Expected dust grain size distributions in galaxies detected by ALMA at
  $z>7$
  The dust properties in high-redshift galaxies provide clues to the origin of
dust in the Universe. Although dust has been detected in galaxies at redshift
$z>7$, it is difficult to constrain the dominant dust sources only from the
total dust amount. Thus, we calculate the evolution of grain size distribution,
expecting that different dust sources predict different grain size
distributions. Using the star formation time-scale and the total baryonic mass
constrained by the data in the literature, we calculate the evolution of grain
size distribution. To explain the total dust masses in ALMA-detected $z>7$
galaxies, the following two solutions are possible: (i) high dust condensation
efficiency in stellar ejecta, and (ii) efficient accretion (dust growth by
accreting the gas-phase metals in the interstellar medium). We find that these
two scenarios predict significantly different grain size distributions: in (i),
the dust is dominated by large grains ($a\gtrsim 0.1~\mu$m, where $a$ is the
grain radius), while in (ii), the small-grain ($a\lesssim 0.01~\mu$m) abundance
is significantly enhanced by accretion. Accordingly, extinction curves are
expected to be much steeper in (ii) than in (i). Thus, we conclude that
extinction curves provide a viable way to distinguish the dominant dust sources
in the early phase of galaxy evolution.
