Extended Data Fig. 8: Astrometric characterization of ZTF J1406+1222.

a, The measured Gaia eDR3 J2016 position of the sdK is shown by the blue circles and the measured position of the variable black widow component is illustrated by the red diamonds. The magenta stars represent the projected J2021.5 position of the sdK, given the proper motion in its Gaia astrometric solution. The solid black line shows the position angle between the two Gaia source positions. The pink star indicates the position of the source in an SDSS u image obtained in J2003.4, and the black star indicates the source position in the SDSS z image at this epoch. Because the black widow component dominates in the u band, and the sdK in the z band, these positions should approximately reflect the positions of the two components in J2003.4, and the dashed arrows indicate that these sources are co-moving, having both translated their positions considerably since that epoch (by about an arcsecond). b, The black points indicate the measured centroid of the point spread function of the variable source with respect to a reference star on the HiPERCAM r-band images. This centroid moves back and forth between the two sources of luminosity as the black widow component brightens and fades, and gives a precise estimate of the position angle between the two sources when the data were obtained, at epoch J2021.5. The solid blue line is a linear fit to the data used to derive a slope to measure this position angle, the value of which is shown in the legend. The slope is consistent with the J2016 position angle and clearly inconsistent with only the sdK having moved since epoch J2016.0, demonstrating that the two sources must indeed be co-moving, and thus part of a hierarchical triple system.