The maser receiver produced a 50 K overall system temperature and a 16 MHz bandwidth. Its gain was controlled by a noise-adding radiometer designed by M. J. Yerbury. Unlike a conventional Dicke-switch radiometer, which balances the detected baseline level but does not stabilize the receiver gain at all, the noise adding radiometer reduced receiver gain changes to less than 1 %) per night, greatly simplifying the flux density calibration procedure. Each galaxy was observed with one or more 80 second sidereal-rate drift scans centered on its accurately known optical position (Dressel and Condon 1976). During a typical night 130 galaxies and 10 calibration sources were so observed. A 3.4 K thermal noise diode was fired several times per night to verify the receiver gain stability. Most galaxies were observed only once but those near the 15 mJy detection limit were reobserved whenever time permitted. The raw scan data, smoothed with an RC = 2 second time constant, were recorded digitally on magnetic tape for processing on the observatory's CDC 3300 computer. A linear baseline was fitted to the first and last 15 second data segments and subtracted. If one of these segments was confused, a zero-slope baseline was fitted to the other and subtracted. Then the scan was smoothed by convolution with the time-symmetric filter function, shown in Figure 1 along with the antenna point-source response. The filter was chosen so that its Fourier transform (Fig. 1) is nearly unity for all postdetection signal frequencies resulting from a drift scan across any nonfluctuating source and falls rapidly to zero at higher frequencies (v > 0.1 Hz). Unlike least-squares fitting of a Gaussian or similar beam shape to the source response, this filtering procedure reduces noise without attenuating the antenna response to high spatial frequencies. The effective beamwidth is not broadened at all, so the confusion error is minimized. The amplitude of the filtered data is an accurate measure of the source intensity; no further fitting is required. The filtered data for a representative scan on the 15 mJy galaxy U06120 are shown in Figure 2. Because the effects of pointing errors are greater than those due to gradients in noise and confusion for sources stronger than the survey limit, the flux density of each source was actually taken to be proportional to the maximum value of the filtered scan data within a "window" extending about 3.0 seconds of time on either side of the expected position. Seeking the peak in this way introduces a small bias which was removed as described below. Next, the gain correction curves for diurnal thermal deformations (Fig. 3) and spillover (Fig. 4) were determined simultaneously by an iterative procedure involving the calibration source scans. The individual calibration source intensities in arbitrary units were converted to antenna temperatures via the 3.4 K calibration signals used each night. Trial gain curves were introduced and adjusted until the system sensitivity, corrected by the two curves, was independent of time and zenith angle. The residuals indicate that these curves have been determined to about 1 % rms. After these gain corrections had been applied to all scans, the system gain in arbitrary "counts" per jansky was determined for each night's data from the principal flux density calibration sources listed in Table 1. Our flux density scale is based on that of Kellermann, Pauliny-Toth, and Williams (1969). The scan intensities were then converted to flux densities. The final data-reduction step is a correction for the bias that was introduced by taking the maximum response within a narrow window centered on the expected source position, rather than the response exactly on position. The functional dependence of the bias flux density B on the true source flux density S was estimated theoretically, and the numerical scaling constants were measured from long scans of randomly chosen areas of sky. Within the narrow window the Gaussian source response can be approximated by a parabola, and the heavily filtered noise and confusion
TABLE 1 Principal Calibration Sources =============================== Source 2380 Flux (Jy) -------------------------------- 3C 43 1.87 3C 48 9.91 3C 175 1.42 3C 286 11.06 3C 395 2.74 3C 441 1.66contribution is adequately represented by a straight line whose ordinate at the window center is randomly distributed with zero mean value. Using the measured values of noise and confusion from $III, we obtain B = 6.7(S^2 + 21)^-1/2, where B and S are millijanskys. This equation was verified by reductions of artificial sources of various flux densities which were added to the long background scans. For the actual galaxy scans, the initial flux density estimate was used for S, unless it was negative, in which case S = 0 was used.
The final peak flux densities are listed in Table 2.
III. ERROR ANALYSIS
The major contributions to the peak flux density errors can be divided into two groups - those which are directly proportional to the source flux density and those which are independent of it. The intensity-proportional errors are due to antenna pointing errors, uncalibrated receiver gain changes, and uncertainties in the corrections for zenith angle and time (thermal) dependences of antenna gain. Receiver noise and confusion produce intensity-independent errors. Telescope pointing errors are responsible for nearly all of the intensity-proportional error. Observations of about 40 unresolved secondary calibration sources whose positions are known with 5" or better accuracy show that the rms pointing error was 18" in each coordinate during the first observing run and 16" in the second, accounting for nearly all of the 5 % and 4 % rms flux density errors, respectively. The pointing errors are strongly correlated for successive scans of the same source made at similar zenith and azimuth angles, so that repeated observations do not reduce the intensity-proportional error significantly. Since the receiver gain was very stable and about 10 calibration scans were made per night, the receiver gain calibration error is less than 2 %. The spillover and timedependent thermal deformation gain-correction curves are at least this accurate also.The rms noise and confusion errors were determined by direct measurement because simple calculations of these quantities often give values which are much too small. Two sidereal-rate drift scans were made covering the same strip of sky on two different nights. These strips were broken into 242 80 second segments and reduced in the same way as the normal galaxy scans. The contributions due to noise and confusion can be isolated by comparing the flux densities S1 and S2 measured at each position on nights 1 and 2, respectively, since the noise errors are independent from one night to the next, while the confusion errors are nearly identical. Thus the normalized probability distribution of S = 2^-1/2 (S1 - S2) shown in Figure 5 is the single-scan noise error distribution. It is Gaussian, as expected, and its rms width is 2.7 mJy. The distribution of S = (S1 + S2)/2 without bias removal is also plotted in Figure 5. It is the convolution of a Gaussian noise distribution of rms width 1.9 mJy with the confusion error distribution whose " median standard deviation " must also be about 1.9 mJy to account for the total width of 2.7 mJy. (The "median standard deviation" is half the flux density range centered on the median containing two-thirds of the points in the distribution. It is equivalent to the rms for a Gaussian distribution, but it is not so sensitive to the long tail of a confusion distribution.)
The intensity-proportional, confusion, and noise errors are independent, so that the total flux density error can be written as
Sigma = [(e*S)^2 + 2^2 + 3^2/N]^1/2 mJy,
where e = 0.05 for observations made during the first session and e = 0.04 for those in the second, S is the measured flux density in millijanskys, and N is the number of scans on the source. The errors computed from this equation are listed in Table 2. In a few cases higher errors have been assigned because the baselines appeared unusually irregular.
The east-west angular diameters of all sources with peak flux densities greater than 50 mJy were estimated from broadening of the 2.7' beam. To produce detectable broadening, a source stronger than 100 mJy must have a half-power diameter greater than 1.2', and a 50 to 100 mJy source must be at least 1.9' in diameter. Twenty-eight sources of the former class, and three of the latter, were resolved and are listed with their measured half-power diameters in Table 3.
Most of the resolved sources are associated with two distinctly different types of galaxies: spirals with eastwest optical diameters greater than 4', and elliptical/SO galaxies of various optical sizes. Figure 6 is a histogram showing the distribution of the ratio R of radio to optical diameters of all spirals with optical major diameters greater than 5' and peak flux densities over 50 mJy. The unshaded areas indicate upper limits. R never exceeds about 1/2. Since the optical diameters (taken from the UGC catalog) are typically twice as large as the bright parts of the optical images on the Sky Survey prints, it appears that the half-power diameters of radio sources in spiral galaxies are smaller than or equal to the optical "half-power" diameters. The integrated flux densities of most of the remaining weaker sources in spiral galaxies should therefore be only slightly higher than the peak flux densities listed in Table 2.
The elliptical and SO galaxies have ejected a number of radio sources beyond their optical boundaries. Two-thirds of the sources stronger than 100 mJy and identified with elliptical galaxies are resolved, so that many peak flux densities of the 38 weaker detected ellipticals may be significantly below the integrated flux densities.
Of the remaining five resolved sources, three are associated with multiple systems and two have been produced by compact galaxies of unknown Hubble type.This research was supported in part by the National Science Foundation grant AST 75-1 1 139. We thank the NAIC staff, especially Dr. M. M. Davis, for help with the observations. L. L. D. thanks Dr. Vigdor Teplitz, head of the VPI & SU Department of Physics, for hospitality.
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FIG.1.-- The smoothing filter and antenna beam in time and frequency domains. Abscissae: time (s) and frequency (Hz). Ordinates: normalized gain.
FIG. 2.-- A typical scan after filtering and baseline removal. Abscissa: time after transit (seconds). Ordinate: peak flux density (mJy).
FIG. 3. -- Duirnal gain curve
FIG. 4. -- Spillover gain curve
FIG. 5. -- Noise and confusion error distributions
FIG. 6. -- Distribution of the radio-to-optical diameter ratio...