The nature of the infrared counterpart and of the optical nebula associated with the Central Compact Object in Vela Jr.

The X-ray source CXO\, J085201.4$-$461753in the few kyr-old Vela Jr. supernova remnant (G266.2-1.2) belongs to the peculiar class of isolated neutron stars dubbed "Central Compact Objects" (CCOs). At variance with the other CCOs, which are only detected in the X-rays, \cxo\ has been possibly detected also at other wavelengths. In particular, a candidate near-infrared counterpart (H = 21.6 $\pm$0.1) was detected by the Very Large Telescope (VLT) in addition to a 6\arcsec-wide nebula detected in H$\alpha$, interpreted as a velocity-driven bow-shock. Here, we present new near-infrared and optical VLT observations of the candidate counterpart to \cxo\ and its nebula to confirm the proposed associations. Moreover, we used archival Chandra observations to measure for the first time the CXO\, J085201.4$-$461753 proper motion. The comparison between the two sets of near-infrared VLT images, taken 10.56 year apart, do not show evidence of proper motion for the candidate counterpart to CXO\, J085201.4$-$461753, expected from its 4\arcmin\ offset from the SNR geometrical centre, with a $3\sigma$ upper limit of $\sim 10$ mas yr$^{-1}$. This is much smaller than the expected proper motion of $\sim$50--100 mas yr$^{-1}$, which, in turn, is below the $3\sigma$ upper limit of $\sim$ 300 mas yr$^{-1}$ that we obtained with Chandra. At the same time, VLT spectroscopy resolved the nebula optical emission, which is dominated by the NII doublet at 6548 and 6584 \AA\ and not by H$\alpha$. To summarise, we conclude that the proposed near-infrared counterpart is likely unassociated with \cxo\ and that the nebula is not a velocity-driven bow-shock.