First-principles modeling of three-body interactions in highly compressed solid helium

We present a new set of three-body interaction models based on the Bruch-McGee (BM) potential that are suitable for the study of the energy, structural and elastic properties of solid 4He at high pressure. Our ab initio three-body potentials are obtained from the fit to total energies and atomic forces computed with the van der Waals density functional theory method due to Grimme, and represent an improvement with respect to previously reported three-body interaction models. In particular, we show that some of the introduced BM parametrizations reproduce closely the experimental equation of state and bulk modulus of solid helium up to a pressure of ~ 60 GPa, when used in combination with standard pairwise interaction models in diffusion Monte Carlo simulations. Importantly, we find that recent predictions reporting a surprisingly small variation of the kinetic energy and Lindeman ratio on quantum crystals under increasing pressure are likely to be artifacts produced by the use of incomplete interaction models. Also, we show that the experimental variation of the shear modulus, C44, at P < 25 GPa can be quantitatively described with the new set of three-body BM potentials. At higher pressures, however, the agreement between our C44 results and experiments deteriorates and thus we argue that higher order many-body terms in the expansion of the atomic interactions probably are necessary in order to better describe elasticity in very dense solid 4He.Comment: 11 pages, 7 figure

Modelling ion populations in astrophysical plasmas: carbon in the solar transition region

The aim of this work is to improve the modelling of ion populations in higher density, lower temperature astrophysical plasmas, of the type commonly found in lower solar and stellar atmospheres. Ion population models for these regions frequently employ the coronal approximation, which assumes conditions more suitable to the upper solar atmosphere, where high temperatures and lower densities prevail. Using the coronal approximation for modelling the solar transition region gives theoretical lines intensities for the Li-like and Na-like isoelectronic sequences which can be factors of 2-5 times lower than observed. The works of Burgess & Summers (1969) and Nussbaumer & Storey (1975) showed the important part ions in excited levels play when included in the modelling. Their models, however, used approximations for the atomic rates to determine the ion balance. Presented here is the first stage in updating these earlier models of carbon by using rates from up-to-date atomic calculations and more recent photo-ionising radiances for the quiet Sun. Where such atomic rates are not readily available, in the case of electron-impact direct ionisation and excitation--auto-ionisation, new calculations have been made and compared to theoretical and experimental studies. The effects each atomic process has on the ion populations as density changes is demonstrated, and final results from the modelling are compared to the earlier works. Lastly, the new results for ion populations are used to predict line intensities for the solar transition region in the quiet Sun, and these are compared with predictions from coronal-approximation modelling and with observations. Significant improvements in the predicted line intensities are seen in comparison to those obtained from zero-density modelling of carbon.Comment: Draft accepted by A&A, 13 pages, 15 figure

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

The temperature and chronology of heavy-element synthesis in low-mass stars

Roughly half of the heavy elements (atomic mass greater than that of iron) are believed to be synthesized in the late evolutionary stages of stars with masses between 0.8 and 8 solar masses. Deep inside the star, nuclei (mainly iron) capture neutrons and progressively build up (through the slow-neutron-capture process, or s-process) heavier elements that are subsequently brought to the stellar surface by convection. Two neutron sources, activated at distinct temperatures, have been proposed: 13C and 22Ne, each releasing one neutron per alpha-particle (4He) captured. To explain the measured stellar abundances, stellar evolution models invoking the 13C neutron source (which operates at temperatures of about one hundred million kelvin) are favoured. Isotopic ratios in primitive meteorites, however, reflecting nucleosynthesis in the previous generations of stars that contributed material to the Solar System, point to higher temperatures (more than three hundred million kelvin), requiring at least a late activation of 22Ne. Here we report a determination of the s-process temperature directly in evolved low-mass giant stars, using zirconium and niobium abundances, independently of stellar evolution models. The derived temperature supports 13C as the s-process neutron source. The radioactive pair 93Zr-93Nb used to estimate the s-process temperature also provides, together with the pair 99Tc-99Ru, chronometric information on the time elapsed since the start of the s-process, which we determine to be one million to three million years.Comment: 30 pages, 10 figure

Atomic data for the astrophysics : Fe XII soft X-ray lines.

We present new large-scale R-matrix (up to n = 4) and distorted-wave (DW, up to n = 6) scattering calculations for electron collisional excitation of Fe xii. The first aim is to provide accurate atomic data for the soft X-rays, where strong decays from the n = 4 levels are present. As found in previous work on Fe x, resonances attached to n = 4 levels increase the cross-sections for excitations from the ground state to some n = 4 levels, when compared to DW calculations. Cascading from higher levels is also important. We provide a number of models and line intensities, and list a number of strong unidentified lines. The second aim is to assess the effects of the large R-matrix calculation on the n = 3 transitions. Compared to our previous (n = 3) R-matrix calculation, we find overall excellent agreement to within a few percent, however a few key density diagnostic EUV intensities differ by about 60% at coronal densities. The new atomic data result in lower electron densities, resolving previous discrepancies with solar observations

Low-energy Population III supernovae and the origin of extremely metal-poor stars

Some ancient, dim, metal-poor stars may have formed in the ashes of the first supernovae (SNe). If their chemical abundances can be reconciled with the elemental yields of specific Population III (Pop III) explosions, they could reveal the properties of primordial stars. But multidimensional simulations of such explosions are required to predict their yields because dynamical instabilities can dredge material up from deep in the ejecta that would otherwise be predicted to fall back on to the central remnant and be lost in one-dimensional (1D) models. We have performed two-dimensional (2D) numerical simulations of two low-energy Pop III SNe, a 12.4 Msun explosion and a 60 Msun explosion, and find that they produce elemental yields that are a good fit to those measured in the most iron-poor star discovered to date, SMSS J031300.36-670839.3 (J031300). Fallback on to the compact remnant in these weak explosions accounts for the lack of measurable iron in J031300 and its low iron-group abundances in general. Our 2D explosions produce higher abundances of heavy elements (atomic number Z > 20) than their 1D counterparts due to dredge-up by fluid instabilities. Since almost no Ni is ejected by these weak SNe, their low luminosities will prevent their detection in the near-infrared with the James Webb Space Telescope and future 30-m telescopes on the ground. The only evidence that they ever occurred will be in the fossil abundance record.Comment: Accepted to MNRA

Atomic calculation for the atmospheres of strongly-magnetized neutron stars

Complete modeling of radiative transfer in neutron star atmospheres is in progress, taking into account the anisotropy induced by magnetic fields, non-ideal effects and general relativity. As part of our modeling, we present a novel atomic calculation method producing an extensive atomic data set including energy values and oscillator strengths in the so-called Landau regime ($B > 4.7\times10^9Z^2$ G). Conventional atmosphere models for B=0 are not applicable to typical field strengths of cooling neutron stars ($B \sim10^{12}-10^{13}$ G), since an atom no longer keeps its spherical shape. The elemental composition and the configuration of the magnetic field in the atmosphere are presently unknown, so that atomic data must be produced for ground and excited states of several ions as a function of magnetic field. To accomplish this efficiently, we minimized the iterations in the Hartree equation and treated exchange terms and higher Landau states by perturbation methods. This method has the effect of reducing the computation time significantly. Inclusion of higher Landau states gives us much more accurate data for inner orbitals unlike other methods based on the adiabatic approximation. While existing atomic data in the Landau regime are available only for low $Z$ atoms, our method can be used in elements up to Fe with sufficient accuracy to be of use for spectroscopic missions such as {\it Chandra}, {\it XMM-Newton} and next-generation X-ray telescopes.Comment: 19 pages, AASTeX, 4 figures, accepted for publication in Ap