Wind-wind collision in the eta Carinae binary system - III. The HeII 4686 line profile

We modeled the HeII 4686 line profiles observed in the eta Carinae binary system close to the 2003.5 spectroscopic event, assuming that they were formed in the shocked gas that flows at both sides of the contact surface formed by wind-wind collision. We used a constant flow velocity and added turbulence in the form of a gaussian velocity distribution. We allowed emission from both the primary and secondary shocks but introduced infinite opacity at the contact surface, implying that only the side of the contact cone visible to the observer contributed to the line profile. Using the orbital parameters of the binary system derived from the 7 mm light curve during the last spectroscopic event (Paper II) we were able to reproduce the line profiles obtained with the HST at different epochs, as well as the line mean velocities obtained with ground based telescopes. A very important feature of our model is that the line profile depends on the inclination of the orbital plane; we found that to explain the latitude dependent mean velocity of the line, scattered into the line of sight by the Homunculus, the orbit inclination should be close to 90 degrees, meaning that it does not lie in the Homunculus equatorial plane, as usually assumed. This inclination, together with the relative position of the stars during the spectroscopic events, allowed us to explain most of the observational features, like the variation of the Purple Haze with the orbital phase, and to conciliate the X-ray absorption with the postulated shell effect used to explain the optical and UV light curves.Comment: to appear in the MNRA

Disconnecting strongly regular graphs

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner $2$-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency

WR 7a: a V Sagittae or a qWR star?

The star WR 7a, also known as SPH 2, has a spectrum that resembles that of V Sagittae stars although no O VI emission has been reported. The Temporal Variance Spectrum - TVS - analysis of our data shows weak but strongly variable emission of O VI lines which is below the noise level in the intensity spectrum. Contrary to what is seen in V Sagittae stars, optical photometric monitoring shows very little, if any, flickering. We found evidence of periodic variability. The most likely photometric period is P(phot) = 0.227(14) d, while radial velocities suggest a period of P(spec) = 0.204(13) d. One-day aliases of these periods can not be ruled out. We call attention to similarities with HD 45166 and DI Cru (= WR 46), where multiple periods are present. They may be associated to the binary motion or to non-radial oscillations. In contrast to a previous conclusion by Pereira et al. (1998), we show that WR 7a contains hydrogen. The spectrum of the primary star seems to be detectable as the N V 4604A absorption line is visible. If so, it means that the wind is optically thin in the continuum and that it is likely to be a helium main sequence star. Given the similarity to HD 45166, we suggests that WR 7a may be a qWR - quasi Wolf-Rayet - star. Its classification is WN4h/CE in the Smith et al. (1996) three dimensional classification system.Comment: 6 pages, 6 figures, preprint of an article accepted for publication in Monthly Notices of The Royal Astronomical Societ

Exploiting neutron-rich radioactive ion beams to constrain the symmetry energy

The Modular Neutron Array (MoNA) and 4 Tm Sweeper magnet were used to measure the free neutrons and heavy charged particles from the radioactive ion beam induced 32Mg + 9Be reaction. The fragmentation reaction was simulated with the Constrained Molecular Dynamics model(CoMD), which demonstrated that the of the heavy fragments and free neutron multiplicities were observables sensitive to the density dependence of the symmetry energy at sub-saturation densities. Through comparison of these simulations with the experimental data constraints on the density dependence of the symmetry energy were extracted. The advantage of radioactive ion beams as a probe of the symmetry energy is demonstrated through examination of CoMD calculations for stable and radioactive beam induced reactions

Problems on q-Analogs in Coding Theory

The interest in $q$-analogs of codes and designs has been increased in the last few years as a consequence of their new application in error-correction for random network coding. There are many interesting theoretical, algebraic, and combinatorial coding problems concerning these q-analogs which remained unsolved. The first goal of this paper is to make a short summary of the large amount of research which was done in the area mainly in the last few years and to provide most of the relevant references. The second goal of this paper is to present one hundred open questions and problems for future research, whose solution will advance the knowledge in this area. The third goal of this paper is to present and start some directions in solving some of these problems.Comment: arXiv admin note: text overlap with arXiv:0805.3528 by other author