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We present explicit formulas for arbitrary-order derivatives of the energy, grand potential, electron density, and higher-order response functions with respect to the number of electrons, and the chemical potential for any smooth and differentiable model of the energy versus the number of electrons. The resulting expressions for global reactivity descriptors (hyperhardnesses and hypersoftnesses), local reactivity descriptors (hyperFukui functions and local hypersoftnesses), and nonlocal response functions are easy to evaluate computationally. Specifically, the explicit formulas for global/local/nonlocal hypersoftnesses of arbitrary order are derived using Bell polynomials. Explicit expressions for global and local hypersoftness indicators up to fifth order are presented. [ABSTRACT FROM AUTHOR]

We present spatially and velocity-resolved echelle spectroscopy for NGC 7009 obtained with the UVES spectrograph at the European Southern Observatory's Very Large Telescope. Our objective is to analyze the kinematics of emission lines excited by recombination and collisions with electrons to determine whether similarities or differences could be useful in elucidating the well-known abundance discrepancy derived from them. We construct position–velocity maps for recombination, fluorescence, charge transfer, and collisionally excited lines. We find a plasma component emitting in the C II, N II, O II, and Ne II recombination lines whose kinematics are discrepant: they are incompatible with the ionization structure derived from all other evidence and the kinematics derived from all of these lines are unexpectedly very similar. We find direct evidence for a recombination contribution to [N II] λ5755. Once taken into account, the electron temperatures from [N II], [O III], and [Ne III] agree at a given position and velocity. The electron densities derived from [O II] and [Ar IV] are consistent with direct imaging and the distribution of hydrogen emission. The kinematics of the C II, N II, O II, and Ne ii lines does not coincide with the kinematics of the [O III] and [Ne III] forbidden emission, indicating that there is an additional plasma component to the recombination emission that arises from a different volume from that giving rise to the forbidden emission from the parent ions within NGC 7009. Thus, the chemical abundances derived from either type of line are correct only for the plasma component from which they arise. Apart from [N II] λ5755, we find no anomaly with the forbidden lines usually used to determine chemical abundances in ionized nebulae, so the abundances derived from them should be reliable for the medium from which they arise. [ABSTRACT FROM AUTHOR]

We have selected a group of 100 evolved planetary nebulae (PNe) and study their kinematics based upon spatiallyresolved, long-slit, echelle spectroscopy. The data have been drawn from the San PedroMártir Kinematic Catalogue of PNe. The aim is to characterize in detail the global kinematics of PNe at advanced stages of evolution with the largest sample of homogenous data used to date for this purpose. The results reveal two groups that share kinematics, morphology, and photo-ionization characteristics of the nebular shell and central star luminosities at the different late stages under study. The typical flow velocities we measure are usually larger than seen in earlier evolutionary stages, with the largest velocities occurring in objects with very weak or absent [N ii] λ6584 line emission, by all indications the least evolved objects in our sample. The most evolved objects expand more slowly. This apparent deceleration during the final stage of PNe evolution is predicted by hydrodynamical models, but other explanations are also possible. These results provide a template for comparison with the predictions of theoretical models. [ABSTRACT FROM AUTHOR]

We present analytical and numerical models of the bright long GRB 210822A at z  = 1.736. The intrinsic extreme brightness exhibited in the optical, which is very similar to other bright GRBs (e.g. GRBs 080319B, 130427A, 160625A 190114C, and 221009A), makes GRB 210822A an ideal case for studying the evolution of this particular kind of GRB. We use optical data from the RATIR instrument starting at T + 315.9 s, with publicly available optical data from other ground-based observatories, as well as Swift /UVOT, and X-ray data from the Swift /XRT instrument. The temporal profiles and spectral properties during the late stages align consistently with the conventional forward shock model, complemented by a reverse shock element that dominates optical emissions during the initial phases (T < 300 s). Furthermore, we observe a break at T  = 80 000 s that we interpreted as evidence of a jet break, which constrains the opening angle to be about θj = (3–5) degrees. Finally, we apply a machine-learning technique to model the multiwavelength light curve of GRB 210822A using the afterglowpy library. We estimate the angle of sight θobs = (6.4 ± 0.1) × 10−1 degrees, the energy E 0 = (7.9 ± 1.6) × 1053 erg, the electron index p  = 2.54 ± 0.10, the thermal energy fraction in electrons ϵe = (4.63 ± 0.91) × 10−5 and in the magnetic field ϵB = (8.66 ± 1.01) × 10−6, the efficiency χ = 0.89 ± 0.01, and the density of the surrounding medium n 0 = 0.85 ± 0.01 cm−3. [ABSTRACT FROM AUTHOR]

IOData is a free and open‐source Python library for parsing, storing, and converting various file formats commonly used by quantum chemistry, molecular dynamics, and plane‐wave density‐functional‐theory software programs. In addition, IOData supports a flexible framework for generating input files for various software packages. While designed and released for stand‐alone use, its original purpose was to facilitate the interoperability of various modules in the HORTON and ChemTools software packages with external (third‐party) molecular quantum chemistry and solid‐state density‐functional‐theory packages. IOData is designed to be easy to use, maintain, and extend; this is why we wrote IOData in Python and adopted many principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. This article is the official release note of the IOData library. [ABSTRACT FROM AUTHOR]