Roche tomography of cataclysmic variables – I. Artefacts and techniques

Roche tomography is a technique used for imaging the Roche-lobe-filling secondary stars in cataclysmic variables (CVs). In order to interpret Roche tomograms correctly, one must determine whether features in the reconstruction are real, or the result of statistical or systematic errors. We explore the effects of systematic errors using reconstructions of simulated data sets, and show that systematic errors result in characteristic distortions of the final reconstructions that can be identified and corrected. In addition, we present a new method of estimating statistical errors on tomographic reconstructions using a Monte Carlo bootstrapping algorithm, and show this method to be much more reliable than Monte Carlo methods which 'jiggle' the data points in accordance with the size of their error bars.     

Roche tomography of cataclysmic variables – II. Images of the secondary stars in AM Her, QQ Vul, IP Peg and HU Aqr

We present a set of Roche tomography reconstructions of the secondary stars in the cataclysmic variables AM Her, QQ Vul, IP Peg and HU Aqr. The image reconstructions show distinct asymmetries in the irradiation pattern for all four systems that can be attributed to shielding of the secondary star by the accretion stream/column in AM Her, QQ Vul and HU Aqr, and increased irradiation by the bright-spot in IP Peg. We use the entropy landscape technique to derive accurate system parameters (   M ₁, M ₂  , i and γ) for the four binaries. In principle, this technique should provide the most reliable mass determinations available, since the intensity distribution across the secondary star is known. We also find that the intensity distribution can systematically affect the value of γ derived from circular orbit fits to radial velocity variations.     

Roche tomography of cataclysmic variables – III. Star-spots on AE Aqr

We present a Roche tomography reconstruction of the secondary star in the cataclysmic variable AE Aqr. The tomogram reveals several surface inhomogeneities that are due to the presence of large, cool star-spots. In addition to a number of lower latitude spots, the maps also show the presence of a large, high-latitude spot similar to that seen in Doppler images of rapidly rotating isolated stars, and a relative paucity of spots at a latitude of 40°. In total, we estimate that some 18 per cent of the Northern hemisphere of AE Aqr is spotted.
We have also applied the entropy landscape technique to determine accurate parameters for the binary system. We obtain optimal masses   M ₁= 0.74 M_⊙, M ₂= 0.50 M_⊙  , a systemic velocity  γ=−63 km s⁻¹  and an orbital inclination   i = 66°  .
Given that this is the first study to successfully image star-spots on the secondary star in a cataclysmic variable, we discuss the role that further studies of this kind may play in our understanding of these binaries.     

Indirect imaging of polars

Tomographic techniques of different flavour offer enormous diagnostic power for the analysis of magnetic cataclysmic binaries, particularly those of AM Herculis type, the so‐called polars. The three main ingredients of such systems, the donor star, the accretor and the accretion stream between the two stars, are investigated by Doppler tomography, Roche tomography and eclipse mapping methods. The indirect imaging methods reveal the structure, extent and ionization conditions in the accretion stream, they reveal the extent of the irradiation zone on the secondary star and constrain the mass ratio and the orbital inclination of the binary. We describe a new code for Roche tomography, the achievements and limitations of straight Doppler tomography and a new mapping technique tentatively called curtain tomography. This new technique will map emission line profiles to an accretion curtain making full use of the velocity and the photometric information. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

BVR observations and period variation of the near-contact binary ZZ Aurigae

BVR light curves of ZZ Aurigae were obtained with the 60-cm Cassegrain reflector at the Sobaek Observatory, Korea, between 2000 February and 2001 February. All collected times of minimum light, including our observations, were used for the period study. The period variation could be of quasi-sinusoidal form superposed on an upward parabola. A continuous period increase of  d P /d t =+2.3 × 10⁻⁸ d yr⁻¹  was determined for ZZ Aur. The period of quasi-sinusoidal variation is about ∼26–31 yr. Photometric solutions were found using the Wilson–Devinney method. The Roche configuration of ZZ Aur is that of an Algol-type semidetached system where the primary star nearly fills its Roche lobe and the secondary star fills its lobe. The spot model was used to explain the asymmetry in the light curve known as the O'Connell effect.     

UBV photometry, UV spectroscopy and radio observations of the peculiar binary V Sagittae

We have performed high-speed UBV photometric observations on the peculiar binary V Sagittae. Using three new eclipse timings we update the orbital ephemeris and convert it to a dynamical time-scale (TDB). We also searched for quasi-periodic oscillations but did not detect them. Using the Wilson–Devinney algorithm we have modelled the light curve to find the stellar parameters of V Sge. We find that the system is a detached binary but that the primary star is very close to filling its Roche lobe, while the secondary star fills 90 per cent of its Roche lobe volume. We find temperatures of the primary and the secondary star to be T ₁=41 000 K and T ₂=22 000 K. We find i =72° and masses of 0.8 M_⊙ and 3.3 M_⊙ for the primary and secondary stars respectively. De-archived Hubble Space Telescope ( HST ) spectroscopy of V Sge shows evidence of mass loss via a wind or winds. In addition we report radio observations of V Sge during an optical high state at 2 cm, 3.6 cm and 6 cm wavelengths. The 3.6 cm emission is increased by a factor of more than six compared with an earlier detection in a previous optical high state.     

BL Andromedae and GW Tauri: close binary stars in a key evolutionary stage

A photoelectric light curve of BL And is presented along with the first CCD light curve of GW Tau. Both objects are short-period eclipsing binaries and were observed in 2003 or 2004. Photometric elements were computed using the latest version of the Wilson–Van Hamme code. The results reveal that BL And is a semidetached system with the primary component filling its Roche lobe and the secondary one almost filling but still detached, while GW Tau is a marginal-contact binary system with a small degree of contact ( f = 10.9 per cent) and a large temperature difference of about 3100 K. All available eclipse times, including new ones, were analysed for each system. It was found that the orbital period of BL And is decreasing at the rate of  d P /d t =−2.36 × 10⁻⁸ (±0.09) d yr⁻¹  while that of GW Tau may be decreasing or oscillating. We think period decrease is more probable. The derived configuration and secular period decrease for BL And combined with the asymmetry of the light curve indicate that this system may evolve from the present semidetached phase into a contact stage, with mass transfer from the primary component to the secondary one through the L ₁ point, or that it might just undergo the broken stage predicted by the theory of thermal relaxation oscillations. In contrast, GW Tau is a marginal-contact binary in poor thermal contact and may be at the beginning of the contact phase.     

Mass transfer in eccentric binaries: the new oil-on-water smoothed particle hydrodynamics technique

To measure the onset of mass transfer in eccentric binaries, we have developed a two-phase smoothed particle hydrodynamics (SPH) technique. Mass transfer is important in the evolution of close binaries, and a key issue is to determine the separation at which mass transfer begins. The circular case is well understood and can be treated through the use of the Roche formalism. To treat the eccentric case, we use a newly developed two-phase system. The body of the donor star is made up from high-mass water particles, whilst the atmosphere is modelled with low-mass oil particles. Both sets of particles take part fully in SPH interactions. To test the technique, we model circular mass-transfer binaries containing a  0.6 M_⊙  donor star and a  1 M_⊙  white dwarf; such binaries are thought to form cataclysmic variable (CV) systems. We find that we can reproduce a reasonable CV mass-transfer rate, and that our extended atmosphere gives a separation that is too large by approximately 16 per cent, although its pressure scale height is considerably exaggerated. We use the technique to measure the semimajor axis required for the onset of mass transfer in binaries with a mass ratio of   q = 0.6  and a range of eccentricities. Comparing to the value obtained by considering the instantaneous Roche lobe at pericentre, we find that the radius of the star required for mass transfer to begin decreases systematically with increasing eccentricity.     

Large-scale circulations and energy transport in contact binaries

A hydrodynamic model for the energy transport between the components of a contact binary is presented. Energy is transported by a large-scale, steady circulation carrying high entropy matter from the primary to secondary component. The circulation is driven by the baroclinic structure of the common envelope, which is a direct consequence of the non-uniform heating at the inner critical Roche lobes due to unequal emergent energy fluxes of the components. The mass stream flowing around the secondary is bound to the equatorial region by the Coriolis force and its width is determined primarily by the flow velocity. Its bottom is separated from the underlying secondary's convection zone by a radiative transition layer acting as an insulator. For a typically observed degree of contact the heat capacity of the stream matter is much larger than radiative losses during its flow around the secondary. As a result, its effective temperature and entropy decrease very little before it returns to the primary. The existence of the stream changes insignificantly specific entropies of both convective envelopes and sizes of the components. Substantial oversize of the secondaries, required by the Roche geometry, cannot be explained in this way. The situation can, however, be explained by assuming that the primary is a main-sequence star whereas the secondary is in an advanced evolutionary stage with hydrogen depleted in its core. Such a configuration is reached past mass transfer with mass ratio reversal. Good agreement with observations is demonstrated by model calculations applied to actual W UMa-type binaries. In particular, a presence of the equatorial bulge moving with a relative velocity of  10–30 km s^−!  around both components of AW UMa is accounted for.     

Tomography of stellar non‐radial pulsations

The stellar surface imaging technique is used for studying stellar non‐radial pulsations on the basis of inversions of time series of variable line profiles without making assumptions on the specific shape of the pulsations. The inversion results in an image of the stellar surface in which sectoral and tesseral modes can be distinguished in many cases and the pulsational degree and the azimuthal order can be determined. The capability of the technique is studied with simulated data. Then, the surface imaging technique is applied to high‐resolution spectra of the rapidly rotating Beta Cep‐type star ω¹ Sco, which shows strong line‐profile variations. Stellar surface imaging is concluded to be a useful technique for pulsation‐mode identification. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of neutron stars in high-mass X-ray binaries

We consider the evolution of neutron stars during the X-ray phase of high-mass binaries. Calculations are performed assuming a crustal origin of the magnetic field. A strong wind from the companion can significantly influence the magnetic and spin behaviour of a neutron star even during the main-sequence life of the companion. In the course of evolution, the neutron star passes through four evolutionary phases ('isolated pulsar', propeller, wind accretion, and Roche lobe overflow). The model considered can naturally account for the observed magnetic fields and spin periods of neutron stars, as well as the existence of pulsating and non-pulsating X-ray sources in high-mass binaries. Calculations also predict the existence of a particular sort of high-mass binary with a secondary that fills its Roche lobe and a neutron star that does not accrete the overflowing matter because of fast spin.     

Differential rotation of cool active stars

The surface differential rotation of active solar‐type stars can be investigated by means of Doppler and Zeeman‐Doppler Imaging, both techniques enabling one to estimate the short‐term temporal evolution of photospheric structures (cools spots or magnetic regions). After describing the main modeling tools recently developed to guarantee a precise analysis of differential rotation in this framework, we detail the main results obtained for a small number of active G and K fast rotating stars. We evoke in particular some preliminary trends that can be derived from this sample, bearing the promise that major advances in this field will be achieved with the new generation of spectropolarimeters (ESPaDOnS/CFHT, NARVAL/TBL). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The light curve of the companion to PSR B1957+20

We present a new analysis of the light curve for the secondary star in the eclipsing binary millisecond pulsar system PSR B1957+20. Combining previous data and new data points at minimum from the Hubble Space Telescope , we have 100 per cent coverage in the R -band. We also have a number of new K _s-band data points, which we use to constrain the infrared magnitude of the system. We model this with the eclipsing light-curve (ELC) code. From the modelling with the ELC code we obtain colour information about the secondary at minimum light in BVRI and K . For our best-fitting model we are able to constrain the system inclination to 65°± 2° for pulsar masses ranging from 1.3 to  1.9  M_⊙  . The pulsar mass is unconstrained. We also find that the secondary star is not filling its Roche lobe. The temperature of the unirradiated side of the companion is in agreement with previous estimates and we find that the observed temperature gradient across the secondary star is physically sustainable.     

A non-main-sequence secondary in SY Cancri

Simultaneous spectroscopic and photometric observations of the Z Cam type dwarf nova SY Cancri were used to obtain absolute flux calibrations. A comparison of the photometric calibration with a wide-slit spectrophotometric calibration showed that either method is equally satisfactory. A radial velocity study of the secondary star, made using the far-red Na  i doublet, yielded a semi-amplitude of   K ₂= 127 ± 23 km s⁻¹  . Taking the published value of  86 ± 9 km s⁻¹  for K ₁ gives a mass ratio of   q = M ₂/ M ₁= 0.68 ± 0.14  ; this is very different from the value of  1.13 ± 0.35  quoted in the literature. Using the new lower mass ratio, and constraining the mass of the white dwarf to be within reasonable limits, then leads to a mass for the secondary star that is substantially less than would be expected for its orbital period if it satisfied a main-sequence mass–radius relationship. We find a spectral type of M0 that is consistent with that expected for a main-sequence star of the low mass we have found. However, in order to fill its Roche lobe, the secondary must be significantly larger than a main-sequence star of that mass and spectral type. The secondary is definitely not a normal main-sequence star.     

Time series photometric spot modelling – V. Phase coherence of spots on UZ Librae

We present spot models for nine years of continuous VI_c photometry of UZ Lib from 1993–2001. The relatively stable double‐humped light curve shape suggests extreme phase coherence. From the spot‐modelling analysis, we found that the major spots or spot groups are always located on the hemisphere facing the secondary star and exactly in the opposite hemisphere anti‐facing the secondary. Several single‐humped light curves and our suggested binary scenario rule out a pure ellipsoidal variability as the cause of the double‐humped light curve shape. We try to explain this preferred spot pattern with a magnetic‐field structure that connects the two components, as suggested earlier for RS CVn stars in general. A possible 4.8 years spot cycle is found from the long‐term brightness variations but needs confirmation. We rediscuss the basic astrophysical data of UZ Lib. The Hipparcos parallax is likely wrong, a possible reason could be that UZ Lib is e.g., a triple system.     

Preliminary results on the fundamental parameters of the eclipsing binary V398 Lacertae

The Hipparcos Space Astrometry Mission photometric observations of V398 Lac, led to the discovery of its variability, allowing to classify it as an eclipsing binary with an orbital period of about 5.4 days. This prompted us to acquire highresolution échelle spectra with the aim of performing accurate radial velocity measurements and to determine the main physical parameters of the system's components. We present, for the first time, a double‐lined radial velocity curve and determine the orbital and physical parameters of the two components, that can be classified both as late B‐type stars. In particular, we obtained an orbital inclination i ∼ 85°. With this value of the inclination, we deduced masses M₁ = 3.83±0.35 M_⊙ andM₂ = 3.29±0.32 M_⊙, and radii R₁ = 4.89±0.18 R_⊙ and R₂ = 2.45±0.11 R_⊙ for the more massive and less massive components, respectively. Both components are well inside their own Roche lobes. The mass ratio is M₂/M₁ ∼ 0.86. We derived also the projected rotational velocities as v₁ sin i = 79±2 km s^–1 and v² sin i = 19±2 km s^–1. Our measurements indicate that the rotation of the primary star is essentially pseudo‐synchronized with the orbital velocity at the periastron, while the secondary appears to rotate very slowly and has not yet attained synchronization. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Physical parameters of the O6.5V+B1V eclipsing binary system LS 1135

The 'All Sky Automated Survey' (ASAS) photometric observations of LS 1135, an O-type single-lined binary (SB1) system with an orbital period of 2.7 d, show that the system is also eclipsing performing a numerical model of this binary based on the Wilson–Devinney method. We obtained an orbital inclination     . With this value of the inclination, we deduced masses   M ₁∼ 30 ± 1 M_⊙  and   M ₂∼ 9 ± 1 M_⊙  , and radii   R ₁∼ 12 ± 1 R_⊙  and   R ₂∼ 5 ± 1 R_⊙  for primary and secondary components, respectively. Both the components are well inside their respective Roche lobes. Fixing the T _eff of the primary to the value corresponding to its spectral type (O6.5V), the T _eff obtained for the secondary component corresponds approximately to a spectral type of B1V. The mass ratio   M ₂/ M ₁∼ 0.3  is among the lowest known values for spectroscopic binaries with O-type components.     

Near-contact binaries among short-period Algols: the case of BF Velorum with a pulsating component

A photometric analysis of the short-period Algol eclipsing binary system BF Velorum based for the first time on complete BVRI CCD light curves is presented. The new photometric solution obtained with the Wilson-Devinney program reveals that BF Vel is a near-contact semi-detached system with its secondary component filling its Roche lobe. Moreover, we discovered pulsations of one member of the binary system, the analysis of which shows main frequencies of 44.9386 and 33.6731 cycles/day. Absolute elements of the system were calculated, and the evolutionary status of its members was estimated.      

The ever challenging emission‐line binary β Lyrae

A brief history of investigations of Lyr, an emission‐line binary and one of the first ever discovered Be stars is presented. A rather fast progress in the understanding of this enigmatic object during the past fifteen years is then discussed in some detail. The current picture of β Lyr is that it is an eclipsing binary in a stage of mass transfer between the components. The mass‐losing star is a B6‐8II object, with a mass of about 3 M_⊙, which is filling the Roche lobe and sending material towards its more massive companion at a rate of about 2 × 10^—5 M_⊙ yr^—1. This leads to the observed rapid increase of the orbital period at a rate of 19 s per year. The mass‐gaining star is as early B star with a mass of about 13 M_⊙. It is completely hidden inside an opaque accretion disk, jet‐like structures, perpendicular to the orbital plane and a light‐scattering halo above the poles of the star. The observed radiation of the disk corresponds to an effective temperature which is much lower than what would correspond to an early B star. The disk shields the radiation of the central star in the directions along the orbital plane and redistributes it in the directions perpendicular to it. That is why the mass‐losing star appears brighter of the two in the optical region of the spectrum. At present, rather reliable estimates of all basic properties of the binary and its components are available. However, in spite of great progress in understanding the system in recent years, some disagreement between the existing models and observed phase variations still remains, both for continuum and line spectrum, which deserves further effort.     

Numerical solutions of the equation concerning small adiabatic oscillations of pulsating components in double star systems

The equation governing small adiabatic radial oscillations for pulsating components in close binary stars modelled by tidally and rotationally distorted Roche geometry is solved numerically. With assumed initial conditions, solutions for systems with different mass ratios are presented. The changes in relative wave amplitude with various parameters are shown. The variation of the ratio of the pulsation frequencies of distorted to undistorted stars for given mass ratio of the binary systems is also investigated. Observational evidence is examined by using two data sets that show the modelled effects, by taking into account likely practical factors. The results show that the measured frequencies and amplitudes of surface waves can vary slightly for distorted stars in comparison to undistorted ones (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)