Hubble Space Telescope Snapshot Survey for Resolved Companions of Galactic Cepheids: Final Results.

Cepheids in multiple systems provide information on the outcome of the formation of massive stars. They can also lead to exotic end-stage objects. This study concludes our survey of 70 galactic Cepheids using the {\it Hubble Space Telescope\} (\HST) Wide Field Camera~3 (WFC3) with images at two wavelengths to identify companions closer than $5\arcsec$. In the entire WFC3 survey we identify 16 probable companions for 13 Cepheids. The seven Cepheids having resolved candidate companions within $2"$ all have the surprising property of themselves being spectroscopic binaries (as compared with a 29\% incidence of spectroscopic binaries in the general Cepheid population). That is a strong suggestion that an inner binary is linked to the scenario of a third companion within a few hundred~AU\null. This characteristic is continued for more widely separated companions. Under a model where the outer companion is formed first, it is unlikely that it can anticipate a subsequent inner binary. Rather it is more likely that a triple system has undergone dynamical interaction, resulting in one star moving outward to its current location. {\it Chandra\} and {\it Gaia\} data as well as radial velocities and \HSTSTIS and {\it IUE\} spectra are used to derive properties of the components of the Cepheid systems. The colors of the companion candidates show a change in distribution at approximately 2000~AU separations, from a range including both hot and cool colors for closer companions, to only low-mass companions for wider separations.