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The impact of fallback on the compact remnants and chemical yields of core-collapse supernovae

Fallback in core-collapse supernovae plays a crucial role in determining the properties of the compact remnants and of the ejecta composition. We perform three-dimensional simulations of mixing and fallback for selected non-rotating supernova models to study how explosion energy and asymmetries correlate with the remnant mass, remnant kick, and remnant spin. We find that the strongest kick and spin is imparted by partial fallback in an asymmetric explosion. Black hole (BH) kicks of several hundred $\mathrm{km}\,\mathrm{s}^{-1}$ and spin parameters of $\mathord{\sim}0.25$ can be obtained in this scenario. If the initial explosion energy barely exceeds the envelope binding energy, stronger fallback results, and the remnant kick and spin remain small. If the explosion energy is high with respect to the envelope binding energy, there is little fallback with a small effect on the remnant kick, but the spin-up by fallback can be substantial. For a non-rotating $12\,\mathrm{M}_\odot$ progenitor, we find that the neutron star (NS) is spun up to millisecond periods. The high specific angular momentum of the fallback material can also lead to disk formation around black holes. Fallback may thus be a pathway towards millisecond-magnetar or collapsar-type engines for hypernovae and gamma-ray bursts that does not require rapid progenitor rotation. Within our small set of simulations, none reproduced the peculiar layered fallback necessary to explain the metal-rich iron-poor composition of many carbon-enhanced metal-poor (CEMP) stars. Models with different explosion energy and different realisations of asymmetries may, however, be compatible with CEMP abundance patterns.