(OCR by H.Andernach 8/97;)
(Coodinates columns by S.Trushkin 11/98;)
The reduction and calibration techniques are described in Section 2, and Section 3 deals with the method of deriving angular diameters and the fraction of the total flux density of a source which scintillates. Section 4 comprises the catalogue of ~1500 4C sources, roughly 60 per cent of which scintillate. It should be emphasized that many of the observed diameters may be due to interstellar scattering rather than to the intrinsic source size.
The half-power beamwidth of the 18000 m^2 array at declination delta is 0.28d*sec(delta) in right ascension and 4.9d*sec(52d-delta) in declination, whereas the spacing of adjacent declination strips is 2.76deg*sec (52d-delta). Thus there was some redundancy in observations on adjacent declination strips.
The scintillation index, F, is defined by
F = D_S/S
where D_S is the rms variation of flux density due to scintillation and S is the flux density. For each receiver D_S was measured, as described in Paper I, by using a high-pass filter with a low-frequency cut-off at 0.02 Hz to separate the scintillating component from the output. After further amplification the signals were rectified and integrated with a time constant of 15 S, sampled at D_S intervals, and recorded sequentially on a single-punched tape. The sampling interval gave slightly more than 3 sec(delta) readings during the drift-time of a source at declination delta through the reception pattern. The reduction of ~1 per cent in D_S caused by removal of the low-frequency component may be ignored. The non-filtered, filtered and integrated signals were recorded on Evershed three-track chart recorders ( see Fig. I(a), (b), (c) ) to facilitate calibration and also detection of interference.
The variations of spectral index with galactic latitude determined by Bridle (1968) indicate that the correction to (2) is negligible over most of the sky and amounts to only ~10 per cent towards the galactic plane. Thus the scaling provided by (2) is sufficiently accurate for our purposes, and has been applied without further corrections, to derive the sensitivity of the telescope (see Fig. 2). Apart from some regions near the galactic plane where the background temperature may change significantly in one beam area, the calibration is believed to be accurate to ~10 per cent.
This calibration was used in conjunction with the output of the integrator circuit (see Fig.I(c)) to determine D_S for each source as follows: Let J be the level at the output of the integrator circuit, and J = <J> if the input consists solely of background noise. In the presence of a scintillating source the increase of the integrator output is then J -<J> which may be converted into D_S using the above calibration and the measured response of the filter, amplifier and integrator circuits.
The magnitude of <J> in the absence of obvious scintillating sources was next found and used to compute J - <J> for each source. The values of J - <J>. for intense scintillating sources were then transcribed on to magnetic tape and subsequently erased from the integrated record. A typical record after the removal of these is shown in Fig. I(d).
The separate records of J - <J> for each declination strip were then added and their sum convolved with a function corresponding to the response of the array to a source during transit, in order to obtain the maximum signal/noise ratio allowed by information theory. An example of the records at this stage is shown in Fig. 1(e). This analysis gave the maximum integration time for detecting weak scintillating sources and the threshold sensitivity may be estimated as follows:
Let D_S define the scintillating flux of a given source, and D_Sn the system noise for a receiver time constant T1. The random fluctuations at the output of the final integrator, for a time constant T2, will have a value
(J - <J>)_rms = D_Sn*sqrt(T1/T2)
In deriving this result e assume, for convenience, that the output of the final rectifier and integrator is J = D_S, although the detector will be to some extent non-linear. .N scintillating source will be at the limit of detection when
J_(s+n) - J_n ~ (J - <J>)_rms
Since the scintillating flux and the system noise are uncorrelated the mean fluctuating signal is D_S^2 + D_Sn^2. and hence
[ formula ]
giving
[ formula ] The addition of repeated observations, combined with the convolution mentioned above, gives a further increase of integration time and we have [ formula ] as the detection limit, where 7'i s the total integration time. This relation corresponds to a signal noise ratio of unity and we assume that a source is unlikely to escape detection if D_S > 2sigma.
Now at 81.5 MHz D_Sn is largely determined by the galactic background temperature, while D_S depends upon solar elongation and is also a function of the ratio source coordinates. contours indicating D_S = 2*sigma are shown in Fig 3.
The individual values of J - <J> for each repeated observation of every source were converted to scintillating fluxes as described in Section 2(ii) and the variation of D_S with solar elongation for each source was plotted by computer (see Fig. 4).
The scintillating flux curves were then used in conjunction with the chart recordings to distinguish between genuine scintillating sources and random fluctuations on the records. The four highest computed values of DS were checked on the charts to eliminate interference which might have escaped declination in stage one. All suspected scintillators which showed an increase in scintillating flux with decreasing elongation~n were then classified according to the following scheme, which is summarized in Table 1:
[Table 1]
The scintillating sources are assigned to classes A, B or C depending on whether they arc strong, moderate or weak scintillators respectively. Some sources, which showed only a marginal increase in scintillation with decreasing elongation, are classed as probable scintillators. An example of a source in each class is given in Fig. 4. There are - 750 sources in classes A, B and C which arc undoubtedly scintillators and of these - 95 per cent are property associated with 4C sources (sec Section 2(v)). In class P only ~80 per cent are properly associated with 4C sources.
[formula]
Calculations by Little & Hewish (1966) and Readhead (1972) of the variation of with e for a number of different source models show that the shape of the F(e) curve is very similar for the different models. In the following discussion we have therefore assumed, for convenience, that all sources consist of a circularly symmetrical Gaussian component, of diameter theta and flux S_1, and a non-scintillating component of diameter > 2" and flux S_2 (see Fig. 5). The effect of this assumption on the interpretation of the observations is discussed later. It should be noted that a Gaussian brightness distribution is a good approximation for sources which are significantly broadened by interstellar scattering.
We now consider separately the strongly scintillating sources, corresponding to classes A and B, and the weakly scintillating sources corresponding to classes C and P:
[formula]
In this simple model R is equal to the ratio of the flux in the scintillating component to the total flux of the source, i.e.
[formula]
[formula]
In some cases, where theta, is so large that the upper limit to R given by equation (4) is > 1, and therefore useless, we may derive a more stringent upper limit, theta_u', to the angular diameter by setting
[formula]
A lower limit to R may be obtained by comparing the observed scintillation index with that of a point source,
[formula]
Thus for sources with D_S ~= D_Sn it is possible to derive an upper limit to the angular diameter, theta by two independent methods. In addition a useful lower limit to R can be derived in all cases, while only in certain cases can a useful upper limit to R be derived.
Since it is known that many extragalactic radio sources contain two or more components of comparable flux density and angular Size', it is important to estimate how the complexity of a source might affect the values of R and theta derived from our simple model. Consider two possibilities, sketched in Fig.6, such that the flux S1 is contained in (i) N components of diameter theta separated by angle S( > 1") which exceeds the resolution of the scintillation method, and (ii) N components of negligible diameter contained within an angle < I". Elementary considerations then show that for model (i) the correct value of ~ is obtained but R is reduced by a factor 1/sqrt(N), while for model (ii) R is underestimated by some factor and the apparent diameter is that corresponding to the group (Little & Hewish 1968).
These examples show that the values of R derived on the assumption of our two-component model will tend to underestimate the total flux contained in fine structure, while fine structure contained within an angle of about 1" will be regarded as a single extended source.
(i) The right ascension (in hours and minutes) and declination (in degrees) at epoch 1950.0.
(ii) The 4C number of the source. Sources which are not associated with sources in the 4C catalogue are denoted by U. The 3C number of the source is also given. In cases where a scintillating source is associated with a source which is not in the 3C or 4C catalogue the finding survey is denoted as follows: WKB, refers to the 38 MHz survey of Williams, Kenderdine & Baldwin; MSH, refers to the 85 MHz survey of Mills, Slee & Hill; PKS, refers to the 408 MHz Parkes survey.
(iii) The equivalent Gaussian diameter, theta, in seconds of arc. Non-scintillating sources are denoted by NS.
(iv) The fraction R of the flux density in the scintillating component". In the case of non-scintillating sources this is the upper limit on the fraction with structure < 0.5".
(v) The total flux, S, followed by a letter indicating the source of the 81.5 MHz flux: A, Artjukh et al. ; C, Collins; E, Extrapolated from 178 MHz assuming alpha = 0.75; I, Interpolated between 38 MHz and 8 MHz; P, Parker (1968); S, Smith; SS, Scott & Shakeshaft.
(vi) The maximum observed scintillating flux, in flux units (10^26 W m^-2 Hz^-1). (Jy)
(vii) The elongation, e_1, at which maximum scintillation occurs.
(viii) The source classification, see table 1.
(ix) Other 4C sources in the same beam area an asterisk indicates that the confusing source also scintillates.
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