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Multi-Frequency Optical-Depth Maps and the Case for Free-Free Absorption in Two Compact Symmetric Radio Sources: the CSO candidate J1324+4048 and the CSO J0029+3457

We obtained dual-polarization VLBI observations at six frequencies of the compact symmetric object J0029+3457 and the CSO candidate J1324+4048. By comparing the three lower-frequency maps with extrapolations of the high frequency maps we produced maps of the optical depth as a function of frequency. The morphology of the optical-depth maps of J1324+4048 is strikingly smooth, suggestive of a foreground screen of absorbing gas. The spectra at the intensity peaks fit a simple free-free absorption model, with a reduced chi square ~ 2, better than a simple synchrotron self-absorption model, in which the reduced chi square ~ 3.5 - 5.5. We conclude that the case for free-free absorption in J1324+4048 is strong. The optical-depth maps of J0029+3457 exhibit structure, but the morphology does not correlate with that in the intensity maps. The fit of the spectra at the peaks to a simple free-free absorption model yields a reduced chi square ~ 1, but since the turnover is gradual the fit is relatively insensitive to the input parameters. We find that free-free absorption by a thin amount of gas in J0029+3457 is likely, but not definitive. One compact feature in J0029+3457 has an inverted spectrum even at the highest frequencies. We infer this to be the location of the core and estimate an upper limit to the magnetic field of order 3 Gauss at a radius of order 1 pc. In comparison with maps from observations at earlier epochs, no apparent growth in either J1324+4048 or J0029+3457 is apparent, with upper limits of 0.03 and 0.02 mas per yr, corresponding to maximum linear separation speeds of 0.6c and 0.4c.