The orbital period of the long-period and colliding-wind binary WR 146 from radio interferometry of the shock cone

We report the first measurement of the orbital period of a long-period colliding-wind binary (CWB) system WR 146, derived by tracing the rotational morphology of its wind-colliding region (WCR) and the relative orientation of the two binary components. This result is based on our imaging observations using the Very Long Baseline Array (VLBA) and the European Very Long Baseline Interferometry (VLBI) Network (EVN), combined with archival data from VLBA, EVN, the Very Large Array (VLA), the enhanced Multi-Element Radio-Linked Interferometer Network (eMERLIN) arrays, and optical images from the Hubble Space Telescope (HST). We evaluated two methods for determining the binary's orbital period based on the images of the WCR: (I) fitting the shock cone of the WCR and (II) stacking images using the cross-correlation function. Using these techniques, we find orbital period estimates of 810+120-90 years from method I and 1120+540-270 years from method II, both of which support a long orbital period of approximately 1,000 years. Furthermore, we analyzed archival spectral data of WR 146 to estimate the stellar wind velocities of the binary components, finding no significant orbital phase lag between the binary orientation and the WCR rotation. We also estimate the range of the binary's mass using the currently measured parameters.