3 Source radio spectral index analysis

Multi-frequency analysis gives a far better understanding of the nature of discrete sources. The MCs are essentially transparent to radio emission, and all catalogues of MC sources contain not only sources located within the Clouds, but also background sources lying behind and seen through the Clouds. With this in mind, sources in the direction of the Clouds may be divided into three groups:

1.

non-thermal sources, such as:

a)

background quasars and galaxies

b)

SNRs in the Clouds and

2.

thermal sources, such as Hii regions in the Clouds.

This paper uses the results of the six radio surveys to deduce the spectral index for each object and then uses the spectral index estimate in a "first-pass'' classification of each source into these three categories. The uncertainties in the observed flux densities lead to the uncertainties in the estimated spectral index and subsequently to uncertainties in classification. The uncertainties and the calibration of the flux-density scale for the our six surveys (1.40, 2.30, 2.45, 4.75, 4.85 and 8.85 GHz) are discussed in Papers IV, IVa and V.

3.1 Estimating the spectral index

Estimates of the spectral index ($\alpha$) of each radio source are based on flux densities obtained from our survey results (Papers IV, IVa and V) and from a range of radio-frequency catalogues that have been published (Tables 1, 2, 3 and 4). The spectral index $\alpha$ is defined by the relation $S_{\nu}\sim \nu^{\alpha}$,where $S_{\nu}$ is the integrated flux density and $\nu$ is frequency.

The integrated flux densities at the various frequencies were plotted as Log($S_{\nu}$) versus Log($\rm \nu_{GHz}$). For 422 radio sources in the field of the LMC (Table 5), straight lines were fitted with a simple linear regression to produce the best estimates of spectral index. For 162 sources in the field of the SMC (out of 224) we estimated the spectral index (Table 6).

For some sources a simple power-law spectrum could not be applied and these sources were examined individually (two-point spectral indices have been computed) and remarked on in Cols. 19 and 16 of Tables 5 and 6, respectively. No spectral index was calculated for 61 LMC and 62 SMC sources as these sources were seen either only at the two closely-spaced frequencies of 4.75 GHz and 4.85 GHz (20 sources for the LMC and 5 for the SMC) or at only one of the Parkes radio frequencies (41 towards the LMC and 57 towards the SMC). The errors in spectral index ($\Delta\alpha$) have been deduced from the linear-regression uncertainty, given the scatter in flux density.

Tables 5 and 6 gives the source names which have been adopted from Papers IV and V (Col. 1), the flux density at each radio frequency (Cols. 2-15 for the Table 5 and Cols. 2-12 for the Table 6), the spectral index $\alpha$and uncertainty $\Delta\alpha$ (Cols. 17 for the Table 5 and Col. 14 for the Table 6). Columns 18 (Table 5) and 15 (Table 6) list, where known, the published source type (Hii region, SNR or background). Note that capitals (BG, SNR and Hii) are used for classifications from previous works, and lower case (bg, snr and hii) for sources classified here. The question-mark indicates probable but not certain classification. Columns 19 (Table 5) and 16 (Table 6) give the reference for this source designation. Columns 20 (Table 5) and 17 (Table 6) give some comments, where SB (X) stands for "X-ray bright superbubble'' and SGS stands for "supergiant shell'' (Chu et al. 1994). Columns 21 (Table 5) and 18 (Table 6) contain the spectral index from previous work.

Tables 5 and 6 include sources observed over a range of wavelengths - X-ray, H$\alpha$, optical, infrared and radio continuum. Of the 483 radio sources catalogued towards the LMC and the 224 towards the SMC, we have compared and identified sources with various ranges of catalogues (for details see Table 7). These identifications have been included in Papers IV, IVa and V (Table 7).

  

Table 7: Identification of Parkes radio sources with other MCs catalogues

$^{ \dag }$ DEM sources often contain more than one Henize source, e.g. DEM L10=N 79A,B,C,D,E. Therefore, DEM detected more sources in the MCs than Henize (1956).
$^{ \ddag }$Three objects from MC catalogue out of the LMC field and two double.

3.2 Comparison with other published spectral indices

Spectral indices for 74 "well-known'' sources towards the LMC and for 46 sources towards the SMC were compared with spectral indices for the same sources previously published (McGee & Newton 1972; McGee et al. 1976; Milne et al. 1980; Mills et al. 1984b; Mathewson et al. 1983, 1984, 1985; Loiseau et al. 1987).

Figures 1a and 1b show the correlation between the results of previous work and those estimated here. There is an obvious agreement between the two determinations of spectral index, with the difference ("old'' - "new'')=0.03$\pm$0.02 for the LMC and -0.07$\pm$0.04 for the SMC. The standard deviation of the difference is 0.17 for the LMC and 0.27 for the SMC.

  

Figure 1: Radio spectral index comparison for the LMC a) and the SMC b). Comparison of the radio spectra from previous work and this work. Asterisks represent SNRs; filled squares - Hii regions and open triangles - background sources

3.3 Source radio spectral-index classification

McGee & Newton (1972) divided all radio sources towards the LMC into three groups, based on their radio spectrum, as follows:

1.

background sources with $-1.8<\alpha<-0.6$

2.

SNRs with a steep spectrum, $-0.8<\alpha<-0.2$ and

3.

Hii regions with a flat spectrum, $\alpha\gt-0.2$.

We use this criterion as a starting point to developing more precise criteria.

3.3.1 Spectral-index distribution of the sources towards the LMC

Figures 2a, 2b, and 2c show histograms of the source spectral-index distribution obtained for these sources using our determination of the spectral index. From the histograms it can be seen that the known Hii regions have flat spectra ($\rm \alpha_{mean}$=-0.15 with standard deviation of 0.31) and that SNRs and background sources have steeper spectra ($\rm \alpha_{mean}$=-0.43$\pm$0.19 and $\rm \alpha_{mean}$=-0.59$\pm$0.48 respectively) (see Table 8).

  

Figure 2: Distributions of radio spectral index (this study) for the LMC sources which are classified in previous work (Hii regions a), SNRs b) and background sources c))

Note that the SD of $\alpha$ for background sources is far larger than for the SNRs and Hii regions. The reason for this is probably that background sources could be divided into two groups: one with steep spectra and the other with flat spectra. Variability of the background sources should be taken into account in understanding the large SD in $\alpha$.Source flux densities at different frequencies at different times for variable sources can give misleading spectral-index estimates.

3.3.2 Spectral-index distribution of the sources towards the SMC

In the same way as for the LMC, in Figs. 3a, 3b and 3c are shown spectral index histograms of the same sources using the spectral index calculated in Sect. 3.1. (Table 6). From these histograms it can be seen that the known SMC Hii regions have flat spectra ($\rm \alpha_{mean}$=0.03$\pm$0.09 with standard deviation of 0.34) and that SNRs and background sources have steeper spectra ($\rm \alpha_{mean}$=-0.22$\pm$0.07 and $\rm \alpha_{mean}$=-0.45$\pm$0.06 respectively) (see Table 9). Again, Table 9 also shows that SD for background sources are far larger than for the SNRs and Hii regions. The explanation for this is the same as for the LMC (see previous section).

  

Figure 3: Distributions of radio spectral index (this study) for the SMC sources which are classified in previous work (Hii regions a), SNRs b) and background sources c))

  

Table 8: Spectral index distribution by source type in the LMC

  

Table 9: Spectral index distribution by source type in the SMC

3.3.3 Conclusions about the radio spectral index distribution

Sources cannot easily be classified by radio spectral index alone because of large overlaps in spectral indices between the various source types (also see Rosado et al. 1993b). In particular, SNRs and background sources (radio galaxies and quasars) have similar spectra resulting from synchrotron radiation. Furthermore, Hii regions and SNRs are often associated, since a number of SNR in the MCs are embedded in or near to Hii regions. It is thus not surprising that it is not possible to make an accurate classification on the basis of radio spectral index alone.

The distribution of spectral index for all of the 422 LMC and 164 SMC sources is given in Figs. 4a and 4b. The distribution is broad, covering the range $\alpha$=-2.2 to 1.1 for the LMC and $\alpha$=-2.2 to 1.5 for the SMC. However, most sources (86% in the LMC and 77% in the SMC) fall in the range -1.1 and 0.1.

  

Figure 4: Distributions of radio spectral index for the LMC a) and for the SMC b)

The mean spectral index for all sources towards the LMC is - 0.53$\pm$0.02 (SD=0.46) and towards the SMC is -0.73$\pm$0.05 (SD=0.61). There is no significant difference in the mean spectral index after excluding of known background sources ($\rm \alpha_{mean}$=- 0.51$\pm$0.02 with standard deviation 0.47 for the LMC and $\rm \alpha_{mean}$=-0.50$\pm$0.05 with standard deviation 0.62 for the SMC). The mean spectral index for all sources towards the MCs agree well with the overall spectral index including the diffuse component estimated by Haynes et al. (1991) and Klein et al. (1989, 1991). Their results are -0.52$\pm$0.05 for the LMC and -0.78$\pm$0.11 for the SMC.

Based on the classification scheme introduced by McGee & Newton (1972), 57% of sources towards the LMC and 61% sources towards the SMC show steep spectra ($\alpha \le$-0.45), and 27% of LMC and 21% of SMC sources have flat spectra ($\alpha \ge$-0.20). The remaining sources, 16% for the LMC and 18% for the SMC, fall in the ambiguous region where $\alpha$ is between -0.44 and -0.21.