Planetary detection efficiency of the magnification 3000 microlensing event OGLE-2004-BLG-343

OGLE-2004-BLG-343 was a microlensing event with peak magnification A(max) = 3000 +/- 1100, by far the highest magnification event ever analyzed and hence potentially extremely sensitive to planets orbiting the lens star. Due to human error, intensive monitoring did not begin until 43 minutes after peak, at which point the magnification had fallen to A similar to 1200, still by far the highest ever observed. As the light curve does not show significant deviations due to a planet, we place upper limits on the presence of such planets by extending the method of Yoo et al. (2004b), which combines light-curve analysis with priors from a Galactic model of the source and lens populations, to take account of finite-source effects. This is the first event so analyzed for which finite-source effects are important, and hence we develop two new techniques for evaluating these effects. Somewhat surprisingly, we find that OGLE-2004-BLG-343 is no more sensitive to planets than two previously analyzed events with A(max) similar to 100, despite the fact that it was observed at similar to 12 times higher magnification. However, we show that had the event been observed over its peak, it would have been sensitive to almost all Neptune-mass planets over a factor of 5 of projected separation and even would have had some sensitivity to Earth-mass planets. This shows that some microlensing events being detected in current experiments are sensitive to very low mass planets. We also give suggestions on how extremely high magnification events can be more promptly monitored in the future.