Very Long Baseline Interferometry Measured Proper Motion and Parallax of the {$\gamma$}-Ray Millisecond Pulsar PSR J0218+4232

PSR J0218+4232 is a millisecond pulsar (MSP) with a flux density similar to 0.9 mJy at 1.4 GHz. It is very bright in the high-energy X-ray and gamma-ray domains. We conducted an astrometric program using the European VLBI Network (EVN) at 1.6 GHz to measure its proper motion and parallax. A model-independent distance would also help constrain its gamma-ray luminosity. We achieved a detection of signal-to-noise ratio S/N > 37 for the weak pulsar in all five epochs. Using an extragalactic radio source lying 20 arcmin away from the pulsar, we estimate the pulsar's proper motion to be mu(alpha) cos delta = 5.35 +/- 0.05 mas yr (1) and mu(delta) = -3.74 +/- 0.12 mas yr (1), and a parallax of pi = 0.16 +/- 0.09 mas. The very long baseline interferometry (VLBI) proper motion has significantly improved upon the estimates from long-term pulsar timing observations. The VLBI parallax provides the first model-independent distance constraints: d = 6.3(-2.3)(+8.0) kpc, with a corresponding 3 sigma lower-limit of d = 2.3 kpc. This is the first pulsar trigonometric parallax measurement based solely on EVN observations. Using the derived distance, we believe that PSR J0218+4232 is the most energetic gamma-ray MSP known to date. The luminosity based on even our 3 sigma lower-limit distance is high enough to pose challenges to the conventional outer gap and slot gap models.