arXiv subjects

René D. Rohrmann

Publications and source records attributed to René D. Rohrmann.

16 recordsLinked to original sources

arXiv2026

Hydrogen photoionization in a magnetized medium: the rigid-wavefunction approach revisited

Realistic modeling of stellar spectra requires accurate radiative opacity coefficients. Owing to the fragmentary nature of existing data from rigorous quantum-mechanical calculations, photoionization coefficients based on the rigid-wavefunction approximation remain the only practical option for studies of magnetic white dwarfs. Although variants of this approach have been widely used in spectral analyses for decades, a complete and explicit treatment of degeneracy-level breaking has not previously been presented. In this work, we provide a comprehensive description of this procedure, including explicit expressions for the photoionization probability of individual bound-free transitions as functions of magnetic field strength and radiation polarization. We also evaluate the occupation numbers of bound states in a magnetized gas under ionization equilibrium, enabling the calculation of absolute photoionization opacities. Because high-lying atomic states are strongly perturbed by the magnetic field and ultimately dissolved, substantial modifications of the monochromatic absorption are found even for fields below 10 MG--a regime where fully rigorous quantum calculations are numerically demanding and have not yet been applied. Over a wide range of magnetic field strengths, pronounced dichroic features appear in the hydrogen continuum absorption.

astro-ph.SR↗

arXiv2024

Strong signature of right-handed circularly polarized photoionization close to the cyclotron line in the atmosphere of magnetic white dwarfs

Magnetic fields break the symmetry of the interaction of atoms with photons with different polarizations, yielding chirality and anisotropy properties. The dependence of the absorption spectrum on the polarization, a phenomenon known as dichroism, is present in the atmosphere of magnetic white dwarfs. Its evaluation for processes in the continuum spectrum has been elusive so far due to the absence of appropriate ionization equilibrium models and incomplete data on photoionization cross sections. We combined rigorous solutions to the equilibrium of atomic populations with approximate cross sections to calculate the absolute opacity due to photoionization in a magnetized hydrogen gas. We predict a strong right-handed circularly polarized absorption ($χ^+$) formed blueward of the cyclotron resonance for fields from about 14 to several hundred megagauss. In energies lower than the cyclotron fundamental, this absorption shows a deep trough with respect to linear and left-handed circular polarizations that steepens with the field strength. The jump in $χ^+$ is due to the confluence of a large number of photoionization continua produced by right-handed circularly polarized transitions from atomic states with a nonnegative magnetic quantum number toward different Landau levels.

astro-ph.SR↗

arXiv2024

A numerical code for the analysis of magnetic white dwarf spectra that includes field effects on the chemical equilibrium

We present a new magnetic-atmosphere model code for obtaining synthetic spectral fluxes of hydrogen-rich magnetic white dwarfs. To date, observed spectra have been analyzed with models that neglect the magnetic field's effects on the atomic populations. In this work, we incorporate state-of-art theory in the evaluation of numerical densities of atoms, free electrons, and ions in local thermodynamical equilibrium under the action of a magnetic field. The energy distribution of atoms is rigorously evaluated for arbitrary field strength. This energy pattern includes going from tightly bound states to metastable or truly bound, highly excited states embedded in the continuum, that is, over the first Landau level. Finite nuclear mass effects and the coupling between the internal atomic structure and the motion of the atom across the magnetic field are also considered. Synthetic fluxes are generated with integrations of numerical solutions of polarized radiative transfer over the visible stellar disk using a spherical t-design method. The atmosphere code is tested with observations from the Sloan Digital Sky Survey for a group of known magnetic white dwarfs. Physical stellar parameters are obtained from least-squares fits to the observed energy distribution and compared with results of previous works. We show that the use of zerofield ionization equilibrium in spectral analyses can lead to underestimated effective temperatures for highly magnetic white dwarfs.

astro-ph.SR↗

arXiv2022

Rayleigh scattering from hydrogen atoms including resonances and high photon energies

The non-relativistic cross section from Rayleigh scattering by hydrogen atoms in the ground state is calculated over a wide range of photon energies ($< 0.8$ keV). Evaluations are performed in terms of the real and imaginary components of the atomic polarizability. The sum over intermediate states that characterizes this second-order radiative process is performed using exact analytic expressions for oscillator strengths of bound and continuum states. Damping terms associated with the finite lifetimes of excited states and their splitting into two fine-structure levels ($p_{1/2}$ and $p_{3/2}$) are taken into account in resonance cross sections. Fitting formulas required for cross-section evaluation are presented for incident photon energy i) redward of the first resonance (Lyman-$α_{1/2}$), ii) in the spectral region corresponding to resonances (for an arbitrary number of them), and iii) above the ionization threshold.

physics.atom-ph↗

arXiv2020

Hydrogen ionization equilibrium in magnetic fields

We assess the partition function and ionization degree of magnetized hydrogen atoms at thermodynamic equilibrium for a wide range of field intensities, $B\approx 10^5$-$10^{12}$~G. Evaluations include fitting formulae for an arbitrary number of binding energies, the coupling between the internal atomic structure and the center-of-mass motion across the magnetic field, and the formation of the so-called decentered states (bound states with the electron shifted from the Coulomb well). Non-ideal gas effects are treated within the occupational probability method. We also present general mathematical expressions for the bound state correspondence between the limits of zero-field and high-field. This let us evaluate the atomic partition function in a continuous way from the Zeeman perturbative regime to very strong fields. Results are shown for conditions found in atmospheres of magnetic white dwarf stars (MWDs), with temperatures $T\approx 5000$-$80000$~K and densities $ρ\approx 10^{-12}$-$10^{-3}$~g~cm$^3$. Our evaluations show a marked reduction of the gas ionization due to the magnetic field in the atmospheres of strong MWDs. We also found that decentered states could be present in the atmospheres of currently known hot MWDs, giving a significant contribution to the partition function in the strongest magnetized atmospheres.

astro-ph.SR↗

arXiv2019

On the evolution of ultra-massive white dwarfs

Ultra-massive white dwarfs are powerful tools to study various physical processes in the Asymptotic Giant Branch (AGB), type Ia supernova explosions and the theory of crystallization through white dwarf asteroseismology. Despite the interest in these white dwarfs, there are few evolutionary studies in the literature devoted to them. Here, we present new ultra-massive white dwarf evolutionary sequences that constitute an improvement over previous ones. In these new sequences, we take into account for the first time the process of phase separation expected during the crystallization stage of these white dwarfs, by relying on the most up-to-date phase diagram of dense oxygen/neon mixtures. Realistic chemical profiles resulting from the full computation of progenitor evolution during the semidegenerate carbon burning along the super-AGB phase are also considered in our sequences. Outer boundary conditions for our evolving models are provided by detailed non-gray white dwarf model atmospheres for hydrogen and helium composition. We assessed the impact of all these improvements on the evolutionary properties of ultra-massive white dwarfs, providing up-dated evolutionary sequences for these stars. We conclude that crystallization is expected to affect the majority of the massive white dwarfs observed with effective temperatures below $40\,000\, \rm K$. Moreover, the calculation of the phase separation process induced by crystallization is necessary to accurately determine the cooling age and the mass-radius relation of massive white dwarfs. We also provide colors in the GAIA photometric bands for our H-rich white dwarf evolutionary sequences on the basis of new models atmospheres. Finally, these new white dwarf sequences provide a new theoretical frame to perform asteroseismological studies on the recently detected ultra-massive pulsating white dwarfs.

astro-ph.SR↗

arXiv2017

Rayleigh scattering in dense fluid helium

Iglesias et al. (2002) showed that the Rayleigh scattering from helium atoms decreases by collective effects in the atmospheres of cool white dwarf stars. Their study is here extended to consider an accurate evaluation of the atomic polarizability and the density effects involved in the Rayleigh cross section over a wide density-temperature region. The dynamic dipole polarizability of helium atoms in the ground state is determinated with the oscillator-strength distribution approach. The spectral density of oscillator strength considered includes most significant single and doubly excited transitions to discrete and continuum energies. Static and dynamic polarizability results are confronted with experiments and other theoretical evaluations shown a very good agreement. In addition, the refractive index of helium is evaluated with the Lorentz-Lorenz equation and shows a satisfactory agreement with the most recent experiments. The effect of spatial correlation of atoms on the Rayleigh scattering is calculated with Monte Carlo simulations and effective energy potentials that represent the particle interactions, covering fluid densities between 0.005 and a few g/cm$^3$ and temperatures between $1000$ K and $15000$ K. We provide analytical fits from which the Rayleigh cross section of fluid helium can be easily calculated at wavelength $λ>505.35$ Å. Collision-induced light scattering was estimated to be the dominant scattering process at densities greater than 1-2 g/cm$^3$ depending on the temperature.

astro-ph.SR↗

arXiv2017

Evolutionary sequences for hydrogen-deficient white dwarfs

We present a set of full evolutionary sequences for white dwarfs with hydrogen-deficient atmospheres. We take into account the evolutionary history of the progenitor stars, all the relevant energy sources involved in the cooling, element diffusion in the very outer layers, and outer boundary conditions provided by new and detailed non-gray white dwarf model atmospheres for pure helium composition. These model atmospheres are based on the most up-to-date physical inputs. Our calculations extend down to very low effective temperatures, of $\sim 2\,500$~K, provide a homogeneous set of evolutionary cooling tracks that are appropriate for mass and age determinations of old hydrogen-deficient white dwarfs, and represent a clear improvement over previous efforts, which were computed using gray atmospheres.

astro-ph.SR↗

arXiv2015

Equation of state for five-dimensional hyperspheres from the chemical-potential route

We use the Percus-Yevick approach in the chemical-potential route to evaluate the equation of state of hard hyperspheres in five dimensions. The evaluation requires the derivation of an analytical expression for the contact value of the pair distribution function between particles of the bulk fluid and a solute particle with arbitrary size. The equation of state is compared with those obtained from the conventional virial and compressibility thermodynamic routes and the associated virial coefficients are computed. The pressure calculated from all routes is exact up to third density order, but it deviates with respect to simulation data as density increases, the compressibility and the chemical-potential routes exhibiting smaller deviations than the virial route. Accurate linear interpolations between the compressibility route and either the chemical-potential route or the virial one are constructed.

cond-mat.stat-mech↗

arXiv2014

Equation of state of sticky-hard-sphere fluids in the chemical-potential route

The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route ($μ$ route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxter's model) are derived within the Percus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the $μ$ route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the $μ$ route yields a general better description than the virial, energy, compressibility, and zero-separation routes.

cond-mat.soft↗

arXiv2013

Chemical-potential route for multicomponent fluids

The chemical potentials of multicomponent fluids are derived in terms of the pair correlation functions for arbitrary number of components, interaction potentials, and dimensionality. The formally exact result is particularized to hard-sphere mixtures with zero or positive nonadditivity. As a simple application, the chemical potentials of three-dimensional additive hard-sphere mixtures are derived from the Percus-Yevick theory and the associated equation of state is obtained. This Percus-Yevick chemical-route equation of state is shown to be more accurate than the virial equation of state. An interpolation between the chemical-potential and compressibility routes exhibits a better performance than the well-known Boublík-Mansoori-Carnahan-Starling-Leland equation of state.

cond-mat.stat-mech↗

arXiv2012

Synthetic Light Curves for Born Again Events: Preliminary Results

The development of surveys which will be able to cover a large region of the sky several times per year will allow the massive detection of transient events taking place in timescales of years. In addition, the projected full digitalization of the Harvard plate collection will open a new window to identify slow transients taking place in timescales of centuries. In particular, these projects will allow the detection of stars undergoing slow eruptions as those expected during late helium flashes in the post-AGB evolution. In order to identify those transients which correspond with late helium flashes the development of synthetic light curves of those events is mandatory. In this connection we present preliminary results of a project aimed at computing grids of theoretical light curves of born again stars.

astro-ph.SR↗

arXiv2012

Conditional pair distributions in many-body systems: Exact results for Poisson ensembles

We introduce a conditional pair distribution function (CPDF) which characterizes the probability density of finding an object (e.g., a particle in a fluid) to certain distance of other, with each of these two having a nearest neighbor to a fixed but otherwise arbitrary distance. This function describes special four-body configurations, but also contains contributions due to the so-called mutual nearest neighbor (two-body) and shared neighbor (three-body) configurations. The CPDF is introduced to improve a Helmholtz free energy method based on space partitions. We derive exact expressions of the CPDF and various associated quantities for randomly distributed, non-interacting points at Euclidean spaces of one, two and three dimensions. Results may be of interest in many diverse scientific fields, from fluid physics to social and biological sciences.

cond-mat.stat-mech↗

arXiv2011

Exact solution of the Percus-Yevick integral equation for fluid mixtures of hard hyperspheres

Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E \textbf{83}, 011201 (2011)]. It is demonstrated here that the RFA technique yields the exact solution of the Percus-Yevick (PY) closure to the Ornstein-Zernike (OZ) equation for binary mixtures at arbitrary odd dimensions. The proof relies mainly on the Fourier transforms $\hat{c}_{ij}(k)$ of the direct correlation functions defined by the OZ relation. From the analysis of the poles of $\hat{c}_{ij}(k)$ we show that the direct correlation functions evaluated by the RFA method vanish outside the hard core, as required by the PY theory.

cond-mat.stat-mech↗

arXiv2011

Multicomponent fluids of hard hyperspheres in odd dimensions

Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of state, structure factors, radial distribution functions, and direct correlations functions of additive mixtures of hard hyperspheres with any number of components and in arbitrary odd-dimension space. The method gives the exact solution of the Ornstein--Zernike equation coupled with the Percus--Yevick closure, thus extending to arbitrary odd dimension the solution for hard-sphere mixtures [J. L. Lebowitz, Phys.\ Rev.\ \textbf{133}, 895 (1964)]. Explicit evaluations for binary mixtures in five dimensions are performed. The results are compared with computer simulations and a good agreement is found.

cond-mat.soft↗

arXiv2010

A white dwarf cooling age of 8 Gyr for NGC 6791 from physical separation processes

NGC 6791 is a well studied open cluster1 that it is so close to us that can be imaged down to very faint luminosities. The main sequence turn-off age (~8 Gyr) and the age derived from the termination of the white dwarf cooling sequence (~6 Gyr) are significantly different. One possible explanation is that as white dwarfs cool, one of the ashes of helium burning, 22Ne, sinks in the deep interior of these stars. At lower temperatures, white dwarfs are expected to crystallise and phase separation of the main constituents of the core of a typical white dwarf, 12C and 16O, is expected to occur. This sequence of events is expected to introduce significant delays in the cooling times, but has not hitherto been proven. Here we report that, as theoretically anticipated, physical separation processes occur in the cores of white dwarfs, solving the age discrepancy for NGC 6791.

astro-ph.SR↗