Electron impact excitation of Te IV and V and Level Resolved R-matrix Photoionization of Te I - IV with application to modelling of AT2017gfo

This paper presents new R-matrix and MCDHF atomic data for tellurium ions (Te I–V), including electron-impact excitation and photoionization cross-sections, to improve kilonova spectral modeling and investigate Te IV's potential contribution to the 1.08 μm emission feature in AT2017gfo.

The Gist

Imagine the universe as a giant, chaotic kitchen where stars are constantly cooking up new elements. When two neutron stars crash into each other, it's like a cosmic explosion that throws a massive "kitchen fire" into space. This event, known as a kilonova, creates a cloud of debris (ejecta) filled with heavy, exotic ingredients that don't usually exist on Earth.

One of the most famous of these cosmic explosions was AT2017gfo. Astronomers are trying to figure out exactly what ingredients were in that cloud by looking at the light it emitted. It's like trying to guess the recipe of a soup just by looking at the steam rising from the pot. To do this, they need a "cookbook" of atomic data—a list of how every specific element behaves when it gets hot, hits electrons, or gets hit by light.

The Problem:
For a long time, the "cookbook" for heavy elements like Tellurium (Te) was missing pages. Scientists had to guess the behavior of these atoms using rough approximations (like guessing a recipe based on a similar, simpler dish). This made it hard to accurately model what was happening in the explosion.

The Solution (This Paper):
This paper is like a team of expert chefs (physicists) writing a brand-new, highly detailed chapter for the cookbook, specifically for Tellurium. They didn't guess; they used a super-precise mathematical method called the R-matrix (think of it as a high-tech simulation lab) to calculate exactly how Tellurium atoms react.

Here is a breakdown of what they did, using simple analogies:

1. Building the Atomic "Skeleton" (Atomic Structure)

Before you can predict how a car drives, you need to know how the engine is built. The authors used a powerful computer code (called grasp0) to build a detailed 3D model of Tellurium atoms that have lost some of their electrons (ions).

• The Analogy: Imagine Tellurium as a complex Lego structure. The authors figured out exactly how the bricks (electrons) are arranged in different configurations. They checked their work against real-world experiments to make sure their Lego models were accurate.

2. Simulating the "Bump" (Electron Impact Excitation)

In the hot cloud of the explosion, atoms are constantly getting bumped by flying electrons. When an electron hits an atom, it can knock the atom's internal parts into a higher energy state, causing the atom to glow (emit light) when it settles back down.

• The Analogy: Think of the Tellurium atom as a bell. The flying electrons are people running by and hitting the bell. The authors calculated exactly how hard the bell rings (how much light it emits) depending on how fast the runner is (the electron's energy). They did this for Tellurium in different states of charge (Te IV and Te V).

3. Simulating the "Sunlight" (Photoionization)

Sometimes, instead of a bump, a photon (a particle of light) hits the atom and knocks an electron completely out of the atom. This is called photoionization.

• The Analogy: Imagine the atom is a house with a door. A photon is a strong wind. If the wind is strong enough, it blows the door (electron) off the hinges. The authors calculated exactly how much "wind" (light energy) is needed to blow the door off for different Tellurium atoms. This is crucial for understanding the early stages of the explosion when the light is very intense.

4. The Big Mystery: The 1.08 Micron Glitch

The most exciting part of the paper is solving a mystery about the light from AT2017gfo.

• The Mystery: Astronomers saw a specific glow in the light at a wavelength of 1.08 micrometers (a specific color of infrared light) about a week after the explosion.
• The Old Theory: They thought this was caused by Strontium (Sr), a lighter element. But the Strontium model had some flaws; it predicted other glows that weren't actually there.
• The New Theory: The authors asked, "What if Tellurium is the culprit?"
  • They found that a specific transition in Tellurium IV (a Tellurium atom that has lost 3 electrons) creates a glow exactly at 1.08 micrometers.
  • The Catch: Tellurium IV is a "hot" ion. It usually needs a very hot environment to exist. However, the explosion environment is complex. The authors suggest that while Strontium might explain the early flash (the P-Cygni feature), Tellurium IV might be responsible for the later glowing emission, provided the explosion has just the right mix of heat and density.

Why Does This Matter?

This paper is a "data dump" for the scientific community.

• For Astronomers: They can now plug these precise numbers into their supercomputer simulations to see if the Tellurium theory fits the real data better than the Strontium theory.
• For Physics: It proves that we can model these heavy, complex atoms without guessing. It moves us from "approximate recipes" to "exact blueprints."

In Summary:
The authors built a precise digital model of Tellurium atoms, calculated how they react to heat and light, and used this data to suggest that Tellurium might be the hidden ingredient causing a specific glow in a famous cosmic explosion. It's a step toward understanding exactly how the universe creates the heavy elements that make up our world.

Technical Summary

1. Problem Statement

Spectral modeling of kilonovae (KNe), such as the neutron star merger event AT2017gfo, requires extensive and accurate atomic data for heavy elements (high $Z$), particularly those associated with the $r$-process nucleosynthesis. Tellurium (Te, $Z=52$) is a key element located at the second peak of the $r$-process abundance pattern and is hypothesized to contribute significantly to the ejecta mass.

However, existing models often rely on approximate hydrogenic calculations or semi-empirical formulae (e.g., van Regemorter, Axelrod) for collisional excitation and photoionization. These approximations lack the precision required for non-local thermodynamic equilibrium (NLTE) modeling of complex ejecta compositions. Specifically, there was a lack of high-precision $R$-matrix data for higher ionization stages of Tellurium (Te iv and v) and level-resolved photoionization cross-sections for Te i–iv, which are critical for modeling different evolutionary phases of the kilonova.

2. Methodology

The authors employed a multi-stage computational approach combining advanced atomic structure calculations with scattering theory:

• Atomic Structure Modeling:

  • Used the GRASP0 package (Multi-Configuration-Dirac-Hartree-Fock approach) to generate optimized single-electron orbitals and configuration state functions (CSFs).
  • Te iv Model: Included 21 non-relativistic valence configurations (e.g., $4d^{10}5s^2\{4f, 5p, \dots\}$) resulting in 21 CSFs.
  • Te v Model: Included 27 non-relativistic valence configurations.
  • Validated energy levels against experimental data (Crooker & Joshi 1964; Tauheed et al. 1999/2000) and theoretical benchmarks (Ekman et al. 2013).
  • Calculated Einstein $A$-values for radiative transitions, applying wavelength shifts to match spectroscopic values where available.

• Electron-Impact Excitation (Collisions):

  • Utilized the $R$-matrix method (via the DARC codes) to calculate collision strengths ($\Omega$) for Te iv and v.
  • Employed close-coupling expansions with 100 target levels and 20 continuum basis orbitals.
  • Calculated partial waves up to $2J=62$ (with top-up rules for higher $J$) over energy ranges of 0–3.6 Ry (Te iv) and 0–6.4 Ry (Te v).
  • Thermally averaged collision strengths ($\Upsilon$) were computed using Maxwellian distributions to derive effective collision rates for various electron temperatures.

• Photoionization:

  • Performed level-resolved $R$-matrix photoionization calculations for Te i through Te iv using the DARC implementation.
  • Calculated cross-sections ($\sigma_{PI}$) for transitions from ground and metastable states of the parent ion to the continuum of the residual ion.
  • Included resonances and core-excitations by constructing large Hamiltonian matrices (up to ~69,000 $\times$ 69,000 for Te i) and using fine energy meshes.

• Spectral Modeling:

  • Integrated the new excitation rates into the ColRadPy collisional-radiative model.
  • Generated synthetic spectra for Te iii and Te iv to compare with observational data of AT2017gfo, specifically investigating the 1.08 $\mu$m emission feature.

3. Key Contributions

• First $R$-matrix Photoionization for Te: This work presents the first level-resolved photoionization cross-sections for Te i–iv specifically tailored for kilonova applications.
• High-Precision Data for Te iv and v: Provided the first comprehensive set of electron-impact excitation rates and radiative data for Te iv and v using the $R$-matrix method, moving beyond semi-empirical approximations.
• Validation: The atomic structure models were rigorously validated against experimental energy levels and alternative codes (FAC, GRASP2K), showing excellent agreement even with significantly smaller configuration expansions than previous large-scale studies.
• Public Data Release: All effective collision strengths (in ADf04 format) and photoionization cross-sections are made available via OPEN-ADAS and supplementary materials, facilitating immediate use by the astrophysical community.

4. Key Results

• Atomic Structure:

  • Te iv: Computed energy levels agreed with experimental data within 0.002–0.09 Ry. The calculated Einstein $A$-value for the forbidden transition $5s^2 5p \ ^2P^o_{3/2} \to \ ^2P^o_{1/2}$ (1.08 $\mu$m) was $7.03 \text{ s}^{-1}$, matching the literature value of $7.09 \text{ s}^{-1}$.
  • Te v: Good agreement found for low-lying levels compared to experimental and theoretical benchmarks, despite the compact model size (267 CSFs) compared to previous large-scale calculations (~600,000 CSFs).

• Collisional-Radiative Modeling of AT2017gfo:

  • The 1.08 $\mu$m Feature: The study investigated the origin of the emission feature at 1.08 $\mu$m observed in AT2017gfo at mid-epochs (~7 days). While Sr ii is the accepted cause of the early P-Cygni feature, the authors found that Te iv could plausibly contribute to the later, emission-dominated phase.
  • Feasibility: Under NLTE conditions (specifically with non-thermal ionization from radioactive decay), a mass of $\sim 2.5 \times 10^{-3} M_\odot$ of Te iv at $T_e \approx 3000$ K and $n_e \approx 2 \times 10^7 \text{ cm}^{-3}$ could reproduce the observed line luminosity ($\sim 2.0 \times 10^{39} \text{ erg s}^{-1}$).
  • Advantage over Sr ii: Unlike Sr ii, which produces contaminant lines at other wavelengths, Te iv at these temperatures produces a clean 1.08 $\mu$m feature without significant pollution, making it a viable candidate for the late-time emission.
  • Te iii vs. Te iv: While Te iii also has a line near 1.08 $\mu$m, it requires conditions that would grossly overestimate the 2.1 $\mu$m feature. Te iv offers a better fit for the specific 1.08 $\mu$m feature without conflicting with other observations.

• Photoionization Cross-Sections:

  • Calculated cross-sections for Te i–iv across photon energies of 0–6 Ry (and up to 8 Ry for Te iii/iv).
  • Identified broad resonances around 3.0–3.05 Ry corresponding to photo-excitation of the 5s inner shell.

5. Significance

This paper significantly advances the atomic data infrastructure required for modeling heavy-element kilonovae. By replacing approximate hydrogenic data with rigorous $R$-matrix calculations, the authors enable more accurate spectral synthesis and radiative transfer simulations.

The specific identification of Te iv as a potential contributor to the 1.08 $\mu$m emission feature in AT2017gfo provides a new avenue for interpreting kilonova spectra. It suggests that higher ionization states (Te iv) may persist longer than LTE predictions due to non-thermal ionization, playing a crucial role in the nebular phase of the ejecta. The release of this data allows the community to move away from semi-empirical approximations, leading to more robust constraints on the $r$-process nucleosynthesis yields and the physical conditions of neutron star merger ejecta.