  Molecular emission was imaged with ALMA from numerous components near and
within bright H2-emitting knots and absorbing dust globules in the Crab Nebula.
These observations provide a critical test of how energetic photons and
particles produced in a young supernova remnant interact with gas, cleanly
differentiating between competing models. The four fields targeted show
contrasting properties but within them, seventeen distinct molecular clouds are
identified with CO emission; a few also show emission from HCO+, SiO and/or SO.
These observations are compared with Cloudy models of these knots. It has been
suggested that the Crab filaments present an exotic environment in which H2
emission comes from a mostly-neutral zone probably heated by cosmic rays
produced in the supernova surrounding a cool core of molecular gas. Our model
is consistent with the observed CO J=3-2 line strength. These molecular line
emitting knots in the Crab present a novel phase of the ISM representative of
many important astrophysical environments.
