Investigating the structure of the accretion disc in WZ Sge from multiwaveband time-resolved spectroscopic observations – II

We present our second paper describing multiwaveband time-resolved spectroscopy of WZ Sge. We analyse the evolution of both optical and IR emission lines throughout the orbital period and find evidence, in the Balmer lines, for an optically thin accretion disc and an optically thick hotspot. Optical and IR emission lines are used to compute radial velocity curves. Fits to our radial velocity measurements give an internally inconsistent set of values for K ₁, γ and the phase of red-to-blue crossing. We present a probable explanation for these discrepancies, and provide evidence for similar behaviour in other short orbital period dwarf novae. Selected optical and IR spectra are measured to determine the accretion disc radii. Values for the disc radii are found to be strongly dependent on the assumed WD mass and binary orbital inclination. However, the separation of the peaks in the optical emission line (i.e., an indication of the outer disc radius) has been found to be constant during all phases of the supercycle period over the last 40 years.     

The stream impact region in the disc of WZ Sge

We report the observation of new features in the spectrum of the cataclysmic variable WZ Sge. The disc eclipse is seen as a well-defined structure in the Hα line. From phases 0.25 to 0.5 an absorption feature of the same shape as the emission S wave is seen in this line, but redshifted by ∼ 200 km s⁻¹. Two possible interpretations of this feature are given, both of which imply that it originates at the impact point of the stream on the disc edge. In addition, evidence is found for substructure in the velocity map of the spot. Emission from line-emitting post-shock material, extending to about 60° downstream from the continuum hotspot, is seen in the Doppler map in the form of a tail extending from the hotspot. A theoretical estimate shows that such a tail is to be expected as a consequence of the post-impact hydrodynamics of the stream. A new determination of the system parameters is made. They agree with those of Gilliland et al.; in particular, the data support a high primary mass. The variation of Hα surface brightness with distance from the primary is flatter, in the inner regions, than the r ^−1.5 dependence found by Horne for other cataclysmic variables in quiescence.     

Erratum: Spiral structure in the accretion disc of the binary IP Pegasi

The paper 'Spiral structure in the accretion disc of the binary IP Pegasi' was published in Mon. Not. R. Astron. Soc. 290 , L28–L32 (1997). Figs 1 and 2 of the paper (grey-scale images) did not reproduce well, and are reprinted here (Fig. 1 overleaf). Colour versions of the images are available on the World Wide Web:http://www-star.st-and.ac.uk/^∼ds10/spirals.html     

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.     

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.     

Simulations of spiral structure in the accretion disc of IP Pegasi during outburst

We consider the implications of the detection of spiral structure in the accretion disc of the binary IP Pegasi. We use numerical simulations of the development of a disc outburst to construct predicted Doppler tomograms, which are found to be in close agreement with the observations if the spiral pattern arises as a transient feature when the disc expands viscously at the start of the outburst. The good agreement of such viscous disc simulations with the data is consistent with models in which most of the angular momentum transport in the disc originates in internal stresses rather than globally excited waves or shocks. Future detailed observations of the development of transient spiral features offer the potential to measure the dependence of the disc viscosity on the local physical conditions in the disc.     

Post-common-envelope binaries from SDSS – I. 101 white dwarf main-sequence binaries with multiple Sloan Digital Sky Survey spectroscopy

We present a detailed analysis of 101 white dwarf main-sequence binaries (WDMS) from the Sloan Digital Sky Survey (SDSS) for which multiple SDSS spectra are available. We detect significant radial velocity variations in 18 WDMS, identifying them as post-common-envelope binaries (PCEBs) or strong PCEB candidates. Strict upper limits to the orbital periods are calculated, ranging from 0.43 to 7880 d. Given the sparse temporal sampling and relatively low spectral resolution of the SDSS spectra, our results imply a PCEB fraction of ≳15 per cent among the WDMS in the SDSS data base. Using a spectral decomposition/fitting technique we determined the white dwarf effective temperatures and surface gravities, masses and secondary star spectral types for all WDMS in our sample. Two independent distance estimates are obtained from the flux-scaling factors between the WDMS spectra, and the white dwarf models and main-sequence star templates, respectively. Approximately one-third of the systems in our sample show a significant discrepancy between the two distance estimates. In the majority of discrepant cases, the distance estimate based on the secondary star is too large. A possible explanation for this behaviour is that the secondary star spectral types that we determined from the SDSS spectra are systematically too early by one to two spectral classes. This behaviour could be explained by stellar activity, if covering a significant fraction of the star by cool dark spots will raise the temperature of the interspot regions. Finally, we discuss the selection effects of the WDMS sample provided by the SDSS project.     

Indirect imaging of the accretion stream in eclipsing polars – III. HU Aquarii low state

We apply our technique for indirect imaging of the accretion stream to the polar HU Aqr, using eclipse profiles observed when the system was in a low-accretion state. The eclipse profile is different from that in the high state, and more variable from cycle to cycle. We find that the stream maps are brightest near the white dwarf and there is no significant brightening in the threading region. In the low state the stream threads on to the magnetic field closer to the L₁ point than in the high state, with a footpoint of the accreting field line at high latitude. We then produce maps of the accretion region from polarimetry using Stokes imaging. These show that the majority of the accretion occurs near the equator. The difference between the maps may be explained if most of the stream material is not emitting significantly in the low state. If so, neither the stream eclipse mapping nor Doppler tomography techniques will trace the bulk of the accretion flow between the two stars.     

On the accretion mode of the intermediate polar V1025 Centauri

The long white-dwarf spin periods in the magnetic cataclysmic variables EX Hya and V1025 Cen imply that if the systems possess accretion discs then they cannot be in equilibrium. It has been suggested that instead they are discless accretors in which the spin-up torques resulting from accretion are balanced by the ejection of part of the accretion flow back towards the secondary. We present phase-resolved spectroscopy of V1025 Cen aimed at deducing the nature of the accretion flow, and compare this with simulations of a discless accretor. We find that both the conventional disc-fed model and the discless-accretor model have strengths and weaknesses, and that further work is needed before we can decide which applies to V1025 Cen.     

Mass transfer in tidally unstable compact binaries

The 2001 outburst of WZ Sagittae has shown the most compelling evidence yet for an enhancement of the mass-transfer rate from the donor star during a dwarf nova outburst in the form of hotspot brightening. I show that, even in this extreme case, the brightening can be attributed to tidal heating near the interaction point of an accretion stream with the expanding edge of an eccentric accretion disc, with no need at all for an increase in the mass-transfer rate. Furthermore, I confirm previous suggestions that an increase in mass-transfer rate through the stream damps any eccentricity in an accretion disc and suppresses the appearance of superhumps, in contradiction to observations. Tidal heating is expected to be most significant in systems with small mass ratios. It follows that systems like WZ Sagittae – which has a tiny mass ratio – are those most likely to show a brightening in the hotspot region.     

Indirect imaging of the accretion stream in eclipsing polars – II. HU Aquarii

We apply our technique for indirect imaging of the accretion stream to the polar HU Aquarii, using eclipse profiles observed when the system was in a high accretion state. The accretion stream is relatively luminous, contributing as much as the accretion region on the white dwarf, or more, to the overall system brightness. We model the eclipse profiles using a model stream consisting of a ballistic trajectory from the L1 point followed by a magnetically channelled trajectory that follows a dipole field line out of the orbital plane. We perform model fits using two geometries: a stream that accretes on to both footpoints of the field line, and a stream that accretes only on to the footpoint of the field line above the orbital plane. The stream images indicate that the distribution of emission along the stream is not a simple function of the radial distance from the white dwarf. The stream is redirected by the magnetic field of the white dwarf at a distance 1.0–1.3×10¹⁰ cm from the white dwarf; this implies a mass transfer rate in the range 8–76×10¹⁶ g s⁻¹. The absorption dips in the light curve indicate that the magnetically entrained part of the stream moves from 42° to 48° from the line of centres over the three nights of observation. This is in close agreement with the results of the one-footpoint models, suggesting that this is the more appropriate geometry for these data. The stream images show that, in almost all sections of the stream, the flux peaks in B and is successively fainter in U , V and R .     

Infrared spectroscopy of cataclysmic variables – III. Dwarf novae below the period gap and nova-like variables

We present K -band spectra of the short-period dwarf novae YZ Cnc, LY Hya, BK Lyn, T Leo, SW UMa and WZ Sge, the nova-like variables DW UMa, V1315 Aql, RW Tri, VY Scl, UU Aqr and GP Com, and a series of field dwarf stars with spectral types ranging from K2 to M6.
The spectra of the dwarf novae are dominated by emission lines of H  i and He  i . The large velocity and equivalent widths of these lines, in conjunction with the fact that the lines are double-peaked in the highest inclination systems, indicate an accretion disc origin. In the case of YZ Cnc and T Leo, for which we obtained time-resolved data covering a complete orbital cycle, the emission lines show modulations in their equivalent widths that are most probably associated with the bright spot (the region where the gas stream collides with the accretion disc). There are no clear detections of the secondary star in any of the dwarf novae below the period gap, yielding upper limits of 10–30 per cent for the contribution of the secondary star to the observed K -band flux. In conjunction with the K -band magnitudes of the dwarf novae, we use the derived secondary star contributions to calculate lower limits to the distances to these systems.
The spectra of the nova-like variables are dominated by broad, single-peaked emission lines of H  i and He  i – even the eclipsing systems we observed do not show the double-peaked profiles predicted by standard accretion disc theory. With the exception of RW Tri, which exhibits Na  i , Ca  i and ¹²CO absorption features consistent with a M0V secondary contributing 65 per cent of the observed K -band flux, we find no evidence for the secondary star in any of the nova-like variables. The implications of this result are discussed.     

The effective temperature distribution of steady-state, mass-losing accretion discs

Mass loss appears to be a common phenomenon among astrophysical accretion disc systems. An outflow emanating from an accretion disc can act as a sink for mass, angular momentum and energy, and can therefore alter the dissipation rates and effective temperatures across the disc. Here, the radial distributions of dissipation rate and effective temperature across a Keplerian, steady-state, mass-losing accretion disc are derived, using a simple, parametric approach that is sufficiently general to be applicable to many types of dynamical disc–wind models.
Effective temperature distributions for mass-losing accretion discs in cataclysmic variables are shown explicitly, with parameters chosen to describe both radiation-driven and centrifugally driven outflows. For realistic wind mass-loss rates of a few per cent, only centrifugally driven outflows – particularly those in which mass loss is concentrated in the inner disc – are likely to alter the effective temperature distribution of the disc significantly. Accretion discs that drive such outflows could produce spectra and eclipse light curves that are noticeably different from those produced by standard, conservative discs.