Which planets best liberate phosphate for prebiotic chemistry?

Conditions at the surface of terrestrial type worlds inhabitable by Earth-like life are hugely variable. Earth itself has explored much of this extensive parameter space over time, as evidenced via the rock record, which contains evidence of both multi-million year global glaciations as well as hot house conditions. The area of emergent land,  the partial pressure of atmospheric carbon dioxide, and the geochemistry of crustal rocks have all evolved, and imply that terrestrial type exoplanets may be extremely diverse. Unfortunately, all of these parameters remain uncertain for Earth during the Era of Prebiotic chemistry. Understanding how the availability of critical molecules for prebiotic chemistry vary as a function of planetary conditions is therefore crucial for constructing self-consistent scenarios for the origin of life. We focus on phosphate, modelling 1) mineral hosts in crustal rocks, 2) the weathering of those minerals as a function of atmospheric composition, 3) the lithological composition of continental crust, 4) the ratio of continental crust to oceanic crust, 5) the ratio of emergent to submerged crust, and 6) the efficiency of sedimentary crustal reworking. Recent work has suggested that phosphate may be most available on worlds with high atmospheric pCO₂, where abundant dissolved inorganic carbon in surface waters can help solubilise the P-bearing phase apatite.  Provocatively, our modelling suggests that, on primitive worlds where apatite is rare, the weathering of rock-forming silicate and carbonate minerals may supply higher P fluxes - up to an order of magnitude higher than weathering of apatite rich crust at low pCO₂, and roughly competitive with or, for mafic crust rich in basaltic glass, 1-2 orders of magnitue higher than the weathering of apatite rich crust at high pCO₂. Finally, our results also strongly suggest that high rates of sedimentary reworking are needed to access the highest P weathering fluxes on Earth-like worlds. Our results point towards settings of active sedimentary cycling as crucial for fuelling prebiotic chemistry with endogenous P sources, and reveal a broad mineralogical and climatic parameter space for Earth-like worlds under which that chemistry may have plausibly taken place.