Intensity calibration of the HI survey of galaxies during commissioning of the Green Bank Telescope (GBT) is tied to the NVSS flux density scale. About five dozen continuum sources with flux densities between 2.2 and 6.0 Jy were selected to avoid significant multi-source confusion with the nine-arcminute GBT beam. The continuum calibrators were observed with the same spectrometer and receiver configuration as was used to measure the HI line profiles in the survey, with the exception that the spectrometer bandwidth was always 40 MHz centered on 1403 MHz to span most of the range of frequencies observed with smaller bandwidths.
The calibrator observing sequence was 2 minutes off, 2 minutes on, and 2 minutes off source in spectral line mode. The first off position was 38 arcminutes toward lower right ascension than the source position, and the second off was the same distance toward greater right ascension. The hour angle track was, therefore, not exactly the same for the three observed positions for high declination objects, but this did not appear to degrade the spectral baselines significantly. The first task in the calibrator data reduction was to visually inspect the difference spectrum between the two off positions. The difference spectrum offset was typically less than about 60 mJy, as is expected from confusion noise with the GBT beam size, but a few offsets were as high as 300 mJy. These large offsets were possibly due to a moderately strong source in one of the off positions or, more likely, a bit of radiation from the sun during the day. Since the observed source flux density was about 3 Jy, even the largest off-source baseline offset, after the two off spectra were averaged together, caused about 5% error in the measure source intensity. More typically, this source of error amounted to less than 1%. The statistics of the calibrator source measurements were not significantly improved by throwing out observations with larger off-position differences so all data were retained.
The primary objective of the calibrator observations was to transfer the continuum flux density scale directly to the internal receiver secondary calibrator noise sources. This was done by firing the noise source at a one-Hertz, 50% duty cycle rate during the continuum measurements and storing the cal-on and cal-off spectra separately. Then the noise source equivalent flux density spectrum was computed from
Scal = Ssource * (off_src_cal_on - off_src_cal_off) / (on_src_cal_off - off_src_cal_off)where the off-source spectra are averages of the two off positions.
Continuum source flux densities were corrected for linear polarization for each of the two linearly polarized receiver channels using the polarized flux density and position angle published in the NVSS. The frequency dependences of the continuum radio source intensities were computed using a spectral index derived from the NVSS and the Green Bank, 4.85 GHz survey flux densities.
All of the measurements were made at pointing elevations above 30 degrees so atmospheric attenuation was neglected. Other measurements of aperture efficiency confirm the GBT design predictions that there should be no significant antenna gain variation with antenna elevation at 1.4 GHz.
Figures 1 and 2 show the distributions of measured equivalent flux density for the internal noise sources in the two receiver channels averaged across the 40 MHz spectrometer bandpass. If we ignore a few outlier values in these histograms, the standard deviation in the two plots is roughly 4% of the median value. This is somewhat higher than we expect from confusion and other measurement errors. A few of the continuum sources are probably variable, particularly the outliers in Figures 1 and 2, but it is hard to say how much of the scatter in these two plots is due to source variability. The median values of 0.8803 and 0.9448 Jy for the average equivalent flux density for the internal noise sources are probably accurate to a couple of percent.
Figures 3 and 4 show the noise source flux densities measured with five radio sources on two different days. Values for the same object are connected by a line, and they are plotted as a function of spectrometer sampler total power to check for amplitude non-linearities that might be associated with the A/D converters. The largest difference between two measurements is about 5%. There is some indication of a dependence on sampler input level, but the sign of the slope in the two channels is different, and the small number of points does not make a conclusive case, so no sampler-power dependence has been applied to the flux density calibration. The value difference between the two measurements in each pair is larger than can be explained by the spectra quality or pointing errors so the scatter in the calibration measurements is not fully understood as of this writing.
As a further check on system linearity, all of the measured receiver noise flux densities are plotted versus spectrometer sampler total power and versus continuum source flux density in Figures 5 and 6 and 7 and 8, respectively. We expect any non-linearities to be a second-order effect since the receiver noise source and the continuum radio source power are measured on the same part of the sampler conversion curve in each measurement. No significant trend is evident in any of these four plots.
We expect some frequency dependence of the receiver noise source intensity and, possibly, of the antenna response to a radio source in its main beam. Figures 9 and 10 show two example spectra where small slopes in the noise source equivalent flux densities are evident. A few of the spectra measured on other radio sources show somewhat more curvature or sinusoidal patterns at the one or two percent level. Aside from a slope across the spectra, no consistent pattern was seen in the collection of spectra so the frequency dependence characterization has been confined to a measured average spectral index. Figures 11 and 12 show the distributions of spectral indices derived from the measured ratio of powers in 3-MHz spectral bands centered on 1388 and 1417 MHz as defined by
spectral_index = log(P1 / P2) / log(F1 / F2)where P1 and P2 are measured noise powers at frequencies F1 and F2, respectively. A frequency ratio of 2% is a very short lever arm for a spectral index measurement, but the results show moderately well-determined slopes in the spectra. The median spectral indices are +0.66 and -0.58 for the two respective receiver channels across the measured frequency range. As a check on the spectral index corrections of the continuum radio source intensities, the measured receiver noise spectral indices are plotted against radio source spectral index in Figure 13. No systematic residual error is seen.
During the survey a difference in calibrated spectral line flux densities between the two spectrometer channels was discovered. This was traced to a nonlinearity in the channel 1 IF electronics in the FFT spectral processor. The average ratio of measured flux density from the two receiver channels was about 1.27, but it could vary from about 1.15 to 1.35, possibly as a function of time of day. All data taken before February 5, 2002 suffered from this nonlinear defect. After this date there still appeared to be a difference in the measured flux density from the two channels of about 10%. To provide as much information on the calibrated flux densities as possible, both channel values are reported along with the best estimate of the combined value after correcting for the ratio of the two measured values. The channel 2 value is believed to be closer to the true value so the channel 1 values were multiplied by a scale factor before averaging thb=e spectra from the two channels. This ratio depends on the date of observation and has been derived separately for different groups of data. Overall, the final flux densities for the averaged spectra are believed to be accurate to about 10% unless the line profiles had a low signal-to-noise ratio.
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