Non-local Thermodynamic Equilibrium Research Articles

Hunting pre-stellar cores with APEX IRAS16293E (Oph464)

Pre-stellar cores are the first steps in the process of star and planet formation. However, the dynamical and chemical evolution of pre-stellar cores is still not well understood. Our partial knowledge of the chemical and physical structure of pre-stellar cores, as well as how they are fed and influenced by the surrounding environment, limits the level of knowledge that we can achieve at later stages in the star and planet formation process, from protostellar cores to exoplanets. Our aims are to estimate the central density of the pre-stellar core IRAS16293E and to carry out an inventory of molecular species towards the density peak of the core. We observed high-J rotational transitions of N_2H^+ and N_2D^+, and several other molecular lines towards the dust emission peak using the Atacama Pathfinder EXperiment (APEX) telescope, and derived the density and temperature profiles of the core using far-infrared surface brightness maps from Herschel. The N_2H^+ and N_2D^+ lines were analysed by non-local thermodynamic equilibrium (non-LTE) radiative transfer modelling. Our best-fit core model consists of a static inner region, embedded in an infalling envelope with an inner radius of approximately 3000 au (21" at 141 pc). The observed high-J lines of N_2H^+ and N_2D^+ (with critical densities greater than 10^6 cm^-3) turn out to be very sensitive to depletion; the present single-dish observations are best explained with no depletion of N_2H^+ and N_2D^+ in the inner core. The N_2D^+/N_2H^+ ratio that best reproduces our observations is 0.44, one of the highest observed to date in pre-stellar cores. Additionally, half of the molecules that we observed are deuterated isotopologues, confirming the high level of deuteration towards this source. Non-LTE radiative transfer modelling of N_2H^+ and N_2D^+ lines proved to be an excellent diagnostic of the chemical structure (i.e. molecular freeze-out) and dynamics (infall velocity profile) of a pre-stellar core. Probing the physical conditions immediately before the protostellar collapse is a necessary reference for theoretical studies and simulations with the aim of understanding the earliest stages of star and planet formation and the timescale of this process.

Actinide signatures in low electron fraction kilonova ejecta

ABSTRACT Neutron star (NS) mergers are known to produce heavy elements through rapid neutron capture (r-process) nucleosynthesis. Actinides are expected to be created solely by the r-process in the most neutron-rich environments. Confirming if NS mergers provide the requisite conditions for actinide creation is therefore central to determining their origin in the Universe. Actinide signatures in kilonova (KN) spectra may yield an answer, provided adequate models are available in order to interpret observational data. In this study, we investigate actinide signatures in neutron-rich merger ejecta. We use three ejecta models with different compositions and radioactive power, generated by nucleosynthesis calculations using the same initial electron fraction ($Y_e = 0.15$) but with different nuclear physics inputs and thermodynamic expansion history. These are evolved from 10 to 100 d after merger using the sumo non-local thermodynamic equilibrium (NLTE) radiative transfer code. We highlight how uncertainties in nuclear properties, as well as choices in thermodynamic trajectory, may yield entirely different outputs for equal values of $Y_e$. We consider an actinide-free model and two actinide-rich models, and find that the emergent spectra and light-curve evolution are significantly different depending on the amount of actinides present, and the overall decay properties of the models. We also present potential key actinide spectral signatures, of which doubly ionized $_{89}$Ac and $_{90}$Th may be particularly interesting as spectral indicators of actinide presence in KN ejecta.

Probing Na in giant exoplanets with ESPRESSO and 3D NLTE stellar spectra

Context. Neutral sodium was the first atom that was detected in an exoplanetary atmosphere using the transmission spectroscopy technique. To date, it remains the most successfully detected species due to its strong doublet in the optical at 5890 Å and 5896 Å. However, the center-to-limb variation (CLV) of these lines in the host star can bias the Na I detection. When combined with the Rossiter-McLaughlin (RM) effect, the CLV can mimic or obscure a planetary absorption feature if it is not properly accounted for. Aims. This work aims to investigate the impact of three-dimensional (3D) radiation hydrodynamic stellar atmospheres and non-local thermodynamic equilibrium (NLTE) radiative transfer on the modeling of the CLV+RM effect in single-line transmission spectroscopy to improve the detection and characterization of exoplanet atmospheres. Methods. We produced a grid of 3D NLTE synthetic spectra for Na I for FGK-type dwarfs within the following parameter space: Teff = 4500–6500 K, log g = 4.0–5.0, and [Fe/H] = [−0.5, 0, 0.5]. This grid was then interpolated to match the stellar parameters of four stars hosting well-known giant exoplanets, generating stellar spectra to correct for the CLV+RM effect in their transmission spectra. We used archival observations taken with the high-resolution ESPRESSO spectrograph. Results. Our work confirms the Na I detections in three systems, namely WASP-52b, WASP-76b, and WASP-127b, also improving the accuracy of the measured absorption depth. Furthermore, we find that 3D NLTE stellar models can explain the spectral features in the transmission spectra of HD 209458b without the need for any planetary absorption. In the grid of stellar synthetic spectra, we observe that the CLV effect is stronger for stars with low Teff and high log g. However, the combined effect of CLV and RM is highly dependent on the orbital geometry of the planet-star system. Conclusions. With the continuous improvement of instrumentation, it is crucial to use the most accurate stellar models available to correct for the CLV+RM effect in high-resolution transmission spectra to achieve the best possible characterization of exoplanet atmospheres. This will be fundamental in preparation for instruments such as ANDES at the Extremely Large Telescope to fully exploit its capabilities in the near future. We make our grid of 3D NLTE synthetic spectra for Na I publicly available.

The GAPS programme at TNG

Ultra-hot Jupiters (UHJs) are gas giant planets orbiting close to their host star, with equilibrium temperatures exceeding 2000 K, and among the most studied planets in terms of their atmospheric composition. Thanks to a new generation of ultra-stable high-resolution spectrographs, it is possible to detect the signal from the individual lines of the species in the exoplanetary atmospheres. We employed two techniques in this study. First, we used transmission spectroscopy, which involved examining the spectra around single lines of Fe II. Then we carried out a set of cross-correlation studies for two UHJs: KELT-9b and KELT-20b. Both planets orbit fast-rotating stars, which resulted in the detection of the strong Rossiter-McLaughlin (RM) effect and center-to-limb variations in the transmission spectrum. These effects had to be corrected to ensure a precise analysis. Using the transmission spectroscopy method, we detected 21 single lines of Fe II in the atmosphere of KELT-9b. All of the detected lines are blue-shifted, suggesting strong day-to-night side atmospheric winds. The cross-correlation method leads to the detection of the blue-shifted signal with a signal-to-noise ratio (S/N) of 13.46. Our results are in agreement with models based on non-local thermodynamical equilibrium (NLTE) effects, with a mean micro-turbulence of νmic = 2.73 ± 1.5 km s−1 and macro-turbulence of νmac = 8.22 ± 3.85 km s−1. In the atmosphere of KELT-20b, we detected 17 single lines of Fe II. Considering different measurements of the systemic velocity of the system, we conclude that the existence of winds in the atmosphere of KELT-20b cannot be determined conclusively. The detected signal with the cross-correlation method presents a S/N of 11.51. The results are consistent with NLTE effects, including means of νmic = 3.04 ± 0.35 km s−1 and νmac = 6.76 ± 1.17 km s−1.

Enabling the Assimilation of CrIS Shortwave Infrared Observations in Global NWP at NOAA. Part I: Background and Methods

Abstract Radiance observations from Earth-observing satellites have a significant positive impact on numerical weather prediction (NWP) forecasts, but some spectral regions are not fully exploited. Observations from hyperspectral infrared (IR) sounders in the longwave region (650–1100 cm−1), for instance, are routinely assimilated in many NWP models, but observations in the shortwave region (2155–2550 cm−1) are not. Each of these regions provides information on the temperature structure of the atmosphere, but the shortwave IR (SWIR) region is considered challenging to assimilate due to noise-equivalent delta temperature (NEDT) that is highly variable depending on scene brightness temperature and to phenomena that are difficult to model, like nonlocal thermodynamic equilibrium (NLTE) and solar reflectance. With recent advances in small-satellite technology, SWIR temperature sounders may provide an agile and cost-effective complement to the current constellation of IR sounders. Therefore, a better understanding of the use and impact of SWIR observations in data assimilation for NWP is warranted. In Part I of this study, as presented here, the amount of unique information [as determined by empirical orthogonal decomposition (EOD)] made available to a data assimilation system by Cross-track Infrared Sounder (CrIS) SWIR observations is reviewed, recent advancements to the Community Radiative Transfer Model (CRTM) for the simulation of CrIS shortwave radiances are tested, and enhancements to NOAA’s Global Data Assimilation System (GDAS) for the assimilation of CrIS SWIR observations are implemented and evaluated. Part II of this study, which seeks to assess the value of assimilating shortwave IR observations in global NWP, is also introduced.

Helium features are inconsistent with the spectral evolution of the kilonova AT2017gfo

The spectral features observed in kilonovae have revealed the elemental composition and the velocity structures of matter ejected from neutron star mergers. In the spectra of the kilonova AT2017gfo, a P Cygni line at about 1 μm has been linked to Sr II, providing the first direct evidence of freshly synthesised r-process material. An alternative interpretation of this feature has been proposed – He Iλ1083.3 nm under certain non-local thermodynamic equilibrium conditions. A key way to robustly discriminate between these identifications, and indeed other proposed identifications, is to analyse the temporal emergence and evolution of the feature. In this analysis, we trace the earliest appearance of the observed feature and detail its spectro-temporal evolution, which we compare with a collisional-radiative model of helium. We show that the 1 μm P Cygni line is inconsistent with a He I interpretation both in emergence time and in subsequent spectral evolution. Self-consistent helium masses cannot reproduce the observed feature due to the diminishing strength of radiative pathways out of triplet helium.

Free–Free Gaunt Factors for Atmospheres of Accreting Pulsars Observable with X-Ray Space Missions

Free–free Gaunt factors for X-ray absorption by hot plasma in the presence of a strong magnetic field are reported. Modified formulae are used for application to the nonlocal thermodynamic equilibrium conditions found in accreting pulsar atmospheres. Given upcoming global X-ray polarimetric space missions, these can be used for the construction of an absorption matrix in discrete-ordinate polarized radiative transfer.

Extension of the multilevel radiative transfer code PyRaTE to model linear polarization of molecular lines

Context. Linear polarization of spectral lines, commonly known as the Goldreich-Kylafis effect within the star formation community, is one of the most underutilized techniques for probing magnetic fields in the dense and cold interstellar medium. Aims. In this study, we implement linear polarization of molecular spectral lines into the multilevel, non-local thermodynamic equilibrium radiative transfer code PYRATE. Methods. Different modes of polarized radiation are treated individually, with separate optical depths computed for each polarization direction. Our implementation is valid in the so-called strong magnetic field limit and is exact for either a system satisfying the large-velocity-gradient approximation, and/or for any system with a uniform magnetic field. We benchmark our implementation against analytical results and provide tests for various limiting cases. Results. In agreement with previous theoretical results, we find that in the multilevel case the amount of fractional polarization decreases when compared to the two-level approximation, but this result is subject to the relative importance between radiative and collisional processes. Finally, we post-process an axially symmetric, nonideal magnetohydrodynamic chemo-dynamical simulation of a collapsing prestellar core and provide theoretical predictions regarding the shape (as a function of velocity) of the polarization fraction of CO during the early stages in the evolution of molecular clouds.

Revisiting rotationally excited CH at radio wavelengths: A case study towards W51

Context. Ever since they were first detected in the interstellar medium, the radio wavelength (3.3 GHz) hyperfine-structure splitting transitions in the rotational ground state of CH were observed to show anomalous excitation. Astonishingly, this behaviour was uniformly observed towards a variety of different sources probing a wide range of physical conditions. While the observed level inversion could be explained globally by a pumping scheme involving collisions, a description of the extent of ‘over-excitation’ observed in individual sources required the inclusion of radiative processes, involving transitions at higher rotational levels. Therefore, a complete description of the excitation mechanism in the CH ground state, observed towards individual sources entails observational constraints from the rotationally excited levels of CH and in particular that of its first rotationally excited state (2Π3/2, N = 1, J = 3/2). Aims. Given the limited detections of these lines, the objective of this work is to characterise the physical and excitation properties of the rotationally excited lines of CH between the Λ-doublet levels of its 2Π3/2, N = 1, J = 3/2 state near 700 MHz, and investigate their influence on the pumping mechanisms of the ground-state lines of CH. Methods. This work presents the first interferometric search for the rotationally excited lines of CH between the Λ-doublet levels of its 2Π3/2, N = 1, J = 3/2 state near 700 MHz carried out using the upgraded Giant Metrewave Radio Telescope (uGMRT) array towards six star-forming regions, W51 E, Sgr B2 (M), M8, M17, W43, and DR21 Main. Results. We detected the two main hyperfine structure lines within the first rotationally excited state of CH, in absorption towards W51 E. To jointly model the physical and excitation conditions traced by lines from both the ground and first rotationally excited states of CH, we performed non-local thermodynamic equilibrium (LTE) radiative transfer calculations using the code MOLPOP-CEP. These models account for the effects of line overlap and are aided by column density constraints from the far-infrared (FIR) wavelength rotational transitions of CH that connect to the ground state and use collisional rate coefficients for collisions of CH with H, H2 and electrons (the latter was computed in this work using cross-sections estimated within the Born approximation). Conclusions. The non-LTE analysis revealed that physical properties typical of diffuse and translucent clouds best reproduced the higher rates of level inversion seen in the ground-state lines at 3.3 GHz, observed at velocities near 66 km s−1 along the sightline towards W51 E. In contrast, the excited lines near 700 MHz were only excited in much denser environments with nH ~ 105 cm−3 towards which the anomalous excitation in two of the three ground state lines is quenched, but not in the 3.264 GHz line. This is in alignment with our observations and suggests that while FIR pumping and line overlap effects are essential for exciting and producing line inversion in the ground state, excitation to the first rotational level is dominated by collisional excitation from the ground state. For the rotationally excited state of CH, the models indicated low excitation temperatures and column densities of 2 × 1014 cm−2. Furthermore, modelling these lines helps us understand the complexities of the spectral features observed in the 532/536 GHz rotational transitions of CH. These transitions, connecting sub-levels of the first rotationally excited state to the ground state, play a crucial role in trapping FIR radiation and enhancing the degree of inversion seen in the ground state lines. Based on the physical conditions constrained, we predict the potential of detecting hyperfine-splitting transitions arising from higher rotationally excited transitions of CH in the context of their current non-detections.

A platform for non-local thermodynamic equilibrium atomic physics research using the buried layer target approach at a kJ level laser facility.

We present a design and first use of a kJ level laser facility for research of non-local thermodynamic equilibrium atomic physics using the buried layer target method. The target design included a metal layer buried inside a plastic tamper with thicknesses tailored to the expected laser intensities. The target was illuminated from each side by two laser beams with intensities of 0.5-5 × 1014 W/cm2. The advanced diagnostic suite included static and time-resolved imagers and spectrometers with various spectral resolutions. A 3D printed dual elliptically curved spectrometer is presented, and its results are compared to a traditional crystal spectrometer. Experimental results and radiation hydrodynamic simulations demonstrate that the target achieved the desired thermodynamic conditions of ne ≈ 1021-1022 cm-3 and Te ≈ 1-2keV.

The temporal and spatial variations of lithium abundance in the Galactic disc

ABSTRACT This study investigates the temporal and spatial variations in lithium abundance within the Milky Way using a sample of 22 034 main-sequence turn-off (MSTO) stars and subgiants, characterized by precise stellar ages, 3D non-local thermodynamic equilibrium lithium abundances, and birth radii. Our results reveal a complex variation in lithium abundance with stellar age: a gradual increase from 14 to 6 Gyr, followed by a decline between 6 and 4.5 Gyr, and a rapid increase thereafter. We find that young Li-rich stars (ages $\lt $ 4 Gyr, A(Li) $\gt $ 2.7 dex) predominantly originate from the outer disc. By binning the sample according to guiding centre radius and z$_{\rm max}$, we observe that these young Li-rich stars migrate radially to the local and inner discs. In addition, the stars originating from the inner disc experienced a rapid Li enrichment process between 8 and 6 Gyr. Our analysis suggests that the age range of Li-dip stars is 4–5 Gyr, encompassing evolution stages from MSTO stars to subgiants. The Galactic radial profile of A(Li) (with respect to birth radius), as a function of age, reveals three distinct periods: 14–6 Gyr ago, 6–4 Gyr ago, and 4–1 Gyr ago. Initially, the lithium abundance gradient is positive, indicating increasing Li abundance with birth radius. During the second period, it transitions to a negative and broken gradient, mainly affected by Li-dip stars. In the final period, the gradient reverts to a positive trend.

The long-term influence of a magnetar power in stripped-envelope supernovae. Radiative-transfer modeling of He-star explosions from 1 to 10 years

Much interest surrounds the nature of the compact remnant that formed in core collapse supernovae (SNe). One means to constrain its nature is to search for signatures of power injection from the remnant in the SN observables years after explosion. In this work, we conduct a large grid of 1D nonlocal thermodynamic equilibrium radiative transfer calculations of He-star explosions under the influence of magnetar-power injection from post-explosion age of about one to ten years. Our results for SN observables vary with He-star mass, SN age, injected power, or ejecta clumping. At high mass (model he12p00), the ejecta coolants are primarily O and Ne, with and dominating in the optical, and with strong in the infrared -- this line may carry more than half the total SN luminosity. For lower He-star masses (models he6p00 and he3p30), a greater diversity of coolants appear, in particular Fe, S, Ar, or Ni from the Si- and Fe-rich regions. All models tend to rise in ionization in time, with twice-ionized species (i.e., O Ne S or Fe dominating at sim \,10\,yr, although this ionization is significantly reduced if clumping is introduced. Our treatment of magnetar power in the form of high-energy electrons or X-ray irradiation yields similar results -- no X-rays emerge from our ejecta even at ten years because of high-optical depth in the kilo-electronvolt range. An uncertainty of our work concerns the power deposition profile, which is not known from first principles, although this profile could be constrained from observations. Our magnetar-powered model he8p00 with moderate clumping yields a good match to the optical and near-infrared observations of Type Ib SN\,2012au at both 289--335\,d (power of $1-2 and 2269\,d (power of 1040\ Unless overly ionized (i.e., if the optical spectrum shows only strong we find that all massive magnetar-powered ejecta should be infrared luminous at 5--10\,yr through strong line emission.

Quantum rotational dynamics of linear C5 at low interstellar temperatures for H2 collision.

The quantum dynamics of carbon chains through H2 and He collisions in the interstellar medium (ISM) is an important step toward accurate modeling of their abundance in non-local thermodynamic equilibrium conditions. The C5(Σg+1) molecule is the longest pure carbon chain detected in the ISM to date. While He collisions are computationally easy to perform, the collision with much more abundant H2 is both complicated and computationally demanding. Using templates for approximating p-H2 collisional rates, such as scaling He rates and using a reduced 4D → 2D potential energy surface (PES), has limited applicability. On the other hand, any such approximation does not exist for o-H2. Therefore, a full rotational dynamics of C5 with both p- and o-H2 is performed considering both molecules as rigid-rotors. The PES is calculated using CCSD(T)-F12a/AVTZ, and a neural network fitting model has been carefully chosen to strictly obey spectroscopic accuracy and augment the PES. The augmented PES is then expanded into radial terms using the bispherical harmonics function, and close coupling calculations have been done to get the cross sections and, subsequently, rate coefficients for various rotational transitions of C5.

Study of soft X-ray radiation of plasma produced by interaction of laser radiation with copper targets at the “Kanal-2” facility

As part of the work on creating an x-ray microscope, experimental and theoretical studies of laser plasma of solid copper targets in the soft x-ray range were carried out. With a laser pulse duration of 2.5 ns (FWHM), the power density of the Nd:glass laser on the target is varied in the range 0.8 × 1013–4.2 × 1013 W/cm2. Experimental results demonstrated the presence of intense plasma emission in spectral ranges of water and carbon windows, and the number of photons of the most intense lines was calculated. Spatio-temporal studies of copper plasma have demonstrated intense emission in the wavelength range shorter than 15 Å, and the images of plasma emission in time-integrated and linear sweep modes are shown. The simulations of the interaction of the specified laser radiation flux with copper targets were carried out taking into account the transfer of self-radiation in plasma. The non-local thermodynamic equilibrium optical properties of the plasma were used. As a result of calculations, profiles of density, temperature, electron thermal conductivity flux, emissivity of plasma, and self-radiation flux were obtained. The calculated spectrum of the outgoing radiation is consistent with that obtained at the experiment.

Quantitative spectroscopy of multiple OB stars

Context. The majority of massive stars are located in binary or multiple star systems. Compared to single stars, these objects pose additional challenges to quantitative analyses based on model atmospheres. In particular, little information is currently available on the chemical composition of such systems. Aims. The members of the quadruple star system HD 37061, which excites the H II region Messier 43 in Orion, are fully characterised. Accurate and precise abundances for all elements with lines traceable in the optical spectrum are derived for the first time. Methods. A hybrid non-local thermodynamic equilibrium (non-LTE) approach, using line-blanketed hydrostatic model atmospheres computed with the ATLAS12 code in combination with non-LTE line-formation calculations with DETAIL and SURFACE, was employed. A high-resolution composite spectrum was analysed for the atmospheric parameters and elemental abundances of the individual stars. Fundamental stellar parameters were derived based on stellar evolution tracks, and the interstellar reddening was characterised. Results. We determined the fundamental parameters and chemical abundances for three stars in the HD 37061 system. The fourth and faintest star in the system shows no distinct spectral features, as a result of its fast rotation. However, this star has noticeable effects on the continuum. The derived element abundances and determined ages of the individual stars are consistent with each other, and the abundances coincide with the cosmic abundance standard. We find an excellent agreement between our spectroscopic distance and the Gaia Data Release 3 parallax distance.

Collisional and radiative data for tellurium ions in kilonovae modelling and laboratory benchmarks

ABSTRACT Tellurium is a primary candidate for the identification of the 2.1 $\, \mu$m emission line in kilonovae (KNe) spectra AT2017gfo and GRB230307A. Despite this, there is currently an insufficient amount of atomic data available for this species. We calculate the required atomic structure and collisional data, particularly the data required for accurate non-local-thermodynamic-equilibrium (NLTE) modelling of the low temperatures and densities in KNe. We use a multiconfigurational Dirac–Hartree–Fock method to produce optimized one-electron orbitals for Te i-iii. As a result energy levels and Einstein A-coefficients for Te i-iii have been calculated. These orbitals are then employed within Dirac R-matrix collision calculations to provide electron-impact-excitation collision strengths that were subsequently averaged according to a thermal Maxwellian distribution. Subsequent tardis simulations using this new atomic data reveal no significant changes to the synthetic spectra due to the very minor contribution of Te at early epochs. NLTE simulations with the colradpy package reveal optically thin spectra consistent with the increasing prominence of the Te iii 2.1 $\, \mu$m line as the KNe ejecta cools. This is reinforced by the estimation of luminosities at nebular KNe conditions. New line ratios for both observation and laboratory benchmarks of the atomic data are proposed.

Full non-LTE spectral line formation

In the present paper we consider the full nonlocal thermodynamic equilibrium (non-LTE) radiation transfer problem. This formalism allows us to account for deviation from equilibrium distribution of both the radiation field and the massive particles. In the present study, two-level atoms with broadened upper level represent the massive particles. In the absence of velocity-changing collisions, we demonstrate the analytic equivalence of the full non-LTE source function with the corresponding standard non-LTE partial frequency redistribution (PFR) model. We present an iterative method based on operator splitting techniques that can be used to numerically solve the problem at hand. We benchmark it against the standard non-LTE transfer problem for a two-level atom with PFR. We illustrate the deviation of the velocity distribution function of excited atoms from the equilibrium distribution. We also discuss the dependence of the emission profile and the velocity distribution function on elastic collisions and velocity-changing collisions.

TIC 441725813: A new bright hybrid hot B subdwarf pulsator with differential core versus envelope rotation

Context. The Transiting Exoplanet Survey Satellite (TESS) performs high-precision photometry over almost the whole sky primarily in search of exoplanet transits. It also provides exquisite data to study stellar variability, in particular for pulsating hot B subdwarf (sdB) stars. Aims. We present a detailed analysis of a new hybrid (p- and g-mode) sdB pulsator, TIC 441725813 (TYC 4427-1021-1), discovered and monitored by TESS for 670 days. Methods. The TESS light curves available for this star were analysed using prewhitening techniques to extract mode frequencies accurately. The pulsation spectrum was then interpreted through methods that include asymptotic period spacing relationships and the identification of rotational multiplets. We also exploited a high signal-to-noise ratio (S/N), low-resolution spectrum of TIC 441725813 using grids of non-local thermodynamic equilibrium (NLTE) model atmospheres to derive its atmospheric parameters. Results. The light curve analysis reveals that frequencies are mostly found in the g-mode region, but several p-modes are also detected, indicating that TIC 441725813 is a hybrid sdB pulsator. We identify 25 frequencies that can be associated with ℓ = 1 g-modes, 15 frequencies corresponding to ℓ = 2 g-modes, and six frequencies characteristic of p-modes. Interestingly, several frequency multiplets interpreted as rotational splittings of deep-probing g-modes indicate a slow rotation period of at least 85.3 ± 3.6 day, while splittings of mostly envelope-probing p-modes suggest a significantly shorter rotation period of 17.9 ± 0.7 day, which implies the core (mainly the helium mantle with possibly the deeper partially mixed helium-burning core that it surrounds) rotates at least 4.7 times slower than the envelope. The radial velocity curves indicate that TIC 441725813 is in a close binary system with a low-luminosity companion, possibly a white dwarf. While elusive in the available TESS photometry, a low-frequency signal that would correspond to a period of ∼6.7 h is found, albeit at a low S/N. Furthermore, we estimate the inclination angle to be ∼60° by two independent means. Conclusions. TIC 441725813 is a particularly interesting sdB star whose envelope rotates faster than the core. We hypothesise that this might be caused by the effects of a tidal interaction with a companion, although in the present case, the presence of such a companion will have to be further investigated. This analysis paves the way towards a more detailed seismic probing of TIC 441725813 using optimisation techniques, which will be presented in a second paper.

Jacobian-free Newton-Krylov method for multilevel nonlocal thermal equilibrium radiative transfer problems

Context. The calculation of the emerging radiation from a model atmosphere requires knowledge of the emissivity and absorption coefficients, which are proportional to the atomic level population densities of the levels involved in each transition. Due to the intricate interdependence of the radiation field and the physical state of the atoms, iterative methods are required in order to calculate the atomic level population densities. A variety of different methods have been proposed to solve this problem, which is known as the nonlocal thermodynamical equilibrium (NLTE) problem. Aims. Our goal is to develop an efficient and rapidly converging method to solve the NLTE problem under the assumption of statistical equilibrium. In particular, we explore whether the Jacobian-Free Newton-Krylov (JFNK) method can be used. This method does not require an explicit construction of the Jacobian matrix because it estimates the new correction with the Krylov-subspace method. Methods. We implemented an NLTE radiative transfer code with overlapping bound-bound and bound-free transitions. This solved the statistical equilibrium equations using a JFNK method, assuming a depth-stratified plane-parallel atmosphere. As a reference, we also implemented the Rybicki & Hummer (1992) method based on linearization and operator splitting. Results. Our tests with the Fontenla, Avrett and Loeser C model atmosphere (FAL-C) and two different six-level Ca II and H I atoms show that the JFNK method can converge faster than our reference case by up to a factor 2. This number is evaluated in terms of the total number of evaluations of the formal solution of the radiative transfer equation for all frequencies and directions. This method can also reach a lower residual error compared to the reference case. Conclusions. The JFNK method we developed poses a new alternative to solving the NLTE problem. Because it is not based on operator splitting with a local approximate operator, it can improve the convergence of the NLTE problem in highly scattering cases. One major advantage of this method is that it is expected to allow for a direct implementation of more complex problems, such as overlapping transitions from different active atoms, charge conservation, or a more efficient treatment of partial redistribution, without having to explicitly linearize the equations.

Three-Dimensional Nonlocal Thermodynamic Equilibrium Abundance Analyses of Late-Type Stars

The chemical compositions of stars encode the history of the universe and are thus fundamental for advancing our knowledge of astrophysics and cosmology. However, measurements of elemental abundance ratios, and our interpretations of them, strongly depend on the physical assumptions that dictate the generation of synthetic stellar spectra. Three-dimensional radiation-hydrodynamic (3D RHD) box-in-a-star simulations of stellar atmospheres offer a more realistic representation of surface convection occurring in late-type stars than do traditional one-dimensional (1D) hydrostatic models. As evident from a multitude of observational tests, the coupling of 3D RHD models with line formation in nonlocal thermodynamic equilibrium (non-LTE) today provides a solid foundation for abundance analysis for many elements. This review describes the ongoing and transformational work to advance the state of the art and replace 1D LTE spectrum synthesis with its 3D non-LTE counterpart. In summary: ▪3D and non-LTE effects are intricately coupled, and consistent modeling thereof is necessary for high-precision abundances; such modeling is currently feasible for individual elements in large surveys. Mean 3D (〈3D〉) models are not adequate as substitutes.▪The solar abundance debate is presently dominated by choices and systematic uncertainties that are not specific to 3D non-LTE modeling.▪3D non-LTE abundance corrections have a profound impact on our understanding of FGK-type stars, exoplanets, and the nucleosynthetic origins of the elements.