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.