Using high-precision astrometric optical observations from the Walter Baade Magellan Telescope in conjunction with high-resolution very long baseline interferometric ( VLBI ) radio imaging with the Very Long Baseline Array ( VLBA ) , we have located the core of the X-ray binary system XTE J1752-223 .
Compact radio emission from the core was detected following the state transition from the soft to the hard X-ray state .
Its position to the south-east of all previously-detected jet components mandated a re-analysis of the existing VLBI data .
Our analysis suggests that the outburst comprised at least two ejection events prior to 2010 February 26 .
No radio-emitting components were detected to the south-east of the core at any epoch , suggesting that the receding jets were Doppler-deboosted below our sensitivity limit .
From the ratio of the brightness of the detected components to the measured upper limits for the receding ejecta , we constrain the jet speed \beta > 0.66 and the inclination angle to the line of sight \theta < 49 ^ { \circ } .
Assuming that the initial ejection event occurred at the transition from the hard intermediate state to the soft intermediate state , an initial period of ballistic motion followed by a Sedov phase ( i.e .
self-similar adiabatic expansion ) appears to fit the motion of the ejecta better than a uniform deceleration model .
The accurate core location can provide a long time baseline for a future proper motion determination should the system show a second outburst , providing insights into the formation mechanism of the compact object .