Constraining the orbital orientation of η Carinae from H Paschen lines

During the past decade, several observational and theoretical works have provided evidence of the binary nature of η Carinae. Nevertheless, there is still no direct determination of the orbital parameters, and the different current models give contradictory results. The orbit is, in general, assumed to coincide with the Homunculus equator although the observations are not conclusive. Among all systems, η Car has the advantage that it is possible to observe both the direct emission of line transitions in the central source and its reflection by the Homunculus, which is dependent on the orbital inclination. In this work, we studied the orbital phase-dependent hydrogen Paschen spectra reflected by the south-east lobe of the Homunculus to constrain the orbital parameters of η Car and determine its inclination with respect to the Homunculus axis. Assuming that the emission excess originates in the wind–wind shock region, we were able to model the latitude dependence of the spectral line profiles. For the first time, we were able to estimate the orbital inclination of η Car with respect to the observer and to the Homunculus axis. The best fit occurs for an orbital inclination to the line of sight of   i ∼ 60°± 10°  , and   i *∼ 35°± 10°  with respect to the Homunculus axis, indicating that the angular momenta of the central object and the orbit are not aligned. We were also able to fix the phase angle of conjunction as  ∼−40°  , showing that periastron passage occurs shortly after conjunction.     

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.     

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.     

A first orbital solution for the very massive 30 Dor main-sequence WN6h+O binary R145

We report the results of a spectroscopic and polarimetric study of the massive, hydrogen-rich WN6h stars R144 (HD 38282 = BAT99-118 = Brey 89) and R145 (HDE 269928 = BAT99-119 = Brey 90) in the Large Magellanic Cloud. Both stars have been suspected to be binaries by previous studies (R144: Schnurr et al.; R145: Moffat). We have combined radial-velocity (RV) data from these two studies with previously unpublished polarimetric data. For R145, we were able to establish, for the first time, an orbital period of 158.8 d, along with the full set of orbital parameters, including the inclination angle i , which was found to be   i = 38°± 9°  . By applying a modified version of the shift-and-add method developed by Demers et al., we were able to isolate the spectral signature of the very faint line companion star. With the RV amplitudes of both components in R145, we were thus able to estimate their absolute masses. We find minimum masses   M _WRsin³ i = 116 ± 33 M_⊙  and   M _Osin³ i = 48 ± 20 M_⊙  for the WR and the O component, respectively. Thus, if the low-inclination angle were correct, resulting absolute masses of the components would be at least 300 and  125 M_⊙  , respectively. However, such high masses are not supported by brightness considerations when R145 is compared to systems with known very high masses such as NGC 3603-A1 or WR20a. An inclination angle close to  90°  would remedy the situation, but is excluded by the currently available data. More and better data are thus required to firmly establish the nature of this puzzling, yet potentially very massive and important system. As to R144, however, the combined data sets are not sufficient to find any periodicity.     

The massive double-lined O-type binary HD 165052

We present a new optical spectroscopic study of the O-type binary HD 165052 based on high- and intermediate-resolution CCD observations. We re-investigated the spectral classification of the binary components, obtaining spectral types of O6.5 V and O7.5 V for the primary and secondary, respectively, finding that both stars display weak C  iii λ 5696 emission in their spectra. We also determined a radial-velocity orbit for HD 165052 with a period of  2.95510±0.00001 d  , and semi-amplitudes of 94.8 and  104.7±0.5 km s^-1  , resulting in a mass ratio   Q =0.9  . From a comparison with previous radial-velocity determinations, we found evidence of apsidal motion in the system. Several signatures of wind–wind collision, such as phase-locked variability of the X-ray flux and the Struve–Sahade effect, are also considered. It was also found that the reddening in the region should be normal, in contrast with previous determinations.     

A first detailed study of the colliding wind WR+O binary WR 30a

We present a detailed, extensive investigation of the photometric and spectroscopic behaviour of WR 30a. This star is definitely a binary system with a period around 4.6 d. We propose the value         . The identification of the components as WO4+O5((f)) indicates a massive evolved binary system; the O5 component is a main-sequence or, more likely, a giant star. The radial velocities of the O star yield a circular orbit with an amplitude         and a mass function of 0.013     . The spectrum of WR 30a exhibits strong profile variations of the broad emission lines that are phase-locked with the orbital period. We report the detection of the orbital motion of the WO component with     , but this should be confirmed by further observations. If correct, it implies a mass ratio     . The star exhibits sinusoidal light variations of amplitude 0.024 mag peak-to-peak with the minimum of light occurring slightly after the conjunction with the O star in front. On the basis of the phase-locked profile variations of the C  iv λ 4658 blend in the spectrum of the WO, we conclude that a wind–wind collision phenomenon is present in the system. We discuss some possibilities for the geometry of the interaction region.     

Transit timing effects due to an exomoon – II

In our previous paper, we evaluated the transit duration variation (TDV) effect for a co-aligned planet-moon system at an orbital inclination of   i = 90°  . Here, we will consider the effect for the more general case of   i ≤ 90°  and an exomoon inclined from the planet-star plane by Euler rotation angles  α, β  and γ. We find that the TDV signal has two major components, one due to the velocity variation effect described in our first paper and one new component due to transit impact parameter variation. By evaluating the dominant terms, we find the two effects are additive for prograde exomoon orbits, and deductive for retrograde orbits. This asymmetry could allow for future determination of the orbital sense of motion. We re-evaluate the ratio of TDV and transit timing variation effects, η, in the more general case of an inclined planetary orbit with a circular orbiting moon and find that it is still possible to directly determine the moon's orbital separation from just the ratio of the two amplitudes, as first proposed in our previous paper.     

Spectroscopic solution of the star QX Cas

High-resolution spectroscopic observations around the Hα line of the binary star QX Cas covering the whole orbital period are presented. Our radial velocity solution, the first ever determined, requires an eccentric orbit with the following orbital parameters: eccentricity,   e = 0.22 ± 0.01  ; longitude of periastron,  ω= 45°± 5°  ; semi-amplitudes of the radial velocity curves of the primary and secondary stars,   K ₁ sin  i = 125.8 ± 0.9 km s⁻¹  and   K ₂ sin  i = 144.8 ± 1.1 km s⁻¹  ; gamma velocity,   V ₀= 65.1 ± 0.5 km s⁻¹  ; and mass ratio,   q = 0.869 ± 0.013  . The corresponding lower limits of the masses of the components and their separation are         , and   a sin  i = 31.34 ± 0.48 R_⊙  .     

Aquila X-1: a low-inclination soft X-ray transient

We have obtained I -band photometry of the neutron star X-ray transient Aql X-1 during quiescence. We find a periodicity at 2.487 cycles d⁻¹, which we interpret as twice the orbital frequency (19.30±0.05 h). Folding the data on the orbital period, we model the light-curve variations as the ellipsoidal modulation of the secondary star. We determine the binary inclination to be 20°–30° (90 per cent confidence) and also determine the 95 per cent upper limits to the radial velocity semi-amplitude and rotational broadening of the secondary star to be 117 and 50 km s⁻¹, respectively.     

Theoretical X-ray line profiles from colliding wind binaries

We present theoretical X-ray line profiles from a range of model colliding wind systems. In particular, we investigate the effects of varying the stellar mass-loss rates, the wind speeds and the viewing orientation. We find that a wide range of theoretical line profile shapes is possible, varying with orbital inclination and phase. At or near conjunction, the lines have approximately Gaussian profiles, with small widths  (HWHM ∼ 0.1 v _∞)  and definite blueshifts or redshifts (depending on whether the star with the weaker wind is in front or behind). When the system is viewed at quadrature, the lines are generally much broader  (HWHM ∼ v _∞)  , flat-topped and unshifted. Local absorption can have a major effect on the observed profiles – in systems with mass-loss rates of a few times  10⁻⁶ M_⊙ yr⁻¹  the lower energy lines  ( E  ≲ 1 keV)  are particularly affected. This generally results in blueward-skewed profiles, especially when the system is viewed through the dense wind of the primary. The orbital variation of the linewidths and shifts is reduced in a low-inclination binary. The extreme case is a binary with   i = 0°  , for which we would expect no line profile variation.     

Physical properties of active stars and stellar systems

We study spectra of 18 active stars and stellar systems, drawn from lists of known active binaries or newly discovered extreme-ultraviolet and soft X-ray sources. Using spectral synthesis and template modelling, we measure (often for the first time) a variety of physical properties of the stars, including spectral types, luminosities and v  sin  i values. We report direct observation of previously undetected secondary components in three systems, and refine the orbital elements for two of these (HR 7275 and HD 217344).     

Precession and nutation in the η Carinae binary system: evidence from the X-ray light curve

It is believed that η Carinae is actually a massive binary system, with the wind–wind interaction responsible for the strong X-ray emission. Although the overall shape of the X-ray light curve can be explained by the high eccentricity of the binary orbit, other features like the asymmetry near periastron passage and the short quasi-periodic oscillations seen at those epochs have not yet been accounted for. In this paper we explain these features assuming that the rotation axis of η Carinae is not perpendicular to the orbital plane of the binary system. As a consequence, the companion star will face η Carinae on the orbital plane at different latitudes for different orbital phases and, since both the mass-loss rate and the wind velocity are latitude dependent, they would produce the observed asymmetries in the X-ray flux. We were able to reproduce the main features of the X-ray light curve assuming that the rotation axis of η Carinae forms an angle of  29°± 4°  with the axis of the binary orbit. We also explained the short quasi-periodic oscillations by assuming nutation of the rotation axis, with an amplitude of about  5°  and a period of about 22 days. The nutation parameters, as well as the precession of the apsis, with a period of about 274 years, are consistent with what is expected from the torques induced by the companion star.     

uvbyβ photometry of the short-period binary VV Ursae Majoris

We present well-sampled uvby light curves, supplemented by a few β filter measurements, of the Algol binary VV UMa. The light curves are analysed using two different codes to derive the orbital and absolute stellar parameters of this binary. We find reasonably good fits to the light curves and determine the stellar effective temperatures T _eff,1≃9000–9600 K , and T _eff,2≃5300–5600 K with a mass ratio q ≃0.35 . From the light-curve fits we discard the possibility of an anomalous gravity-darkening exponent for the secondary star of this system, as previously suggested.
We find evidence of short-term, small-amplitude variations in the brightness of the system. Two periodicities of about 1.10 and 0.51 h seem to be present in the data for at least two different nights, even within the secondary eclipse. This suggests that VV UMa may be a new Algol binary with a low-amplitude variable primary star, but new data collected during longer observing runs are necessary to confirm the pulsating nature of the brightness 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.     

The radial velocity of the companion star in the low-mass X-ray binary 2S 0921–630: limits on the mass of the compact object

In this paper we report on optical spectroscopic observations of the low-mass X-ray binary 2S 0921–630 obtained with the Very Large Telescope. We found sinusoidal radial velocity variations of the companion star with a semi-amplitude of  99.1 ± 3.1 km s⁻¹  modulated on a period of 9.006 ± 0.007 d, consistent with the orbital period found previously for this source, and a systemic velocity of  44.4 ± 2.4 km s⁻¹  . Owing to X-ray irradiation, the centre of light measured by the absorption lines from the companion star is probably shifted with respect to the centre of mass. We try to correct for this using the so-called K -correction. Conservatively applying the maximum correction possible and using the previously measured rotational velocity of the companion star, we find a lower limit to the mass of the compact object in 2S 0921–630 of   M_X sin³ i > 1.90 ± 0.25 M_⊙  (1σ errors). The inclination in this system is well constrained since partial eclipses have been observed in X-ray and optical bands. For inclinations in the range  60° < i < 90°  we find  1.90 ± 0.25 < M_X < 2.9 ± 0.4 M_⊙  . However, using this maximum K -correction we find that the ratio between the mass of the companion star and that of the compact object, q , is 1.32 ± 0.37, implying super-Eddington mass-transfer rates; however, evidence for that has not been found in 2S 0921–630. We conclude that the compact object in 2S 0921–630 is either a (massive) neutron star or a low-mass black hole.     

The mass of the neutron star in the binary millisecond pulsar PSR J 1012 + 5307

We have measured the radial velocity variation of the white dwarf secondary in the binary system containing the millisecond pulsar PSR J 1012 + 5307. Combined with the orbital parameters of the radio pulsar, we infer a mass ratio q (≡ M ₁/ M ₂) = 10.5 ± 0.5. Our optical spectroscopy has also allowed us to determine the mass of the white dwarf companion by fitting the spectrum to a grid of DA model atmospheres: we estimate M ₂ = 0.16 ± 0.02 M⊙, and hence the mass of the neutron star is 1.64 ± 0.22 M⊙, where the error is dominated by that of M ₂. The orbital inclination is 52 ± 4°. For an initial neutron star mass of ∼ 1.4 M⊙, only a few tenths of a solar mass at most has been successfully accreted over the lifetime of the progenitor low-mass X-ray binary. If the initial mass of the secondary was ∼ 1 M⊙, our result suggests that the mass transfer may have been non-conservative.     

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.     

Modelling the spectra of colliding winds in the Wolf–Rayet WC7+O binaries WR 42 and WR 79

We have obtained complete phase coverage of the WC7+O binaries WR 42 = HD 97152 and WR 79 = HD 152270 with high signal-to-noise ratio (S/N), moderate-resolution spectra. Remarkable orbital phase-locked profile variations of the C  iii λ 5696 line are observed and interpreted as arising from colliding wind effects. Within this scenario, we have modelled the spectra using a purely geometrical model that assumes a cone-shaped wind–wind interaction region which partially wraps around the O star. Such modelling holds the exciting promise of revealing a number of interesting parameters for WR+O binaries, such as the orbital inclination, the streaming velocity of material in the interaction region and the ratio of wind momentum flux. Knowledge of these parameters in turn leads to the possibility of a better understanding of WR star masses, mass-loss rates and wind region characteristics.     

Modelling the binary progenitor of Supernova 1993J

We have developed a detailed stellar evolution code capable of following the simultaneous evolution of both stars in a binary system, together with their orbital properties. To demonstrate the capabilities of the code, we investigate potential progenitors for the Type IIb Supernova 1993J, which is believed to have been an interacting binary system prior to its primary exploding. We use our detailed binary stellar evolution code to model this system to determine the possible range of primary and secondary masses that could have produced the observed characteristics of this system, with particular reference to the secondary. Using the luminosities and temperatures for both stars (as determined by Maund et al.) and the remaining mass of the hydrogen envelope of the primary at the time of explosion, we find that if mass transfer is 100 per cent efficient, the observations can be reproduced by a system consisting of a  15 M_⊙  primary and a  14 M_⊙  secondary in an orbit with an initial period of 2100 days. With a mass transfer efficiency of 50 per cent, a more massive system consisting of a  17 M_⊙  primary and a  16 M_⊙  secondary in an initial orbit of 2360 days is needed. We also investigate some of the uncertainties in the evolution, including the effects of tidal interaction, convective overshooting and thermohaline mixing.     

The secondary stars in cataclysmic variables and low-mass X-ray binaries

We critically re-examine the available data on the spectral types, masses and radii of the secondary stars in cataclysmic variables (CVs) and low-mass X-ray binaries (LMXBs), using the new catalogue of Ritter &38; Kolb as a starting point. We find there are 55 reliable spectral type determinations and only 14 reliable mass determinations of CV secondary stars (10 and 5, respectively, in the case of LMXBs). We derive new spectral type–period, mass–radius, mass–period and radius–period relations, and compare them with theoretical predictions. We find that CV secondary stars with orbital periods shorter than 7–8 h are, as a group, indistinguishable from main-sequence stars in detached binaries. We find that it is not valid, however, to estimate the mass from the spectral type of the secondary star in CVs or LMXBs. We find that LMXB secondary stars show some evidence for evolution, with secondary stars which are slightly too large for their mass. We show how the masses and radii of the secondary stars in CVs can be used to test the validity of the disrupted magnetic braking model of CV evolution, but we find that the currently available data are not sufficiently accurate or numerous to allow such an analysis. As well as considering secondary star masses, we also discuss the masses of the white dwarfs in CVs, and find mean values of ⁻ M  = 0.69 ± 0.13 M_⊙ below the period gap, and ⁻ M  = 0.80 ± 0.22 M_⊙ above the period gap.