The Canada-France Imaging Survey: Reconstructing the Milky Way Star
  Formation History from its White Dwarf Population
  As the remnants of stars with initial masses $\lesssim$ 8 M$_{\odot}$, white
dwarfs contain valuable information on the formation histories of stellar
populations. In this paper, we use deep, high-quality, u-band photometry from
the Canada France Imaging Survey (CFIS), griz photometry from Pan-STARRS 1
(PS1), as well as proper motions from Gaia DR2, to select 25,156 white dwarf
candidates over $\sim$4500 deg$^2$ using a reduced proper motion diagram. We
develop a new white dwarf population synthesis code that returns mock
observations of the Galactic field white dwarf population for a given star
formation history, while simultaneously taking into account the geometry of the
Milky Way, survey parameters, and selection effects. We use this model to
derive the star formation histories of the thin disk, thick disk, and stellar
halo. Our results show that the Milky Way disk began forming stars (11.3 $\pm$
0.5) Gyr ago, with a peak rate of (8.8 $\pm$ 1.4) M$_{\odot}$yr$^{-1}$ at (9.8
$\pm$ 0.4) Gyr, before a slow decline to a constant rate until the present day
--- consistent with recent results suggesting a merging event with a satellite
galaxy. Studying the residuals between the data and best-fit model shows
evidence for a slight increase in star formation over the past 3 Gyr. We fit
the local fraction of helium-atmosphere white dwarfs to be (21 $\pm$ 3) %.
Incorporating this methodology with data from future wide-field surveys such as
LSST, Euclid, CASTOR, and WFIRST should provide an unprecedented view into the
formation of the Milky Way at its earliest epoch through its white dwarfs.
