  Extended nebular filaments are seen at optical wavelengths in NGC 1275, the
central galaxy in the Perseus cluster. The agents responsible for the
excitation of these filaments remain poorly understood. In this paper we
investigate possible mechanisms for powering the filaments, using measurements
from an extensive spectroscopic data set acquired at the Lick Observatory 3-m
Shane telescope. The results show that the filaments are in an extremely low
ionization and excitation state. The high signal-to-noise ratio of the spectra
allows us to measure or place sensitive upper limits on weak but important
diagnostic lines. We compare the observed line intensity ratios to the
predictions of various ionization models, including photoionization by an
active galactic nucleus, shock heating, stellar photoionization, and
photoionization by the intracluster medium. We also investigate possible roles
for cluster extreme-ultraviolet emission, and filtering of cluster soft X-ray
emission by an ionized screen, in the energetics of the filaments. None of
these mechanisms provides an entirely satisfactory explanation for the physical
state of the nebulae. Heating and ionization by reconnection of the
intracluster magnetic field remains a potentially viable alternative, which
merits further investigation through Faraday rotation studies.
