Radio Planetary Nebulae in the Large Magellanic Cloud

We present 21 new radio-continuum detections at catalogued planetary nebula (PN) positions in the Large Magellanic Cloud (LMC) using all presently available data from the Australia Telescope Online Archive at 3, 6, 13 and 20 cm. Additionally, 11 previously detected LMC radio PNe are re-examined with $ 7 $ detections confirmed and reported here. An additional three PNe from our previous surveys are also studied. The last of the 11 previous detections is now classified as a compact \HII\ region which makes for a total sample of 31 radio PNe in the LMC. The radio-surface brightness to diameter ($\Sigma$-D) relation is parametrised as $\Sigma \propto {D^{ - \beta }}$. With the available 6~cm $\Sigma$-$D$ data we construct $\Sigma$-$D$ samples from 28 LMC PNe and 9 Small Magellanic Cloud (SMC) radio detected PNe. The results of our sampled PNe in the Magellanic Clouds (MCs) are comparable to previous measurements of the Galactic PNe. We obtain $\beta=2.9\pm0.4$ for the MC PNe compared to $\beta = 3.1\pm0.4$ for the Galaxy. For a better insight into sample completeness and evolutionary features we reconstruct the $\Sigma$-$D$ data probability density function (PDF). The PDF analysis implies that PNe are not likely to follow linear evolutionary paths. To estimate the significance of sensitivity selection effects we perform a Monte Carlo sensitivity simulation on the $\Sigma$-$D$ data. The results suggest that selection effects are significant for values larger than $\beta \sim 2.6$ and that a measured slope of $\beta=2.9$ should correspond to a sensitivity-free value of $\sim 3.4$.