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The radio surface brightness-to-diameter ({\Sigma} - D) relation forsupernova remnants (SNRs) in the starburst galaxy M82 is analyzed in astatistically more robust manner than in the previous studies that mainlydiscussed sample quality and related selection effects. The statistics of datafits in log {\Sigma} - log D plane are analyzed by using vertical (standard)and orthogonal regressions. As the parameter values of D - {\Sigma} and{\Sigma} - D fits are invariant within the estimated uncertainties fororthogonal regressions, slopes of the empirical {\Sigma} - D relations shouldbe determined by using the orthogonal regression fitting procedure. Thusobtained {\Sigma} - D relations for samples which are not under severeinfluence of the selection effects could be used for estimating SNR distances.Using the orthogonal regression fitting procedure {\Sigma} - D slope {\beta}\approx 3.9 is obtained for the sample of 31 SNRs in M82. The results ofimplemented Monte Carlo simulations show that the sensitivity selection effectdoes not significantly influence the slope of M82 relation. This relation couldbe used for estimation of distances to SNRs that evolve in denser interstellarenvironment, with number denisty up to 1000 particles per cm3 .

astrophysical journal/the astrophysical journal

The orthogonal fitting procedure for determination of the empirical  {\Sigma} - D relations for supernova remnants: application to starburst  galaxy M82