Accretion disks with masses ~0.001-0.1 Msun form during the merger of neutron star (NS)-NS and black hole-NS binaries. Initially, such hyper-accreting disks cool efficiently by neutrino emission and their composition is driven neutron-rich by pair captures under degenerate conditions. However, as the disk viscously spreads and its temperature drops, cooling becomes inefficient and the disk becomes advective. Analytic arguments and numerical simulations suggest that once this occurs, powerful winds likely drive away most of the disks remaining mass. We calculate the thermal evolution and nuclear composition of viscously spreading accretion disks formed from compact object mergers using one-dimensional height-integrated simulations. We show that freeze-out from weak equilibrium necessarily accompanies the disks late-time transition to an advective state. As a result, hyper-accreting disks generically freeze out neutron-rich (with electron fraction Ye ~ 0.2-0.4), and their late-time outflows robustly synthesize rare neutron-rich isotopes. Using the measured abundances of these isotopes in our solar system, we constrain the compact object merger rate in the Milky Way to be < 1e-5 (M_d,0/0.1 Msun)^(-1) per year, where M_d,0 is the average initial mass of the accretion disk. Thus, either the NS-NS merger rate is at the low end of current estimates or the average disk mass produced during a typical merger is << 0.1 Msun. We also show that if most short duration gamma-ray bursts (GRBs) are produced by compact object mergers, their beaming fraction must exceed f_b ~ 0.13(M_d,0/0.1 Msun), corresponding to a jet half-opening angle > 30(M_d,0/0.1 Msun)^(1/2) degrees. This is consistent with other evidence that short duration GRB outflows are less collimated than those produced in long duration GRBs.
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