Extreme Magnification Microlensing Event OGLE-2008-BLG-279: Strong Limits on Planetary Companions to the Lens Star

We analyze the extreme high-magnification microlensing event OGLE-2008-BLG-279, which peaked at a maximum magnification of A ~ 1600 on 30 May 2008. The peak of this event exhibits both finite-source effects and terrestrial parallax, from which we determine the mass of the lens, M_l=0.64 +/- 0.10 M_Sun, and its distance, D_l = 4.0 +/- 0.6. We rule out Jupiter-mass planetary companions to the lens star for projected separations in the range 0.5-20 AU. More generally, we find that this event was sensitive to planets with masses as small as 0.2 M_Earth ~= 2 M_Mars with projected separations near the Einstein ring (~3 AU).