Radio and X-ray variability in the Seyfert galaxy NGC 4051

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 2000-01. The X-ray observations were made with the Proportional Counter Array on the Rossi Timing X-ray Explorer (RXTE) and radio observations were made at 8.4 and 4.8 GHz with the Very Large Array (VLA). In the X-ray band NGC 4051 behaves very much like the analogue of 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 well-separated compact components almost in a line. This structure resembles the core and outer hot spots seen in powerful, jet-dominated, extragalactic radio sources and, although no jet is visible in NGC 4051, suggests that a weak jet may exist. However it has not previously been clear whether the nucleus is currently active in the radio band and whether there is any link between the radio and X-ray emission processes. 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 differing 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 per cent) over the 16-month period and is consistent with being constant. Within the 6 A configuration observations where we have greatest sensitivity we see marginal evidence for radio core variability of similar to 25 per cent (similar to 0.12 mJy at 8.4 GHz) on a 2-week time-scale, correlated with X-ray variations. These percentage variations are similar to those of the Seyfert galaxy NGC 5548, which is 10 times brighter. 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, although sensitivity is somewhat reduced, there is no sign of correlated X-ray/radio variability. NGC 4051 is one decade lower in radio luminosity than the radio/X-ray/mass fundamental plane for jet-dominated hard-state black holes, although the scatter around the plane is of the same order. The lack of radio variability commonly seen in hard-state GBHs may be explained by orientation effects. Another possibility, consistent with the lack of radio variability, is that the radio emission arises from the X-ray corona although, in that case, the linear structure of the compact radio components is hard to explain. A combination of corona and jet may explain the observations