Collapsars Are Not Heavy $r$-Process Factories

Abstract

Collapsar disks are proposed sources of $r$-process elements, but neutron-rich disk ejecta require gas to be both neutronized in the disk and ejected before accretion. The magnetic field that enables ejection also thickens the disk and accelerates the inflow, lowering both the density and the time available for weak processing. To compute the resulting neutronization, we evolve the electron fraction of the inflowing gas, adopting at each radius the temperature that maximizes the net neutronization rate for the local density and instantaneous composition. This yields a lower limit on $Y_{\mathrm{e}}$ that is independent of the disk's thermal history. We adopt an optimistic unbinding radius of $R_{\mathrm{unb}}=10r_g$ for all magnetic fluxes capable of launching outflows. Combining this ejection condition with favorable assumptions of low black hole mass, ejection of midplane gas, and the upper end of the $\gamma$-ray burst (GRB) engine-power scale, which limits the accretion rate to ${\dot{M}}_{\mathrm{BH}}\lesssim 0.4M_{\odot }{\mathrm{s}}^{-1}$, gives a fiducial lower bound $Y_{\mathrm{e}}\gtrsim 0.33$, above the characteristic $Y_{\mathrm{e}}\approx 0.25$ threshold for heavy $r$-process production. Stronger magnetic flux, toward which jet-launching engines evolve, raises the lower bound to $Y_{\mathrm{e}}\gtrsim 0.49$. We conclude that collapsar disk outflows cannot supply the heavy $r$-process yields invoked for a dominant enrichment channel. Only engines with unusually high accretion rates, potentially including exceptionally luminous GRBs, such as GRB 221009A, and direct-horizon collapsars, may produce heavy $r$-process ejecta.