Impact of dust size distribution including large dust grains on magnetic resistivity: an analytical approach

Abstract

This paper investigates the impact of dust size distribution on magnetic resistivity. In particular, we focus on its impact when the maximum dust size significantly increases from sub-micron. The first half of the paper describes our calculation method for magnetic resistivity based on the model of \citet{1987ApJ...320..803D} and shows that the method reproduces the results of a more realistic chemical reaction network calculations reasonably well. Then, we describe the results of the resistivity calculations for dust distributions with large maximum dust grains. Our results show that resistivity tends to decrease with dust growth, which is particularly true when the dust size power exponent $q$ is $q=2.5$. On the other hand, the decrease is less pronounced when the dust size power exponent $q$ is $q=3.5$, i.e., when the small dust is also responsible for the dust cross-section. Our results suggest that detailed dust coagulation and fragmentation processes play a vital role in the magnetic resistivities in protostar formation.