The proper motion of the galactic center pulsar relative to Sagittarius A

We measure the proper motion of the pulsar PSR J1745-2900 relative to the Galactic center massive black hole, Sgr A∗, using the Very Long Baseline Array (VLBA). The pulsar has a transverse velocity of 236 ± 11 km s-1 at position angle 22 ± 2 deg east of north at a projected separation of 0.097 pc from Sgr A∗. Given the unknown radial velocity, this transverse velocity measurement does not conclusively prove that the pulsar is bound to Sgr A∗; however, the probability of chance alignment is very small. We do show that the velocity and position are consistent with a bound orbit originating in the clockwise disk of massive stars orbiting Sgr A∗ and a natal velocity kick of ≲ 500 km s-1. An origin among the isotropic stellar cluster is possible but less probable. If the pulsar remains radio-bright, multiyear astrometry of PSR J1745-2900 can detect its acceleration and determine the full three-dimensional orbit. We also demonstrate that PSR J1745-2900 exhibits the same angular broadening as Sgr A∗ over a wavelength range of 3.6 cm to 0.7 cm, further confirming that the two sources share the same interstellar scattering properties. Finally, we place the first limits on the presence of a wavelength-dependent shift in the position of Sgr A∗, i.e., the core shift, one of the expected properties of optically thick jet emission. Our results for PSR J1745-2900 support the hypothesis that Galactic center pulsars will originate from the stellar disk and deepen the mystery regarding the small number of detected Galactic center pulsars