  Main-belt asteroid (6478) Gault unexpectedly sprouted two tails in late 2018
and early 2019, identifying it as a new active asteroid. Here we present
observations obtained by the 1.2-m Zwicky Transient Facility survey telescope
that provide detailed time-series coverage of the onset and evolution of
Gault's activity. Gault exhibited two brightening events, with the first one
starting on 2018 Oct. 18$\pm5$ days and a second one starting on 2018 Dec.
24$\pm1$ days. The amounts of mass released are $2\times10^7$ kg and
$1\times10^6$ kg, respectively. Based on photometric measurements, each event
persisted for about a month. Gault's color has not changed appreciably over
time, with a pre-outburst color of $g_\mathrm{PS1}-r_\mathrm{PS1}=0.50\pm0.04$
and $g_\mathrm{PS1}-r_\mathrm{PS1}=0.46\pm0.04$ during the two outbursts.
Simulations of dust dynamics shows that the ejecta consists of dust grains of
up to 10 $\mu$m in size that are ejected at low velocities below
$1~\mathrm{m~s^{-1}}$ regardless of particle sizes. This is consistent with
non-sublimation-driven ejection events. The size distribution of the dust
exhibits a broken power-law, with particles at 10--20 $\mu$m following a
power-law of $-2.5$ to $-3.0$, while larger particles follow a steeper slope of
$-4.0$. The derived properties can be explained by either rotational excitation
of the nucleus or a merger of a near-contact binary, with the latter scenario
to be statistically more likely.
