Abstract. We present new optical spectroscopy of the eclipsing binary pulsar Sk 160/SMC X-1. From the He I absorption lines, taking heating corrections into account, we determine the radial velocity semi-amplitude of Sk 160 to be 21.8 ± 1.8 km s −1 . Assuming Sk 160 fills its Roche-lobe, the inclination angle of the system is i = 65.3• ± 1.3• and in this case we obtain upper limits for the mass of the neutron star as M x = 1.21 ± 0.10 M and for Sk 160 as M o = 16.6 ± 0.4 M . However if we assume that the inclination angle is i = 90• , then the ratio of the radius of Sk 160 to the radius of its Roche-lobe is β = 0.79 ± 0.02, and the lower limits for the masses of the two stars are M x = 0.91 ± 0.08 M and M o = 12.5 ± 0.1 M . We also show that the He II 4686 Å emission line tracks the motion of the neutron star, but with a radial velocity amplitude somewhat less than that of the neutron star itself. We suggest that this emission may arise from a hotspot where material accreting via Roche lobe overflow impacts the outer edge of an accretion disc.

Context. The early-type binary MY Cam belongs to the young open cluster Alicante 1, embedded in Cam OB3. Aims. MY Cam consists of two early-O type main-sequence stars and shows a photometric modulation suggesting an orbital period slightly above one day. We intend to confirm this orbital period and derive orbital and stellar parameters. Methods. Timing analysis of a very exhaustive (4607 points) light curve indicates a period of 1.1754514 ± 0.0000015 d. Highresolution spectra and the cross-correlation technique implemented in the todcor program were used to derive radial velocities and obtain the corresponding radial velocity curves for MY Cam. Modelling with the stellar atmosphere code fastwind was used to obtain stellar parameters and create templates for cross-correlation. Stellar and orbital parameters were derived using the WilsonDevinney code, such that a complete solution to the binary system could be described. Results. The determined masses of the primary and secondary stars in MY Cam are 37.7 ± 1.6 and 31.6 ± 1.4 M , respectively. The corresponding temperatures, derived from the model atmosphere fit, are 42 000 and 39 000 K, with the more massive component being hotter. Both stars are overfilling their Roche lobes, sharing a common envelope. Conclusions. MY Cam contains the most massive dwarf O-type stars found so far in an eclipsing binary. Both components are still on the main sequence, and probably not far from the zero-age main sequence. The system is a likely merger progenitor, owing to its very short period.

New high resolution, optical spectroscopy of the high mass X-ray binary LMC X-3, shows the spectral type of the donor star changes with phase due to irradiation by the X-ray source. We find the spectral type is likely to be B5V, and only appears as B3V when viewing the heated side of the donor. Combining our measurements with those previously published, and taking into account the effects of X-ray irradiation, results in a value for the donor star radial velocity semi-amplitude of 256.7 4.9 o K  km/s. We find the mass of the black hole lies in the range 9.5 13.6x M M M  .

The radius of the proton is a topic of debate and has yet to be confirmed. Measurements from different techniques yield conflicting values, with some experimental methods yielding a value in disagreement with the standard model. This review article outlines the current status of the experimental results and summarizes the possible solutions to this puzzle.

We address the ~122 orders of magnitude discrepancy between the vacuum energy density at the cosmological scale and the vacuum density predicted by quantum field theory. This disagreement is known as the cosmological constant problem or the "vacuum catastrophe". Utilizing a generalized holographic model, we consider the total mass-energy density in the geometry of a spherical shell universe (as a first order approximation) and find an exact solution for the currently observed critical density of the universe. We discuss the validity of such an approach and consider its implications to cosmogenesis and universal evolution.