Enhancing LSST Science with Euclid Synergy

This white paper is the result of the Tri-Agency Working Group (TAG) appointed to develop synergies between missions and is intended to clarify what LSST observations are needed in order to maximally enhance the combined science output of LSST and Euclid. To facilitate LSST planning we provide a range of possible LSST surveys with clear metrics based on the improvement in the Dark Energy figure of merit (FOM). To provide a quantifiable metric we present five survey options using only between 0.3 and 3.8% of the LSST 10 year survey. We also provide information so that the LSST DDF cadence can possibly be matched to those of emph{Euclid} in common deep fields, SXDS, COSMOS, CDFS, and a proposed new LSST deep field (near the Akari Deep Field South). Co-coordination of observations from the Large Synoptic Survey Telescope (LSST) and Euclid will lead to a significant number of synergies. The combination of optical multi-band imaging from LSST with high resolution optical and near-infrared photometry and spectroscopy from emph{Euclid} will not only improve constraints on Dark Energy, but provide a wealth of science on the Milky Way, local group, local large scale structure, and even on first galaxies during the epoch of reionization. A detailed paper has been published on the Dark Energy science case (Rhodes et al.) by a joint LSST/Euclid working group as well as a white paper describing LSST/Euclid/WFIRST synergies (Jain et al.), and we will briefly describe other science cases here. A companion white paper argues the general science case for an extension of the LSST footprint to the north at airmass < 1.8, and we support the white papers for southern extensions of the LSST survey.