In the core-degenerate (CD) scenario for the formation of Type Ia supernovae (SNe Ia) the Chandrasekhar or super-Chandrasekhar mass white dwarf (WD) is formed at the termination of the common envelope phase or during the planetary nebula phase, from a merger of a WD companion with the hot core of a massive asymptotic giant branch (AGB) star. The WD is destroyed and accreted onto the more massive core. In the CD scenario the rapidly rotating WD is formed shortly after the stellar formation episode, and the delay from stellar formation to explosion is basically determined by the spin-down time of the rapidly rotating merger remnant. The spin-down is due to the magneto-dipole radiation torque. Several properties of the CD scenario make it attractive compared with the double-degenerate (DD) scenario. (1) Off-center ignition of carbon during the merger process is not likely to occur. (2) No large envelope is formed. Hence avoiding too much mass loss that might bring the merger remnant below the critical mass. (3) This model explains the finding that more luminous SNe Ia occur preferentially in star forming galaxies.

We have begun new studies of the evolution of thermonuclear runaways (TNRs) in the accreted envelopes of white dwarfs (WDs). Here we focus on the recent outbursts of RS Oph (2006), U Sco (2010) and T Pyx (2011). U Sco explodes about every 10 years and the ejected material from the WD is helium rich. It has a short orbital period for recurrent novae (RNe) but the secondary is likely to be evolved. The WD is thought to be close in mass to the Chandrasekhar limit. T Pyx has just suffered its first outburst since 1966 and it was predicted to never experience another outburst. It has a short orbital period and has formed dust in the ejecta as this paper was being written. One important question is the secular evolution of the WD. Do the repeated outbursts cause the WD to gain or lose mass? If it is gaining mass, it could eventually reach the Chandrasekhar limit and become a Type Ia supernova (SNe Ia) if it can hide the hydrogen and helium in the system. Here, we report on our latest studies of TNRs in accreted envelopes on WDs using a variety of initial WD masses, luminosities, and mass accretion rates. Of great importance to our conclusions, we assume a solar composition (Lodders abundance distribution). We use our 1-D hydro code, NOVA, that includes the Hix and Thielemann nuclear reaction network, the Iliadis reaction rate library, the Timmes equation of state, OPAL opacities, and the new convection of Arnett, Meakin, and Young. We report on the amount of ejected mass, evolution time to explode, and whether or not the WD is growing or losing mass.

The model of a young star with a low-mass secondary component (q = M2/M1 ≤ 0.1) accreting matter from a circumbinary (CB) disc is considered. It is assumed that the orbit and the CB disc can be coplanar and non-coplanar. The model parameters were varied within the following ranges: the component mass ratio q ranged from 0.1 to 0.003, the eccentricity e varied from 0 to 0.7, the inclination of the orbit plane to the CB disc ranged from 0 to 10 degrees, and the parameter that defines the viscosity of the system was also varied. A number of hydrodynamics models of such a system have been calculated by the SPH method and then the variations of the circumstellar extinction and phase brightness curves were determined. The calculated brightness curves differ in shape and amplitude and it depends on the model parameters and the orientation of the system relative to the observer. The results were used to analyze the cyclic activity of UX Ori type stars.

In 1905, Henri Poincaré predicted the existence of gravitational waves and assumed their speed equal to the speed of light. If additionally the gravitational aberration would have the same magnitude as the aberration of light, we would observe several paradoxical phenomena. For instance, the orbit of two bodies would be unstable, since two attractive forces arise that are not in line and hence form a couple. This will be modelled by a nonautonomous system of ordinary differential equations with delay. In fact, any positive value of the gravitational aberration increases the angular momentum of such a system and this may contribute to the expansion of the universe. We found a remarkable coincidence between the Hubble constant and the increasing distance of the Moon from the Earth.

In 2000, Carlip showed that in general relativity gravitational aberration is almost cancelled out by velocity–dependent interactions. We show how the actual value of the gravitational aberration can be obtained by measurement of a single angle at a suitable time t* corresponding to the perihelion of an elliptic orbit. We also derive an a priori error estimate that expresses how accurately t* has to be determined to obtain the gravitational aberration to a prescribed tolerance.

In close binary systems of O-type stars, the individual stellar winds will collide between the stars to form shock fronts. The existence of the shock region can be established through observations of excess X-ray emission and orbital phase-related variations in UV wind features and optical emission lines. Here I report on work in progress on the orbital variations of the UV wind lines in a large sample of O-binaries that have been observed with the International Ultraviolet Explorer satellite. In most of these binaries, the blue absorption trough of the P-Cygni lines weakens when the strong wind component is behind its companion, in accordance with expectations for colliding winds. I describe how the radial velocity variations of the wind features differ from the orbital motions. Finally I discuss observations of Hα emission in these systems, with emphasis on HD 47129 (Plaskett's star). Such optical emission lines act as a probe of high density regions in the winds.

WR stars obey M-L-·-Teff-R-chemistry relations, which are in general model independent (with the exception of chemistry). The processes of WR formation (stellar winds, hydrodynamical mixing, binary mass transfer etc.) influence, however, the domain of parameters occupied by WR stars. We specifically examine the distribution of luminosities and H-contents of WN stars, which both support heavy mass loss rates, or possibly mixing, in the main sequence and WNL phases. Detailed studies of the number ratios WR/O, WC/WN, WC/WR, etc. are made for galaxies at various metallicities Z which exhibit extremely different WR populations. Good agreement of models and observations is found. It is also shown that the data are better explained if a certain fraction Φ (less than 10%) of the O-stars become WR stars, preferentially of type WNE as a result of Roche lobe overflow (RLOF) in binaries. This result necessarily implies that the fraction of WR stars, owing their existence to RLOF, is variable with Z, being nearly 100% at low Z and much smaller at high Z. We also identify several hydrodynamical developments physically required in stellar models. Among them, we collect the available observational and theoretical arguments supporting an important role of mixing in massive star evolution.

I review the properties of the X-ray source Cygnus X-3, and the evidence that is available that indicates that its companion is a Wolf-Rayet star. I focus on the interpretation of spectra of its infrared counterpart. Considering all data, I conclude that the companion is indeed a WR star, and I discuss the ramifications of this conclusion for our understanding of WR stars in general.