A numerical study of the rotational behavior of the white dwarf in DQ Herculis, II: the turn-over scenario

The optical pulsations in DQ Her are universally believed to be due to emission from the magnetic poles of the white dwarf. However, there is no way for a pulsation to be seen if the magnetic axis and the spin axis are aligned; whether the optical pulsation is seen directly from the magnetic poles or as a result of re-processing this beam from sides in an accretion disc, the magnetic and spin axes must be offset. This fact explains why the `oblique rotator' model has been adopted as a standard model for the DQ Her primary. In a recent paper, we have computed several axisymmetric models simulating the DQ Her white dwarf before its `turn-over' (where the term `turn-over' describes the process by which the magnetic axis gets inclining relative to the spin axis at a gradually increasing angle, the so-called `turn-over angle'). For such models, we have found that the moment of inertia along the rotation axis, I ₃₃, is less than the moment(s) of inertia along the two other principal axes, I ₁₁=I ₂₂. The situation I ₁₁>I ₃₃ is known as `dynamical asymmetry', and can cause a spontaneous turn-over of the magnetic axis with respect to the rotation axis . Consequently, the DQ Her white dwarf is either an oblique rotator undergoing its turn-over phase, or it is already qalmostequal a `perpendicular rotator', i.e., its turn-over angle is almost equal to 90^°. Assuming the first case, we study numerically the so-called `turn-over scenario', that is, a scenario on rotational evolution in which the turn-over phase is taken into account. We give emphasis on computations concerning the spin-down time rate of the DQ Her white dwarf due to turn-over (not to be confused with its spin-uptime rate due to accretion) for several possible values of the magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.     

Late evolution of cataclysmic variables: the loss of AM Her systems

The white dwarf in AM Her systems is strongly magnetic and keeps in synchronous rotation with the orbit by magnetic coupling to the secondary star. As the latter evolves through mass loss to a cool, degenerate brown dwarf it can no longer sustain its own magnetic field and coupling is lost. Angular momentum accreted then spins up the white dwarf and the system no longer appears as an AM Her system. Possible consequences are run-away mass transfer and mass ejection from the system. Some of the unusual cataclysmic variable systems at low orbital periods may be the outcome of this evolution.     

Evidence for pole switching in the magnetic cataclysmic variable BY Camelopardalis

An analysis of X-ray and optical light curves of the magnetic cataclysmic variable (MCV) BY Cam is presented. This system is one of three MCVs in which the spin period of the white dwarf and the binary orbital period differ by ∼1 per cent. As such these 'BY Cam' stars are important objects with which to probe the field structure of the magnetic white dwarf and ultimately the nature of synchronization of AM Her binaries. We confirm asynchronous rotation of the magnetic white dwarf with respect to the binary. We find evidence that the accretion stream accretes directly on to the white dwarf as in AM Her systems, but further, the stream impacts on to different magnetic poles over the course of the beat period. We present evidence that the optical and hard X-ray light curves modulate in phase, but together they are out of phase with the soft X-ray light curve. We confirm the spin down of the white dwarf which is expected to lead to the synchronization of the spin and orbital periods of BY Cam.     

Ubvri photometry of nova 1934 dq her during 1982–1995: Brightness variability

The principal results of a photometric investigation of Nova 1934 DQ Her during 1982–1995 are presented. Simultaneous high-speed UBVRI photometry was used to investigate for the first time the behavior of its brightness on time scales from several days to several years. Relationships are found between the changes in brightness of DQ Her in various regions of the spectrum and the corresponding changes in the energy distribution of its radiation. The observed variations in brightness of the system are caused by the variability in the radiation from the accretion disk with the white dwarf at the center. The brightness variations on the time scale of several days to several dozen days, may be caused by changes in the rate of accretion from the disk onto the white dwarf due to inherent disk instability or by irregular delivery of material in the jet from the red dwarf. Cyclic variations in brightness of DQ Her with an amplitude of several tenths of a magnitude and a characteristic time of about 5 yr, as well as the cyclic variations of the parameter "O-C" with the same characteristic time and amplitude of about 2–4 min may be the response of the accretion disk to activity of the red dwarf itself.Translated fromAstrofizika, Vol. 39, No. 1, pp. 41–55, January–March, 1996.     

The relation between the long-term X-ray and optical activity of the polar AM Her (RX J1816.2 + 4952)

We analyze the relation between the long-term (1996–2009) activity of the polar AM Her in the optical and hard X-ray spectral regions. We investigate the mean values of the intensities in the individual high-state episodes. We made use of the ASM/RXTE observations for a time-series analysis of the long-term variations in the 1.5–12 keV band. The optical data came from the AFOEV database. We reveal a complicated relation between the optical (I_O) and hard X-ray intensity (I_X). We argue that our observations cannot be explained by the variations of the orbital modulation in the high-state. Also, the precession of the spin axis of the white dwarf or asynchronous rotation of this object are unlikely in our case. We show that the basic properties of the emitting region (s) is (are) established in the early phase (several days long) of the high-state episode but they are not reproduced for every episode. The increase of the mass transfer rate from the donor that switches the polar from the low to the high-state also establishes a division of the emission released during the accretion process into various spectral regions that is valid only for a given episode. These results enable us a better understanding of the multifrequency behavior of polars on long time-scales.     

Search for and study of photometric variability in magnetic white dwarfs

We report the results of photometric observations of a number of magnetic white dwarfs in order to search for photometric variability in these stars. These V-band observations revealed significant variability in the classical highly magnetized white dwarf GRW+70?8247 with a likely period from several days to several dozen days and a half-amplitude of about 0_. ^m 04. Our observations also revealed the variability of the well-known white dwarf GD229. The half amplitude of its photometric variability is equal to about 0_. ^m 005, and the likely period of this degenerate star lies in the 10–20 day interval. This variability is most likely due to the rotation of the stars considered.We also discuss the peculiarities of the photometric variability in a number of other white dwarfs. We present the updated “magnetic field–rotation period” diagram for the white dwarfs.     

Helical magnetorotational instability of Taylor‐Couette flows in the Rayleigh limit and for quasi‐Kepler rotation

The magnetorotational instability (MRI) of differential rotation under the simultaneous presence of axial and azimuthal components of the (current‐free) magnetic field is considered. For rotation with uniform specific angular momentum the MHD equations for axisymmetric perturbations are solved in a local short‐wave approximation. All the solutions are overstable for B_z · B_ϕ ≠ 0 with eigenfrequencies approaching the viscous frequency. For more flat rotation laws the results of the local approximation do not comply with the results of a global calculation of the MHD instability of Taylor‐Couette flows between rotating cylinders. – With B_ϕ and B_z of the same order the traveling‐mode solutions are also prefered for flat rotation laws such as the quasi‐Kepler rotation. For magnetic Prandtl number Pm → 0 they scale with the Reynolds number of rotation rather than with the magnetic Reynolds number (as for standard MRI) so that they can easily be realized in MHD laboratory experiments. – Regarding the nonaxisymmetric modes one finds a remarkable influence of the ratio B_ϕ/B_z only for the extrema. For B_ϕ ≫ B_z and for not too small Pm the nonaxisymmetric modes dominate the traveling axisymmetric modes. For standard MRI with B_z ≫ B_ϕ, however, the critical Reynolds numbers of the nonaxisymmetric modes exceed the values for the axisymmetric modes by many orders so that they are never prefered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

VSX J074727.6 + 065050: A dwarf nova with a non-radially pulsating white dwarf primary

High speed photometric observations of the dwarf nova VSX J074727.6 + 065050 made in December 2009 during quiescence show an orbital modulation at P _orb =85.6 min. They also show that the star is a member of the relatively rare CV/ZZ group, i.e. the accreting white dwarf primary has non-radial pulsations. The two regions of oscillating power are at 684 s and 238 s. There is some evidence for hidden ∼1 μHz fine structure splitting, which has been seen in three other CV/ZZ stars.     

Capture radius and synchronization of the white dwarf in the unique magnetic cataclysmic system V1432 Aql

Results from two-color VR photometry of the unique cataclysmic magnetic variable star V1432 Aql and a theoretical model of these data are presented. The accuracy is improved by using the “mean-weighted comparison star” method. The derivative of the rotational period is dP/dt = −1.11(±0.016)·10⁻⁸. The characteristic synchronization time for the rotational and orbital motions of the white dwarf is 96.7±1.5 years, in good agreement with theory for the acceleration of an asynchronous propeller owing to the angular momentum of accreting matter. A third type of minimum detected in the light curve is interpreted in terms of the presence of an arc, or ring, rather than an accretion disk. A theoretical model is developed for determining the capture radius of accreted matter by the magnetic field of the white dwarf using the phase difference between the two types of minima associated with the axial rotation. This parameter is estimated to be 16–28 times the radius of the white dwarf for an inclined column model. A dependence of the main characteristics of the system on the mass of the white dwarf is derived which yields better values for the range of this quantity than those determined by indirect methods. For the assumed masses (M₁ = 0.9 M_⊙ and M₂ = 0.3 M_⊙) the estimated accretion rate is ∼7×10⁻¹⁰ M_⊙. It is shown that in a synchronizing polar the contribution to the change in the period by the variation in the angular momentum of the white dwarf is negligible compared to the accretion torque. In the future multicolor monitoring is needed for studying the spin-orbital synchronization and periodic changes in the accretion structure caused by “spinning” of the white dwarf. __________ Translated from Astrofizika, Vol. 50, No. 1, pp. 135–159 (February 2007).     

Exact MHD solutions for rotating,magnetic stars

Simple exact solutions of the magnetohydrodynamic equations are found for rotating, magnetic stars. The velocity and magnetic field are axisymmetric and purely toroidal, and the magnetic energy density equals the kinetic energy density. For constant mass density, the solution reduces to that of Chandrasekhar (1956), which is stable even against non-axisymmetric perturbations. For an ideal gas equation of state, the condition for radiative thermal equilibrium is solved to lowest order in the non-spherical perturbation. The velocity, magnetic field and non-spherical pressure and temperature perturbations all vanish within cones centered around the rotation axis, |cos |>x _i a zero of a Legendre polynomial. Low-order, long-period stellar oscillations may be excited by MHD instabilities near the equatorial region which become damped near the axis.     

Models of rapidly rotating neutron stars: remnants of accretion-induced collapse

Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion-induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high-density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis. The ratio of the rotational kinetic energy to the gravitational potential energy of these neutron stars ranges from 0.13 to 0.26, suggesting that some of these objects may have a non-axisymmetric dynamical instability that could emit a significant amount of gravitational radiation.     

Equilibrium Structures of Differentially Rotating and Tidally Distorted White Dwarf Models of Stars

In this paper we present a method for computing the equilibrium structures and various physical parameters of a primary component of the binary system assuming that the primary is more massive than the secondary and is rotating differentially according to the law of the w² = b₀ + b₁ × s² + b₂ × s⁴, w being the angular velocity of rotation of a fluid element distant s from the axis of rotation and b₀, b₁, b₂ suitably chosen numerical constants. This method utilizes the averaging approach of Kippenhahn and Thomas (1997) and the concept of Roche equipotentials in a manner earlier used by Mohan et al. (1997) to incorporate the effects of rotation and tidal distortions on the equilibrium structures of certain rotationally and tidally distorted stellar models. The use of the method has been illustrated by applying it to obtain the structures and some observable parameters of certain differentially rotating and tidally distorted binary systems whose primary component is assumed to be a white dwarf star.     

Structure of envelopes ejected by Novae

The paper contains an analysis of the structure of envelopes ejected during the outbursts of Novae. The data used for this purpose: (a) Direct photographs of envelopes and the photographs taken with the use of different colour filters; (b) Spectra of envelopes. The envelope of DQ Her is studied most carefully. The analysis of all available data for the envelopes around DQ Her and V 603 Aql permits us to outline a morphological model of these envelopes, see Figure 3. It appears, that the structure of both these envelopes is approximately identical and that the difference in the observed properties of the photographic images of the nebulae (Figure 2 and Figure 4) is connected with a difference in the orientation of the polar axes of the envelopes relative to the line of sight. The envelope ejected during the outburst of T Aur (Figure 5) reveals the same properties, which are characteristic for the envelopes of DQ Her and V 603 Aql.From this we conclude that the distribution of gases inside the envelopes of the majority of Novae is approximately of the same character. This speaks in favour of the presence of certain forces around many Novae, which guide the motion of ejected plasma along some quite definite directions inside rather small solid angles. It seems that the only conceivable forces of this type may be the forces of a magnetic nature. This hypothesis for example permits us to explain the difference between the envelope of GK Per (Figure 1) and the envelopes of DQ Her, V 603 Aql, T Aur (Figures 2, 4 and 5).Comparing the velocity of expansion of the envelope of DQ Her and the rate of change of its angular size we computed that the distance to DQ Her is equal to 320 pc.On the base of photographs of the envelope of DQ Her it is found that in 1968 the fluxF _H of radiation in the H-line was equal to (6±2)×10^–12 ergs/cm²sec, whereas the mass of the envelope was equal to 10²⁹ G and its electronic concentrationn _e to 2×10³ cm^–3. Several hypotheses, which may explain the stratification of emission from different elements inside the envelope are discussed.     

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).     

Multicolor Photometric Study of the NOVA V1494 Aql in 2002

R and I band CCD observations of the nova V1494 Aql during July-November 2002 are reported and the V, R, and I light curves are analyzed. The orbital light curve of this nova has an eclipse-like form with two unequal humps before and after the eclipse. The approach to the eclipse lasts twice as long as the emergence from it. The overall duration of the eclipse is about 0.45P _orb. The depth of eclipse increases with wavelength and averages 0^m.3 (V), 0^m.5 (R), and 0^m.7 (I). The secondary, shallow minimum has an average depth of 0^m.1 in R and I and about 0^m.03 in V. The hump at phase 0.65 is higher than the one at phase 0.17. The most probable explanation for the observed variations in the light with the phase of the orbital period may be self eclipsing of the accretion column in the magnetic exploding variable (white dwarf) together with partial eclipsing of the accretion region by the secondary component.     

ROSAT observations of V471 Tauri, showing that stellar activity is determined by rotation, not age

I present pointed ROSAT PSPC observations of the pre-cataclysmic binary V471 Tauri. The hard X-ray emission (>0.4 keV) is not eclipsed by the K star, demonstrating conclusively that this component cannot be emitted by the white dwarf. Instead I show that its spectrum and luminosity are consistent with coronal emission from the tidally spun-up K star. The star is more active than other K stars in the Hyades, but equally active as K stars in the Pleiades with the same rotation periods, demonstrating that rotation — and not age — is the key parameter in determining the level of stellar activity.   The soft X-ray emission (<0.4 keV) is emitted predominately by the white dwarf and is modulated on its spin period. I find that the pulse profile is stable on time-scales of hours and years, supporting the idea that it is caused by the opacity of accreted material. The profile itself shows that the magnetic field configuration of the white dwarf is dipolar and that the magnetic axis passes through the centre of the star.   There is an absorption feature in the light curve of the white dwarf, which occurs at a time when our line of sight passes within a stellar radius of the K star. The column density and duration of this feature imply a volume and mass for the absorber that are similar to those of coronal mass ejections of the Sun.   Finally I suggest that the spin–orbit beat period detected in the optical by Clemens et al. may be the result of the interaction of the K-star wind with the magnetic field of the white dwarf.     

Magnetic fields and rotation of the white dwarfs 40 Eri B and WD 0009+501

We describe the results of our magnetometric monitoring of two white dwarfs: 40 Eri B and WD 0009+501. We found periodic variations in the longitudinal magnetic field of 40 Eri B. The field variability with an amplitude of ～4 kG and a zero mean is discussed in terms of an oblique rotator model. The rotation period is ～5 h 17 min, but there is another period of 2 h 25 min that may be related to nondipolar field components. The published projected rotational velocities of 40 Eri B measured from a narrow non-LTE Hα peak V sin i?8 km s^?1 are in good agreement with our measurements of the magnetic field and the rotation period. The combined effect of magnetic and rotational broadening of the central Hα component constrains the rotation period, P? 5.2 h. We discovered the rotation period (1.83 h) of the magnetic white dwarf WD 0009+501. The period was found from the periodically varying magnetic field of the star with a mean 〈B_e〉 = ?42.3±5.4 kG and a half-amplitude of 32.0±6.8 kG.     

Magnetic Model of HD 2453

A model is constructed for the magnetic field of the star HD 2453, which has a very long rotation period (P=521^d). It is found that the structure of the field corresponds to the model of a dipole shifted by r=0.09R from the center. The angle of inclination of the axis of the dipole to the axis of rotation, =5°; that is, the star is viewed almost from its equator of rotation and magnetic equator. This explains the low amplitude of the phase dependence of the magnetic field, Be(P), and the low amplitude of the photometric variability. The field at the magnetic poles is equal to Bp=+4400 and -7660 G. The magnetic field parameters turn out to be close to those obtained by Landstreet and Mathys assuming a dipole-quadrupole-octupole model. A Mercator map of the magnetic field distribution of HD 2453 is produced.     

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.     

IGR J16547-1916/1RXS J165443.5-191620—a new intermediate polar from the INTEGRAL galactic survey

We present the results of our optical identification of the X-ray source IGR J16547-1916 detected by the INTEGRAL observatory during a deep all-sky survey. Analysis of the spectroscopic data from the SWIFT and INTEGRAL observatories in the X-ray energy band and from the BTA (Special Astrophysical Observatory) telescope in the optical band has shown that the source is most likely an intermediate polar—an accreting white dwarf with the mass ofM _WD μ 0.85M _⊙ binary system. Subsequent studies of the object’s rapid variability with the RTT-150 telescope have confirmed this conclusion by revealing periodic pulsations of its optical emission with a period of ≈550 s.