Expansion Opacity Research Articles

Comparative study of kilonova opacities for three elements of the sixth period (hafnium, osmium, and gold) from new atomic structure calculations in Hf I–IV, Os I–IV, and Au I–IV

Aims. It is now well established that a large amount of heavy (trans-iron) elements are produced during neutron star (NS) mergers. These elements can be detected in the spectra of the kilonova emitted from the post-merger ejected materials. Due to the high level densities that characterize the complex configurations belonging to heavy elements, thus giving rise to millions of absorption lines, the kilonova ejecta opacity is of significant importance. The elements that contribute the most to the latter are those with an unfilled nd subshell belonging to the fifth and the sixth rows of the periodic table, and those with an unfilled nf subshell belonging to the lanthanide and actinide groups. The aim of the present work is to make a new contribution to this field by performing large-scale atomic structure calculations in three specific sixth-row 5d elements, namely hafnium, osmium, and gold, in the first four charge stages (I–IV), and by computing the corresponding opacities, while focusing on the importance of the atomic models used. Methods. The pseudo-relativistic Hartree–Fock (HFR) method, including extended sets of interacting configurations, was used for the atomic structure and radiative parameter calculations, while the expansion formalism was used to estimate the opacities. Results. Theoretical energy levels, wavelengths, and oscillator strengths were computed for millions of spectral lines in Hf I–IV, Os I–IV, and Au I–IV ions, the reliability of these parameters being assessed through detailed comparisons with previously published experimental and theoretical results. The newly obtained atomic data were then used to calculate expansion opacities for typical kilonova conditions expected one day after the NS merger; these are a density of ρ = 10−13 g cm−3 and temperatures ranging from T = 5000 K to T = 15 000 K. Some agreements and differences were found when comparing our results with available data, highlighting the importance of using sufficiently complete atomic models for the determination of opacities.

Overview of the contributions from all lanthanide elements to kilonova opacity in the temperature range from 25 000 to 40 000 K

Context. It is now well established that the neutron star (NS) merger is at the origin of the production of trans-iron heavy elements in the universe. These elements are therefore present in large quantities in the ejected matter, whose electromagnetic radiation, called kilonova, is characterized by a significant opacity due to the high density of spectral lines belonging to many heavy ions. Among these, the lanthanide ions play an essential role since, with their open 4f subshell, they have a considerable number of transitions that can absorb emitted light. The knowledge of the atomic structure and the radiative parameters of these ions as well as the determination of the corresponding opacities is therefore of paramount importance for the spectral analysis of kilonovae. Aims. The main goal of the present work is to determine the relative contributions of the different lanthanide elements to the opacity of the emission spectrum of a kilonova in its early phase, that is, a few hours after the NS merger, where the conditions are such that the temperature is between 25 000 and 40 000 K. At these temperatures, the lanthanide ions whose charge states are between V and VII are predominant. Methods. We used the pseudo-relativistic Hartree–Fock (HFR) method extensively to calculate the relevant atomic data (energy levels, wavelengths, and oscillator strengths) in La-Lu V-VII ions. The corresponding monochromatic opacities were estimated from the expansion formalism. Results. We calculated the spectroscopic parameters for a total of more than 800 million radiative transitions in all the ions considered. These data were used to estimate the expansion opacities and Planck mean opacities for all the lanthanide elements at early-phase kilonova conditions between 25 000 and 40 000 K, making it possible to deduce the respective contributions of each element as a function of temperature. Atomic calculations were also carried out with the fully relativistic Multiconfiguration Dirac-Hartree-Fock (MCDHF) method in the specific case of the Yb V ion, as the available experimental data had not yet been compared with the theoretical calculations in our previous studies on lanthanide ions.

Statistical RTA simulations of atomic data for astrophysical opacity modeling in the context of kilonova emission

When considering some complex lanthanide ions characterized by a half-filled 4f subshell, the atomic structure Hamiltonian matrix sizes are so large that their diagonalization is challenging and therefore the atomic data of these ions are only used to compute the expansion opacity of a kilonova with difficulty. To avoid this problem, we propose a statistical simulation method to compute kilonova expansion opacities based on the resolved transition array (RTA) method of Bauche et al (1991 Phys. Rev. A 44 5707). The atomic structure relativistic Hartree–Fock (HFR) method has been employed to compute the radial integrals necessary for our statistical RTA simulations where the atomic data are randomly drawn using their corresponding statistical distributions and to determine the exact expansion opacities where the atomic data are obtained by the diagonalization of the Hamiltonian matrix. The statistical RTA simulations carried out for two specific ions, i.e. Sm VIII and Eu VI, for which it is still possible to diagonalize the Hamiltonian matrix, reproduce well the expansion opacities computed using HFR atomic data. Based on this good agreements, the statistical RTA method was used to compute the expansion opacity of Dy VIII, which is determined through diagonalization with difficulty. The proposed statistical RTA simulation method allows the computation of reliable astrophysical expansion opacities which are of paramount importance for kilonova light curve modeling and spectral analysis.

Shock cooling emission from explosions of red supergiants: II. An analytic model of deviations from blackbody emission

ABSTRACT Light emission in the first hours and days following core-collapse supernovae (SNe) is dominated by the escape of photons from the expanding shock-heated envelope. In a preceding paper, Paper I, we provided a simple analytic description of the time-dependent luminosity, L, and colour temperature, Tcol, valid up to H recombination (T ≈ 0.7 eV), for explosions of red supergiants with convective polytropic envelopes without significant circumstellar medium (CSM). The analytic description was calibrated against ‘grey’ (frequency-independent) photon diffusion numeric calculations. Here, we present the results of a large set of 1D multigroup (frequency-dependent) calculations, for a wide range of progenitor parameters (mass, radius, core/envelope mass ratios, metalicity) and explosion energies, using opacity tables that we constructed (and made publicly available), including the contributions of bound–bound and bound–free transitions. We provide an analytic description of the small, ${\simeq}10\ \hbox{per cent}$ deviations of the spectrum from blackbody at low frequencies, hν < 3Tcol, and an improved (over Paper I) description of ‘line dampening’ for hν > 3Tcol. We show that the effects of deviations from initial polytropic density distribution are small, and so are the effects of ‘expansion opacity’ and deviations from LTE ionization and excitation (within our model assumptions). A recent study of a large set of type II SN observations finds that our model accounts well for the early multiband data of more than 50 per cent of observed SNe (the others are likely affected by thick CSM), enabling the inference of progenitor properties, explosion velocity, and relative extinction.

Atomic data and expansion opacity calculations in two representative 4d transition elements, niobium and silver, of interest for kilonovae studies

Aims. Neutron star (NS) mergers are thought to be a source of heavy trans-iron element production. The latter can be detected in the spectra of the ejected materials, from which bright electromagnetic radiation is emitted. This latter is due to the radioactive decay of the produced heavy r-process nuclei and is known as kilonova. Because of their complex atomic structures – characterized by configurations involving unfilled nd or nf subshells – the heavy elements of the kilonova ejecta often give rise to numerous absorption lines generating significant opacities. The determination of the latter, which are of paramount importance for the analysis of kilonova light curves, requires knowledge of the radiative parameters of the spectral lines belonging to the ions expected to be present in the kilonova ejecta. The aim of the present work is to provide new atomic opacity data for two representative 4d elements, niobium (Nb) and silver (Ag), in their first four charge states, namely for Nb I–IV and Ag I–IV. Methods. Large-scale calculations based on the pseudo-relativistic Hartree-Fock (HFR) method were performed to obtain the atomic structure and radiative parameters while the expansion formalism was used to estimate the opacities. Results. Wavelengths and oscillator strengths were computed for several million spectral lines in Nb I–IV and Ag I–IV ions. The reliability of these parameters was estimated by comparison with the few previously published experimental and theoretical results. The newly obtained atomic data were then used to calculate expansion opacities for typical kilonova conditions expected one day after NS merger, a density of ρ = 10−13 g cm−3, and temperatures ranging from T = 5000 K to T =15 000 K.

Self-consistent 3D Radiative Transfer for Kilonovae: Directional Spectra from Merger Simulations

We present 3D radiative transfer calculations for the ejecta from a neutron star merger that include line-by-line opacities for tens of millions of bound–bound transitions, composition from an r-process nuclear network, and time-dependent thermalization of decay products from individual α and β − decay reactions. In contrast to expansion opacities and other wavelength-binned treatments, a line-by-line treatment enables us to include fluorescence effects and associate spectral features with the emitting and absorbing lines of individual elements. We find variations in the synthetic observables with both the polar and azimuthal viewing angles. The spectra exhibit blended features with strong interactions by Ce iii, Sr ii, Y ii, and Zr ii that vary with time and viewing direction. We demonstrate the importance of wavelength calibration of atomic data using a model with calibrated Sr, Y, and Zr data, and find major differences in the resulting spectra, including a better agreement with AT2017gfo. The synthetic spectra for a near-polar inclination show a feature at around 8000 Å, similar to AT2017gfo. However, they evolve on a more rapid timescale, likely due to the low ejecta mass (0.005 M ☉) as we take into account only the early ejecta. The comparatively featureless spectra for equatorial observers gives a tentative prediction that future observations of edge-on kilonovae will appear substantially different from AT2017gfo. We also show that 1D models obtained by spherically averaging the 3D ejecta lead to dramatically different direction-integrated luminosities and spectra compared to full 3D calculations.

Expansion and line-binned opacities of samarium ions for the analysis of early kilonova emission from neutron star mergers

ABSTRACTOpacity calculations performed within the expansion and the line-binned formalisms are reported for Sm V–X ions in this paper. These were determined by means of new large-scale atomic structure and radiative rate computations carried out using the pseudo-relativistic Hartree-Fock (HFR) method from which energy levels, wavelengths, and oscillator strengths were deduced for more than 100 millions of spectral lines in the considered samarium ions. In the absence of any experimental data, the reliability of HFR results was roughly estimated by comparison with those obtained with an independent theoretical approach, namely the fully relativistic multiconfiguration Dirac-Hartree-Fock method, in Sm VI and Sm VII. The opacities were estimated for typical conditions corresponding to early phases of kilonovae following neutron star mergers, i.e. for a density ρ = 10−10 g cm−3, a time after the merger t = 0.1 day and temperatures ranging from 25 000 to 70 000 K. In addition, the atomic calculations allowed us to establish the ground level for each of the Sm ions considered (still unknown until now), as well as reliable partition functions that are crucial for the determination of the ionization balance by solving the Saha equation and for accurate opacity calculations.

Relativistic Atomic Structure of Au IV and the Os Isoelectronic Sequence: Opacity Data for Kilonova Ejecta

Direct detection of gravitational waves (GWs) on 17 August 2017, propagating from a binary neutron star merger, or a “kilonova”, opened the era of multimessenger astronomy. The ejected material from neutron star mergers, or “kilonova”, is a good candidate for optical and near infrared follow-up observations after the detection of GWs. The kilonova from the ejecta of GW1780817 provided the first evidence for the astrophysical site of the synthesis of heavy nuclei through the rapid neutron capture process or r-process. Since properties of the emission are largely affected by opacities of the ejected material, enhancements in the available r-process data is important for neutron star merger modeling. However, given the complexity of the electronic structure of these heavy elements, considerable efforts are still needed to converge to a reliable set of atomic structure data. The aim of this work is to alleviate this situation for low charge state elements in the Os-like isoelectronic sequence. In this regard, the general-purpose relativistic atomic structure packages (GRASP0 and GRASP2K) were used to obtain energy levels and transition probabilities (E1 and M1). We provide line lists and expansion opacities for a range of r-process elements. We focus here on the Os isoelectronic sequence (Os I, Ir II, Pt III, Au IV, Hg V). The results are benchmarked against existing experimental data and prior calculations, and predictions of emission spectra relevant to kilonovae are provided. Fine-structure (M1) lines in the infrared potentially observable by the James Webb Space Telescope are highlighted.

NLTE effects on kilonova expansion opacities

ABSTRACT A binary neutron star merger produces a rapidly evolving transient known as a kilonova (KN), which peaks a few days after merger. Modelling of KNe has often been approached assuming local thermodynamic equilibrium (LTE) conditions in the ejecta. We present the first analysis of non-local thermodynamic equilibrium (NLTE) level populations, using the spectral synthesis code sumo, and compare these to LTE values. We investigate the importance of the radiation field by conducting NLTE excitation calculations with and without radiative transfer. Level populations, in particular higher lying ones, start to show deviations from LTE several days after merger. Excitation is lower in NLTE for the majority of ions and states, and this tends to give lower expansion opacities. While the difference is small for the first few days, it grows to factors 2–10 after this. Our results are important both for demonstrating validity of LTE expansion opacities for an initial phase (less than a week), while highlighting the need for NLTE modelling during later phases. Considering also NLTE ionization, our results indicate that NLTE can give both higher or lower opacities, depending on composition and wavelength, sometimes by orders of magnitudes.

Преобразование уравнения переноса к виду, удобному для расчёта в расширяющейся среде

The work analytically studies the effect of “expansion opacity” in the envelope of supernovae. Between separate lines of different frequencies, shifted due to the Doppler effect, nonlocal radiative interaction occurs. In the case of a large number of bound-bound transitions, opacity is increased when the plasma expands with a non-uniform velocity field. A method is proposed for transforming the transport equation, allowing correctly calculate the average values characterizing the radiation field, as well as the averaged opacity in such media.

Large-scale atomic data calculations in Ce V – X ions for application to early kilonova emission from neutron star mergers

ABSTRACT New radiative parameters (wavelengths, transition probabilities, and oscillator strengths) are reported in the present paper for a large number of spectral lines in moderately charged cerium ions, from Ce V to Ce X. These results were obtained through large-scale atomic structure calculations carried out using three different and independent theoretical approaches, namely the relativistic Hartree–Fock method, including core-polarization corrections (HFR + CPOL), the multiconfiguration Dirac–Hartree–Fock method, and the Particle-Hole Configuration Interaction (PH-CI) method implemented in the AMBiT code. The accuracy of the results was assessed through detailed comparisons between the data deduced from these methods and with the few theoretical and experimental data previously published. For the six cerium ions considered, the most complete and reliable sets of transition wavelengths and rates were then used to calculate the expansion opacities characterizing the early phases of kilonovae following neutron star mergers, i.e. for typical conditions corresponding to temperatures T > 20 000 K, a density ρ = 10−10 g cm−3 and a time after the merger t = 0.1 d.

Expansion opacity in laboratory conditions

Radiation–matter interaction depends mainly on the state of matter (its density, temperature, etc.), and also on the radiation spectrum. The opacity of thick plasma also depends on plasma velocity—the Doppler effect shifts atomic lines. For the cases when there are many bound–bound transitions, i.e., the plenty of lines contribute to the opacity, the latter is enhanced when the plasma expands with a nonuniform velocity field. It is known as “expansion opacity” in the literature. Existing models are discrepant and predict diverse results in some cases. Here, we present a rigorous derivation of the effect and show that the effect is available for experimental study at modern laser facilities. The plasma created by a Cu target irradiated with an ∼100 J nanosecond laser pulse is rich in lines and has enough expansion velocity so that its opacity is increased in the spectral range ∼102−103 eV by the order of magnitude. The possible experimental measurement of the effect is briefly discussed.

Multiconfiguration Dirac–Hartree–Fock radiative parameters for emission lines in Ce ii–ivions and cerium opacity calculations for kilonovae

ABSTRACTLarge-scale calculations of atomic structures and radiative properties have been carried out for singly, doubly, and trebly ionized cerium. For this purpose, the purely relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method was used, taking into account the effects of valence–valence and core–valence electronic correlations in detail. The results obtained were then used to calculate the expansion opacities characterizing the kilonovae observed as a result of neutron star mergers. Comparisons with previously published experimental and theoretical studies have shown that the results presented in this work are the most complete currently available, in terms of quantity and quality, concerning the atomic data and monochromatic opacities for Ce ii, Ce iii, and Ce iv ions.

A line-binned treatment of opacities for the spectra and light curves from neutron star mergers

ABSTRACT The electromagnetic observations of GW170817 were able to dramatically increase our understanding of neutron star mergers beyond what we learned from gravitational waves alone. These observations provided insight on all aspects of the merger from the nature of the gamma-ray burst to the characteristics of the ejected material. The ejecta of neutron star mergers are expected to produce such electromagnetic transients, called kilonovae or macronovae. Characteristics of the ejecta include large velocity gradients, relative to supernovae, and the presence of heavy r-process elements, which pose significant challenges to the accurate calculation of radiative opacities and radiation transport. For example, these opacities include a dense forest of bound–bound features arising from near-neutral lanthanide and actinide elements. Here we investigate the use of fine-structure, line-binned opacities that preserve the integral of the opacity over frequency. Advantages of this area-preserving approach over the traditional expansion–opacity formalism include the ability to pre-calculate opacity tables that are independent of the type of hydrodynamic expansion and thus eliminate the computational expense of calculating opacities within radiation-transport simulations. Tabular opacities are generated for all 14 lanthanides as well as a representative actinide element, uranium. We demonstrate that spectral simulations produced with the line-binned opacities agree well with results produced with the more accurate continuous Monte Carlo Sobolev approach, as well as with the commonly used expansion–opacity formalism. The agreement between the line-binned and expansion–opacity results is explained as arising from the similarity in their opacities in the limit of low optical depth, where radiation transport is important in the ejecta. Additional investigations illustrate the convergence of opacity with respect to the number of included lines, and elucidate sensitivities to different atomic physics approximations, such as fully and semirelativistic approaches.

Line Expansion Opacity in Relativistically Expanding Media

Abstract Spectral lines of heavy atomic elements in the ejecta of supernovae and neutron star mergers can have important contribution to the opacity of the ejecta matter even when the abundance of the elements is very small. Under favorable conditions, the line expansion opacity arising from spectral lines and the expansion of the medium can be orders of magnitude larger than the opacity of electron scattering. In this paper, we derive the formulae for evaluating the line expansion opacity and its Rosseland mean in an expanding medium in the framework of special relativity, which can be considered as a generalization of previous work in the Newtonian approximation. Then we compare the derived relativistic formulae to the Newtonian ones to explore the relativistic effect on the opacity and test the new formulae with the spectral lines of some heavy atomic elements. We also derive some approximation formulae for the Rosseland mean of the line expansion opacity that are easy to use in numerical works while still maintaining a high-enough accuracy relative to exact solutions. The formulae derived in this paper are expected to have important applications in radiative problems related to relativistic astrophysical phenomena such as neutron star mergers, supernovae, and gamma-ray bursts where relativistic or subrelativistic expansions are involved.

A 3-week-old Preterm Infant Who Has Severe Lung Disease

A 3-week-old preterm infant presents with severe lung disease. ### Prenatal History: ### Birth History: The infant was intubated in the delivery room, received one dose of surfactant, and was placed on conventional mechanical ventilation because of severe respiratory distress syndrome. Findings on chest radiography were consistent with respiratory distress syndrome (Fig. 1). The patient was treated with two additional doses of surfactant. Figure 1. Chest radiography demonstrates diminished lung expansion and diffuse bilateral reticulogranular opacities, larger on the right, compatible with severe respiratory distress syndrome. Note the endotracheal tube. Despite management with conventional ventilation the infant’s respiratory status continues to worsen. Surgical patent ductus arteriosus ligation …

Time‐dependent Monte Carlo Radiative Transfer Calculations for Three‐dimensional Supernova Spectra, Light Curves, and Polarization

We discuss Monte Carlo techniques for addressing the three-dimensional time-dependent radiative transfer problem in rapidly expanding supernova atmospheres. The transfer code SEDONA has been developed to calculate the light curves, spectra, and polarization of aspherical supernova models. From the onset of free expansion in the supernova ejecta, SEDONA solves the radiative transfer problem self-consistently, including a detailed treatment of gamma-ray transfer from radioactive decay and with a radiative equilibrium solution of the temperature structure. Line fluorescence processes can also be treated directly. No free parameters need be adjusted in the radiative transfer calculation, providing a direct link between multidimensional hydrodynamic explosion models and observations. We describe the computational techniques applied in SEDONA and verify the code by comparison to existing calculations. We find that convergence of the Monte Carlo method is rapid and stable even for complicated multidimensional configurations. We also investigate the accuracy of a few commonly applied approximations in supernova transfer, namely, the stationarity approximation and the two-level atom expansion opacity formalism.

The diffusion of radiation in moving media

For a given velocity and temperature field in a differentially moving 3D medium, the vector of the radiative flux is derived in the diffusion approximation. Due to the dependence of the velocity gradient on the direction, the associated effective opacity in general is a tensor. In the limit of small velocity gradients analytical expression are obtained which allow us to discuss the cases when the direction of the flux vector deviates from that of the temperature gradient. Furthermore the radiative flux is calculated for infinitely sharp, Poisson distributed spectral lines resulting in simple expressions that provide basic insight into the effect of the motions. In particular, it is shown how incomplete line lists affect the radiative flux as a function of the velocity gradient. Finally, the connection between our formalism and the concept of the expansion opacity introduced by Karp et al. ([CITE]) is discussed.

The Physics of Type Ia Supernova Light Curves. II. Opacity and Diffusion

We examine the nature of the opacity and radiation transport in Type Ia supernovae. The dominant opacity arises from line transitions. We discuss the nature of line opacities and diffusion in expanding media and the appropriateness of various mean and expansion opacities used in light-curve calculations. Fluorescence is shown to be the dominant physical process governing the rate at which energy escapes the supernova. We present a sample light curve that was obtained using a time-dependent solution of the radiative transport equation with a spectral resolution of 80 km s-1 and employing an LTE equation of state. The result compares favorably with light curves and spectra of typical supernovae and is used to illustrate the physics controlling the evolution of the light curve and especially the secondary maxima seen in infrared photometry.

Explosion Models for Type IA Supernovae: A Comparison with Observed Light Curves, Distances, H 0, and Q 0

Theoretical monochromatic light curves and photospheric expansion velocities are compared with observations of 27 Type Ia supernovae (SNe Ia). A set of 37 models has been considered which encompasses all currently discussed explosion scenarios for Type Ia supernovae including deflagrations, detonations, delayed detonations, pulsating delayed detonations and tamped detonations of Chandra- mass, and Helium detonations of low mass white dwarfs. The explosions are calculated using one-dimensional Lagrangian hydro and radiation-hydro codes with incorporated nuclear networks. Subsequently, light curves are constructed using our LC scheme which includes an implicit radiation transport, expansion opacities, a Monte-Carlo $\gamma $-ray transport, and molecular and dust formation. For some supernovae, results of detailed non-LTE calculations have been considered. Observational properties of our series of models are discussed, the relation between the absolute brightness, post-maximum decline rates, the colors at several moments of time, etc. All models with a Ni production larger than 0.4 solar masses produce light curves of similar brightness. The influence of the cosmological red shift on the light curves and on the correction for interstellar reddening is discussed. Based on data rectification of the standard deviation, a quantitative procedure to fit the observations has been used to the determine the free parameters, i.e. the correct model, the distance, the reddening, and the time of the explosion. The results are discussed in detail and applied to determine Ho and qo.