Radio observations are an effective tool to discover particle acceleration regions in colliding-wind binaries, through detection of synchrotron radiation; these regions are natural laboratories for the study of relativistic particles. Wind-collision region (WCR) models can reproduce the radio continuum spectra of massive binaries that contain both thermal and non-thermal radio emission; however, key constraints for models come from high-resolution imaging. Only five WCRs have been resolved to date at radio frequencies at milliarcsec (mas) angular scales. The source HD 93129A, prototype of the very few known O2 I stars, is a promising target for study: recently, a second massive, early-type star about 50 mas away was discovered, and a non-thermal radio source detected in the region. Preliminary long-baseline array data suggest that a significant fraction of the radio emission from the system comes from a putative WCR. We sought evidence that HD 93129A is a massive binary system with colliding stellar winds that produce non-thermal radiation, through spatially resolved images of the radio emitting regions. We completed observations with the Australian Long Baseline Array (LBA) to resolve the system at mas angular resolutions and reduced archival Australia Telescope Compact Array (ATCA) data to derive the total radio emission. We also compiled optical astrometric data of the system in a homogeneous way. We reduced historical Hubble Space Telescope data and obtained absolute and relative astrometry with milliarcsec accuracy. The astrometric analysis leads us to conclude that the two stars in HD 93129A form a gravitationally bound system. The LBA data reveal an extended arc-shaped non-thermal source between the two stars, indicative of a WCR. The wind momentum-rate ratio of the two stellar winds is estimated. The ATCA data show a point source with a change in flux level ...
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