The alpha -element abundances in the most oxygen-poor planetary nebula PNG 135.9+55.9

We present extensive new spectroscopy and imaging of PNG 135.9+55.9. We use these data as constraints to pho- toionization models to derive limits on the oxygen abundance. We find that PNG 135.9+55.9 has an oxygen abundance less than 1/50 of the solar value. Our models favour a value of 12+ log O=H between 5.8 and 6.5 dex, confirming that PNG 135.9+55.9 is the most oxygen-poor planetary nebula known (Tovmassian et al. 2001). We also derive Ne=O= 0:5 0:3, S=O< 0:094, and Ar=O < 0:23. Although the value of Ne/O is nominally high, it need not imply that the progenitor of PNG 135.9+55.9 converted any of its initial oxygen abundance to neon. The helium abundance appears to be very low, He=H 0:08, but a pre- cise determination will require a much more detailed study. We find that H=H is lower than expected and perhaps variable, a finding for which we have no clear explanation.