The galaxy CXOC J100043.1 020637, also known as CID-42, is a highly unusual object. As an apparent galaxy merger remnant, it displays signatures of both an inspiraling, kiloparsec-scale active galactic nucleus (AGN) pair and of a recoiling AGN with a kick velocity of ≳ 1300 km s-1. Among recoiling AGN candidates, CID-42 alone has both spatial offsets (in optical and X-ray bands) and spectroscopic offsets. In order to constrain the relative likelihood of both scenarios, we develop models using hydrodynamic galaxy merger simulations coupled with radiative transfer calculations. Our gas-rich, major merger models are generally well matched to the galactic morphology and to the inferred stellar mass and star formation rate. We show that a recoiling supermassive black hole (SMBH) in CID-42 should be observable as an AGN at the time of observation. However, in order for the recoiling AGN to produce narrow-line emission, it must be observed shortly after the kick while it still inhabits a dense gaseous region, implying a large total kick velocity (vk ≳ 2000 km s-1). For the dual AGN scenario, an unusually large broad-line offset is required, and the best match to the observed morphology requires a galaxy that is less luminous than CID-42. Further, the lack of X-ray emission from one of the two optical nuclei is not easily attributed to an intrinsically quiescent SMBH or to a Compton thick galactic environment. While the current data do not allow either the recoiling or the dual AGN scenario for CID-42 to be excluded, our models highlight the most relevant parameters for distinguishing these possibilities with future observations. In particular, high-quality, spatially resolved spectra that can pinpoint the origin of the broad-line and narrow-line features will be critical for determining the nature of this unique source.
