Dust evolution during a protostellar collapse: Influence on the coupling between the neutral gas and magnetic field

The extent of the coupling between the magnetic field and the gas during the collapsing phase of star-forming cores is strongly affected by the dust size distribution, which is expected to evolve by means of coagulation, fragmentation, and other collision outcomes. We aim to investigate the influence of key parameters on the evolution of the dust distribution, as well as on the magnetic resistivities during protostellar collapse. We performed a set of collapsing single-zone simulations with shark. The code computes the evolution of the dust distribution, accounting for different grain growth and destruction processes, with the grain collisions being driven by brownian motion, turbulence, and ambipolar drift. It also computes the charges carried by each grain species and the ion and electron densities, as well as the magnetic resistivities. We find that the dust distribution significantly evolves during the protostellar collapse, shaping the magnetic resistivities. The peak size of the distribution, population of small grains, and, consequently, the magnetic resistivities are controlled by both coagulation and fragmentation rates. Under standard assumptions, the small grains coagulate very early as they collide by ambipolar drift, yielding magnetic resistivities that are many orders of magnitude apart from the non-evolving dust case. In particular, the ambipolar resistivity, AD, is very high prior to n_ H cm^. As a consequence, magnetic braking is expected to be ineffective. In this case, large size protoplanetary discs should result, which is inconsistent with recent observations. To alleviate this tension, we identified mechanisms that are capable of reducing the ambipolar resistivity during the ensuing protostellar collapse. Among them, electrostatic repulsion and grain-grain erosion feature as the most promising approaches. The evolution of the magnetic resistivities during the protostellar collapse and consequently the shape of the magnetic field in the early life of the protoplanetary disc strongly depends on the possibility to repopulate the small grains or to prevent their early coagulation. Therefore, it is crucial to better constrain the collision outcomes and the dust grain's elastic properties, especially the grain's surface energy based on both theoretical and experimental approaches.