Formation of black holes in the pair-instability mass gap: Hydrodynamical simulation of a massive star collision

The detection of GW190521 by the LIGO-Virgo collaboration proved the existence of black holes in the theoretically predicted pair-instability gap of their mass spectrum. Some recent studies suggest that such massive black holes could be produced by the collision of an evolved star with a carbon-oxygen core and a main sequence star. Such a post-coalescence star could end its life avoiding the pair-instability regime and with a direct collapse of its very massive envelope. It is still not clear, however, how the collision shapes the structure of the newly produced star and how much mass is actually lost in the impact. We investigated this issue by means of hydrodynamical simulations with the smoothed particle hydrodynamics code StarSmasher, finding that the collision can remove up to 12% of the initial mass of the colliding stars. This is a non-negligible percentage of the initial mass and could affect the further evolution of the stellar remnant, particularly in terms of the final mass of a possibly forming black hole, if the core avoids the pair-instability regime. We also found that the main sequence star can plunge down to the outer boundary of the carbon-oxygen core of the primary, changing the inner chemical composition of the remnant. The collision expels the outer layers of the primary, leaving a remnant with an helium-enriched envelope (reaching He fractions of about 0.4 at the surface). These more complex abundance profiles can be directly used in stellar evolution simulations of the collision product.Comment: 7 pages, 5 figures. Comments welcome

Zero Temperature Phases of the Electron Gas

The stability of different phases of the three-dimensional non-relativistic electron gas is analyzed using stochastic methods. With decreasing density, we observe a {\it continuous} transition from the paramagnetic to the ferromagnetic fluid, with an intermediate stability range ($25\pm 5 \leq r_s\leq 35 \pm 5$) for the {\it partially} spin-polarized liquid. The freezing transition into a ferromagnetic Wigner crystal occurs at $r_s=65 \pm 10$. We discuss the relative stability of different magnetic structures in the solid phase, as well as the possibility of disordered phases.Comment: 4 pages, REVTEX, 3 ps figure

Diffusion Monte Carlo study of circular quantum dots

We present ground and excited state energies obtained from Diffusion Monte Carlo (DMC) calculations, using accurate multiconfiguration wave functions, for $N$ electrons ($N\le13$) confined to a circular quantum dot. We analyze the electron-electron pair correlation functions and compare the density and correlation energies to the predictions of local spin density approximation theory (LSDA). The DMC estimated change in electrochemical potential as function of the number of electrons in the dot is compared to that from LSDA and Hartree-Fock (HF) calculations.Comment: 7 pages, 4 eps figures. To be published in Phys. Rev. B, September 15th 2000. See erratum cond-mat/030571

Sparse random matrices and vibrational spectra of amorphous solids

A random matrix approach is used to analyze the vibrational properties of amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n independent non-zero elements in each row. The average values =0 and dispersion =V^2 for all non-zero elements. The density of vibrational states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle law with radius independent of N. We argue that for n^2 << N this model can be used to describe the interaction of atoms in amorphous solids. The level statistics of matrix M is well described by the Wigner surmise and corresponds to repulsion of eigenfrequencies. The participation ratio for the major part of vibrational modes in three dimensional system is about 0.2 - 0.3 and independent of N. Together with term repulsion it indicates clearly to the delocalization of vibrational excitations. We show that these vibrations spread in space by means of diffusion. In this respect they are similar to diffusons introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous silicon. Our results are in a qualitative and sometimes in a quantitative agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure

Structure and Dynamics of Liquid Iron under Earth's Core Conditions

First-principles molecular dynamics simulations based on density-functional theory and the projector augmented wave (PAW) technique have been used to study the structural and dynamical properties of liquid iron under Earth's core conditions. As evidence for the accuracy of the techniques, we present PAW results for a range of solid-state properties of low- and high-pressure iron, and compare them with experimental values and the results of other first-principles calculations. In the liquid-state simulations, we address particular effort to the study of finite-size effects, Brillouin-zone sampling and other sources of technical error. Results for the radial distribution function, the diffusion coefficient and the shear viscosity are presented for a wide range of thermodynamic states relevant to the Earth's core. Throughout this range, liquid iron is a close-packed simple liquid with a diffusion coefficient and viscosity similar to those of typical simple liquids under ambient conditions.Comment: 13 pages, 8 figure

Density-functional-based predictions of Raman and IR spectra for small Si clusters

We have used a density-functional-based approach to study the response of silicon clusters to applied electric fields. For the dynamical response, we have calculated the Raman activities and infrared (IR) intensities for all of the vibrational modes of several clusters (SiN with N=3-8, 10, 13, 20, and 21) using the local density approximation (LDA). For the smaller clusters (N=3-8) our results are in good agreement with previous quantum-chemical calculations and experimental measurements, establishing that LDA-based IR and Raman data can be used in conjunction with measured spectra to determine the structure of clusters observed in experiment. To illustrate the potential of the method for larger clusters, we present calculated IR and Raman data for two low-energy isomers of Si10 and for the lowest-energy structure of Si13 found to date. For the static response, we compare our calculated polarizabilities for N=10, 13, 20, and 21 to recent experimental measurements. The calculated results are in rough agreement with experiment, but show less variation with cluster size than the measurements. Taken together, our results show that LDA calculations can offer a powerful means for establishing the structures of experimentally fabricated clusters and nanoscale systems

Effect of hydrogen on ground state structures of small silicon clusters

We present results for ground state structures of small Si$_{n}$H (2 \leq \emph{n} \leq 10) clusters using the Car-Parrinello molecular dynamics. In particular, we focus on how the addition of a hydrogen atom affects the ground state geometry, total energy and the first excited electronic level gap of an Si$_{n}$ cluster. We discuss the nature of bonding of hydrogen in these clusters. We find that hydrogen bonds with two silicon atoms only in Si$_{2}$H, Si$_{3}$H and Si$_{5}$H clusters, while in other clusters (i.e. Si$_{4}$H, Si$_{6}$H, Si$_{7}$H, Si$_{8}$H, Si$_{9}$H and Si$_{10}$H) hydrogen is bonded to only one silicon atom. Also in the case of a compact and closed silicon cluster hydrogen bonds to the cluster from outside. We find that the first excited electronic level gap of Si$_{n}$ and Si$_{n}$H fluctuates as a function of size and this may provide a first principles basis for the short-range potential fluctuations in hydrogenated amorphous silicon. Our results show that the addition of a single hydrogen can cause large changes in the electronic structure of a silicon cluster, though the geometry is not much affected. Our calculation of the lowest energy fragmentation products of Si$_{n}$H clusters shows that hydrogen is easily removed from Si$_{n}$H clusters.Comment: one latex file named script.tex including table and figure caption. Six postscript figure files. figure_1a.ps and figure_1b.ps are files representing Fig. 1 in the main tex

Anharmonicity, vibrational instability and Boson peak in glasses

We show that a {\em vibrational instability} of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency $\omega_c$, proportional to the strength of interaction. The DOS of the new {\em harmonic modes} is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter -- the Boson peak frequency, $\omega_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $\propto\omega^4$ at low frequencies and linear in $\omega$ in the interval $\omega_b \ll \omega \ll \omega_c$. Our results are in an excellent agreement with recent experimental studies.Comment: LaTeX, 8 pages, 6 figure

Surface reconstruction induced geometries of Si clusters

We discuss a generalization of the surface reconstruction arguments for the structure of intermediate size Si clusters, which leads to model geometries for the sizes 33, 39 (two isomers), 45 (two isomers), 49 (two isomers), 57 and 61 (two isomers). The common feature in all these models is a structure that closely resembles the most stable reconstruction of Si surfaces, surrounding a core of bulk-like tetrahedrally bonded atoms. We investigate the energetics and the electronic structure of these models through first-principles density functional theory calculations. These models may be useful in understanding experimental results on the reactivity of Si clusters and their shape as inferred from mobility measurements.Comment: 9 figures (available from the author upon request) Submitted to Phys. Rev.

Atomic structure and segregation in alkali-metal heteroclusters

The ground-state atomic and electronic distributions in NamCsn clusters with composition m=n and m=2n have been calculated by minimizing the total cluster energy using the density-functional formalism. The approximation is made by replacing the total external potential of the ions by its spherical average around the cluster center during the iterative process of solving the Kohn-Sham equations for each geometry tested. In the size range studied here (up to 90 atoms per cluster), the cluster is composed of well-separated homoatomic Na and Cs shells, the external one always being a Cs shell. We have also found that the cohesive energy goes rapidly to the bulk limit. An analysis of the geometries shows strong cluster reconstruction with increasing size. By comparing the geometry of pure Nan with that of the Nan core in NanCsn for clusters formed by only an inner Na layer and an outer Cs layer, we have observed that the Nan core adopts a geometry different in most cases from that of the free Nan cluster, and such that the number of faces of the polyhedron formed by the Nan core is as close as possible to the number of external Cs atoms, in order to accomodate these Cs atoms on top of the faces of the polyhedron