The origin of the magnetic fields in white dwarfs

Magnetic white dwarfs with fields in excess of ∼10⁶ G (the high field magnetic white dwarfs; HFMWDs) constitute about ∼10 per cent of all white dwarfs and show a mass distribution with a mean mass of  ∼0.93 M_⊙  compared to  ∼0.56 M_⊙  for all white dwarfs. We investigate two possible explanations for these observations. First, that the initial–final mass relationship (IFMR) is influenced by the presence of a magnetic field and that the observed HFMWDs originate from stars on the main sequence that are recognized as magnetic (the chemically peculiar A and B stars). Secondly, that the IFMR is essentially unaffected by the presence of a magnetic field, and that the observed HFMWDs have progenitors that are not restricted to these groups of stars. Our calculations argue against the former hypothesis and support the latter. The HFMWDs have a higher than average mass because on the average they have more massive progenitors and not because the IFMR is significantly affected by the magnetic field. A requirement of our model is that ∼40 per cent of main-sequence stars more massive than  ∼4.5 M_⊙  must either have magnetic fields in the range of ∼10–100 G, which is below the current level of detection, or generate fields during subsequent stellar evolution towards the white dwarf phase. In the former case, the magnetic fields of the HFMWDs could be fossil remnants from the main-sequence phase consistent with the approximate magnetic flux conservation.     

Magnetic fields and rotation in white dwarfs and neutron stars

Recent spectropolarimetric observations of Ap and Bp stars with improved sensitivity have suggested that most Ap and Bp stars are magnetic with dipolar fields of at least a few hundred gauss. These new estimates suggest that the range of magnetic fluxes found for the majority of magnetic white dwarfs is similar to that of main-sequence Ap–Bp stars, thus strengthening the empirical evidence for an evolutionary link between magnetism on the main sequence and magnetism in white dwarfs. We draw parallels between the magnetic white dwarfs and the magnetic neutron stars and argue that the observed range of magnetic fields in isolated neutron stars  ( B_p ∼ 10¹¹–10¹⁵ G)  could also be explained if their mainly O-type progenitors have effective dipolar fields in the range of a few gauss to a few kilogauss, assuming approximate magnetic flux conservation with the upper limit being consistent with the recent measurement of a field of   B_p ∼ 1100 G  for θ Orion C.
In the magnetic field–rotation diagram, the magnetic white dwarfs can be divided into three groups of different origin: a significant group of strongly magnetized slow rotators  ( P _rot∼ 50 –100 yr)  that have originated from single-star evolution, a group of strongly magnetized fast rotators  ( P _rot∼ 700 s)  , typified by EUVE J0317–853, that have originated from a merger, and a group of modest rotators ( P _rot∼ hours–days) of mixed origin (single-star and CV-type binary evolution). We propose that the neutron stars may similarly divide into distinct classes at birth , and suggest that the magnetars may be the counterparts of the slowly rotating high-field magnetic white dwarfs.     

The evolution of iron-core white dwarfs

Recent measurements by Hipparcos present observational evidence supporting the existence of some white dwarf (WD) stars with iron-rich core composition. In connection with this, the present paper is aimed at exploring the structure and evolution of iron-core WDs by means of a detailed and updated evolutionary code. In particular, we examined the evolution of the central conditions, neutrino luminosity, surface gravity, crystallization, internal luminosity profile and ages. We find that the evolution of iron-rich WDs is markedly different from that of their carbon–oxygen counterparts. In particular, cooling is strongly accelerated (up to a factor of 5 for models with pure iron composition) as compared with the standard case. Thus, if iron WDs were very numerous, some of them would have had time enough to evolve at lower luminosities than that corresponding to the fall-off in the observed WD luminosity function.     

Theoretical model of a magnetic white dwarf

In this paper a theoretical model of a magnetic white dwarf is studied. All numerical calculations are performed under the assumption of a spherically symmetric star. The obtained equation of state is stiffer with the increase of value of the magnetic field (B). Numerical values of the maximum mass and radius are presented. The influence of the magnetic field on the results is evident. Finally the departure from the condition of isothermality of a degenerate electron gas in the gravitational field is discussed.     

Combination frequencies in the Fourier spectra of white dwarfs

Combination frequencies are observed in the Fourier spectra of pulsating DA and DB white dwarfs, along with frequencies that are associated with stellar gravity modes. They appear at the sum and difference frequencies of the stellar modes. Brickhill proposed that the combination frequencies result from mixing of the eigenmode signals by a depth-varying surface convection zone when undergoing pulsation. The depth changes cause time-dependent thermal impedance.
Following Brickhill's proposal, we developed analytical expressions for the amplitudes and phases of these combination frequencies. The parameters that appear in these expressions are the depth of the stellar convection zone when at rest, the sensitivity of this depth towards changes in the stellar effective temperature, the inclination angle of the stellar pulsation axis with respect to the line of sight, and lastly the spherical degrees of the eigenmodes involved in the mixing. Adopting credible values for these parameters, we apply our expressions to DA and DB variable white dwarfs. We find reasonable agreement between theory and observation, although some discrepancies remain unexplained. It is possible to identify the spherical degrees of the pulsation modes using the combination frequencies.     

Gravitational radiation from differentially rotating and oscillating white dwarfs

We examine the possible emission of gravitational waves from white dwarfs undergoing self-similar oscillations driven by the energy released during relaxation of their differential rotation. Two distributions of the initial angular momentum are considered. It is assumed that 1% of the energy dissipated by a rotating white dwarf is converted into the energy of self-similar oscillations and, therefore, into gravitational radiation. The relative amplitude of the gravitational radiation from an isolated white dwarf at a distance of 50 pc is found to be less than 10⁻²⁷. The emission from the galactic population of white dwarfs may create a background which overlaps the random cosmological background of gravitational radiation for the improved decihertz detectors currently being proposed. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 231–242 (May 2006).     

Hydrogen-model atmospheres for white dwarf stars

We present a detailed calculation of model atmospheres for DA white dwarfs. Our atmosphere code solves the atmosphere structure in local thermodynamic equilibrium with a standard partial linearization technique, which takes into account the energy transfer by radiation and convection. This code incorporates recent improved and extended data base of collision-induced absorption by molecular hydrogen. We analyse the thermodynamic structure and emergent flux of atmospheres in the range 2500 T _eff60 000 K and 6.5log  g 9.0. Bolometric correction and colour indices are provided for a subsample of the model grid. Comparison of the colours is made with published observational material and results of other recent model calculations.
Motivated by the increasing interest in helium-core white dwarfs, we analyse the photometric characteristics of these stars during their cooling, using evolutionary models recently available. Effective temperatures, surface gravities, masses and ages have been determined for some helium-core white dwarf candidates, and their possible binary nature is briefly discussed.     

Circumstellar features in hot DA white dwarfs

We present a phenomenological study of highly ionized, non-photospheric absorption features in high spectral resolution vacuum ultraviolet spectra of 23 hot DA white dwarfs. Prior to this study, four of the survey objects (Feige 24, REJ 0457−281, G191−B2B and REJ 1614−085) were known to possess these features. We find four new objects with multiple components in one or more of the principal resonance lines: REJ 1738+665, Ton 021, REJ 0558−373 and WD 2218+706. A fifth object, REJ 2156−546, also shows some evidence of multiple components, though further observations are required to confirm the detection. We discuss possible origins for these features including ionization of the local interstellar environment, the presence of material inside the gravitational well of the white dwarf, mass loss in a stellar wind and the existence of material in an ancient planetary nebula around the star. We propose ionization of the local interstellar medium as the origin of these features in G191−B2B and REJ 1738+665, and demonstrate the need for higher-resolution spectroscopy of the sample, to detect multiple interstellar medium velocity components and to identify circumstellar features that may lie close to the photospheric velocity.     

Full evolution of low-mass white dwarfs with helium and oxygen cores

We study the full evolution of low-mass white dwarfs with helium and oxygen cores. We revisit the age dichotomy observed in many white dwarf companions to millisecond pulsar on the basis of white dwarf configurations derived from binary evolution computations. We evolve 11 dwarf sequences for helium cores with final masses of 0.1604, 0.1869, 0.2026, 0.2495, 0.3056, 0.3333, 0.3515, 0.3844, 0.3986, 0.4160 and  0.4481 M_⊙  . In addition, we compute the evolution of five sequences for oxygen cores with final masses of 0.3515, 0.3844, 0.3986, 0.4160 and  0.4481 M_⊙  . A metallicity of   Z = 0.02  is assumed. Gravitational settling, chemical and thermal diffusion are accounted for during the white dwarf regime. Our study reinforces the result that diffusion processes are a key ingredient in explaining the observed age and envelope dichotomy in low-mass helium-core white dwarfs, a conclusion we arrived at earlier on the basis of a simplified treatment for the binary evolution of progenitor stars. We determine the mass threshold where the age dichotomy occurs. For the oxygen white dwarf sequences, we report the occurrence of diffusion-induced, hydrogen-shell flashes, which, as in the case of their helium counterparts, strongly influence the late stages of white dwarf cooling. Finally, we present our results as a set of white dwarf mass–radius relations for helium and oxygen cores.     

Evolutionary calculations of carbon dredge-up in helium envelope white dwarfs

We investigate the evolution of cooling helium atmosphere white dwarfs using a full evolutionary code, specifically developed to follow the effects of element diffusion and gravitational settling on white dwarf cooling. The major difference between this work and previous work is that we use more recent opacity data from the OPAL project. Since, in general, these opacities are higher than those available 10 years ago, at a given effective temperature, convection zones go deeper than in models with older opacity data. Thus convective dredge-up of observationally detectable carbon in helium atmosphere white dwarfs can occur for thicker helium layers than found by Pelletier et al. We find that the range of observed C to He ratios in different DQ white dwarfs of similar effective temperature is well explained by a range of initial helium layer mass between 10⁻³ and 10⁻² M⊙, in good agreement with stellar evolution theory, assuming a typical white dwarf mass of 0.6 M⊙. We also predict that oxygen will be present in DQ white dwarf atmospheres in detectable amounts if the helium layer mass is near the lower limit compatible with stellar evolution theory. Determination of the oxygen abundance has the potential of providing information on the profile of oxygen in the core and hence on the important ¹²C(α,γ)¹⁶O reaction rate.     

Gravitational radiation from white dwarfs with rough surfaces

A white dwarf rotating at a maximal angular velocity can take a form of a triaxial ellipsoid due to the rotation and to the presence of mountains on its surface. Such an object emits gravitational waves at a frequency of 2, where is the angular velocity of rotation, and the source of the radiated energy is the rotational kinetic energy. It is shown that the gravitational waves from rapidly rotating white dwarfs at an average distance of 50 pc from an terrestrial observer have an amplitude on the order of 10^–24, so they can be detected by the new generation of detectors. Gravitational radiation from a pulsating white dwarf with a rough surface is also examined. It is shown that quasiradial pulsations of a white dwarf are long-lived; that is, once perturbed, a white dwarf will emit gravitational waves during all lifetime.Translated from Astrofizika, Vol. 48, No. 1, pp. 69–78 (February 2005).     

Gravitational radiation from strongly magnetized white dwarfs

The magnetic fields of white dwarfs distort their shape generating an anisotropic moment of inertia. A magnetized white dwarf that rotates obliquely relative to the symmetry axis has a mass quadrupole moment that varies in time, so it will emit gravitational radiation. The Laser Interferometer Space Antenna ( LISA ) mission may be able to detect the gravitational waves from two nearby, rapidly rotating white dwarfs.     

A new magnetic white dwarf: PG 2329+267

We have discovered that the white dwarf PG 2329+267 is magnetic, and, assuming a centred dipole structure, has a dipole magnetic field strength of approximately 2.3 MG. This makes it one of only approximately 4 per cent of isolated white dwarfs with a detectable magnetic field. Linear Zeeman splitting, as well as quadratic Zeeman shifts, is evident in the hydrogen Balmer sequence and circular spectropolarimetry reveals ∼10 per cent circular polarization in the two displaced σ components of Hα. We suggest from comparison with spectra of white dwarfs of known mass that PG 2329+267 is more massive than typical isolated white dwarfs, in agreement with the hypothesis that magnetic white dwarfs evolve from magnetic chemically peculiar Ap and Bp type main-sequence stars.