| Summary: | This thesis is an investigation into the emission from an individual Narrow Line Seyfert 1 (NLS1) Active Galactic Nuclei (AGN) NGC 4051. NLS1s have all the properties of Seyfert galaxies but show peculiar characteristics, including the narrowest Balmer lines, strongest Fe II emission and extreme properties in the X-rays. NGC 4051, is one of the most X-ray bright Seyferts and it has been studied extensively by a number of X-ray observatories. Recent studies have also revealed that Seyfert cores are variable at radio wavelengths, however, there are very few Seyfert radio variability investigations, and this is one of the first that also investigates the radio/X-ray (jet/disc) coupling. It has been known for some time that both the X-ray and continuum radio observations provide an optimal tool to access the innermost regions of the AGN. A combination of X-ray, radio and optical data is used here to give an in depth analysis of both the core and extended emission regions of NLS1 NGC 4051. This work reveals that there is no clear evidence for radio variability in the core emission of NGC 4051 at 8.4 GHz with the possible exception of very low amplitude » 0.12 mJy variations detected in VLA A configuration. Deep VLA observations reveal a mean spectral index value of a » −0.3 for the core, suggesting a self absorbed jet. The surrounding radio emission has steeper spectral index values in the range of −0.5 < a < −1.6 which suggests the extended radio emission is optically thin synchrotron emission. During the A configuration observations both VLA radio data sets (2000-2001 and 2008-2009) reveal a very weak positive correlation between the radio and much larger amplitude X-ray variations but there is no evidence for a b value much greater than » 0.1 for the LR µ LbX relationship, which is consistent with a constant radio luminosity for the core. Collimated VLBI structure is detected which hints at the presence of an unseen jet. The proposed jet is of non-negligible power and estimates of the buoyancy speed of the lobes, and the break timescales from the radio spectral index provide evidence for radio activity in NGC 4051 occurring on timescales greater than > 106 years. Also, a change in the relative distance of the SW hotspot with respect to the core (seen in VLBI images) gives an apparent jet velocity 0.012 pc yr−1, equivalent to a speed of 11,700 kms−1 (» 0.04 c). Deep VLA radio imaging of NGC 4051 shows double lobed radio emission, which lies along the same PA as optical [OIII] emission. The nucleus of the [OIII] emission is coincident with the core radio emission. This structure suggests the presence of a double sided ionisation cone, where both radio and optical emission are collimated by the same disc or tori.
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