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NAIC REPORT March 1975

J. M. Durdin and D. Pleticha

National Astronomy and Ionosphere Center Cornell University, Ithaca, New York

J. J. Condon

National Radio Astronomy Observatory, Charlottesville, Virginia

M. J. Yerbury and D. L. Jauncey

National Astronomy and Ionosphere Center
Cornell-Sydney University Astronomy Center
Cornell University, Ithaca, New York

C. Hazard

Institute of Astronomy, Madingley Road, Cambridge, England

ABSTRACT. The techniques developed for observation, source parameter estimation, and calibration with a multiple beam system limited by confusion noise are described. A list contains the fluxes and positions of 3118 radio sources stronger than 0.35 Jy in the surveyed region: 0hRA<12h,-2d<DEC<+18d. Virtually all the time independent, linearly polarized continuum emission as seen by the 12.6' beams is available in a computer accessible map.


It has long been recognised that, in principle, the use of multiple feeds with a spherical reflector allows significant advantages in speed and in positional accuracy over a single beam. Using this technique to produce a radio survey is analogous to the use of a Schmidt camera in optical astronomy. The goal of the National Astronomy and Ionosphere Center (NAIC) 611 MHz multi-beam sky survey has been to demonstrate the practicality of such a system and to produce a resolution limited map of a large area of sky.

A multiple feed system for the 1000 ft Arecibo reflector was constructed using point feeds several years ago; however, cross-coupling between the feeds and receiver instabilities did not at that time allow a useful survey to be made. Since then, the development of high gain, linearly polarised line feeds (LaLonde and Harris 1970) and of very stable transistorised receivers (Yerbury 1972) made feasible the construction of a usable multiple feed array.

The meridian transit mode of observation yielded a beam-convolved sky brightness temperature at each observed point in the survey region shown in Figure 1. The positional accuracy was limited by internal calibration to about 10" rather than by telescope pointing errors. Long term stability of the receivers made it possible to display regions of up to several hours of time without loss of sensitivity. Figure 2 is a composite of some of the analog data depicting the observed radio sky in the vicinity of the Galactic anti-center.

Methods were developed for determining, as accurately as possible, positions, fluxes, and error estimates of all sources detected in the confusion limited data. These techniques were applied to the more than 3000 sources stronger than 0.35 Jy at 611 MHz. The source parameters and their associated errors are listed in Table 3.

Some actual and potential uses of the data should be mentioned. The relatively large area uniformly surveyed (about 1 steradian) makes the data useful for isotropy studies, particularly as the sensitivity

is such that the observed sources are distributed over a very large volume of space. The correlation of position with observed sky bright- ness temperature for classes of objects gives statistical information on the radio emission of those objects. The survey data may also be used to detect variability in sources, and to produce Galactic structure maps for one linear polarisation of the continuum emission.

The majority of sources in the list are extragalactic, unresolved, and previously uncatalogued; the list is a radio-complete sample for which it is likely that a substantial fraction will correspond to high redshift objects. The optical identification of the sources will provide information free of the selection effects usually present in optical samples. For this purpose, a simple, accurate measuring machine for use with the Palomar Sky Survey has been constructed (Jauncey and Durdin 1974


The equipment used to make the observations consisted of an array of ten line feeds with the electric polarisation vector in the east-west plane. An independent total power receiver was connected to each feed. Two parallel rows of five feeds each were positioned so that the beams were uniformly spaced in declination by 8.4 and Stationary, that is, the telescope was used as a meridian transit instrument. The beam power pattern of each feed was approximately Gaussian and circularly symmetric with a half power beam width of about 12.6'. The resultant undersampling in declination led to an effective declination beam width of about 14.7'.

The use of total power receivers for continuum radio astronomy is somewhat unusual and merits some discussion. Balanced systems, such as the Dicke or correlation radiometer, stabilise the baseline against gain and receiver noise power variations at the expense of an appreciable increase in system temperature. Usually, frequent gain calibration is required for these systems because gain variations can occur unnoticed; inevitably, such calibrations increase the effective system temperature still further. Therefore, it is best to use a gain-stable radiometer in a continuum survey instrument (Yerbury 1972).

For the multi-beam system, highly stable, total power radiometers were developed. System temperatures of about 250 K were measured, and the r.m.s. baseline variation over a period of several hours was about 0.1 K. In fact, the overall system stability was limited more by antenna gain changes than by receiver performance. The observing equipment is described in more detail elsewhere (Condon et.al. 1974).

Observations were made at night to minimize gain changes due to thermal distortion of the reflector. On each of thirty nights during November and December, 1972, a strip of sky 1.4 degrees in declination by about 12 hours in right ascension was surveyed. The previous night observations were overlapped by five beams to provide double coverage as depicted in Figure 1.

Data was taken by rapidly sampling each receiver output with analog-to-digital converters and recording them on magnetic tape using a program on the NAIC's CDC 3300 computer which simultaneously tested the data channels to give warning of possible receiver failures. Multiple channel observations made almost all types of interference easily recognisable. Sampling at a rate many times faster than beam critical sampling also allowed the removal of impulse interference. The majority of detected interference was caused by tropical electrical storms, and was deleted from the data before further processing.

Final smoothing of the data used an approximately rectangular low-pass filter with a cutoff at (1/12.6') in the spatial frequency domain. Sidereal rate observations do not allow the antenna responses to contain real components above this frequency. After smoothing, relative channel gains and the sensitivity of each night's observations were calibrated as described in section V. Each hour of data was then plotted in profile and as contours, after a constant baseline chosen to ensure continuity across declination was first removed from each channel for that hour (Durdin et al. 1974).


Determining the maximum likelihood (ML) estimates of the position and flux of radio sources from the observed antenna responses in the presence of Gaussian noise is a well understood process, utilising either convolution or least-squares techniques. This is untrue, however where the dominant noise is due to the aggregate of undetectable weak sources, that is, the radio sky confusion. The confusion probability distribution, discussed elsewhere (Condon 1974), is neither normal nor symmetric, and confusion errors, by their nature, are often correlated in "independent" (in a sampling sense) data points. ML estimates of parameters thus cannot be obtained from a least-squares approach, but require knowledge of the multi-variate probability distribution for the correlated errors in adjacent data points.

The problem of numerically determining the ML parameters from the observed data and from the multi-variate error distributions has not been solved. In practice, parameters were estimated by assuming Gaussianly distributed errors. A Monte Carlo analysis then gave estimates for the errors in those parameters. Factors considered in choosing a method to estimate source parameters included:

  1. the accuracy of the estimated parameters,
  2. the completeness of the final source list,
  3. the determining of additional information about the source or about parameter errors, and
  4. the cost of the computer time needed for the method, since several thousands of detected sources were examined.
Different procedures were tried, keeping these factors in mind; however, accuracy was never sacrificed for the sake of cost reduction.

The initial step in estimating the source parameters was to remove a local baseline from each channel. When a deflection above this baseline greater than about 0.2 Jy for point sources was detected, the approximate position of the nearest local maximum was stored for use with beam fitting routines. The extent to which varying the nature and length of the baseline affected the parameter estimates was examined and found not to be critical.

Two entirely different beam-fitting programs were written. The first used a weighted, non-linear least-squares method to fit a theoretical Gaussian beam to a source's two dimensional data matrix. Fitting beams to inserted Monte Carlo sources with known parameters indicated that the parameter errors depended only weakly upon the choice of weight. Allowing the beam widths to be variable parameters did not improve the accuracy of the position estimates as positions and widths are not completely independent in a non-linear fit to a Gaussian beam. Thus reliable width estimates were not available from this method. The chi-squared, a goodness-of-fit measure, was found to be useful in distinguishing strongly confused or resolved sources from unresolved sources.

The second method for estimating source strengths and positions was to determine independently the right ascension position and peak deflection in each of the three adjacent declination channels where the source was strongest. Although intrinsically a non-linear procedure, when three independent data points in each channel were used and three parameters determined (the center position, peak deflection and width of the fitted Gaussian), the fit was, of course, exact. The parameters could be written simply as algebraic functions of the data points.

The source right ascension was then found by weighting the right ascension values from each channel according to the square of their corresponding peak strengths, as dictated by the constant magnitude of confusion "noise". Declination was similarly estimated, and flux was found from the data matrix and the fitted position and width parameters. The advantages of this second method were that: 1) it was far more efficient computationally, 2) it allowed greater completeness in that fewer sources totally failed to fit, and 3) meaningful width estimates were available. Again the chi-squared of the flux fit can be used to separate confused or resolved sources from point sources, but this information is also available more directly from the fitted widths Flux and position errors of point sources depend upon this apparent resolution. This second method of source fitting was used to produce the final source list in Table 3.

Corrections to these fitted fluxes were made due to a baseline bias and due to gain variations caused by thermal distortion of the reflector.

The bias correction for the particular baseline used was a constant negative correction of 0.05 Jy. The gain correction was computed based on a known gain dependence on antenna temperature and based on the mean nightly temperature profile over the observing period.

The uncertainties in the source parameters found by the beam fitting program were determined by studying the errors in measuring the parameters of inserted dummy sources. Also pairs of observations from adjacent declination strips were compared. The errors were found to depend on source flux and on the extent to which the source was broadened by the background of confusing sources. Analytic expressions, empirically found to adequately describe the parameter variances, for an individual source measurement are

rms_RA  = sqrt (.97 - 0.03/S + 0.35/S^2 + 68.0 zRA/S^2 )  sec
rms_DEC = sqrt (90. + 420./S + 330./S^2 + 12000 zDEC/S^2) arcsec

rms_flux = sqrt ( 2.0 + 2.8*S + 2.0*S*S + 27.*(zRA+zDEC) ) mJy

where zRA  = abs( S* (thRA - thRAm ) / thRAm )
      zDEC = abs( S* (thDEC- thDECm) / thDECm)
S is the measured flux at 611 MHz in Janskys thRA, thDEC are the widths of the Gaussian which best fit the source
 thRAm  = mean thRA  = 12.58'
 thDECm = mean thDEC = 14.70'
The families of histograms in Figures 3,4, and 5 give the number of sources as a function of the uncertainty in their parameters.


The NAIC multi-beam source list in Table 3 contains 3118 sources stronger than 0.35 Jansky at 611 MHz.

Positions quoted in the list are for epoch 1950.0. Fluxes are based on the Kellermann, Pauliny-Toth, Williams (KPW) flux scale (KPW 1969). Only sources stronger than 0.35 Jy appear in the list. The "RA-Size-Dec" columns give the full widths of the Gaussians which best fit the observations. A completely unresolved, unconfused source would have its size listed as 12.6' for right ascension and 14.7' for declination. In the "Code" column: "R" denotes the Rosette Nebula, "C" indicates the source is confused (its parameters are more uncertain than the quoted sigmas indicate), "L" indicates that the source is at the position of a strong side lobe of a second source (the fluxes of both sources have been corrected), and the numerals 1 or 2 indicate how many observations were averaged to estimate the source's parameters. The last column gives the date the source was observed (for example, 721118 is 1972 November 18).

A Gaussian beam shape was such a poor approximation to the Rosette Nebula that the fitting procedure failed to determine some of its parameters. The five entries in Table 3 marked with an "R" in the "Code" column give some information about the Rosette Nebula. Four entries listed with a flux of 0.0 Jy are the approximate positions of relative maxima. The entry with an assigned flux of 350. Jy is the position of the central relative minimum. Width information for this entry gives the approximate size of the nebula. Figure 6 shows the 611 MHz contour map of the Rosette Nebula superimposed on a Palomar Sky Survey plate.

For strong, unresolved sources, the Table 3 source list is complete. However it is not intended to be complete for objects highly resolved by a 12.6' beam. Information on extended features should be obtained by examining the contour and projection plots of this survey. The list's lower limit of 0.35 Jy is about five times the average size of the radio sky confusion; of course, toward this weak flux end the list becomes incomplete.

The beam fitting computer program produced a preliminary source list which contained two types of spurious entries: many sources were listed twice, and strong side lobes appeared as sources. Nearly the entire one steradian region was surveyed twice in half-overlapping declination strips 1.4 degrees wide. Sources which occurred between beams two and nine on two consecutive observing nights appeared twice in the preliminary list. This final list contains the weighted means of the two sets of parameters for such sources.

Because the fitting procedure assigned a position and flux to all beam shaped deflections, responses from side lobes produced spurious sources. To identify these entries in the preliminary source list, it was first necessary to accurately determine the side lobe pattern. By examining point source responses, it was noted that each of the ten feeds had approximately the same lobe pattern throughout the survey. Strong sources revealed right ascension and declination feed lobes, and first and second order grating lobes. The old reflector mesh sagged between the parallel north-south main support cables and produced grating lobes (Condon and Niell 1970). A list of the positions and strengths of the 10 strongest lobes is given in Table 1.

After the set of lobes was roughly determined, a computer program used it to filter the lobe responses out of the preliminary source list. Around each prospective source, positions in the source list were examined where lobe producing sources might occur. When such lobe producing sources were found, the flux that their lobe was expected to produce at the position of the prospective source was subtracted from the prospective source's strength. If this corrected flux exceeded 0.35 Jy, the propective source was recognised as a real source superimposed on a lobe of another source. Only in this case was the source retained in the final source list. Since these corrected fluxes are very uncertain, such sources are denoted by an "L" in the "Code" column of the Table 3 source list whenever the amount of the flux correction exceeded half the quoted uncertainty in the flux.


The fluxes and positions of the set of sources in each observed declination strip were calibrated relative to the sources in the overlapping declination strips and also with respect to independently measured calibration standards. In general, the absolute gain and position of a night's data were determined by fitting the night's sources to calibration sources by a weighted least-squares method. The Monte Carlo error estimates given in section III, specified the weights.

Since the survey used ten receiver systems during 30 nights of observing, 300 data strings had to be flux calibrated relative to each other before an absolute calibration was attempted. This was accomplished by determining the P (d) distribution widths which were proportional to the gains of the systems. The P(d) distribution is the confusion probability distribution; this is the probability distribution of getting deflection d from a receiver output after large scale Galactic gradients have been filtered out. The two-thirds width of the P(d) distribution for one channel's 1700 independent responses, and therefore, the gain can be determined with an uncertainty of about 6 percent. To within this accuracy, the ratios of the widths for all pairs of receivers on a night remained constant over the entire observing session.

For a given night, each data string except the first was multiplied by a ratio (which depended on receiver number but not observing night) in order to make its P(d) width agree with the night's first data string's. This left each set of ten data strings internally calibrated but as yet not absolutely calibrated to any standard. Night to night changes which affected all ten systems similarly still had to be corrected for.

The largest contribution to the nightly gain change was due to the antenna system. An observed change in gain of each system by nearly a factor of two as the declinations observed varied from -2d to +18d seems to have been caused by a defocusing of the line feeds when the portion of the reflector they illuminated changed from the north part of the dish down to the central regions. This explanation is consistent with an observed change in angular separation of the two feed banks as a function of declination.

This survey was ultimately calibrated to the KPW flux scale. The secondary calibrators were ten sources measured at Arecibo at 606 MHz based on the KPW scale (Condon, Niell and Jauncey 1971). Marked by an asterisk in Table 2, these sources were too few to be used alone to calibrate all of the declination strips. Since a more complete list of good calibration sources did not exist at 611 MHz, the fluxes of 150 additional sources were independently measured accurate to about 7 percent at Arecibo in the Fall of 1973. Table 2 gives their assigned fluxes. These source were tied to the KPW scale through the ten secondary calibrators. Sources chosen were stronger than about 1 Jy in the Molonglo 408 MHz lists, and were unconfused and unresolved using a beamwidth of 12.6' (Munro 1971, 1972; Bridle ct al. 1972). Each night of observations was absolutely calibrated to about a half dozen of these calibrators falling within its strip.

Fifty to a hundred sources with well determined parameters and stronger than 0.35 Jy were found in the overlapping region on consecutive nights. The two sets of fluxes for these sources were fitted to each other to improve the night to night relative calibration. This relative flux calibration procedure was combined with the absolute flux calibration method in a weighted least-squares manner to produce the final gain calibration.

The primary list of 600 position calibrators was selected from the University of Texas interferometric positions measured accurate to about 2" at 365 MHz (Ghigo and Owen 1973, Douglas et al. 1973). These lists were supplemented by another list compiled at the University of Sydney having positional errors less than 1" (Crawford 1973).

Approximately 20 position calibration sources in each of this curve, declination strips positioned the strip to an accuracy of about 10". Matching each pair of positions for sources occurring on two consecutive nights, allowed these pairs of nights to be aligned with respect to each other to about the same accuracy. Finally, combining these two methods in a least-squares manner allowed the position of any of the 500,000 independent data points to be determined to about 6" in right ascension and to about 8" in declination.

The National Astronomy and Ionosphere Center is operated by Cornell University under contract with the National Science Foundation.

Table 1.

Average Position of Sidelobes as Detected by the Source Fitting Program
                                       RA   Dec  Fractional
       Type of lobe                    (')   (')  strength
first order preceding grating lobe    -56.4   0.0   0.12
first order following grating lobe     56.4   0.0   0.09
second order preceding grating lobe  -112.7   0.0   0.025
second order following grating lobe   112.7   0.0   0.025
preceding feed lobe                   -17.0  -3.5   0.085
following feed lobe                    17.0  -3.5   0.085
first order southern feed lobe         0.0   -22.8  0.08
first order northern feed lobe         0.0    22.8  0.08
second order southern feed lobe        0.0   -44.3  0.06
second order northern feed lobe        0.0    44.3  0.06


Bridle, A. H., Davis, M. M., Fomalont, E. B., and Lequeux J. 1972, A.J., 77, 405.

Condon, J. J. 1974, Ap.J., 18, 279.

Condon, J. J., Durdin, J. M., Hazard, C., Jauncey, D. L., LaLonde, L.M., and Yerbury, M. J. 1974, Astron. Astrophy5. Suppl., 15, 471.

Condon, J. J., and Niell, A. E. 1970, Cornell-Sydney University Astronomy Center, Report No.216 (Ithaca, N.Y.: Cornell University).

Condon, J. J., Niell, A. E., and Jauncey, D. L. 1971, Cornell-Sydney University Astronomy Center, Report No.218 (Ithaca, N.Y.: Cornell University).

Crawford, D. F. 1973, private communication.

Douglas, J. N., Bash, F. N., Ghigo, F. D., Moseley, G. F., and Torrence G. W. 1973, A.J., 78, 1.

Durdin, J. M., Pleticha, D., Condon, J. J., Yerbury, M. J., Jauncey, M.J., and Hazard, C. 1974, National Astronomy and ionosphere Center, Report No.44 (Ithaca, N.Y.: Cornell University).

Ghigo, F. D. and Owen, F. N. 1973, A.J., 78, 848.

Jauncey, D. L., and Durdin, J. M. 1974, Pub. Astron. Soc. Pacific, 86, 826.

Kellermann, K. I., Pauliny-Toth, I. I. K., and Williams, P. J. S. 1969, ApJ 157,1.

LaLonde, L. M. and Harris, D. E. 1970, Proc. IEEE, AP-18, 41.

Munro, R. E. B. 1971, Aust. J. Phys. 24, 617.

Munro, R. E. B. 1972, Aust. J. Phys. Astrophys. Suppl. 22, 1972.

Yerbury, M. J. 1972, Cornell-Sydney University Astronomy Center, Report No.252 (Ithaca, N.Y.: Cornell University).

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