We examine the evolution of the Tully-Fisher relation (TFR) using a sample of 89 field spirals, with 0.1 < z < 1, for which we have measured confident rotation velocities (Vrot). By plotting the residuals from the local TFR versus redshift, or alternatively fitting the TFR to our data in several redshift bins, we find evidence that luminous spiral galaxies are increasingly offset from the local TFR with redshift, reaching a brightening of -1.0+-0.5 mag, for a given Vrot, by approximately z = 1. Since selection effects would generally increase the fraction of intrinsically-bright galaxies at higher redshifts, we argue that the observed evolution is probably an upper limit. Previous studies have used an observed correlation between the TFR residuals and Vrot to argue that low mass galaxies have evolved significantly more than those with higher mass. However, we demonstrate that such a correlation may exist purely due to an intrinsic coupling between the Vrot scatter and TFR residuals, acting in combination with the TFR scatter and restrictions on the magnitude range of the data, and therefore it does not necessarily indicate a physical difference in the evolution of galaxies with different Vrot. Finally, if we interpret the luminosity evolution derived from the TFR as due to the evolution of the star formation rate (SFR) in these luminous spiral galaxies, we find that SFR(z) is proportional to (1+z)^(1.7+-1.1), slower than commonly derived for the overall field galaxy population. This suggests that the rapid evolution in the SFR density of the universe observed since approximately z = 1 is not driven by the evolution of the SFR in individual bright spiral galaxies. (Abridged.)
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