  SPHEREx is a proposed NASA MIDEX mission selected for Phase A study. SPHEREx
would carry out the first all-sky spectral survey in the near infrared. At the
end of its two-year mission, SPHEREx would obtain 0.75-to-5$\mu$m spectra of
every 6.2 arcsec pixel on the sky, with spectral resolution R>35 and a
5-$\sigma$ sensitivity AB$>$19 per spectral/spatial resolution element. More
details concerning SPHEREx are available at http://spherex.caltech.edu. The
SPHEREx team has proposed three specific science investigations to be carried
out with this unique data set: cosmic inflation, interstellar and circumstellar
ices, and the extra-galactic background light. Though these three themes are
undoubtedly compelling, they are far from exhausting the scientific output of
SPHEREx. Indeed, SPHEREx would create a unique all-sky spectral database
including spectra of very large numbers of astronomical and solar system
targets, including both extended and diffuse sources. These spectra would
enable a wide variety of investigations, and the SPHEREx team is dedicated to
making the data available to the community to enable these investigations,
which we refer to as Legacy Science. To that end, we have sponsored two
workshops for the general scientific community to identify the most interesting
Legacy Science themes and to ensure that the SPHEREx data products are
responsive to their needs. In February of 2016, some 50 scientists from all
fields met in Pasadena to develop these themes and to understand their
implications for the SPHEREx mission. The 2016 workshop highlighted many
synergies between SPHEREx and other contemporaneous astronomical missions,
facilities, and databases. Consequently, in January 2018 we convened a second
workshop at the Center for Astrophysics in Cambridge to focus specifically on
these synergies. This white paper reports on the results of the 2018 SPHEREx
workshop.
