On the Distances to the X-Ray Binaries Cygnus X-3 and GRS 1915+105

In this paper we significantly improve estimates of distance to the X-ray binary systems Cyg X-3 and GRS 1915+105. We report a highly accurate trigonometric parallax measurement for Cyg X-3 using the Very Long Baseline Array at 43 GHz, placing the source at a distance of ${9.67}_{-0.48}^{+0.53}$ kpc. We also use Galactic proper motions and line-of-sight radial velocity measurements to determine three-dimensional (3D) kinematic distances to both systems, under the assumption that they have low peculiar velocities. This yields distances of 8.95 ± 0.96 kpc for Cyg X-3 and 9.4 ± 0.6 (statistical) ± 0.8 (systematic) for GRS 1915+105. The good agreement between parallax and 3D kinematic distances validates the assumption of low peculiar velocities, and hence small natal kicks, for both of the systems. For a source with a low peculiar velocity, given its parallax distance, Cyg X-3 should have a V _LSR near -64 ± 5 km s^-1. Our measurements imply a slightly higher inclination angle, and hence lower black hole mass, for GRS 1915+105 than found from previous work by Reid et al. and strengthen arguments from X-ray polarization that Cyg X-3 would be an ultraluminous X-ray source if viewed face-on.