  Passive red galaxies frequently contain warm ionized gas and have spectra
similar to low-ionization nuclear emission-line regions (LINERs). Here we
investigate the nature of the ionizing sources powering this emission, by
comparing nuclear spectroscopy from the Palomar survey with larger aperture
data from the Sloan Digital Sky Survey. We find the line emission in the
majority of passive red galaxies is spatially extended; the Halpha surface
brightness profile depends on radius (r) as r^(-1.28). We detect strong line
ratio gradients with radius in [N II]/Ha, [S II]/Ha, and [O III]/[S II],
requiring the ionization parameter to increase outwards. Combined with a
realistic gas density profile, this outward increasing ionization parameter
convincingly rules out AGN as the dominant ionizing source, and strongly favors
distributed ionizing sources. Sources that follow the stellar density profile
can additionally reproduce the observed luminosity-dependence of the line ratio
gradient. Post-AGB stars provide a natural ionization source candidate, though
they have an ionization parameter deficit. Velocity width differences among
different emission lines disfavor shocks as the dominant ionization mechanism,
and suggest that the interstellar medium in these galaxies contains multiple
components. We conclude that the line emission in most LINER-like galaxies
found in large aperture (>100pc) spectroscopy is not primarily powered by AGN
activity and thus does not trace the AGN bolometric luminosity. However, they
can be used to trace warm gas in these red galaxies.
