Interferometric Monitoring of Gamma-ray Bright AGNs: Measuring the Magnetic Field Strength of 4C +29.45.

We present the results of multi-epoch, multi-frequency monitoring of a blazar 4C +29.45, which was regularly monitored as part of the Interferometric Monitoring of GAmma-ray Bright Active Galactic Nuclei (iMOGABA) program - a key science program of the Korean Very long baseline interferometry Network (KVN). Observations were conducted simultaneously at 22, 43, 86, and 129 GHz during the 4 years from 5 December 2012 to 28 December 2016. We also used additional data from the 15 GHz Owens Valley Radio Observatory (OVRO) monitoring program. From the 15 GHz light curve, we estimated the variability time scales of the source during several radio flux enhancements. We found that the source experienced 6 radio flux enhancements with variability time scales of 9-187 days during the observing period, yielding corresponding variability Doppler factors of 9-27. From the multi-frequency simultaneous KVN observations, we were able to obtain accurate radio spectra of the source and hence to more precisely measure the turnover frequencies $\nu_{\rm r}$ of synchrotron self-absorbed (SSA) emission with a mean value of $\nu_{rm r}$ = 28.9 GHz. Using jet geometry assumptions, we estimated the size of the emitting region at the turnover frequency. We found that the equipartition magnetic field strength is up to two orders of magnitudes higher than the SSA magnetic field strength (0.001-0.1 G). This is consistent with the source being particle dominated. We performed a careful analysis of the systematic errors related to making these estimations. From the results, we concluded that the equipartition region locates upstream the SSA region.