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.
Accepted for publication in ApJ. 14 pages, 8 figures, 2 tables