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Astron. Astrophys. 355, 863-872 (2000)

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2. The data

The 45-MHz observations have been made with the large array of the University of Chile as a part of the Southern Sky Survey (Alvarez et al. 1997). The antenna is a filled array of 528 full-wave dipoles oriented E-W, and has a resolution of [FORMULA] x [FORMULA]. A detailed description of this instrument can be found in May et al. (1984) and Alvarez et al. (1994). The contour map of Cen A, corrected for antenna sidelobes, can be seen in the 45 MHz survey (Alvarez et al. 1997, Fig. 1, p. 320). The source's multiple-lobe structure, readily seen in observations with higher resolution (Fig. 1), is lost in our data because of the instrument's low resolution. As a check of our observations, the data of Cen A at 408 MHz, from the all-sky survey of Haslam et al. (1982), was convolved to our antenna beam resulting in a map almost identical in morphology.

2.1. The total integrated flux density at 45 MHz

The flux densities of extended components have been computed graphically following the standard method of integrating brightness temperature contour maps (e.g. Bracewell 1962, Kraus 1966, Cooper et al. 1965). Since the sources are irregular in shape, the integrals are replaced by summations. There are four main sources of error in this calculation. The first one is the replacement of an integral by a summation; here the closer the contours, the better the approximation. The second one arises from the necessity to close open contours which are usually the external ones and correspond to the lower temperatures, so the error is not expected to be large. The third one is a possible temperature scale error present in the data, and which is usually given by the original authors. And the fourth one is the determination of the limits of the source, or base contour, which is usually not shown in the maps; however, the first contour given corresponds to a low relative temperature so the contribution from the region between the unknown base contour and the first contour is expected to be small. Obviously, the flux calculated from the first contour represents only a lower bound. To estimate this error we have assumed that the area between the base and first contours is the same as that between the first and second contours. This is reasonable unless the temperature gradient changes significantly near the edge of the source.

The 45-MHz map was obtained by removing the background from the original data (Alvarez et al. 1997), using the so-called method of unsharp masking (Sofue & Reich 1979). Due to nearby features, not belonging to the source, a few external contours did not close; however, we did close them reasonably well by following the general trend of adjacent contours. We estimate the error in this process to be less than 10%. Regarding the error associated with the separation of the temperature contours, a first integration was done with a separation of 1000 K, then we repeated the process with 500 K and found a difference of 0.4%. We also found that adopting a base isophote of 500 K, instead of 0 K, yielded an error of 0.7%. Since the error in temperature scale of the Southern Survey (Alvarez et al. 1997) is better than 10%, we have adopted a total error of 15% for the 45-MHz integrated flux density of the Whole Source, which is [FORMULA] Jy.

2.2. Integrated flux densities at other frequencies

From brightness temperature maps, made at different frequencies by other authors, we have computed the integrated flux density of some Cen A components. By graphical integration we determined the flux density of the individual GLs and of the Whole Source at 2650 MHz from Figs. 6(a) and 7(a) in Cooper et al. (1965). Table 1 lists the integrated flux densities of the Whole Source.


[TABLE]

Table 1. Integrated flux density of the Whole Source.
Notes:
a) Error quoted is an estimate only.
b) Error quoted by Cooper et al. (1965).
c) Corrected by Haslam et al. (1981) using Baars et al.'s (1977) temperature scale.
d) Corrected by Cooper et al. (1965).
e) Based on data from Cooper et al. (1965). The error is the sum of: 3% from graphical integration, 2% from closing open contours, and 10% assumed from the brightness temperature scale.
f) The original data have been reduced by 15% by indication of the authors (Junkes, personal communication). The error includes 5% uncertainty in the temperature scale.


The absolute flux densities are extremely difficult to measure, especially at frequencies below 100 MHz where the problems are multiple and severe. The errors of measurement are not always given in the literature by the original authors and, whenever given, the type of error is not specified.

When we have found no error quoted by the original authors or by related works, we have estimated an appropriate value based upon the details of the observation and other available information. For example, Shain (1959) gives an error of 15% at 19.7 MHz (see Table 1). We estimate that the error must be larger at lower frequencies and so we have assigned an uncertainty of 20% to the measurements of Hamilton & Haynes (1968) at 10.0 MHz and Ellis & Hamilton (1966) at 4.7 MHz. In other cases we have adopted different criteria. To assign an error to the 406 MHz total flux of Cooper et al. (1965), we note that the southern survey made by Haslam et al. (1981) at 408 MHz using the same antenna (64-m Parkes Telescope) has a temperature scale error of probably better than 10%, so we have adopted this value. Similarly, we have used the temperature scale errors of the southern surveys by Hill (1968) at 1410 MHz and by Day et al. (1972) at 2700 MHz, also using the Parkes Telescope, to estimate the uncertainties in the measurements of Cooper et al. (1965) at 1410 and 2650 MHz. We have determined these to be 5 and 10%, respectively. To estimate the error in Bolton & Clark's (1960) observations at 960 MHz, we have used the value quoted by Harris & Roberts (1960) in an unrelated work at the same frequency and with the same antenna. In the case of our determination at 2650 MHz, we have added to the temperature scale error the error derived from the graphical integration.

The extragalactic radio source PKS B1318-434 is seen projected on the GLS (Fig. 1). There has been some debate about this source being a hot spot of Cen A (see Junkes et al. 1993). This is a complex radio source and from the available information it seems likely that it is associated with the interacting system NGC 5090-5091 (Smith & Bicknell 1986; Jones & McAdam 1992). Since the contribution of this source to the flux of Cen A is only a fraction of 1% we have made no corrections for it.

We are aware that, to cover the widest range of frequencies, we have had to use results from many different types of instruments. The use of interferometric techniques is of particular concern in the determination of integrated flux densities for very extended sources, like Cen A. This is because extended sources can present large properties of their flux at low spatial frequencies, which are often sampled poorly by interferometers. Of the fourteen measurements presented in Table 1, four were obtained through interferometric methods (Shain 1959; Sheridan 1958; Jones & McAdam 1992; and Rogstad & Ekers 1969). The rest were observed with either single dishes or filled arrays.

Table 1 contains observations made not only with a variety of instruments, but also spanning 40 years. In fact, the majority of the observations were made during the 50's and 60's, particularly those at low frequencies. High quality observations at frequencies below 100 MHz are especially difficult to perform, mainly because of ionospheric effects and interference from both natural and artificial sources. In Fig. 2 we see that, in spite of the uncertainties introduced by the use of so many different types of instruments, the fit of the mean values is good (correlation coefficient 0.998).

[FIGURE] Fig. 2. Integrated flux density spectrum of Cen A (Whole Source). The straight line represents the least-squares fit to the data, given by the equation [FORMULA]. The fit does not include the point at 4.7 MHz since it shows indications of absorption

Table 2 shows the integrated flux densities of the ILs, collected from the literature. The situation in Table 2 is different because the Inner Lobes are small in angular size, and so only three of the twelve measurements were obtained with filled aperture instruments (Cooper et al. 1965; Tateyama & Strauss 1992).


[TABLE]

Table 2. Integrated flux density of the Inner Lobes.
Notes:
a) Deduced from peak ratio.
b) Error quoted is an estimate only.


In Tables 1 and 2 we have tried to avoid duplications between the original flux determinations and those presented in catalogues and compendia. Neither have we attempted to standardize flux density scales; however, we have used revised values whenever available.

The fluxes of the GLs, presented in Table 3, were obtained from observations made with large dishes; however, there are fewer data. Here the uncertainties are larger mainly because of the need to separate the GLs and the Central Region (CR). This is especially the case at the lower frequencies where the resolution is less. The GLs' contours near the CR were interpolated reasonably well by following the external shapes, far from the CR. Also, we checked that the sum of the three parts (GLN, GLS, CR) closely approximated the flux of the Whole Source as derived by us. This is the first time that a determination of the spectrum of the individual GLs has been attempted.


[TABLE]

Table 3. Integrated flux density of the Giant Outer Lobes.
Notes:
a) Error quoted is an estimate only.
b) The error is the sum of: 10% from graphical integration, and 10% assumed from the brightness temperature scale.
c) The error is the sum of: 5% from graphical integration, and 10% assumed from the brightness temperature scale. d) Based on data from Cooper et al. (1965).
e) As corrected by Cooper et al. (1965).
f) The error is the sum of: 7% from graphical integration, and 10% assumed from the brightness temperature scale.
g) The error is the sum of: 4% from graphical integration, and 10% assumed from the brightness temperature scale.
h) The original data have been reduced by 15%, by indication of the authors (Junkes, personal communication). The error includes 5% uncertainty in the temperature scale.


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Online publication: March 21, 2000
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