5 Luminosity functions of SNRs and Hii regions in the MCs

The luminosity of SNRs and Hii regions is important in understanding the physical nature of the sources. For sources of the same distance, such as those in the MCs, the luminosity is directly related to the observed flux without the extra complication of uncertain distance estimates. Therefore, the luminosity function can be obtained much more directly than for our Galaxy.

The luminosity of each radio source is given in WHz^-1 and is defined by the relation:
L=4$\pi$D²S

where D is distance to the Clouds (50 kpc to the LMC and 60 kpc to the SMC; Westerlund 1993) and S is the flux density at the given radio frequency (1 Jy=10^-26 Wm^-2 Hz^-1).

Source flux densities at 4.75 GHz (for the LMC) and 4.85 GHz (for the SMC) were used to estimate the luminosity of each source. The completeness level at the 4.75 GHz LMC surveys is 40 mJy (the 5$\sigma$ level) (for more details see Table 9; Col. 2) and for the 4.85-GHz SMC survey is 25 mJy (the 5$\sigma$ level) (for more details see Table 10; Col. 2). These correspond to completeness levels in luminosity of 1.2$\ 10^{16}$ and 1.1$\ 10^{16}$ WHz^-1 for the LMC and the SMC respectively.

5.1 The luminosity function of SNRs in the LMC

Figures 7a and 7b show the histogram of luminosities for SNRs and SNR candidates in the LMC. We have flux densities at 4.75 GHz for 53 of these. The SNRs without flux density at this frequency, are plotted in the lowest bin in Fig. 7a since they are below the 5$\sigma$level.

  

Figure 7: The luminosity function of SNRs in the LMC. In Fig. 7a the luminosity distribution is plotted on a linear scale and in Fig. 7b it is plotted on a logarithmic scale with logarithmic bins. The vertical dashed line represent the approximate completeness level assuming the S4.75 flux densities to be complete down to $\sim$0.1 Jy

In Fig. 7a the highest luminosity sources are above the plotted range. To show the full range of luminosities, the luminosity distribution is plotted also in Fig. 7b on a logarithmic scale with equal bins in the log domain (rather than linear bins as in Fig. 7a).

As expected, there are more sources with low luminosity than with high luminosity. To quantify the distribution a power law has been fitted and this gives a power-law index of -1.2 (i.e. $N(L)\propto L^{-1.2}$dL). The theory for the evolution of SNR diameters and luminosity is not well understood. However, the expected evolution of SNR diameter and surface brightness is generally described by power laws as a function of time (Lozinskaya 1992). Therefore, the expected evolution of luminosity is a power law with time, and the luminosity function is a power law assuming that SN explosions occur at a constant rate in the LMC.

We do not have either sensitivity or spatial resolution to determine the phase of evolution (Sedov or linear expansion) of any SNRs in the LMC. Confusion (in most cases) with surrounding Hii regions further worsens the situation. Therefore, the luminosity function power-law index estimated here can be understood as an overall power-law index for SNRs in the LMC, combining SNRs in all different phases of evolution.

5.2 The luminosity function of Hii regions in the LMC

The luminosity function of the LMC Hii regions was calculated in a similar way to the LMC SNRs. The 148 Hii regions (and Hii region candidates) in the LMC are plotted in the histogram (Fig. 8a) where we have 124 objects with 4.75-GHz flux densities, and the rest are plotted (as weak sources below the 5$\sigma$ level) in the lowest bin.

Figure 8a does not plot the highest luminosity Hii regions in the LMC and therefore Fig. 8b shows luminosity on a logarithmic scale with log bins. This plot does not include Hii regions which are not detected in the 4.75-GHz survey. Note that the most luminous Hii region is 30 Doradus which is two orders of magnitude stronger than for "typical" Hii regions.

  

Figure 8: The luminosity function of Hii regions in the LMC. In Fig. 8a the luminosity distribution is plotted on a linear scale and in Fig. 8b it is plotted on a logarithmic scale with logarithmic bins. The vertical dashed line represent the approximate completeness level assuming the S4.75 flux densities to be complete down to $\sim$0.1 Jy

The distribution in luminosity has been fitted with an exponential curve ($N(L) \propto$exp(-L/L₀)dL) with characteristic luminosity scale $L_{0}=4.2\ 10^{16}\,$WHz^-1. Ye (1988) fitted the diameter distributions for Hii regions as an exponential function and using a similar method he has also fitted the luminosity distribution with an exponential function for the MCs and other galaxies.

5.3 The luminosity function of SNRs in the SMC

Because of the small number of the SMC SNRs (12), the luminosity function is rather sparse. However, similar histograms to those from Sect. 5.1. are plotted in Figs. 9a and 9b. Despite the small number of sources, the luminosity distribution looks similar to that of the LMC SNRs.

  

Figure 9: The luminosity function of SNRs in the SMC. In Fig. 9a the luminosity distribution is plotted on a linear scale and in Fig. 9b it is plotted on a logarithmic scale with logarithmic bins. The vertical dashed line represent the approximate completeness level assuming the S4.75 flux densities to be complete down to $\sim$0.1 Jy

The luminosity function for SMC SNRs is shown in Fig. 9a. The luminosity distribution is plotted also in Fig. 9b on a logarithmic scale with equal bins in the log domain (rather then linear bins as in Fig. 9a). Only the SNRs detected at the 4.85-GHz survey are plotted in Fig. 9b.

5.4 The luminosity function of Hii regions in the SMC

The number of SMC Hii regions is also small (26); however, the luminosity functions are plotted in Figs. 10a and 10b. The most luminous SMC Hii region is not nearly as bright as 30 Doradus in the LMC.

In Fig. 10a, the histogram is plotted of the SMC Hii region luminosities and Fig. 10b shows the luminosity function on a logarithmic scale with log bins. This plot does not include Hii regions which are not detected at the 4.85-GHz survey.

  

Figure 10: The luminosity function of Hii regions in the SMC. In Fig. 10a the luminosity distribution is plotted on a linear scale and in Fig. 10b it is plotted on a logarithmic scale with logarithmic bins. The vertical dashed line represent the approximate completeness level assuming the S4.75 flux densities to be complete down to $\sim$0.1 Jy