  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 to be greater than 0.66c and the inclination
angle to the line of sight to be less than 49 degrees. 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.

High Energy Astrophysical Phenomena