Confirmation of eclipses in KPD 0422+5421, a binary containing a white dwarf and a subdwarf B star

We report additional photometric CCD observations of KPD 0422+5421, a binary with an orbital period of 2.16 h which contains a subdwarf B star (sdB) and a white dwarf. There are two main results of this work. First, the light curve of KPD 0422+5421 contains two distinct periodic signals, the 2.16-h ellipsoidal modulation discovered by Koen, Orosz & Wade and an additional modulation at 7.8 h. This 7.8-h modulation is clearly not sinusoidal: the rise time is about 0.25 in phase, whereas the decay time is 0.75 in phase. Its amplitude is roughly half of the amplitude of the ellipsoidal modulation. Secondly, after the 7.8-h modulation is removed, the light curve folded on the orbital period clearly shows the signature of the transit of the white dwarf across the face of the sdB star and the signature of the occultation of the white dwarf by the sdB star. We have used the Wilson–Devinney code to model the light curve to obtain the inclination, the mass ratio and the Ω potentials, and a Monte Carlo code to compute confidence limits on interesting system parameters. We find component masses of     and     ( M _total     , 68 per cent confidence limits). If we impose an additional constraint and require the computed mass and radius of the white dwarf to be consistent with a theoretical mass–radius relation, we find     and     (68 per cent confidence limits). In this case the total mass of the system is less than 1.4 M_⊙ at the 99.99 per cent confidence level. We briefly discuss possible interpretations of the 7.8-h modulation and the importance of KPD 0422+5421 as a member of a rare class of evolved binaries.     

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.     

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.     

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.     

Photometry of four binary subdwarf B stars and the nature of their unseen companion stars

We present light curves of four binary subdwarf B stars (sdB), Ton 245, Feige 11, PG 1432+159 and PG 1017−086. We also present new spectroscopic data for PG 1017−086 from which we derive its orbital period,   P =0.073 d  , and the mass function,   f _m=0.0010±0.0002 M_⊙.  This is the shortest period for an sdB binary measured to date. The values of P and f _m for the other sdB binaries have been published elsewhere. We are able to exclude the possibility that the unseen companion stars to Ton 245, Feige 11 and PG 1432+159 are main-sequence stars or subgiant stars from the absence of a sinusoidal signal, which would be caused by the irradiation of such a companion star, i.e. they show no reflection effect. The unseen companion stars in these binaries are likely to be white dwarf stars. In contrast, the reflection effect in PG 1017−086 is clearly seen. The lack of eclipses in this binary combined with other data suggests that the companion is a low-mass M-dwarf or, perhaps, a brown dwarf.     

An iterative filter to reconstruct planetary transit signals in the presence of stellar variability

We report the identification, from a photometric, astrometric and spectroscopic study, of a massive white dwarf member of the nearby, approximately solar metallicity, Coma Berenices open star cluster (Melotte 111). We find the optical to near-infrared energy distribution of WD 1216+260 to be entirely consistent with that of an isolated DA and determine the effective temperature and surface gravity of this object to be   T _eff= 15 739⁺¹⁹⁷₋₁₉₆ K  and  log  g = 8.46^+0.03_−0.02  . We set tight limits on the mass of a putative cool companion,   M ≳ 0.036 M_⊙  (spatially unresolved) and   M ≳ 0.034 M_⊙  (spatially resolved and   a ≲ 2500 au  ). Based on the predictions of CO core, thick H layer evolutionary models we determine the mass and cooling time of WD 1216+260 to be   M _WD= 0.90 ± 0.04 M_⊙  and  τ_cool= 363⁺⁴⁶₋₄₁ Myr  , respectively. For an adopted cluster age of  τ= 500 ± 100 Myr  we infer the mass of its progenitor star to be   M _init= 4.77^+5.37_−0.97 M_⊙  . We briefly discuss this result in the context of the form of the stellar initial mass–final mass relation.     

Orbital solution and fundamental parameters of σ Scorpii

The first orbital solution for the spectroscopic pair in the multiple star system σ Scorpii, determined from measurements with the Sydney University Stellar Interferometer, is presented. The primary component is of β Cephei variable type and has been one of the most intensively studied examples of its class. The orbital solution, when combined with radial velocity results found in the literature, yields a distance of  174⁺²³₋₁₈ pc  , which is consistent with, but more accurate than the Hipparcos value. For the primary component we determine  18.4 ± 5.4 M_⊙, −4.12 ± 0.34 mag  and  12.7 ± 1.8 R_⊙  for the mass, absolute visual magnitude and radius, respectively. A B1 dwarf spectral type and luminosity class for the secondary is proposed from the mass determination of  11.9 ± 3.1 M_⊙  and the estimated system age of 10 Myr.     

The Jeans mass and the origin of the knee in the IMF

We use numerical simulations of the fragmentation of a  1000 M_⊙  molecular cloud and the formation of a stellar cluster to study how the initial conditions for star formation affect the resulting initial mass function (IMF). In particular, we are interested in the relation between the thermal Jeans mass in a cloud and the knee of the IMF, i.e. the mass separating the region with a flat IMF slope from that typified by a steeper, Salpeter-like, slope. In three isothermal simulations with   M _Jeans= 1, 2  and  5 M_⊙  , the number of stars formed, at comparable dynamical times, scales roughly with the number of initial Jeans masses in the cloud. The mean stellar mass also increases (though less than linearly) with the initial Jeans mass in the cloud. It is found that the IMF in each case displays a prominent knee, located roughly at the mass scale of the initial Jeans mass. Thus clouds with higher initial Jeans masses produce IMFs which are shallow to higher masses. This implies that a universal IMF requires a physical mechanism that sets the Jeans mass to be near  1 M_⊙  . Simulations including a barotropic equation of state as suggested by Larson, with cooling at low densities followed by gentle heating at higher densities, are able to produce realistic IMFs with the knee located at  ≈1 M_⊙  , even with an initial   M _Jeans= 5 M_⊙  . We therefore suggest that the observed universality of the IMF in the local Universe does not require any fine tuning of the initial conditions in star forming clouds but is instead imprinted by details of the cooling physics of the collapsing gas.     

The case and fate of HD 75767 – neutron star or supernova?

We report the discovery of the nearby  ( d = 24 pc)  HD 75767 as an eight billion year old quadruple system consisting of a distant M dwarf pair, HD 75767 C–D, in orbit around the known short-period   P = 10.25 d  single-lined binary HD 75767 A–B, the primary of which is a solar-like G star. On the reasonable assumption of synchronous orbital rotation as well as rotational and orbital coplanarity for the inner pair, we get   M _B= 0.96 M_⊙  for the unseen HD 75767 B, that is, the case of a massive white dwarf. Upon future evolution, mass transfer towards HD 75767 B will render the   M _A= 0.96 M_⊙  G-type primary, now a turnoff star, to become a helium white dwarf of   M _A∼ 0.33 M_⊙  . Depending on the mass accretion rate, accretion efficiency and composition of the massive white dwarf, this in turn may result in a collapse of HD 75767 B with the formation of a millisecond pulsar, i.e. the creation of a low-mass binary pulsar (LMBP), or, instead, a Type Ia supernova explosion and the complete disruption of HD 75767 B. Irrespective of which scenario applies, we point to the importance of the distant M dwarfs as the likely agents for the formation of the inner, short-period HD 75767 A–B pair, and hence a path that particularly avoids preceding phases of common envelope evolution.     

Orbital periods of the binary sdB stars PG 0940+068 and PG 1247+554

We have used the radial velocity variations of two sdB stars previously reported to be binaries to establish their orbital periods. They are PG 0940+068 ( P =8.33 d) and PG 1247+554 ( P =0.599 d). The minimum masses of the unseen companions, assuming a mass of 0.5 M_⊙ for the sdB stars, are 0.090±0.003 M. for PG 1247+554 and 0.63±0.02 M_⊙ for PG 0940+068. The nature of the companions is not constrained further by our data.     

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  .     

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.     

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.     

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.     

Radial velocities of pulsating subdwarf B stars: KPD 2109+4401 and PB 8783

High-speed spectroscopy of two pulsating subdwarf B stars, KPD 2109+4401 and PB 8783, is presented. Radial motions are detected with the same frequencies as reported from photometric observations and with amplitudes of ∼2 km s⁻¹ in two or more independent modes. These represent the first direct observations of surface motion arising from multimode non-radial oscillations in subdwarf B stars. In the case of the sdB+F binary PB 8783, the velocities of both components are resolved; high-frequency oscillations are found only in the sdB star and not the F star. There also appears to be evidence for mutual motion of the binary components. If confirmed, it implies that the F-type companion is ≳1.2 times more massive than the sdB star, while the amplitude of the F-star acceleration over 4 h would constrain the orbital period to lie between 0.5 and 3.2 d.     

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.     

HST and ground-based eclipse observations of V2051 Ophiuchi: binary parameters

We report on high-speed eclipse photometry of the dwarf nova V2051 Oph while it was in a low brightness state, at B  ≃ 16.2 mag. In comparison with the average IUE spectra, the ultraviolet continuum and emission lines appear reduced by factors of, respectively, ≃ 4 and ≃ 5. Flickering activity is mostly suppressed and the light curve shows the eclipse of a compact white dwarf at the disc centre which contributes ≃ 60 per cent of the total light at 3900–4300 Å. We use measurements of contact phases in the eclipse light curve to derive the binary geometry and to estimate masses and relevant dimensions. We find a mass ratio of q  = 0.19 ± 0.03 and an inclination of i  = 83 ± 2°. The masses of the component stars are M ₁ = 0.78 ± 0.06 M⊙ and M ₂ = 0.15 ± 0.03 M⊙. Our photometric model predicts K ₁ = 83 ± 12 km s⁻¹ and K ₂ = 436 ± 11 km s⁻¹. The predicted value of K₁ is in accordance with the velocity amplitude obtained from the emission lines after a correction for asymmetric line emission in the disc is made. The secondary of V2051 Oph is significantly more massive than the secondaries of the other ultrashort period dwarf novae. V2051 Oph is probably a relatively young system, with a secondary star that has not had enough time to evolve out of thermal equilibrium.     

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 Galactic hybrid Wolf–Rayet WN 7o/CE + O7V((f)) binary system WR 145

A spectroscopic study of the binary Wolf–Rayet (WR)+O system WR 145 is performed, in order to determine the radial velocity orbits of the individual stars, the angle of orbital inclination and the stellar masses. The emission and absorption components are separated from the original spectra, allowing us to confirm the spectral classification WN 7o/CE of the hybrid WR component and to derive a spectral classification O7V((f)) for the O star. A study of the wind-collision properties is performed. Fitting the radial velocity and full width at half-maximum of the excess emission with Lührs' model results in an inclination angle of   i = 63°  , leading to estimates of the stellar masses:   M _WR= 18 M_⊙  and   M _O= 31 M_⊙  . Both of these masses are compatible with those of other stars of similar types.     

Quantifying the coexistence of massive black holes and dense nuclear star clusters

In large spheroidal stellar systems, such as elliptical galaxies, one invariably finds a  10⁶–10⁹ M_⊙  supermassive black hole at their centre. In contrast, within dwarf elliptical galaxies one predominantly observes a  10⁵–10⁷ M_⊙  nuclear star cluster. To date, few galaxies have been found with both types of nuclei coexisting and even less have had the masses determined for both central components. Here, we identify one dozen galaxies housing nuclear star clusters and supermassive black holes whose masses have been measured. This doubles the known number of such hermaphrodite nuclei – which are expected to be fruitful sources of gravitational radiation. Over the host spheroid (stellar) mass range  10⁸–10¹¹ M_⊙  , we find that a galaxy's nucleus-to-spheroid (baryon) mass ratio is not a constant value but decreases from a few per cent to ∼0.3 per cent such that  log[( M _BH+ M _NC)/ M _sph]=−(0.39 ± 0.07) log[ M _sph/10¹⁰ M_⊙]− (2.18 ± 0.07)  . Once dry merging commences and the nuclear star clusters disappear, this ratio is expected to become a constant value.
As a byproduct of our investigation, we have found that the projected flux from resolved nuclear star clusters is well approximated with Sérsic functions having a range of indices from ∼0.5 to ∼3, the latter index describing the Milky Way's nuclear star cluster.