We present intensive quasi-simultaneous X-ray and radio monitoring of the narrow line Seyfert 1 galaxy NGC 4051, over a 16 month period in 2000-2001. Observations were made with the Rossi Timing X-ray Explorer (RXTE) and the Very Large Array (VLA) at 8.4 and 4.8 GHz. In the X-ray band NGC 4051 behaves much like a Galactic black hole binary (GBH) system in a `soft-state'. In such systems, there has so far been no firm evidence for an active, radio-emitting jet like those found in `hard state' GBHs. VLBI observations of NGC 4051 show three co-linear compact components. This structure resembles the core and outer hot spots seen in powerful, jet-dominated, extragalactic radio sources and suggests the existence of a weak jet. Radio monitoring of the core of NGC 4051 is complicated by the presence of surrounding extended emission and by the changing array configurations of the VLA. Only in the A configuration is the core reasonably resolved. We have carefully removed the contaminations of the core by extended emission in the various arrays. The resulting lightcurve shows no sign of large amplitude variability (i.e. factor 50 %) over the 16 month period. Within the most sensitive configuration (A array) we see marginal evidence for radio core variability of ~25% (~0.12 mJy at 8.4GHz) on a 2-week timescale, correlated with X-ray variations. Even if the radio variations in NGC 4051 are real, the percentage variability is much less than in the X-ray band. Within the B configuration observations, where sensitivity is reduced, there is no sign of correlated X-ray/radio variability. The lack of radio variability in NGC 4051, which we commonly see in `hard state' GBHs, may be explained by orientation effects. Another possibility is that the radio emission arises from the X-ray corona, although the linear structure of the compact radio components here is hard to explain.Comment: 13 pages, 15 figures, 3 tables Accepted to MNRAS November 23. Received 2010 November 23; in original form 2010 August 2

The origin of the low luminosity radio emission in radio-quiet AGN, is unknown. The detection of a positive correlation between the radio and X-ray emission would imply a jet-like origin, similar to that seen in 'hard state' X-ray binary systems. In our previous work, we found no believable radio variability in the well known X-ray bright Seyfert 1 galaxy NGC 4051, despite large amplitude X-ray variability. In this study we have carefully re-analysed radio and X-ray observations using the same methods as our previous work, we again find no evidence for core radio variability.In direct contrast to our findings, another study claim significant radio variability and a distinctive anti-correlation between radio and X-ray data for the same source. The other study report only integral flux values and do not consider the effect of the changing array on the synthesised beam. In both our studies of NGC 4051 we have taken great care to account for the effect that the changing beam size has on the measured radio flux and as a result we are confident that our method gives more accurate values for the intrinsic core radio flux. However, the lack of radio variability we find is hard to reconcile because radio images of NGC 4051 do show jet-like structure. We suggest that the radio structures observed are likely the result of a previous period of higher radio activity and that the current level of radio emission from a compact nuclear jet is low.

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