We explore the impact of incorporating physically motivated ionisation and recombination rates on the history and topology of cosmic reionisation, by incorporating inputs from small-volume hydrodynamic simulations into a semi-numerical code, SimFast21, that evolves reionisation on large scales. We employ radiative hydrodynamic simulations to parameterize the ionisation rate Rion and recombination rate Rrec as functions of halo mass, overdensity and redshift. We find that Rion is super-linearly dependent on halo mass (Rion ~ Mh^1.41), in contrast to previous assumptions. We implement these scalings into SimFast21 to identify the ionized regions. We tune our models to be consistent with recent observations of the optical depth, ionizing emissivity, and neutral fraction by the end of reionisation. We require an average photon escape fraction fesc=0.04 within ~ 0.5 cMpc cells, independent of halo mass or redshift, to simultaneously match these data. We present predictions for the 21cm power spectrum, and show that it is converged with respect to simulation volume. We find that introducing superlinearly mass-dependent ionisations increases the duration of reionisation and boosts the small-scale 21cm power by ~ 2-3 at intermediate phases of reionisation. Introducing inhomogeneous recombinations reduces ionised bubble sizes and suppresses large-scale 21cm power by ~ 2-3. Moreover, gas clumping on sub-cell scales has a minimal effect on the 21cm power, indicating that robust predictions do not depend on the behaviour of kpc-scale structures. The superlinear ionisations significantly increase the median halo mass scale for ionising photon output to >10^10 Mo, giving greater hope for detecting most of ionising sources with next-generation facilities. These results highlight the importance of more accurately treating ionising sources and recombinations for modeling reionisation and its 21cm signal.
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