The Host Galaxy of the Recoiling Black Hole Candidate in 3C 186: An Old
  Major Merger Remnant at the Center of a z=1 Cluster
  3C186, a radio-loud quasar at $z=1.0685$, was previously reported to have
both velocity and spatial offsets from its host galaxy, and has been considered
as a promising candidate for a gravitational wave recoiling black hole
triggered by a black hole merger. Another possible scenario is that 3C186 is in
an on-going galaxy merger, exhibiting a temporary displacement. In this study,
we present analyses of new deep HST/WFC3-IR and ACS images, aiming to
characterize the host galaxy and test this alternative scenario. We carefully
measure the light-weighted center of the host and reveal a significant spatial
offset from the quasar core ($11.1\pm0.1$kpc). The direction of the confirmed
offset aligns almost perpendicularly to the radio jet. We do not find evidence
of a recent merger, such as a young starburst in disturbed outskirts, but only
marginal light concentration in F160W at $\sim30$kpc. The host consists of
matured ($>200$Myr) stellar populations and one compact star-forming region. We
compare with hydro-dynamical simulations and find that those observed features
are consistently seen in late-stage merger remnants. Taken together, those
pieces of evidence indicate that the system is not an on-going/young merger
remnant, suggesting that the recoiling black hole scenario is still a plausible
explanation for the puzzling nature of 3C186.
