Dust coagulation and fragmentation in a collapsing cloud core and their influence on non-ideal magnetohydrodynamic effects

We determine the time evolution of the dust particle size distribution during the collapse of a cloud core, accounting for both dust coagulation and dust fragmentation, to investigate the influence of dust growth on non-ideal magnetohydrodynamic effects.The density evolution of the collapsing core is given by a one-zone model. We assume two types of dust model: dust composed only of silicate (silicate dust) and dust with a surface covered by $\mathrm{H_{2}O}$ ice ($\mathrm{H_{2}O}$ ice dust). When only considering collisional coagulation, the non-ideal magnetohydrodynamic effects are not effective in the high-density region for both the silicate and $\mathrm{H_{2}O}$ ice dust cases. This is because dust coagulation reduces the abundance of small dust particles, resulting in less efficient adsorption of charged particles on the dust surface. For the silicate dust case, when collisional fragmentation is included, the non-ideal magnetohydrodynamic effects do apply at a high density of $n_{\mathrm{H}}>10^{12} \ \mathrm{cm^{-3}}$ because of the abundant production of small dust particles. On the other hand, for the $\mathrm{H_{2}O}$ ice dust case, the production of small dust particles due to fragmentation is not efficient. Therefore, for the $\mathrm{H_{2}O}$ ice dust case, non-ideal magnetohydrodynamic effects apply only in the range $n_{\mathrm{H}}\gtrsim 10^{14} \ \mathrm{cm^{-3}}$, even when collisional fragmentation is considered. Our results suggest that it is necessary to consider both dust collisional coagulation and fragmentation to activate non-ideal magnetohydrodynamic effects, which should play a significant role in the star and disk formation processes.