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\def\gsim{\,\lower.6ex\hbox{$\buildrel>\over\sim$} \,}
We observed the quasar 3C\,345 with ROSAT\/ in the soft X-ray band in June 1990, together with quasi-simultaneous VLBI imaging at 1.7, 5.0, 8.3, 10.7 and 22.2 GHz. These data were obtained to study the inverse-Compton process in the parsec-scale superluminal jet, which simple models suggest is the origin of the X-rays. The X-ray spectrum is well-fitted by a power-law model which includes absorption by the observed Galactic HI column density; there is some indication that the flux density is lower than earlier Einstein\/ measurements.
From the VLBI images, we can deduce the radio spectra and angular sizes of individual features in the jet, though in practice this can be done reliably only for components which appear discrete. At the epoch of the X-ray observation, we measure an inverted spectrum for the nucleus, and a normal spectrum ($\alpha \approx 0.7$) for component `C5'. Using a simple homogeneous-sphere model, we infer a limit of $\delta \gsim 7$ for the Doppler factor of C5, implying a Lorentz factor $\gamma \gsim 3.5$, which is consistent with its measured superluminal motion. C5 may be plausibly modeled as a sphere, but our VLBI images show that the nucleus and other jet features are much more complicated.
We discuss steps toward more sophisticated modeling of the jet physics. We plan to use imaging of the time-varying VLBI structure to calculate X-ray variability -- a key test of the inverse-Compton model.
