radius smaller and larger than $\sim 0.03~\micron$.

Model {#sec:model}
=====

Hydrodynamic simulation
-----------------------

We perform a hydrodynamic simulation of an isolated galaxy using the smoothed particle hydrodynamics (SPH) code <span style="font-variant:small-caps;">gadget3-osaka</span> [A17; @2019MNRAS.484.2632S], which is based on the <span style="font-variant:small-caps;">gadget-3</span> code [originally described in @2005MNRAS.364.1105S]. In our simulation, the star formation and metal/dust production are treated consistently with gravitational/hydrodynamic evolution of a Milky-Way-like isolated galaxy. Dust grains are assumed to be coupled with gas particles (Section \[subsec:size\_distribution\]).

Our present run corresponds to the M12 run in @2019MNRAS.484.2632S, and the total mass of isolated galaxy is $\sim 10^{12}~{\rm M}_{\sun}$. We employ $10^5$ dark matter particles, $10^5$ gas (SPH) particles, $10^5$ and $1.25\times 10^4$ collisionless particles that represent stars in the disc and the bulge, respectively. We adopt a fixed gravitational softening length of $\epsilon_{\rm grav} = 80$pc, but allow the minimum gas smoothing length to reach 10 percent of $\epsilon_{\rm grav}$. The final gas smoothing length reaches $\sim 30$pc as the gas becomes denser owing to radiative cooling.

The difference between this paper and A17 is as follows. We additionally include the metal/dust supply and the feedback from AGB stars. We use the [CELib]{} package [@2017AJ....153...85S] for metal generation and follow 