Determination of the Physical Conditions of the Knots in the Helix Nebula from Optical and Infrared Observations

[Abridged] We use new HST and archived images to clarify the nature of theknots in the Helix Nebula. We employ published far infrared spectrophotometryand existing 2.12 micron images to establish that the population distributionof the lowest ro-vibrational states of H2 is close to the distribution of a gasin LTE at 988 +- 119 K. We derive a total flux from the nebula in H2 lines andcompare this with the power available from the central star for producing thisradiation. We establish that neither soft X-rays nor FUV radiation has enoughenergy to power the H2 radiation, only the stellar EUV radiation shortward of912 Angstrom does. Advection of material from the cold regions of the knotsproduces an extensive zone where both atomic and molecular hydrogen are found,allowing the H2 to directly be heated by Lyman continuum radiation, thusproviding a mechanism that can explain the excitation temperature and surfacebrightness of the cusps and tails. New images of the knot 378-801 reveal thatthe 2.12 micron cusp and tail lie immediately inside the ionized atomic gaszone. This firmly establishes that the "tail" structure is an ionizationbounded radiation shadow behind the optically thick core of the knot. A uniquenew image in the HeII 4686 Angstrom line fails to show any emission from knotsthat might have been found in the He++ core of the nebula. We also re-examinedhigh signal-to-noise ratio ground-based telescope images of this same innerregion and found no evidence of structures that could be related to knots.