The Evolution of Pop III.1 Protostars Powered by Dark Matter Annihilation. II. Dependence on WIMP Properties

The rapid appearance of supermassive black holes (SMBHs) at $z\gtrsim7$ requires efficient pathways to form massive black hole seeds. We investigate whether annihilation of weakly interacting massive particles (WIMPs) can alter primordial (Pop III.1) protostellar evolution sufficiently to enable formation of such `heavy'' seeds. Using the one-dimensional Geneva stellar-evolution code (GENEC) with an implemented Gould single-scatter capture module, we compute a grid of protostellar evolution models covering ambient WIMP mass densities $\rho_\chi=10^{12}$-$10^{16}\ \mathrm{GeV\,cm^{-3}}$, WIMP masses $m_\chi=30$-$3000\ \mathrm{GeV}$, spin-dependent cross sections $\sigma_{\rm SD}=10^{-42}$-$10^{-40}\ \mathrm{cm^2}$, and baryonic accretion rates $\dot{M_*}=(1-3)\times10^{-3}\, M_\odot \,{\rm yr}^{-1}$. We find a robust bifurcation of outcomes. For sufficiently high ambient dark matter density ($\rho_\chi\gtrsim5\times10^{14}\ \mathrm{GeV\,cm^{-3}}$) and capture efficiency ($\sigma_{\rm SD}\gtrsim10^{-41}\ \mathrm{cm^2}$) WIMP annihilation supplies enough energy to inflate protostars onto extended, cool (Hayashi-track) configurations that dramatically suppress ionizing feedback and permit uninterrupted growth to $\sim10^{5}\,M_\odot$. Lighter WIMPs and larger $\sigma_{\rm SD}$ favour earlier and stronger annihilation support; heavier WIMPs delay the effect. For our fiducial case, WIMP masses $<$3 TeV are essential for allowing growth to the supermassive regime, otherwise the protostar evolves to the compact, feedback-limited regime that results in `light'' seeds. These results indicate that, under plausible halo conditions, DM annihilation provides a viable channel for forming heavy black hole seeds.