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Deciphering the formation of supermassive black holes~(SMBHs) is a keyscience goal for upcoming observational facilities. In most theoreticalchannels proposed so far, the seed formation depends crucially on local gasconditions. We systematically characterize the impact of a range of gas basedblack hole seeding prescriptions on SMBH populations using cosmologicalsimulations. Seeds of mass $M_{\mathrm{seed}}\sim 10^3-10^{6}~M_{\odot}/h$ areplaced in halos that exceed critical thresholds for star-forming, metal-poorgas mass and halo mass (defined as $\tilde{M}_{\mathrm{sf,mp}}$ and$\tilde{M}_{\mathrm{h}}$, respectively, in units of $M_{\mathrm{seed}}$). Wequantify the impact of these parameters on the properties of $z\geq7$ SMBHs.Lower seed masses produce much higher BH merger rates (by factors of $\sim10$and $\sim1000$ at $z\sim7$ and $z\sim15$, respectively). For fixed seed mass,we find that $\tilde{M}_{\mathrm{h}}$ has the strongest impact on the BHpopulation at high redshift ($z\gtrsim15$, where a factor of 10 increase in$\tilde{M}_{\mathrm{h}}$ suppresses merger rates by $\gtrsim 100$). At lowerredshift ($z\lesssim15$), we find that $\tilde{M}_{\mathrm{sf,mp}}$ has alarger impact on the BH population. Increasing $\tilde{M}_{\mathrm{sf,mp}}$from $5-150$ suppresses the merger rates by factors of $\sim8$ at $z\sim7-15$.This suggests that the seeding criteria explored here could leave distinctimprints on the redshift distribution of LISA merger rates. In contrast, AGNluminosity functions are much less sensitive to seeding criteria, varying byfactors $\lesssim2-3$ within the seed parameters we have explored. Suchvariations will be challenging to probe even with future sensitive instrumentssuch as Lynx or JWST. Overall, our systematic parameter study provides a usefulbenchmark for development of seed models for large-volume cosmologicalsimulations.

Impact of gas based seeding on supermassive black hole populations at $z\geq7$