A numerical study of the rotational behavior of the white dwarf in DQ Herculis

It is well-known that the optical pulsations in DQ Her are due to emission from the magnetic poles of the white dwarf. As the white dwarf spins on its axis, the magnetic poles sweep into and out of the line of sight due to the fact that the magnetic axis and the spin axis are not aligned, that is, the DQ Her white dwarf is an `oblique rotator'. So, a central question is if an initially axisymmetric model 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 progressively increasing angle, the so-called `turn-over angle') is indeed susceptible to turn-over. For the puprose of resolving this problem, we compute several axisymmetric models of the DQ Her white dwarf. Our results show that, for both the rotation periods proposed on the basis of the observational evidence regarding the optical pulsations of DQ Her (i.e.,71 s or 142 s), the moment of inertia along the rotation axis is less than the corresponding moment of inertia along the remaining two principal axes of the axisymmetric configuration, I ₃₃ > I ₁₁(=I ₂₂). This is because toroidal magnetic field (tending to derive prolate equidensity surfaces) dominates over rotation (tending, in turn, to derive oblate equidensity surfaces), mainly in the interior of the star. The situation I ₁₁ < I ₃₃ is known as `dynamical asymmetry', and can cause a turn-over of the magnetic symmetry axis with respect to the rotation axis, eventually deriving a nonaxisymmetric configuration corresponding to the so-called `perpendicular rotator' with turn-over angle almost equal to 90^°. In this view, our results explain why the DQ Her white dwarf is now an oblique rotator. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

The changing X-ray light curves of the intermediate polar FO Aquarii

Comparison of five X-ray observations of the intermediate polar FO Aqr reveals that the morphology of the X-ray light curve changes considerably with time. In particular, power spectra of the 1988 Ginga   and 1993 ASCA   data reveal strong sideband and orbital variations, whereas the 1990 Ginga   observation does not. This suggests that the amount of stream-fed accretion varies with epoch, and the system was accreting predominantly from a disc in 1990.   In contrast to other intermediate polars, the X-ray spin-pulse profiles show significant variations between observations, ranging from relatively sinusoidal to sawtooth-shaped at medium energies. During the 1988 and 1990 observations a notch is visible at spin phase zero, due to the presence of an interpulse at phase 0.85, which is absent during the other observations. At lower energies a narrow pulse of emission is seen at spin phase 0.2.   We interpret the pulse profile from the 1990 Ginga   observation using a model for accretion from a disc on to a dipolar magnetic field, the axis of which is offset from the white dwarf centre by ∼ 0.15 white dwarf radii. In order to account for the later occurrence of the hardness-ratio maximum in 1988 and 1993, we suggest that the accretion-rate profile changes so that accretion is favoured along the field lines which trail the magnetic pole. This also accounts for the disappearance of the interpulse and notch in 1993.     

Magnetically moderated outbursts of WZ Sagittae

We argue that the quiescent value of the viscosity parameter of the accretion disc in WZ Sge may be  α_cold∼ 0.01  , in agreement with estimates of α_cold for other dwarf novae. Assuming the white dwarf in WZ Sge to be magnetic, we show that, in quiescence, material close to the white dwarf can be propelled to larger radii, depleting the inner accretion disc. The propeller therefore has the effect of stabilizing the inner disc and allowing the outer disc to accumulate mass. The outbursts of WZ Sge are then regulated by the (magnetically determined) evolution of the surface density of the outer disc at a radius close to the tidal limit. Numerical models confirm that the recurrence time can be significantly extended in this way. The outbursts are expected to be superoutbursts since the outer disc radius is forced to exceed the tidal (3:1 resonance) radius. The large, quiescent disc is expected to be massive, and to be able to supply the observed mass accretion rate during outburst. We predict that the long-term spin evolution of the white dwarf spin will involve a long cycle of spin-up and spin-down phases.     

The white dwarf in AE Aqr brakes harder

Taking advantage of the very precise de Jager et al. optical white dwarf orbit and spin ephemerides; ASCA , XMM–Newton and Chandra X-ray observations spread over 10 yr; and a cumulative 27-yr baseline, we have found that in recent years the white dwarf in AE Aqr is spinning down at a rate that is slightly faster than predicted by the de Jager et al. spin ephemeris. At the present time, the observed period evolution is consistent with either a cubic term in the spin ephemeris with     , which is inconsistent in sign and magnitude with magnetic dipole radiation losses, or an additional quadratic term with     , which is consistent with a modest increase in the accretion torques spinning down the white dwarf. Regular monitoring, in the optical, ultraviolet and/or X-rays, is required to track the evolution of the spin period of the white dwarf in AE Aqr.     

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.     

Spectroscopic evidence for two-pole accretion in the intermediate polar RX J0558+5353

We report on time-series optical spectrophotometry of the low-inclination intermediate polar RX  J0558+5353. This object exhibits coherent continuum and Hα line variations on both the orbital and white dwarf spin cycles. Despite the absence of a well-determined conjunction phase, the spectroscopic ephemeris combined with a favourable comparison with better-studied systems suggests that the impact between gas stream and accretion disc, or magnetosphere, drives orbital phenomena. Continuum variations over the spin cycle are consistent with previous broad-band data and indicate that accretion occurs on two poles of the primary star. We find no significant spin pulsations in the integrated line emission, but do detect variations in the resolved line profiles of Hα. Pulsed profiles are also suggestive of two-pole accretion. Double-peaked Hα line profiles and the non-detection of beat behaviour between the orbital and spin frequencies provide evidence for partial-disc transport in the system.     

The evolution of a rapidly accreting helium white dwarf to become a low-luminosity helium star

We have examined the evolution of merged low-mass double white dwarfs which become low-luminosity (or high-gravity) extreme helium stars. We have approximated the merging process by the rapid accretion of matter, consisting mostly of helium, on to a helium white dwarf. After a certain mass is accumulated, a helium shell flash occurs, the radius and luminosity increase and the star becomes a yellow giant. Mass accretion is stopped artificially when the total mass reaches a pre-determined value. As the helium-burning shell moves inwards with repeating shell flashes, the effective temperature gradually increases as the star evolves towards the helium main sequence. When the mass interior to the helium‐burning shell is approximately 0.25 M_⊙, the star enters a regime where it is pulsationally unstable. We have obtained radial pulsation periods for these models.
These models have properties very similar to those of the pulsating helium star V652 Her. We have compared the rate of period change of the theoretical models with that observed in V652 Her, as well as with its position on the Hertzsprung–Russell diagram. We conclude that the merger between two helium white dwarfs can produce a star with properties remarkably similar to those observed in at least one extreme helium star, and is a viable model for their evolutionary origin. Such helium stars will evolve to become hot subdwarfs close to the helium main sequence. We also discuss the number of low-luminosity helium stars in the Galaxy expected for our evolution scenario.     

Analysis of the oscillations in HST observations of the quiescent SU UMa type dwarf nova WZ Sagittae

An analysis of the UV oscillations in WZ Sge is presented, in which we obtain the oscillation amplitude spectra. We find a strong 27.9-s oscillation in our Hubble Space Telescope ( HST ) UV and zeroth-order light curves as well as weaker oscillations at 28.4 s in the UV and 29.1 s in the zeroth order. We find that the main oscillation amplitude spectrum can be fitted with static white dwarf spectra of about 17 000 K, an accretion hotspot of only a few 100 K hotter than the underlying white dwarf temperature or a variety of cool (<14 500 K) white dwarf pulsation amplitude spectra. A pulsating white dwarf can also explain the very blue colour of oscillations of different periods previously found in the optical. Comparing our results with those of Welsh et al., we see that the amplitude spectra of the main oscillations in WZ Sge measured with different periods in data sets from different epochs are similar to each other. Our results raise questions about using the magnetically accreting rotating white dwarf model to explain the oscillations. We suggest that the pulsating white dwarf model is still a viable explanation for the oscillations in WZ Sge.     

ASCA X-ray observations of EX Hya: spin-resolved spectroscopy

We analyse the spectral changes over the spin modulation in the intermediate polar EX Hya using archival ASCA data. We find that the modulation can be modelled as either (1) the effect of occultation of the accretion poles by the limb of the white dwarf, or (2) the effect of phase-dependent photoelectric absorption. We argue, on the basis of the partial X-ray eclipse, that the accretion columns in the system are tall, with shock height ∼ R _wd, and hence that the spin modulation is caused mainly by occultation. We find that the temperature distribution along the accretion shocks is incompatible with the calculations of Aizu, except for a restricted parameter regime with a high M _wd. Hence the material in the shock must cool faster than predicted by theory.     

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).     

Return mapping of phases and the analysis of the gravitational clustering hierarchy

We present spectroscopic and high-speed photometric data of the eclipsing polar V895 Cen. We find that the eclipsed component is consistent with it being the accretion regions on the white dwarf. This is in contrast to Stobie et al. who concluded that the eclipsed component was not the white dwarf. Further, we find no evidence for an accretion disc in our data. From our Doppler tomography results, we find that the white dwarf has   M ≳0.7 M_⊙  . Our indirect imaging of the accretion stream suggests that the stream is brightest close to the white dwarf. When we observed V895 Cen in its highest accretion state, emission was concentrated along field lines leading to the upper pole. There is no evidence for enhanced emission at the magnetic coupling region.     

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 simulation of the magnetic field and spin period evolution of accreting neutron stars

By means of the Monte Carlo method, we simulate the evolutionary distribution of accreting neutron stars (NSs) in the magnetic field versus spin period (B‐P) diagram where the accretion induced magnetic‐field decay model is exploited. The simulated results show that by mass accretion the B‐P distribution of the accreting NS would evolve along the equilibrium period line to a region with low field and short period. The B‐P distributions of the simulated accreting NSs are consistent with those of the observed millisecond pulsars (MSPs) after accretion of ∼ 0.1–0.2 M⊙. We also test the effects of the initial magnetic field and the spin period on the evolved B‐P distribution of the accreting NSs. It is shown that the evolved distributions of the simulated samples are independent of the selection of the initial condition when the NS magnetic field decays to a value less than ∼10¹⁰ G. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cataclysmic variable evolution: AM Her binaries and the period gap

AM Her variables – synchronized magnetic cataclysmic variables (CVs) – exhibit a different period distribution from other CVs across the period gap. We show that non-AM Her systems may infiltrate the longer-period end of the period gap if they are metal-deficient, but that the position and width of the gap in orbital period are otherwise insensitive to other binary parameters (except for the normalization of the braking rate). In AM Her binaries, magnetic braking is reduced as the wind from the secondary star may be trapped within the magnetosphere of the white dwarf primary. This reduced braking fills the period gap from its short-period end as the dipole magnetic moment of the white dwarf increases. The consistency of these models with the observed distribution of CVs, of both AM Her and non-AM Her type, provides compelling evidence supporting magnetic braking as the agent of angular momentum loss among long-period CVs, and its disruption as the explanation of the  2–3 h  period gap among non-magnetic CVs.     

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.     

X-ray confirmation of the new intermediate polar RX J1238–38

By finding a 2147-s X-ray pulsation in the recently identified ROSAT   source RX  1238–38 we confirm that it is a member of the intermediate polar class of cataclysmic variable. We analyse the spectral changes over the white dwarf spin cycle, but are unable to distinguish between competing mechanisms for the cause of the pulsation. RX  1238–38 has an anomalous ratio of spin period to orbital period, similar to that of EX Hya.     

First XMM-Newton observations of strongly magnetic cataclysmic variables – II. Timing studies of DP Leo and WW Hor

XMM-Newton was used to observe two eclipsing, magnetic cataclysmic variables, DP Leo and WW Hor, continuously for three orbital cycles each. Both systems were in an intermediate state of accretion. For WW Hor we also obtained optical light curves with the XMM-Newton Optical Monitor and from ground-based observations. Our analysis of the X-ray and optical light curves allows us to constrain physical and geometrical parameters of the accretion regions and derive orbital parameters and eclipse ephemerides of the systems. For WW Hor we directly measure horizontal and vertical temperature variations in the accretion column. From comparisons with previous observations we find that changes in the accretion spot longitude are correlated with the accretion rate. For DP Leo the shape of the hard X-ray light curve is not as expected for optically thin emission, showing the importance of optical depth effects in the post-shock region. We find that the spin period of the white dwarf is slightly shorter than the orbital period and that the orbital period is decreasing faster than expected for energy loss by gravitational radiation alone.     

The accretion flow in the discless intermediate polar V2400 Ophiuchi

RXTE observations confirm that the X-ray light curve of V2400 Oph is pulsed at the beat cycle, as expected in a discless intermediate polar. There are no X-ray modulations at the orbital or spin cycles, but optical line profiles vary with all three cycles. We construct a model for line-profile variations in a discless accretor, based on the idea that the accretion stream flips from one magnetic pole to the other, and show that this accounts for the observed behaviour over the spin and beat cycles. The minimal variability over the orbital cycle implies that (1) V2400 Oph is at an inclination of only ≈10°, and (2) much of the accretion flow is not in a coherent stream, but is circling the white dwarf, possibly as a ring of denser, diamagnetic blobs. We discuss the light that this sheds on disc formation in intermediate polars.     

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.