Mass transfer in eccentric binary stars

The concept of Roche lobe overflow is fundamental to the theory of interacting binaries. Based on potential theory, it is dependent on all the relevant material corotating in a single frame of reference. Therefore if the mass losing star is asynchronous with the orbital motion or the orbit is eccentric, the simple theory no longer applies and no exact analytical treatment has been found. We use an analytic approximation whose predictions are largely justified by smoothed particle hydrodynamic simulations (SPH). We present SPH simulations of binary systems with the same semi-major axis   a = 5.55 R_⊙  , masses   M ₁= 1 M_⊙, M ₂= 2 M_⊙  and radius   R ₁= 0.89 R_⊙  for the primary star but with different eccentricities   e = 0.4, 0.5, 0.6  and 0.7. In each case the secondary star is treated as a point mass. When   e = 0.4  no mass is lost from the primary while at   e = 0.7  catastrophic mass transfer, partly through the L₂ point, takes place near periastron. This would probably lead to common-envelope evolution if star 1 were a giant or to coalescence for a main-sequence star. In between, at   e ≥ 0.5  , some mass is lost through the L₁ point from the primary close to periastron. However, rather than being all accreted by the secondary, some of the stream appears to leave the system. Our results indicate that the radius of the Roche lobe is similar to circular binaries when calculated for the separation and angular velocity at periastron. Part of the mass loss occurs through the L₂ point.     

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.     

Low- and intermediate-mass close binary evolution and the initial–final mass relation

Using Eggleton's stellar evolution code, we carry out 150 runs of Population I binary evolution calculations with the initial primary mass between 1 and 8 M_⊙, the initial mass ratio     between 1.1 and 4, and the onset of Roche lobe overflow (RLOF) at an early, middle or late Hertzsprung-gap stage. We assume that RLOF is conservative in the calculations, and find that the remnant mass of the primary may change by more than 40 per cent over the range of initial mass ratio or orbital period, for a given primary mass. This is contrary to the often-held belief that the remnant mass depends only on the progenitor mass if mass transfer begins in the Hertzsprung gap. We fit a formula, with an error less than 3.6 per cent, for the remnant (white dwarf) mass as a function of the initial mass M _1i of the primary, the initial mass ratio q _i and the radius of the primary at the onset of RLOF. We also find that a carbon–oxygen white dwarf with mass as low as 0.33 M_⊙ may be formed if the initial mass of the primary is around 2.5 M_⊙.     

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.     

Spectroscopic and photometric observations of the eclipsing star UV Leo

High-resolution spectroscopic observations around the Hα line and BVRI photometry of the eclipsing short-period RS CVn star UV Leo are presented. The simultaneous light-curve solution and radial velocity-curve solution led to the following values of the global parameters of the binary: temperatures   T ₁= 6000 ± 100 K  and   T ₂= 5970 ± 20 K  ; masses   M ₁= 0.976 ± 0.067 M_⊙  and   M ₂= 0.931 ± 0.052 M_⊙  ; separation   a = 3.716 ± 0.048 R_⊙  ; orbital inclination     ; radii   R ₁= 1.115 ± 0.052 R_⊙  and   R ₂= 1.078 ± 0.051 R_⊙  ; equatorial velocities   V ₁= 98.8 ± 2.3 km s⁻¹  and   V ₂= 89.6 ± 2.7 km s⁻¹  . These results lead to the conclusion that the two components of UV Leo are slightly oversized for their masses and lie within the main-sequence band on the mass–radius diagram, close to the isochrone 9 × 10¹⁰ yr.     

The component masses of the cataclysmic variable V347 Puppis

We present time-resolved spectroscopy and photometry of the double-lined eclipsing cataclysmic variable V347 Pup (=LB 1800). There is evidence of irradiation on the inner hemisphere of the secondary star, which we correct for using a model to give a secondary-star radial velocity of   K _R= 198 ± 5 km s⁻¹  . The rotational velocity of the secondary star in V347 Pup is found to be   v sin  i = 131 ± 5 km s⁻¹  and the system inclination is   i = 840 ± 23  . From these parameters we obtain masses of   M ₁= 0.63 ± 0.04 M_⊙  for the white dwarf primary and   M ₂= 0.52 ± 0.06 M_⊙  for the M0.5V secondary star, giving a mass ratio of   q = 0.83 ± 0.05  . On the basis of the component masses, and the spectral type and radius of the secondary star in V347 Pup, we find tentative evidence for an evolved companion. V347 Pup shows many of the characteristics of the SW Sex stars, exhibiting single-peaked emission lines, high-velocity S-wave components and phase-offsets in the radial velocity curve. We find spiral arms in the accretion disc of V347 Pup and measure the disc radius to be close to the maximum allowed in a pressureless disc.     

Cooling curves and initial models for low-mass white dwarfs (<0.25 M⊙) with helium cores

We present a detailed calculation of the evolution of low-mass (<0.25 M_⊙) helium white dwarfs. These white dwarfs (the optical companions to binary millisecond pulsars) are formed via long-term, low-mass binary evolution. After detachment from the Roche lobe, the hot helium cores have a rather thick hydrogen layer with mass between 0.01 and 0.06 M_⊙. As a result of mixing between the core and outer envelope, the surface hydrogen content ( X _surf) is 0.5–0.35 , depending on the initial value of the heavy element Z and the initial secondary mass. We found that the majority of our computed models experience one or two hydrogen shell flashes. We found that the mass of the helium dwarf in which the hydrogen shell flash occurs depends on the chemical composition. The minimum helium white dwarf mass in which a hydrogen flash takes place is 0.213 M_⊙ ( Z =0.003), 0.198 M_⊙ ( Z =0.01), 0.192 M_⊙ ( Z =0.02) or 0.183 M_⊙ ( Z =0.03). The duration of the flashes (independent of chemical composition) is between a few ×10⁶ and a few ×10⁷ yr. In several flashes the white dwarf radius will increase so much that it forces the model to fill its Roche lobe again. Our calculations show that the cooling history of the helium white dwarf depends dramatically on the thickness of the hydrogen layer. We show that the transition from a cooling white dwarf with a temporarily stable hydrogen-burning shell to a cooling white dwarf in which almost all residual hydrogen is lost in a few thermal flashes (via Roche lobe overflow) occurs between 0.183 and 0.213 M_⊙ (depending on the heavy element value).     

Orbital parameters, masses and distance to β Centauri determined with the Sydney University Stellar Interferometer and high-resolution spectroscopy

The bright southern binary star β Centauri (HR 5267) has been observed with the Sydney University Stellar Interferometer (SUSI) and spectroscopically with the European Southern Observatory Coude Auxiliary Telescope and Swiss Euler telescope at La Silla. The interferometric observations have confirmed the binary nature of the primary component and have enabled the determination of the orbital parameters of the system. At the observing wavelength of 442 nm the two components of the primary system have a magnitude difference of  0.15 ± 0.02  . The combination of interferometric and spectroscopic data gives the following results: orbital period  357.00 ± 0.07 d  , semimajor axis  25.30 ± 0.19 mas  , inclination  674 ± 03  , eccentricity  0.821 ± 0.003  , distance  102.3 ± 1.7 pc  , primary and secondary masses   M ₁= M ₂= 9.1 ± 0.3 M_⊙  and absolute visual magnitudes of the primary and secondary   M _{1 V} =−3.85 ± 0.05  and   M _{2 V} =−3.70 ± 0.05  , respectively. The high degree of accuracy of the results offers a fruitful starting point for future asteroseismic modelling of the pulsating binary components.     

Optical spectroscopy and Doppler tomography of Cygnus X-2

We present phase resolved optical spectroscopy and Doppler tomography of V1341 Cygni, the optical counterpart to the neutron star low-mass X-ray binary (LMXB) Cygnus X-2 (Cyg X-2). We derive a radial velocity (RV) curve for the secondary star, finding a projected RV semi-amplitude of   K ₂= 79 ± 3 km s⁻¹  , leading to a mass function of  0.51 ± 0.06 M_⊙, ∼30  per cent lower than the previous estimate. We tentatively attribute the lower value of K ₂ (compared to that obtained by other authors) to variations in the X-ray irradiation of the secondary star at different epochs of observations. The limited phase coverage and/or longer timebase of previous observations may also contribute to the difference in K ₂. Our value for the mass function implies a primary mass of  1.5 ± 0.3 M_⊙  , somewhat lower than previous dynamical estimates, but consistent with the value found by analysis of type-I X-ray bursts from this system. Our Doppler tomography of the broad He  ii λ4686 line reveals that most of the emission from this line is produced on the irradiated face of the donor star, with little emission from the accretion disc. In contrast, the Doppler tomogram of the N  iii λ4640.64 Bowen blend line shows bright emission from near the gas stream/accretion disc impact region, with fainter emission from the gas stream and secondary star. This is the first LMXB for which the Bowen blend is dominated by emission from the gas stream/accretion disc impact region, without comparable emission from the secondary star. This has implications for the interpretation of Bowen blend Doppler tomograms of other LMXBs for which the ephemeris may not be accurately known.     

Optical spectroscopy of the quiescent counterpart to EXO 0748−676

We present phase resolved optical spectroscopy and X-ray timing of the neutron star X-ray binary EXO 0748−676 after the source returned to quiescence in the autumn of 2008. The X-ray light curve displays eclipses consistent in orbital period, orbital phase and duration with the predictions and measurements before the return to quiescence. Hα and He  i emission lines are present in the optical spectra and show the signature of the orbit of the binary companion, placing a lower limit on the radial velocity semi-amplitude of   K ₂ > 405 km s⁻¹  . Both the flux in the continuum and the emission lines show orbital modulations, indicating that we observe the hemisphere of the binary companion that is being irradiated by the neutron star. Effects due to this irradiation preclude a direct measurement of the radial velocity semi-amplitude of the binary companion; in fact, no stellar absorption lines are seen in the spectrum. Nevertheless, our observations place a stringent lower limit on the neutron star mass of   M ₁ > 1.27 M_⊙  . For the canonical neutron star mass of   M ₁= 1.4 M_⊙  , the mass ratio is constrained to  0.075 < q < 0.105  .     

KPD 0422 + 5421: a new short-period subdwarf B/white dwarf binary

The subdwarf B (sdB) star KPD 0422 + 5421 was discovered to be a single-lined spectroscopic binary with a period of P  = 0.090 1795 ± (3 × 10⁻⁷) d (2 h 10 min). The U B light curves display an ellipsoidal modulation with amplitudes of ≈ 0.02 mag. The sdB star contributes nearly all of the observed flux. This and the absence of any reflection effect suggest that the unseen companion star is small (i.e. R _comp ≈ 0.01 R_⊙) and therefore degenerate. We modelled the U B light curves and derived i  = 78.05° ± 0.50° and a mass ratio of q  =  M _comp/ M _sdB = 0.87 ± 0.15. The sdB star fills 69 per cent of its Roche lobe. These quantities may be combined with the mass function of the companion [ f ( M ) = 0.126 ± 0.028 M_⊙] to derive M _sdB = 0.72 ± 0.26 M_⊙ and M _comp = 0.62 ±  0.18 M_⊙. We used model spectra to derive the effective temperature, surface gravity and helium abundance of the sdB star. We found T _eff = 25 000 ± 1500 K, log g  = 5.4 ± 0.1 and [He/H] = −1.0. With a period of 2 h 10 min, KPD 0422 + 5421 has one of the shortest known orbital periods of a detached binary. This system is also one of only a few known binaries that contain a subdwarf B star and a white dwarf. Thus KPD 0422 + 5421 represents a relatively unobserved, and short-lived, stage of binary star evolution.     

Kinematical studies of the low-mass X-ray binary GR Mus (XB 1254–690)

We present simultaneous high-resolution optical spectroscopy and X-ray data of the X-ray binary system GR Mus (XB 1254–690), obtained over a full range of orbital phases. The X-ray observations are used to re-establish the orbital ephemeris for this source. The optical data include the first spectroscopic detection of the donor star in this system through the use of the Doppler Tomography technique on the Bowen fluorescence blend (∼4630–4650 Å). In combination with an estimate for the orbital parameters of the compact object using the wings of the He  ii λ4686 emission line, dynamical mass constraints of  1.20 ≤ M _X /M_⊙≤ 2.64  for the neutron star and  0.45 ≤ M ₂/M_⊙≤ 0.85  for the companion are derived.     

The mass of the neutron star in Centaurus X-3

We report new radial velocity observations of V779 Cen, the optical companion to the X-ray pulsar Cen X-3. Two sets of results at two epochs yield very different radial velocity amplitudes. We demonstrate there are problems with the first set, not least that they are incompatible with the observed duration of the X-ray eclipse for all inclination angles. The anomalously high radial velocities are probably a result of changes in the outflow behaviour of the companion star. Although there is no reason to doubt the results from the second epoch when viewed in isolation, given the anomalous radial velocities of the first epoch, they must be treated with caution. Using these data, the semi-amplitude of the resulting radial velocity curve is found to be 24.4±4.1 km s⁻¹. Given the accurately measured semi-amplitude of the orbit of the pulsar, 414.3±0.9 km s⁻¹, the mass ratio of the system is 0.059±0.010. The inclination of the system is found to be 702±27, assuming that the optical component fills its Roche lobe, and that the system is in synchronous rotation. Hence the mass of the neutron star is 1.21±0.21 M_⊙, and the mass of the optical companion is 20.5±0.7 M_⊙. This is a smaller uncertainty than previously reported values, and is consistent with the canonical neutron star mass of 1.4 M_⊙.
In addition, we use our spectra to determine the spectral class of V779 Cen to be O6-7II-III.     

Gamma-ray emission from pulsars: strength of the acceleration field in the outer gap

In this study we present and re-analyse the historical, 1889–1998, light curve (LC) of the eclipsing symbiotic binary AR Pav. For the first time, we show that the timing of mid-points of eclipses observed during a quiescent phase obeys a quadratic ephemeris, with an initial orbital period P ₀=605.18 d and a rate of period change     .
We determined a distance to the system of 5.8±1.5 kpc, the mass ratio of the giant to the hot star, M _g M _h=0.4±0.1, the mass of the giant, M _g=1.8+1/−0.5 M_⊙ and its radius, R _g=167±15 R_⊙.
During quiescence, the LC has characteristic features similar to those observed in cataclysmic variables (CVs). It can be well reproduced by a model of a large accretion disc surrounding the hot star. However, it is probable that the geometry of the transferred material in the Roche lobe of the accretor in AR Pav is different from that of CVs.
During active phases the shape of the LC changes considerably. A complex wave-like variation developed as a function of the orbital phase with an amplitude of ∼1 mag. It is interpreted in terms of a collisionally heated emission region located on the giant surface and arising from the hot star eruption.     

Violent stellar merger model for transient events

We derive the constraints on the mass ratio for a binary system to merge in a violent process. We find that the secondary-to-primary stellar mass ratio should be  0.003 ≲ ( M ₂/ M ₁) ≲ 0.15  . A more massive secondary star will keep the primary stellar envelope in synchronized rotation with the orbital motion until merger occurs. This implies a very small relative velocity between the secondary star and the primary stellar envelope at the moment of merger, and therefore very weak shock waves, and low-flash luminosity. A too low-mass secondary will release small amount of energy, and will expel small amount of mass, which is unable to form an inflated envelope. It can, however, produce a quite luminous but short flash when colliding with a low-mass main-sequence star.
Violent and luminous mergers, which we term mergebursts, can be observed as V838 Monocerotis-type events, where a star undergoes a fast brightening lasting days to months, with a peak luminosity of up to  ∼10⁶ L_⊙  followed by a slow decline at very low effective temperatures.     

Optical spectroscopy of X-Mega targets – II. The massive double-lined O-type binary HD 93205

A new high-quality set of orbital parameters for the O-type spectroscopic binary HD 93205 has been obtained combining échelle and coudé CCD observations. The radial velocity orbits derived from the He  ii λ 4686 Å (primary component) and He  i λ 4471 Å (secondary component) absorption lines yield semi-amplitudes of 133±2 and 314±2 km s⁻¹ for each binary component, resulting in minimum masses of 31 and 13 M_⊙ ( q =0.42) . We also confirm for the binary components the spectral classification of O3 V+ O8 V previously assigned. Assuming for the O8 V component a 'normal' mass of 22–25 M_⊙ we would derive for the primary O3 V a mass of 'only' 52–60 M_⊙ and an inclination of about 55° for the orbital plane. We have also determined for the first time a period of apsidal motion for this system, namely 185±16 yr using all available radial velocity data sets of HD 93205 (from 1975 to 1999). Phase-locked variations of the X-ray emission of HD 93205 consisting of a rise of the observed X-ray flux near periastron passage are also discussed.     

Superhumps in the helium dwarf nova KL Draconis

We report on the discovery of a 25.5-min superhump period for the suspected helium dwarf nova system KL Draconis in a high state. The presence of superhumps combined with the previously observed helium spectrum and large-amplitude photometric variations confirm that KL Dra is an AM CVn system similar to CR Bootis, V803 Cen and CP Eridani. We also find a low-state photometric period at 25.0 min that we suggest may be the orbital period. With this assumption, we estimate   q =0.075  ,   M ₁=0.76 M_⊙  and   M ₂=0.057 M_⊙  .     

The mass ratio and the orbital parameters of the sdOB binary AA Doradus

The time sequence of 105 spectra covering one full orbital period of AA Dor has been analysed. Direct determination of   V  sin  i   for the sdOB component from 97 spectra outside of the eclipse for the lines Mg  ii 4481 Å and Si  iv 4089 Å clearly indicated a substantially smaller value than estimated before. Detailed modelling of line-profile variations for eight spectra during the eclipse for the Mg  ii 4481 Å line, combined with the out-of-eclipse fits, gave   V  sin  i = 31.8 ± 1.8 km s⁻¹  . The previous determinations of   V  sin  i   , based on the He  ii 4686 Å line, appear to be invalid because of the large natural broadening of the line. With the assumption of the solid-body, synchronous rotation of the sdOB primary, the measured values of the semi-amplitude K ₁ and   V  sin  i   lead to the mass ratio   q = 0.213 ± 0.013  which in turn gives K ₂ and thus the masses and radii of both components. The sdOB component appears to be less massive than assumed before,   M ₁= 0.25 ± 0.05 M_⊙  , but the secondary has its mass–radius parameters close to theoretically predicted for a brown dwarf,   M ₂= 0.054 ± 0.010 M_⊙  and   R ₂= 0.089 ± 0.005 R_⊙  . Our results do not agree with the recent determination of Vŭcković et al. based on a K ₂ estimate from line-profile asymmetries.     

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.     

J-band spectroscopy of cataclysmic variables

We present time-resolved, J ‐band (1.025–1.340 μm) infrared spectra of the short-period dwarf novae (DNe) WZ Sge and VY Aqr, and single spectra of the short-period DN EF Peg and the nova-like variable PX And. There is some evidence in the spectra of VY Aqr and EF Peg that we have detected the secondary star, both in the continuum slope and also through the possible presence of spectral features. The spectra of WZ Sge and PX And, on the other hand, show no evidence for the secondary star, with upper limits for its contribution to the J ‐band light of 10 and 20 per cent respectively. The spectral type of the secondary in WZ Sge is constrained to be later than M7.5V. Using skew mapping, we have been able to derive a value for the radial velocity semi-amplitude of the secondary star in VY Aqr of K _R =320±70 km s⁻¹, which in conjunction with K _W from Thorstensen & Taylor gives a mass ratio of q =0.15±0.04.