We have obtained deep narrowband images in the near-infrared H2 (2.122 microns) emission line for a sample of 15 faint Isaac Newton Telescope Photometric Halpha Survey (IPHAS) bipolar planetary nebulae (PNe) to search for molecular material. H2 emission is found in most of them (14 out of 15), mostly associated with rings at their equatorial regions and with their bipolar lobes. These detections add to the high occurrence of H2 emission among bipolar PNe reported in previous works, resulting from the large reservoir of molecular material in these sources and the suitable excitation conditions for H2 emission. The correlation between detailed bipolar morphology and H2 luminosity is also confirmed: bipolar PNe with broad equatorial rings (R-BPNe) have almost no continuum emission, are H2 brighter and have larger H2/Brgamma line ratio than bipolar PNe with pinched equatorial waists (W-BPNe). The origin of this dichotomy is unclear. The larger size and age of R-BPNe are consistent with shock excitation of H2, whereas ultraviolet pumping is most likely the excitation mechanism in the smaller and younger W-BPNe, which would explain their lower H2 luminosity. Although both types of bipolar PNe seem to proceed from the same progenitor population, this does not imply that R-BPNe descend from W-BPNe. Otherwise, we note that some of the H2-weak bipolar PNe harbor post-common envelope binary systems and symbiotic stars. Finally, we suggest that the long-living H2 emission from R-BPNe arises from a discrete distribution of compact knots embedded within the ionized gas at the equatorial region.

13 pages, 9 figures, Accepted for publication in MNRAS