The close correlation between cooling hows and emission-line nebulae i
n clusters of galaxies has been recognized for over a decade and a hal
f, but the physical reason for this connection remains unclear. Here w
e present deep optical spectra of the nebula in Abell 2597, one of the
nearest strong cooling-flow clusters. These spectra reveal the densit
y, temperature, and metal abundances of the line-emitting gas. The abu
ndances are roughly half-solar, and dust produces an extinction of at
least a magnitude in V. The absence of CO mi lambda 4363 emission rule
s out shocks as a major ionizing mechanism, and the weakness of He II
lambda 4686 rules out a hard ionizing source, such as an active galact
ic nucleus or cooling intracluster gas. Hot stars are therefore the be
st candidate for producing the ionization. However, even the hottest O
stars cannot power a nebula as hot as the one we see. Some other noni
onizing source of heat appears to contribute a comparable amount of po
wer. We show that the energy flux from a confining medium can become i
mportant when the ionization level of a nebula drops to the low levels
seen in cooling-how nebulae. We suggest that this kind of phenomenon,
in which energy fluxes from the surrounding medium augment photoelect
ric heating, might be the common feature underlying the diverse group
of objects classified as LINERS.