- 5.1 The luminosity function of SNRs in the LMC
- 5.2 The luminosity function of Hii regions in the LMC
- 5.3 The luminosity function of SNRs in the SMC
- 5.4 The luminosity function of Hii regions in the SMC

The luminosity of each radio source is given in WHz^{-1} and is defined
by the relation:

*L*=4*D ^{2}*

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 level) (for more
details see Table 9; Col. 2) and for the 4.85-GHz SMC survey is
25 mJy (the 5 level) (for more details see Table 10;
Col. 2). These correspond to completeness levels in luminosity of
1.2 and 1.1 WHz^{-1} for the LMC and
the SMC respectively.

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 S flux densities
to be complete down to 0.1 Jy_{4.75} |

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.
d*L*). 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.

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 S flux densities to be complete
down to 0.1 Jy_{4.75} |

The distribution in luminosity has been fitted with an exponential curve
(exp(-*L*/*L _{0}*)d

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 S flux densities
to be complete down to 0.1 Jy_{4.75} |

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.

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 S flux densities to be complete
down to 0.1 Jy_{4.75} |

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