Structure Of White Dwarfs Research Articles

Development of improved higher-order correction for the NIF opacity spectrometer.

X-ray opacity measurements on the National Ignition Facility (NIF) are in the process of reproducing earlier measurements from the Sandia Z Facility, in particular for oxygen and iron plasmas. These measurements have the potential to revise our understanding of the "solar problem" and of the hot degenerate Q class white dwarf structure by probing plasma conditions near the base of their convection zones. Accurate opacity measurements using soft x-ray Bragg crystal spectrometers require correction for higher-order diffraction effects. Extending prior work in this area [Dutra etal., Review of Scientific Instruments 93, 113527 (2022)], we have developed a new method to remove higher-order spectral components from NIF opacity spectrometer data. By modeling absorption and backlighting continuum spectra and subtracting the second- and third-order components from the measured data, we are able to perform this correction while avoiding imprinting first-order model line features onto the data.

The Impact of Breathing Pulses during Core Helium Burning on the Core Chemical Structure and Pulsations of Hydrogen-rich Atmosphere White Dwarfs

Breathing pulses are mixing episodes that could develop during the core helium-burning phase of low- and intermediate-mass stars. The occurrence of breathing pulses is expected to bear consequences on the formation and evolution of white dwarfs, particularly on the core chemical structure, which can be probed by asteroseismology. We aim to explore the consequences of breathing pulses on the chemical profiles and pulsational properties of variable white dwarf stars with hydrogen-rich envelopes, known as ZZ Ceti stars. We compute stellar models with masses of 1.0M ⊙ and 2.5M ⊙ in the zero-age main sequence and evolve them through the core helium-burning phase to the thermal pulses on the asymptotic giant branch, and finally to advanced stages of white dwarf cooling. We compare the chemical structure of the core of white dwarfs whose progenitors have experienced breathing pulses during the core helium-burning phase with the case in which breathing pulses have not occurred. We find that when breathing pulses occur, the white dwarf cores are larger and the central abundances of oxygen are higher than for the case in which the breathing pulses are suppressed, in line with previous studies. However, the occurrence of breathing pulses is not sufficient to explain the large cores and the excessive oxygen abundances that characterize recently derived asteroseismological models of pulsating white dwarfs. We find absolute differences of up to ∼30 s when we compare pulsation periods of white dwarfs coming from progenitors that have experienced breathing pulses with the case in which the progenitors have not suffered breathing pulses.

General relativistic pulsations of ultra-massive ZZ Ceti stars

ABSTRACT Ultra-massive white dwarf stars are currently being discovered at a considerable rate, thanks to surveys such as the Gaia space mission. These dense and compact stellar remnants likely play a major role in Type Ia supernova explosions. It is possible to probe the interiors of ultra-massive white dwarfs through asteroseismology. In the case of the most massive white dwarfs, general relativity could affect their structure and pulsations substantially. In this work, we present results of relativistic pulsation calculations employing relativistic ultra-massive ONe-core white dwarf models with hydrogen-rich atmospheres and masses ranging from 1.29 to $1.369 \ \mathrm{M}_{\odot }$ with the aim of assessing the impact of general relativity on the adiabatic gravity (g)-mode period spectrum of very high mass ZZ Ceti stars. Employing the relativistic Cowling approximation for the pulsation analysis, we find that the critical buoyancy (Brunt–Väisälä) and acoustic (Lamb) frequencies are larger for the relativistic case, compared to the Newtonian case, due to the relativistic white dwarf models having smaller radii and higher gravities for a fixed stellar mass. In addition, the g-mode periods are shorter in the relativistic case than those in the Newtonian computations, with relative differences of up to ∼$50$ per cent for the highest mass models ($1.369 \ \mathrm{M}_{\odot }$) and for effective temperatures typical of the ZZ Ceti instability strip. Hence, the effects of general relativity on the structure, evolution, and pulsations of white dwarfs with masses larger than ∼$1.29 \ \mathrm{M}_{\odot }$ cannot be ignored in the asteroseismological analysis of ultra-massive ZZ Ceti stars.

Finite temperature considerations in the structure of quadratic GUP-modified white dwarfs

In quantum gravity phenomenology, the effect of the generalized uncertainty principle (GUP) on white dwarf structure has been given much attention in recent literature. However, these studies assume a zero temperature equation of state (EoS), excluding young white dwarfs whose initial temperatures are substantially high. To that cause, this paper calculates the Chandrasekhar EoS and resulting mass-radius relations of finite temperature white dwarfs modified by the quadratic GUP, an approach that extends Heisenberg’s uncertainty principle by a quadratic term in momenta. The EoS was first approximated by treating the quadratic GUP parameter as perturbative, causing the EoS to exhibit expected thermal deviations at low pressures, and conflicting behaviors at high pressures, depending on the order of approximation. We then proceeded with a full numerical simulation of the modified EoS, and showed that in general, finite temperatures cause the EoS at low pressures to soften, while the quadratic GUP stiffens the EoS at high pressures. This modified EoS was then applied to the Tolman–Oppenheimer–Volkoff equations and its classical approximation to obtain the modified mass-radius relations for general relativistic and Newtonian white dwarfs. The relations for both cases were found to exhibit the expected thermal deviations at small masses, where low-mass white dwarfs are shifted to the high-mass regime at large radii, while high-mass white dwarfs acquire larger masses, beyond the Chandrasekhar limit. Additionally, we find that for sufficiently large values of the GUP parameter and temperature, we obtain mass-radius relations that are completely removed from the ideal case, as high-mass deviations due to GUP and low-mass deviations due to temperature are no longer mutually exclusive.

PSR J1910–5959A: A rare gravitational laboratory for testing white dwarf models

Context. PSR J1910−5959A is a binary millisecond pulsar in a 0.837 day circular orbit around a helium white dwarf (HeWD) companion. The position of this pulsar is 6.3 arcmin (∼74 core radii) away from the optical centre of the globular cluster (GC) NGC 6752. Given the large offset, the association of the pulsar with the GC has been debated. Aims. We aim to obtain precise measurements of the masses of the stars in the system along with secular orbital parameters, which will help identify if the system belongs to the GC. Methods. We have made use of archival Parkes 64 m ‘Murriyang’ telescope data and carried out observations with the MeerKAT telescope with different backends and receivers over the last two decades. Pulse times of arrival were obtained from these using standard pulsar data reduction techniques and analysed using state-of-the-art Bayesian pulsar timing techniques. We also performed an analysis of the pulsar’s total intensity and polarisation profile to understand the interstellar scattering along the line of sight, and we determined the pulsar’s geometry by fitting the rotating vector model to the polarisation data. Results. We obtain precise measurements of several post-Keplerian parameters: the range, r = 0.202(6) T⊙, and shape, s = 0.999823(4), of the Shapiro delay, from which we infer: the orbital inclination to be 88.9−0.14+0.15 deg; the masses of the pulsar and the companion to be 1.55(7) M⊙ and 0.202(6) M⊙, respectively; a secular change in the orbital period Ṗb = −53−6.0+7.4 × 10−15 s s−1 that proves the GC association; and a secular change in the projected semi-major axis of the pulsar, ẋ = −40.7−8.2+7.3 × 10−16 s s−1, likely caused by the spin–orbit interaction from a misaligned HeWD spin, at odds with the likely isolated binary evolution of the system. We also discuss some theoretical models for the structure and evolution of white dwarfs in neutron star–white dwarf binaries, using PSR J1910−5959A’s companion as a test bed. Conclusions. PSR J1910−5959A is a rare system for which several parameters of both the pulsar and the HeWD companion can be accurately measured. As such, it is a test bed for discriminating between alternative models of HeWD structure and cooling.

Structure and evolution of ultra-massive white dwarfs in general relativity

Context. Ultra-massive white dwarfs (M⋆ ≳ 1.05 M⊙) are of utmost importance in view of the role they play in type Ia supernovae explosions, merger events, the existence of high-magnetic -field white dwarfs, and the physical processes in the super asymptotic giant branch phase. Aims. We aim to present the first set of constant rest-mass ultra-massive oxygen-neon white dwarf cooling tracks with masses of M⋆ > 1.29 M⊙ which fully take into account the effects of general relativity on their structural and evolutionary properties. Methods. We computed the full evolution sequences of 1.29, 1.31, 1.33, 1.35, and 1.369 M⊙ white dwarfs with the La Plata stellar evolution code, LPCODE. For this work, the standard equations of stellar structure and evolution have been modified to include the effects of general relativity. Specifically, the fully general relativistic partial differential equations governing the evolution of a spherically symmetric star are solved in a way so that they resemble the standard Newtonian equations of stellar structure. For comparison purposes, the same sequences have been computed for the Newtonian case. Results. According to our calculations, the evolutionary properties of the most massive white dwarfs are strongly modified by general relativity effects. In particular, the resulting stellar radius is markedly smaller in the general relativistic case, being up to 25% smaller than predicted by the Newtonian treatment for the more massive ones. We find that oxygen-neon white dwarfs more massive than 1.369 M⊙ become gravitationally unstable with respect to general relativity effects. When core chemical distribution due to phase separation on crystallization is considered, such instability occurs at somewhat lower stellar masses, ≳1.36 M⊙. In addition, cooling times for the most massive white dwarf sequences are about a factor of two smaller than in the Newtonian case at advanced stages of evolution. Finally, a sample of white dwarfs have been identified as ideal candidates to test these general relativistic effects. Conclusions. We conclude that the general relativity effects should be taken into account for an accurate assessment of the structural and evolutionary properties of the most massive white dwarfs. These new ultra-massive white dwarf models constitute a considerable improvement over those computed in the framework of the standard Newtonian theory of stellar interiors.

Asteroseismological Analysis of the DAV HS 0507+0434B: The Influence of Chemical Profile on the Pulsation Periods

Abstract Asteroseismology is a powerful tool to infer the details of the inner chemical structure of white dwarfs. Using the nine observed frequencies of HS 0507+0434B, we explore the influence of the inner chemical profile on the pulsation periods. Based on the evolutionary C/O profile, we modify slightly the C/O core profile and make an asteroseismic analysis for HS 0507+0434B. We find that the trapped mode with the period of 445.3 s is mainly affected by the hydrogen and helium mass fraction. The inner C/O core profile has an influence on all modes extending into the inner core. When we use the iteration method with the optimal C/O core profile, the fit between the theoretical periods and observed ones is significantly improved. For the best-fitting model with the optimal parametric C/O core, there is a smaller C/O ratio and a smaller overshooting zone in the stellar interior. The fundamental parameters of the model with the optimal C/O core are M */M ⊙ ∼ 0.710 ± 0.005, T eff ∼ 12570 ± 106K, log M H / M * ∼ − 8.01 ± 0.08 , and log M He / M * ∼ − 2.51 ± 0.08 .

The Structure and Stability of Massive Hot White Dwarfs

Abstract We investigate the structure and stability against radial oscillations, pycnonuclear reactions, and inverse β-decay of hot white dwarfs. We consider the fluid matter to be made up of nucleons and electrons confined in a Wigner–Seitz cell surrounded by free photons. It is considered that the temperature depends on the mass density considering the presence of an isothermal core. We find that the temperature produces remarkable effects on the equilibrium and radial stability of white dwarfs. The stable equilibrium configuration results are compared with those for white dwarfs estimated from the Extreme Ultraviolet Explorer survey and the Sloan Digital Sky Survey. We derive masses, radii, and central temperatures for the most massive white dwarfs according to the surface gravity and effective temperature reported by the surveys. We note that these massive stars are in the mass region where general relativity effects are important. These stars are near the threshold of instabilities due to radial oscillations, pycnonuclear reactions, and inverse β-decay. Regarding the radial stability of these stars as a function of the temperature, we find that it decreases with the increment of central temperature. We also find that the maximum-mass point and the zero eigenfrequencies of the fundamental mode are determined at the same central energy density. Regarding low-temperature stars, pycnonuclear reactions occur in similar central energy densities, and the central energy density threshold for inverse β-decay is not modified. For T c ≥ 1.0 × 108 [K], the onset of radial instability is attained before pycnonuclear reaction and inverse β-decay.

Effect of Coulomb diffusion of ions on the pulsational properties of DA white dwarfs

Context. Element diffusion is a key physical process that substantially affects the superficial abundances, internal structure, pulsation properties, and evolution of white dwarfs. Aims. We study the effect of Coulomb separation of ions on the cooling times of evolving white dwarfs, their chemical profiles, the Brunt–Väisälä (buoyancy) frequency, and the pulsational periods at the ZZ Ceti instability strip. Methods. We followed the full evolution of white dwarf models in the range 0.5 − 1.3 M⊙ derived from their progenitor history on the basis of a time-dependent element diffusion scheme that incorporates the effect of gravitational settling of ions due to Coulomb interactions at high densities. We compared the results for the evolution and pulsation periods of ZZ Ceti stars with the case where this effect is neglected. Results. We find that Coulomb sedimentation profoundly alters the chemical profiles of ultra-massive (M⋆ ≳ 1 M⊙) white dwarfs throughout their evolution, preventing helium from diffusing inward toward the core, and thus leading to much narrower chemical transition zones. As a result, significant changes in the g-mode pulsation periods as high as 15% are expected for ultra-massive ZZ Ceti stars. For lower mass white dwarfs, the effect of Coulomb separation is much less noticeable. It causes period changes in ZZ Ceti stars that are below the period changes that result from uncertainties in progenitor evolution, but larger than the typical uncertainties of the observed periods. Conclusions. Coulomb diffusion of ions profoundly affects the diffusion flux in ultra-massive white dwarfs, driving the gravitational settling of ions with the same A/Z (mass to charge number). We show that it strongly alters the period spectrum of such white dwarfs, which should be taken into account in detailed asteroseismological analyses of ultra-massive ZZ Ceti stars.

A pulsating white dwarf in an eclipsing binary

White dwarfs are the burnt out cores of Sun-like stars and are the final fate of 97% of all stars in our Galaxy. The internal structure and composition of white dwarfs are hidden by their high gravities, which causes all elements, apart from the lightest ones, to settle out of their atmospheres. The most direct method to probe the inner structure of stars and white dwarfs in detail is via asteroseismology. Here we present the first known pulsating white dwarf in an eclipsing binary system, enabling us to place extremely precise constraints on the mass and radius of the white dwarf from the light curve, independent of the pulsations. This 0.325M$_\odot$ white dwarf --- one member of SDSS J115219.99+024814.4 --- will serve as a powerful benchmark to constrain empirically the core composition of low-mass stellar remnants and investigate the effects of close binary evolution on the internal structure of white dwarfs.

ON SOME EFFECTS IN THE STRUCTURE OF WHITE DWARFS

ON SOME EFFECTS IN THE STRUCTURE OF WHITE DWARFS

Gravitational waves from dynamical tides in white dwarf binaries

Abstract We study the effect of tidal forcing on gravitational wave signals from tidally relaxed white dwarf pairs in the LISA, DECIGO and BBO frequency band (0.1 − 100 mHz). We show that for stars not in hydrostatic equilibrium (in their own rotating frames), tidal forcing will result in energy and angular momentum exchange between the orbit and the stars, thereby deforming the orbit and producing gravitational wave power in harmonics not excited in perfectly circular synchronous binaries. This effect is not present in the usual orbit-averaged treatment of the equilibrium tide, and is analogous to transit timing variations in multiplanet systems. It should be present for all LISA white dwarf pairs since gravitational waves carry away angular momentum faster than tidal torques can act to synchronize the spins, and when mass transfer occurs as it does for at least eight LISA verification binaries. With the strain amplitudes of the excited harmonics depending directly on the density profiles of the stars, gravitational wave astronomy offers the possibility of studying the internal structure of white dwarfs, complimenting information obtained from asteroseismology of pulsating white dwarfs. Since the vast majority of white-dwarf pairs in this frequency band are expected to be in the quasi-circular state, we focus here on these binaries, providing general analytic expressions for the dependence of the induced eccentricity and strain amplitudes on the stellar apsidal motion constants and their radius and mass ratios. Tidal dissipation and gravitation wave damping will affect the results presented here and will be considered elsewhere.

On the recent parametric determination of an asteroseismological model for the DBV star KIC 08626021

Context.Asteroseismology of white dwarf stars is a powerful tool that allows us to reveal the hidden chemical structure of white dwarfs and infer details about their present and past evolution by comparing the observed periods with those obtained from appropriate stellar models. A recent asteroseismological study has reproduced the period spectrum of the helium-rich pulsating white dwarf KIC 08626021 with the unprecedented precision of (Pobs − Pmodel)/Pmodel < 10−8. The chemical structure derived from that asteroseismological analysis is notably different from that expected for a white dwarf according to currently accepted formation channels. It therefore poses a challenge to the theory of stellar evolution.Aims.We explore the relevant micro- and macrophysics processes that act during the formation and evolution of KIC 08626021 and might lead to a chemical structure similar to that found through asteroseismology. We quantify to which extent it is necessary to modify the physical processes that shape the chemical structure in order to reproduce the most important features of the asteroseismic model.Methods.We modeled the previous evolution of KIC 08626021 by exploring specific changes in the12C(α, γ)16O reaction rate, screening processes, microscopic diffusion, and convective boundary mixing during core-He burning.Results.We find that in order to reproduce the core chemical profile derived for KIC 0862602, the12C+αnuclear reaction rate has to be increased by a factor of ∼10 during the helium-core burning, and reduced by a factor of ∼1000 during the following helium-shell burning as compared with the standard predictions for this rate. In addition, the main chemical structures derived for KIC 0862602, such as the very thin helium-pure envelope, the mass of the carbon-oxygen core, and the pure C buffer, cannot be reconciled with our current knowledge of white dwarf formation.Conclusion.We find that within our current understanding of white dwarf formation and evolution, it is difficult to reproduce the most important asteroseismologically derived features of the chemical structure of KIC 08626021.

White dwarfs in de Rham-Gabadadze-Tolley like massive gravity

The existence of possible massive white dwarfs more than the Chandrasekhar limit ($1.45\text{ }{M}_{\ensuremath{\bigodot}}$, in which ${M}_{\ensuremath{\bigodot}}$ is mass of the sun) is a challenging topic. In this regard, and motivated by the important effect of massive graviton on the structure of white dwarfs, we study the white dwarfs in Vegh's massive gravity which is known as one of theories of de Rham, Gabadadze, and Tolley (dRGT) like massive gravity. First, we consider the modified Tolman-Oppenheimer-Volkoff equation in this theory of massive gravity and solve it numerically by using the Chandrasekhar's equation of state. Our results show that the maximum mass of white dwarfs in massive gravity can be more than the Chandrasekhar limit ($M>1.45\text{ }{M}_{\ensuremath{\bigodot}}$), and this result imposes some constraints on parameters of massive gravity. Then, we investigate the effects of various parameters on other properties of the white dwarfs such as mass-radius relation, mass-central density relation, Schwarzschild radius, average density, and Kretschmann scalar. Next, we study dynamical stability condition for super-Chandrasekhar white dwarfs and show that these massive compact objects enjoy dynamical stability. Finally, in order to have a better insight, we compare the super-Chandrasekhar white dwarfs with the obtained massive neutron stars in dRGT like massive theory of gravity.

Modeling anisotropic magnetized white dwarfs with γ metric

The effect of magnetic fields in the Equations of State (EoS) of compact objects is the splitting of the pressure in two components, one parallel and the other perpendicular to the magnetic field. This anisotropy suggests the necessity of using structure equations considering the axial symmetry of the magnetized system. In this work, we consider an axially symmetric metric in spherical coordinates, the $\gamma$-metric, and construct a system of equations to describe the structure of spheroidal compact objects. In addition, we connect the geometrical parameter $\gamma$ linked to the spheroid's radii, with the source of the anisotropy. So, the model relates the shape of the compact object to the physics that determines the properties of the composing matter. To illustrate how our structure equations work, we obtain the mass-radii solutions for magnetized White Dwarfs. Our results show that the main effect of the magnetic field anisotropy in White Dwarfs structure is to cause a deformation of these objects. Since this effect is only relevant at low densities, it does not affect the maximum values of magnetized White Dwarf's masses, which remain under Chandrasekhar limit.

WDEC: A Code for Modeling White Dwarf Structure and Pulsations

Abstract The White Dwarf Evolution Code (WDEC), written in Fortran, makes models of white dwarf stars. It is fast, versatile, and includes the latest physics. The code evolves hot (∼100,000 K) input models down to a chosen effective temperature by relaxing the models to be solutions of the equations of stellar structure. The code can also be used to obtain g-mode oscillation modes for the models. WDEC has a long history going back to the late 1960s. Over the years, it has been updated and re-packaged for modern computer architectures and has specifically been used in computationally intensive asteroseismic fitting. Generations of white dwarf astronomers and dozens of publications have made use of the WDEC, although the last true instrument paper is the original one, published in 1975. This paper discusses the history of the code, necessary to understand why it works the way it does, details the physics and features in the code today, and points the reader to where to find the code and a user guide.

General relativistic effects in the structure of massive white dwarfs

In this work we investigate the structure of white dwarfs using the Tolman–Oppenheimer–Volkoff equations and compare our results with those obtained from Newtonian equations of gravitation in order to put in evidence the importance of general relativity (GR) for the structure of such stars. We consider in this work for the matter inside white dwarfs two equations of state, frequently found in the literature, namely, the Chandrasekhar and Salpeter equations of state. We find that using Newtonian equilibrium equations, the radii of massive white dwarfs ( $$M>1.3M_{\odot }$$ ) are overestimated in comparison with GR outcomes. For a mass of $$1.415M_{\odot }$$ the white dwarf radius predicted by GR is about 33% smaller than the Newtonian one. Hence, in this case, for the surface gravity the difference between the general relativistic and Newtonian outcomes is about 65%. We depict the general relativistic mass–radius diagrams as $$M/M_{\odot }=R/(a+bR+cR^2+dR^3+kR^4)$$ , where a, b, c and d are parameters obtained from a fitting procedure of the numerical results and $$k=(2.08\times 10^{-6}R_{\odot })^{-1}$$ , being $$R_{\odot }$$ the radius of the Sun in km. Lastly, we point out that GR plays an important role to determine any physical quantity that depends, simultaneously, on the mass and radius of massive white dwarfs.

Effects of magnetic fields and slow rotation in white dwarfs

In this work we use Hartle’s formalism to study the effects of rotation in the structure of magnetized white dwarfs within the framework of general relativity. We describe the inner matter by means of an equation of state for electrons under the action of a constant magnetic field, which introduces an anisotropy in the pressures. Solutions correspond to typical densities of white dwarfs and values of magnetic field below [Formula: see text][Formula: see text]G considering perpendicular and parallel pressures independently, as if associated to two different equations of state. Rotation effects obtained account for an increase of the maximum mass for both magnetized and nonmagnetized stable configurations, up to about [Formula: see text]. Further effects studied include the deformation of the stars, which become oblate spheroids and the solutions for other quantities of interest, such as the moment of inertia, quadrupolar momentum and eccentricity. In all cases, rotation effects are dominant with respect to those of the magnetic field.

On the maximum mass of magnetized white dwarfs

We develop a detailed and self-consistent numerical model for extremely-magnetised white dwarfs, which have been proposed as progenitors of overluminous Type Ia supernovae. This model can describe fully-consistent equilibria of magnetic stars in axial symmetry, with rotation, general-relativistic effects and realistic equations of state (including electron-ion interactions and taking into account Landau quantisation of electrons due to the magnetic field). We study the influence of each of these ingredients onto the white dwarf structure and, in particular, on their maximum mass. We perform an extensive stability analysis of such objects, with their highest surface magnetic fields reaching $\sim 10^{13}~G$ (at which point the star adopts a torus-like shape). We confirm previous speculations that although very massive strongly magnetised white dwarfs could potentially exist, the onset of electron captures and pycnonuclear reactions may severely limit their stability. Finally, the emission of gravitational waves by these objects is addressed, showing no possibility of detection by the currently planned space-based detector eLISA.

White Dwarf Pulsars and Very Massive Compact Ultra Magnetized White Dwarfs

In this work, we discuss white dwarf pulsars found recently making also reference of the possibility of some SGRs/AXPs being part of this class of pulsars. We also study the properties of very massive compact ultra magnetized white dwarfs that could be the progenitors candidates of super luminous type Ia supernovae, and also a previous stage of these white dwarf pulsars before the magnetic field decay.The structure of this ultra magnetized white dwarfs is obtained by solving the Einstein-Maxwell equations with a poloidal magnetic field in a fully general relativistic approach. The stellar interior is composed of a regular crystal lattice made of carbon ions immersed in a degenerate relativistic electron gas. We find that magnetized white dwarfs violate the standard Chandrasekhar mass limit significantly. We obtain a maximum white dwarf mass of around [Formula: see text] with an equatorial radius [Formula: see text] Km, a central magnetic field of [Formula: see text] G and [Formula: see text] G at the stellar surface.