Chapter 1

1.1 Use Kepler's third law and the small-angle formula to obtain a = 0.051 AU and α = 2.5 mas, still below the currently attainable spatial resolution.

1.2 Use Kepler's third law to obtain a = 19.87 AU, or a = 4270.9 R⊙. Thus both stars have space to evolve independently. The present age of Sirius A is t = 3.28 × 108 years. Sirius B must be massive enough to evolve to a white dwarf in that time. Hence mB = 2.86 M⊙ is the minimum mass for the progenitor of Sirius B, and it must have lost 1.92 M⊙ through the redgiant wind-driven mass-loss phase and the planetary-nebula phase. Discuss whether or not these figures are in accordance with our knowledge of mass loss at different evolutionary stages.

1.3 A CV is composed of a white dwarf and a low-mass main-sequence star. The white dwarf is the degenerate core remnant of a star that was once a red giant. Hence the need for enough space in the binary to allow evolution through the red-giant phase undisturbed, requiring Roche lobes greater than about 100 R⊙. Thus the initial orbital period must have been years, rather than a few as hours as for W UMa systems.

1.4 High-mass x-ray binary (HMXB): 0 star's main-sequence lifetime about 2 × 106 years; A star's, about 100 times longer. 0 star evolves to red-supergiant stage, losing mass to companion through RLOF and mass-ratio reversal.