We present a systematic study of the Supernova Remnant (SNR) populations in the nearby galaxies NGC 45, NGC 55, NGC 1313, and NGC 7793 based on deep Ha and [S II] imaging. We find 42 candidate and 54 possible candidate SNRs based on the [S II] / Ha > 0.4 criterion, 84 of which are new identifications. We derive the Ha and the joint [S II]-Ha luminosity functions after accounting for incompleteness effects. We find that the Ha luminosity function of the overall sample is described with a skewed Gaussian with a mean equal to log(LHa / 10^(36) erg s^(-1)) = 0.07 and m(log(LHa / 10^(36) erg s^(-1)))) = 0.58. The joint [S II]-Ha function is parameterized by a skewed Gaussian along the log([S II] / 10^(36) erg s^(-1)) = 0.88 x log(LHa / 10^(36) erg s^(-1)) - 0.06 line and a truncated Gaussian with m(log(L[S II] / 10^(36))) = 0.024 and s(log(L[S II] / 10^(36))) = 0.14, on its vertical direction. We also define the excitation function as the number density of SNRs as a function of their [S II]/Ha ratios. This function is represented by a truncated Gaussian with a mean at -0.014. We find a sub-linear [S II]-Ha relation indicating lower excitation for the more luminous objects.
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