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We compare the angular expansion velocities, determined with VLBI, with thelinear expansion velocities measured from optical spectra for supernova 1993Jin the galaxy M81, over the period from 7 d to ~9 yr after shock breakout. Weestimate the distance to SN 1993J using the Expanding Shock Front Method (ESM).We find the best distance estimate is obtained by fitting the angular velocityof a point halfway between the contact surface and outer shock front to themaximum observed hydrogen gas velocity. We obtain a direct, geometric, distanceestimate for M81 of D=3.96+-0.05+-0.29 Mpc with statistical and systematicerror contributions, respectively, corresponding to a total standard error of$+-0.29 Mpc. The upper limit of 4.25 Mpc corresponds to the hydrogen gas withthe highest observed velocity reaching no farther out than the contact surfacea few days after shock breakout. The lower limit of 3.67 Mpc corresponds tothis hydrogen gas reaching as far out as the forward shock for the wholeperiod, which would mean that Rayleigh-Taylor fingers have grown to the forwardshock already a few days after shock breakout. Our distance estimate is 9+-13 %larger than that of 3.63+-0.34 Mpc from the HST Key Project, which is near ourlower limit but within the errors.

SN 1993J VLBI (IV): A Geometric Determination of the Distance to M81 with the Expanding Shock Front Method