A VLBI distance and transverse velocity for PSR B1913+16

Using the Very Long Baseline Array, we have made astrometric observations of the binary pulsar B1913+16 spanning an 18 month period in 2014 - 2015. From these observations we make the first determination of the annual geometric parallax of B1913+16, measuring $\pi= 0.24^{+0.06}_{-0.08}$ milliarcseconds (68% confidence interval). The inferred parallax probability distribution differs significantly from a Gaussian. Using our parallax measurement and prior information on the spatial and luminosity distributions of the millisecond pulsar population, we infer a distance of $d=4.1^{+2.0}_{-0.7}$ kpc, which is significantly closer than the $9.8 \pm 3.1$ kpc suggested by the pulsar's dispersion measure and analyses of the ionized interstellar medium. While the relatively low significance of the parallax detection ($\sim$3$\sigma$) currently precludes an improved test of general relativity using the orbital decay of PSR B1913+16, ongoing observations with improved control of systematic astrometric errors could reach the 10% distance uncertainty required for this goal. The proper motion measured by our VLBI astrometry differs substantially from that obtained by pulsar timing, a discrepancy that has also been found between the proper motion measurements made by interferometers and pulsar timing for some other pulsars and which we speculate is the result of timing noise or dispersion measure variations in the timing data set. Our parallax and proper motion measurements yield a transverse velocityof $15^{+8}_{-4}$ km s$^{-1}$ in the solar reference frame. Analysis incorporating galactic rotation and solar motion finds the space velocity of the pulsar relative to its standard of rest has a component 22$^{+7}_{-3}$ km s$^{-1}$ perpendicular to the galactic plane and components of order 100 km s$^{-1}$ parallel to the galactic plane.