5 GHz SOURCE VARIABILITY AND THE GAIN OF THE NRAO 300 FOOT TELESCOPE


5 GHz SOURCE VARIABILITY AND THE GAIN OF THE NRAO 300 FOOT TELESCOPE

C.L. BENNETT, C.R. LAWRENCE,  B.F. BURKE
Research Laboratory of Electronics, Massachusetts Institute of Technology
Received 1983 June 23; accepted 1983 August 10

ABSTRACT

During the course of the MIT-Green Bank 5 GHz survey on the NRAO 300 foot
(91.4 m) transit telescope, ~2400 observations were made of strong sources
for the purpose of calibration. In this paper we analyze the gain curve
of the 300 foot telescope between -10{deg} and +30{deg}, including its time
stability, and discuss the variability of the 123 calibrator sources
that were observed.

Subject headings: instruments - radio sources: variable

1. INTRODUCTION

The MIT-Green Bank survey of 2.2 sr of sky between -O.5{deg} and
+19.5{deg}, begun in 1979 using the NRAO (1) 300 foot (91.4 m) transit
telescope, is now nearly finished.  During the course of the survey
repeated observations were made of 123 sources, ~1 Jy, for calibration
purposes. These observations were used to determine a pointing
correction and to calibrate the gain of the 300 foot telescope. The
calibrator observations over a period of several years also allow a
study of source variability. In this paper we present first an analysis
of the gain curves of the 300 foot telescope between -10{deg} and
+30{deg}, and then ~2400 measurements of the fluxes of 123 calibrators.
(1) The National Radio Astronomy Observatory is operated by Associated
Universities, Inc., under contract with the National Science Foundation.

2. OBSERVATIONS

Sources from Table 1 of Lawrence et al. (1983) were observed in 1979 July,
1980 April-May, 1980 June-July, 1981 January-February, 1981 August, 1981
September-October, 1981 December-1982 February, and 1983 February. All of
the observations were made with the beam-switched "6-25 receiver" in the
"Sterling mount." The two feeds are separated by 7.6' on the sky, and
the nominal beamwidth (FWHP) of each is 2.8'. The center frequency was
4.775 GHz with a bandwidth of 580 MHz, and the integration time was 0.5s.

The telescope was driven in declination from south to north at 6 times the
sidereal rate, 90"/s. The feeds were rotated to an angle of -12{deg}
(in the sense N through E on the sky), so that a source passing through
the midpoint between the two feeds goes through the half-power point of
first one feed, then the other.

3. ANALYSIS

Calibrator scans were analyzed by cross-correlation with a model beam
as described by Lawrence et a!. (1983). If either of the local minima
of the cross-correlation did not fall within one integration period of
the expected minimum position, based on the feed model, then the scan
was thrown out. This occurred only rarely. The antenna temperature
was calculated from the values at the two minima.  The sources used
to calibrate the gain of the 300 foot telescope are most of those in
Table 1 of Lawrence et al. (1983) for which fluxes are listed. Antenna
temperatures from the cross-correlations were divided by the fluxes from
the table to give gain values. Several models were fitted to the gain
values as a function of declination. The best fit was obtained with the
following polynomial:

G(K/Jy) = G0[1+G2/G0(dec-dec0)^2 + G4/G0(dec-dec0)^4 , (1)

where dec0 = 38.43deg is the declination of the zenith in Green Bank. Although
this model gives a gain curve which is symmetric about the zenith, we have
made observations only in the declination range -10{deg} < DEC < +30{deg}
and cannot comment on the accuracy of the model outside of this range.

The fit was made by reflecting the gain data points about the
zenith declination, followed by a change of variables to x_i = (dec- dec0)/48.43,
so that x(dec_i = -10{deg}) = -1. Since -1 < x_i < 1,
Legendre polynomials could be fitted to the data.  Legendre polynomials
are approximately orthogonal over the x_i's, and their coefficients are
nearly independent. This process automatically forces the gain curve to be
symmetric about dec0, since the odd Legendre polynomials will vanish. The
Legendre coefficients were then converted into the G`s of equation
(1). The results are presented in Table 1, and their time variations
are shown in Figure 1. Figure 2 is representative of the high quality
of all fits. The values of G0 are significantly different for different
times. The variations in G2/G0 =(-5.27+-O.37)x10^-4 and in G4/G0=(7.7+-1.9)x10^-8
are insignificant. Thus, the gain curve used in obtaining the
fluxes in this paper is

G(K/Jy)=G0(t)[1- 5.27x10^-4(dec-38.43deg)^2+
				  +7.7x10^-8(dec -38.43deg)^4], (2)
where G0(t) is given in Table 1.

Table 1. Gain curve coefficients as a function of time

Date    G_0   G2/G_0   G4/G_0
              x10^-4   x10^-8
----+----1----+----2----+----3----+
79.504  0.936  -4.86    5.91  
80.375  1.06   -5.50    8.52  
80.542  0.967  -5.22    7.86  
81.125  0.943  -5.08    6.46  
81.666  0.867  -5.25    7.64  
81.792  0.872  -5.30    8.20  
82.000  0.876  -5.03    6.36  
82.375  0.855  -6.13   12.1  
83.166  0.861  -5.06    6.04
-------------------------------------
NOTE. Differences in G0 are significant. Higher order coefficients are
taken as constants with values G2/G0 = -(5.27+-0.37)x10^{-4} and G4/G0 =
(7.7+-1.9)x10^{-8}.

The important result is that G_0 changes significantly over time, but
G2/G_0 and G4/G_0 do not. In other words, the shape of the gain curve
is constant, but its amplitude changes.  

The antenna temperatures of 2400 observations were converted into fluxes
using equation (2). An editing algorithm eliminated measurements which
were obviously in error, as follows: the mean flux, (S), and the standard
deviation of the mean, sigma_m  were calculated for each source. The most
extreme flux, S_E was thrown out if

|S_E-| > 3max({sigma}_m,O.2), (3)

where max(x,y) chooses the larger value of the two arguments The
quantities  and {sigma}_m were recomputed, and the procedure iterated
until all the measurements passed the test.  Only ~25 observations (~1%)
were thrown out, so this is a mild editing algorithm. The resulting
fluxes and the corresponding dates of observation are shown in Table
2. The uncertainty in a single measurement is declination dependent,
but the measured dispersion for - 1O ; the standard deviation, sigma; the
number of measurements, N; the coefficients A and B as described above;
the percentage deviation in the measurements 100sigma_S/