As part of an ongoing program to use the VLA to set limits on fluctuations in the cosmic microwave background (CMBR), Ed Fomalont, Ken Kellermann, Eric Richards, Rogier Windhorst and I made extended observations of a region centered at (J2000) and The field contained no radio sources with flux density at our observing frequency of 8.4 GHz exceeding 500 ; optical data was available as part of the Medium Deep Survey (see Windhorst et al. (1995)). We combined observations in the C and D configurations of the VLA, giving us a synthesized beam of full width at half maximum and a field of view of to the half power points of primary beam. Our resolution image had an rms sensitivity of 1.5 , making it the most sensitive radio image obtained to date at any frequency or resolution. Lower resolution images were made by applying a gaussian taper to the data. Radio contours of the map are shown in Fig.1, superimposed on the MDS survey image from HST (see Windhorst et al. (1995)). That paper also discusses the optical identifications of the 46 radio sources we detected above a 4.7 flux threshold of 7 .
Figure 1: The 13 MDS field (grey scale) with the radio contours overlaid. The possible S--Z feature, or ``Black Cloud'', is southwest of the image center.
In order to use this image to set limits on , we needed to remove the effect of foreground radio sources and of instrument noise. The obvious sources, those visible in Fig.1 or exceeding were removed as described in Fomalont et al. (1993) or Partridge et al. (1997). We found the position of each source, then performed a CLEAN in a box around each to a predetermined level of , and finally subtracted the visibility function formed from these clean components from the raw visibility to provide a corrected set of visibility data. The resulting map is thus free of bright sources and their side lobes at all resolutions. But we recognized that additional, weaker sources were still present. The variance contributed by these was removed by Monte Carlo simulations. We assumed that the source counts obeyed the law (Kellermann et al. (1997)),
then scattered sources with fluxes ranging from 7 down to 0.1 at random in the map. This allowed us to estimate (see Partridge et al. (1997)) the weak source variance , which was subtracted from the observed map variance.
We also needed to estimate instrument noise. We used several means to do so (see Partridge et al. (1997)); in particular, we constructed a difference map by subtracting one half of the data from the other. In this map, real sky signals subtract out, leaving just instrument noise uniformly spread over the map. Some of the values found by this process are shown in Table 1. Subtracting both the weak source variance and the instrument variance allowed us to estimate the residual variance in the maps. To be conservative in setting upper limits on , we ascribe all of the observed residual variance to fluctuations in the microwave background at the appropriate angular scale. Sky variances were converted to 95% confidence limits on assuming K and using the measured beam solid angle at each resolution.
Table 1: Instrument noise. Corrected for primary beam response. 1993 and 1996 results combined (Fomalont et al. (1993), Partridge et al. (1997)).
We also combined these observations with some made in a different field in order to produce overall limits on total intensity and polarized CMBR fluctuations on a range of angular scales. Results from our work (Partridge et al. (1997)) are displayed in Table 2, along with comparable results from other groups.
Table 2: Observational results, . (a)At 95% confidence. (b) Beam-switch angle.