Binaries Like to be Twins: Implications for Doubly Degenerate Binaries, the Supernova Ia Rate and Other Interacting Binaries

The recent sample of 21 detached eclipsing binaries in the Small Magellanic Cloud (Harries et al. 2003, Hilditch et al. 2005) provides a valuable test of the binary mass function for massive stars. We show that 50% of detached binaries have companions with very similar masses, q=M_2/M_1 > 0.87, where M_1, M_2 denote the masses of the two binary components, M_1 > M_2. A Salpeter relative mass function for the secondary is very strongly excluded, and the data is consistent with a flat mass function containing 55% of the systems and a ``twin'' population with q>0.95 containing the remainder. We also survey the vast existing literature discussing the mass ratio in binaries and conclude that a significant twin population (of more than 20-25%) exists in binaries that are likely to interact across a broad range of stellar masses and metallicity. Interactions involving nearly equal mass stars have distinctly different properties than those involving stars of unequal mass; the secondaries will tend to be evolved and the common envelope evolution is qualitatively different. The implications of such a population for both binary interactions and star formation are substantial, and we present some examples. We argue that twin systems may provide a natural stellar population to explain the recently proposed prompt channel for type Ia SN, and the presence of a twin population dramatically reduces the maximum inferred NS+BH merger rate relative to the NS+NS merger rate. Twins may also be important for understanding the tendency of WD and NS binaries to be nearly equal in mass, and inclusion of twins in population studies will boost the blue straggler production rate.