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tokens: and discuss the future work needed to improve our understanding of r -process enrichment at high redshifts. 2. Method To model the formation of DNSs, we use published results from the StarTrack (Belczynski et al. 2002 , 2006 , 2008 ) population synthesis code. These simulations are described in detail in Dominik et al. ( 2012 ) and include three major improvements over previous StarTrack versions with regards to stellar winds (Belczynski et al. 2010 ), common envelope (CE) formulation, and compact object formation (Fryer et al. 2012 ). We have analyzed the intermediate data from these simulations that are publicly available. 7 7 The public data from the Synthetic Universe Project are available at: www.syntheticuniverse.org . We briefly summarize the method in this section. Each of the models we analyze has 2 × 10 6 binaries, initialized by four different parameters: (i) the primary star’s mass M 1 ; (ii) the mass ratio q = M 2 / M 1 , with M 2 being the mass of the secondary star; (iii) the semimajor axis a of the binary; and (iv) the eccentricity e . The masses of the primary are drawn from the Kroupa initial mass function (IMF) from 5 to 150 M ⊙ . The mass ratio is assumed to have a flat distribution between q = 0–1 with the minimum mass of the secondary considered to be 3 M ⊙ . The distribution of initial binary separation is assumed to be flat in log( a ), and the eccentricity is drawn from thermal equilibrium distribution Ξ( e ) = 2 e , with e ranging from 0 to 1. 2.1. Model Variations A number of parameters are varied among the models, which are meant to parameterize the uncertainties in our understanding of binary neutron star formation. The first parameter that is varied deals with the behavior of binaries when a star enters into a CE with a Hertzsprung gap (HG) donor star; during a CE, a star enters the envelope of its companion, exchanging orbital energy to unbind the donor’s envelope. For giant stars, with a clear core–envelope boundary, the end result of this process (so long as there is enough orbital energy available to keep the system from merging) is a closely bound binary comprised of the accretor star and the giant star’s core. However, HG stars lack well-defined cores, and studies are inconclusive as to whether binaries entering into a CE during this phase can survive without merging (Deloye Taam 2010 ). We note that allowing HG stars to survive a CE significantly increases the merger rates of double black hole binaries to a level that exceeds current LIGO constraints (Belczynski et al. 2007 ), although it matches NSM rate estimates (Chruslinska et al. 2018 ). Two different submodels, A and B, have been analyzed, and treat CE events with HG donor stars differently. Submodel A treats HG stars such that a core could be distinguished from an envelope in their evolutionary phase, hence a successful CE ejection is possible. Submodel B assumes any system entering into a CE with a HG donor will merge. As a second parameter, the