the fundamental interaction of far-ultraviolet photons with molecular clouds. The transitions across the ionization front (IF), dissociation front (DF), and the molecular cloud are studied at high-angular resolution. These transitions are relevant to understanding the effects of radiative feedback from massive stars and the dominant physical and chemical processes that lead to the IR emission that JWST will detect in many Galactic and extragalactic environments. Due to the proximity of the Orion Nebula and the unprecedented angular resolution of JWST, these data reveal that the molecular cloud borders are hyper structured at small angular scales of 0.1-1" (0.0002-0.002 pc or 40-400 au at 414 pc). A diverse set of features are observed such as ridges, waves, globules and photoevaporated protoplanetary disks. At the PDR atomic to molecular transition, several bright features are detected that are associated with the highly irradiated surroundings of the dense molecular condensations and embedded young star. Toward the Orion Bar PDR, a highly sculpted interface is detected with sharp edges and density increases near the IF and DF. This was predicted by previous modeling studies, but the fronts were unresolved in most tracers. A complex, structured, and folded DF surface was traced by the H2 lines. This dataset was used to revisit the commonly adopted 2D PDR structure of the Orion Bar. JWST provides us with a complete view of the PDR, all the way from the PDR edge to the substructured dense region, and this allowed us to determine, in detail, where the emission of the atomic and molecular lines, aromatic bands, and dust originate.

(Abridged) Mid-infrared observations of photodissociation regions (PDRs) are dominated by strong emission features called aromatic infrared bands (AIBs). The most prominent AIBs are found at 3.3, 6.2, 7.7, 8.6, and 11.2 $\mu$m. The most sensitive, highest-resolution infrared spectral imaging data ever taken of the prototypical PDR, the Orion Bar, have been captured by JWST. We provide an inventory of the AIBs found in the Orion Bar, along with mid-IR template spectra from five distinct regions in the Bar: the molecular PDR, the atomic PDR, and the HII region. We use JWST NIRSpec IFU and MIRI MRS observations of the Orion Bar from the JWST Early Release Science Program, PDRs4All (ID: 1288). We extract five template spectra to represent the morphology and environment of the Orion Bar PDR. The superb sensitivity and the spectral and spatial resolution of these JWST observations reveal many details of the AIB emission and enable an improved characterization of their detailed profile shapes and sub-components. While the spectra are dominated by the well-known AIBs at 3.3, 6.2, 7.7, 8.6, 11.2, and 12.7 $\mu$m, a wealth of weaker features and sub-components are present. We report trends in the widths and relative strengths of AIBs across the five template spectra. These trends yield valuable insight into the photochemical evolution of PAHs, such as the evolution responsible for the shift of 11.2 $\mu$m AIB emission from class B$_{11.2}$ in the molecular PDR to class A$_{11.2}$ in the PDR surface layers. This photochemical evolution is driven by the increased importance of FUV processing in the PDR surface layers, resulting in a "weeding out" of the weakest links of the PAH family in these layers. For now, these JWST observations are consistent with a model in which the underlying PAH family is composed of a few species: the so-called 'grandPAHs'., Comment: 25 pages, 10 figures, to appear in A&A

We present JWST images of the well-known planetary nebula NGC 6720 (the Ring Nebula), covering wavelengths from 1.6$\mu$m to 25 $\mu$m. The bright shell is strongly fragmented with some 20 000 dense globules, bright in H$_2$, with a characteristic diameter of 0.2 arcsec and density $n_{\rm H} \sim 10^5$-$10^6$ cm$^{-3}$. The shell contains a thin ring of polycyclic aromatic hydrocarbon (PAH) emission. H$_2$ is found throughout the shell and in the halo. H$_2$ in the halo may be located on the swept-up walls of a biconal polar flow. The central cavity is shown to be filled with high ionization gas and shows two linear structures. The central star is located 2 arcsec from the emission centroid of the cavity and shell. Linear features (`spikes') extend outward from the ring, pointing away from the central star. Hydrodynamical simulations are shown which reproduce the clumping and possibly the spikes. Around ten low-contrast, regularly spaced concentric arc-like features are present; they suggest orbital modulation by a low-mass companion with a period of about 280 yr. A previously known much wider companion is located at a projected separation of about 15 000 au; we show that it is an M2-M4 dwarf. The system is therefore a triple star. These features, including the multiplicity, are similar to those seen in the Southern Ring Nebula (NGC 3132) and may be a common aspect of such nebulae., Comment: 25 pages, 23 figures. Submitted to Monthly Notices of the Royal Astronomical Society. Corrected typos in metadata

This paper proposes pandemic mitigation vaccination policies for Newfoundland and Labrador (NL) based on two compact mixed integer programming (MIP) models of the distance-based critical node detection problem (DCNDP). Our main focus is on two variants of the DCNDP that seek to minimize the number of connections with lengths of at most one (1-DCNDP) and two (2-DCNDP). A polyhedral study for the 1-DCNDP is conducted, and new aggregated inequalities are provided for the 2-DCNDP. The computational experiments show that the 2-DCNDP with aggregated inequalities outperforms the one with disaggregated inequalities for graphs with a density of at least 0.5%. We also study the strategic vaccine allocation problem as a real-world application of the DCNDP and conduct a set of computational experiments on a simulated contact network of NL. Our computational results demonstrate that the DCNDP-based strategies can have a better performance in comparison with the real-world strategies implemented during COVID-19.

We investigate theoretically the circular polarization signals induced by the Zeeman effect in the Fe II lines of the 279.3-280.7 nm spectral range of the CLASP2 space experiment and their suitability to infer solar magnetic fields. To this end, we use a comprehensive Fe II atomic model to solve the problem of the generation and transfer of polarized radiation in semi-empirical models of the solar atmosphere, comparing the region of formation of the Fe II spectral lines with those of the Mg II h and k and the Mn I resonance lines. These are present in the same near ultraviolet (near-UV) spectral region and allowed the mapping of the longitudinal component of the magnetic field ($B_{\rm L}$) through several layers of the solar chromosphere in an active region plage. We compare our synthetic intensity profiles with observations from the IRIS and CLASP2 missions, proving the suitability of our model atom to characterize these Fe II spectral lines. The CLASP2 observations show two Fe II spectral lines at 279.79 and 280.66 nm with significant circular polarization signals. We demonstrate the suitability of the Weak-Field Approximation (WFA) applied to the Stokes $I$ and $V$ profiles of these Fe II lines to infer $B_{\rm L}$ in the plage atmosphere. We conclude that the near-UV spectral region of CLASP2 allows to determine $B_{\rm L}$ from the upper photosphere to the top of the chromosphere of active region plages., Comment: Accepted for publication in The Astrophysical Journal