Impact of grain size distributions on the dust enrichment in high-redshift quasars

In high-redshift ($z>5$) quasars, a large amount of dust ($\textstyle\sim 10^{8} \mathrm{M}_{\sun}$) has been observed. In order to explain the large dust content, we focus on a possibility that grain growth by the accretion of heavy elements is the dominant dust source. We adopt a chemical evolution model applicable to nearby galaxies but utilize parameters adequate to high-$z$ quasars. It is assumed that metals and dust are predominantly ejected by Type II supernovae (SNe). We have found that grain growth strongly depends on the grain size distribution. If we simply use the size distribution of grains ejected from SNe, grain growth is inefficient because of the lack of small grains (i.e.\ small surface-to-volume ratio of the dust grains). However, if we take small grain production by interstellar shattering into consideration, grain growth is efficient enough to account for the rich dust abundance in high-$z$ quasars. Our results not only confirm that grain growth is necessary to explain the large amount of dust in high-$z$ quasars, but also demonstrate that grain size distributions have a critical impact on grain growth.