Median Statistics Estimate of the Distance to M87

Abstract

de Grijs & Bono compiled 211 independent measurements of the distance to galaxy M87 in the Virgo cluster from 15 different tracers and reported 31.03 ± 0.14 mag as the arithmetic mean of a subset of this compilation as the best estimate of the distance. We compute three different central estimates—the arithmetic mean, weighted mean, and the median—and corresponding statistical uncertainty for the full data set as well as three sub-compilations. We find that for all three central estimates the error distributions show that the data sets are significantly non-Gaussian. As a result, we conclude that the median is the most reliable of the three central estimates, as median statistics do not assume Gaussianity. We use median statistics to determine the systematic error on the distance by analyzing the scatter in the 15 tracer subgroup distances. From the 211 distance measurements, we recommend a summary M87 distance modulus of 31.08−0.04+0.05 (statistical) −0.06+0.04 (systematic) mag, or combining the two errors in quadrature 31.08−0.07+0.06 mag, rounded to 16.4 ± 0.5 Mpc, all at 68.27% significance.