  In an effort to examine the relationship between flare flux and corresponding
CME mass, we temporally and spatially correlate all X-ray flares and CMEs in
the LASCO and GOES archives from 1996 to 2006. We cross-reference 6,733 CMEs
having well-measured masses against 12,050 X-ray flares having position
information as determined from their optical counterparts. For a given flare,
we search in time for CMEs which occur 10-80 minutes afterward, and we further
require the flare and CME to occur within +/-45 degrees in position angle on
the solar disk. There are 826 CME/flare pairs which fit these criteria.
Comparing the flare fluxes with CME masses of these paired events, we find CME
mass increases with flare flux, following an approximately log-linear, broken
relationship: in the limit of lower flare fluxes, log(CME mass)~0.68*log(flare
flux), and in the limit of higher flare fluxes, log(CME mass)~0.33*log(flare
flux). We show that this broken power-law, and in particular the flatter slope
at higher flare fluxes, may be due to an observational bias against CMEs
associated with the most energetic flares: halo CMEs. Correcting for this bias
yields a single power-law relationship of the form log(CME mass)~0.70*log(flare
flux). This function describes the relationship between CME mass and flare flux
over at least 3 dex in flare flux, from ~10^-7 to 10^-4 W m^-2.
