NATIONAL RADIO ASTRONOMY OBSERVATORY

Green Bank, West Virginia

DATE:

TO: VLBI Network

FROM: R.J. Maddalena

SUBJECT: NRAO-GB 140-ft telescope calibration, 8.1 GHz, September 1992

Calibration of Antenna Efficiency

The temperatures used throughout the calibration of antenna efficiency, eta_A, were determined from pointing and source temperature measurements obtained during the VLBI session. A total of 594 measurements provided excellent sky coverage (Fig. 1) for a good measurement of efficiency.

The antenna temperatures used in the calibration were not corrected for the effects of the atmosphere. The sources and flux densities given in Table 1, in combination with the weighted average of the measured antenna temperatures for those sources when they were within 1 hour of the meridian, were used to establish the dependence of eta_A on declination at zero hour angle. (eta_A, when the physical aperture of the telescope is used _A equals 1.93 T_A/S where S is the 8.1 GHz flux in Jy.) The flux densities in Table 2 were determined from the meridian efficiency and the weighted average of T_Awhen the source was within 1 hour of the meridian.

The fluxes from table 1 and 2 and the measured T_A at the points indicated in Figure 1 were used to estimate eta_A across the sky; spherical harmonics were then fit to the values of eta_A. The coefficients found from the fit are given in Table 3 while the efficiency surface is shown in Figure 3. The derived efficiency is somewhat higher than what has been derived before, probably because of an error in the noise tube value.

Figures 4 - 29 display as functions of hour angle, the measured and calculated efficiencies located at the indicated declinations.

Table 1: Primary Calibrators

Source Flux Density (Jy)

0133+476 1.23 ą 0.04 (1)

0454+844 0.72 ą 0.02 (1)

1334-127 6.23 ą 0.16 (1)

1921-293 22.6 ą 1.5 (1)

1928+738 4.41 ą 0.23 (1)

2021+61 3.30 ą 0.31 (1)

2136+141 2.63 ą 0.06 (1)

2203-18 4.16 ą 0.58 (2)

3C123 10.5 ą 0.7 (3)

3C179 0.95 ą 0.32 (2)

3C274 47.7 ą 5.7 (3)

3C279 13.6 ą 0.31 (1)

3C286 5.34 ą 0.41 (3)

3C84 43.0 ą 2.62 (1)

BL-LAC 3.37 ą 0.20 (1)

MON R2 7.86 ą 0.39 (1)

NGC 7027 6.66 ą 1.42 (3)

NRAO 150 2.32 ą 0.09 (1)

OQ208 1.70 ą 0.04 (1)

References:

(1) Previous reports on the calibration of the 140-ft telescope.

(2) Kuhr et al. (1981, Astr. Ap. Suppl., 45, 367).

(3) Baars et al. (1977, Astr. Ap., 61, 99).

Table 2: Secondary Calibrators

Source Flux Density (Jy)

0016+731 1.97 ą 0.12

0851+20 2.62 ą 0.06

0917+624 2.17 ą 0.11

3C273 51.0 ą 1.2

3C345 11.4 ą 0.32

3C395 2.13 ą 0.05

3C454.3 11.3 ą 0.24

3C84 33.7 ą 1.0 (*)

4C71.07 2.41 ą 0.14

* 3C84 is a primary calibrator whose flux was probably in error; its flus was corrected to this value prior to the final fit.

Table 3: Result of Fit

A00 = 0.4006 ą 0.0307

A11o = 0.0123 ą 0.0103

A10 = 0.1055 ą 0.0348

A11e = 0.1944 ą 0.0473

A22o = 0.0004 ą 0.0026

A21o = 0.0052 ą 0.0042

A20 = 0.0160 ą 0.0207

A21e =-0.0222 ą 0.0141

A22e =-0.0130 ą 0.0056

A30 =-0.0905 ą 0.0124

eta(theta,phi) = A00Y00 + A11oY11o + A10Y10 + A11eY11e + A22oY22o

+ A21oY21o + A20Y20 + A21eY21e

+ A22eY22e + A30Y30

where: Y00 = 1

Y11o = sin(theta) sin(phi)

Y10 = cos(theta)

Y11e = sin(theta) cos(phi)

Y22o = 3 sin²(theta) sin(2phi)

Y21o = 3 sin(theta) cos(theta) sin(phi)

Y20 = 3/2 cos²(theta) - 1/2

Y21e = 3 sin(theta) cos(theta) cos(phi)

Y22e = 3 sin²(theta) cos(2phi)

Y30 = 5/2 cos³(theta) - 3/2 cos(phi)

and theta= 90-dec, phi = hour angle in degrees.