  A high quality Keck spectrum of the Halpha line in NGC 4395 reveals symmetric
exponential wings, fv\propto e^{-v/sigma}, with sigma~500km/s. The wings extend
out to >2500km/s from the line core, and down to a flux density of <10^-3 of
the peak flux density. Numerical and analytic calculations indicate that
exponential wings are expected for optically thin, isotropic, thermal electron
scattering. Such scattering produces exponential wings with sigma=1.1sigma_e(ln
tau_e^-1)^0.45, where sigma_e is the electron velocity dispersion, and tau_e is
the electron scattering optical depth. The Halpha wings in NGC 4395 are well
fit by an electron scattering model with tau_e=0.34, and an electron
temperature T_e=1.1x10^4K. Such conditions are produced in photoionized gas
with an ionization parameter U=0.3, as expected in the broad line region (BLR).
Similar analysis of the [O III] 5007 line yields tau_e<0.01, consistent with
the lower ionization in the narrow line region. If the electron scattering
interpretation is correct, there should be a tight correlation between tau_e
and the ionizing flux on time scales shorter than the BLR dynamical time, or ~1
week for NGC 4395. In contrast, the value of sigma should remain nearly
constant on these time scales. Such wings may be discernible in other objects
with unusually narrow Balmer lines, and they can provide a useful direct probe
of T_e and tau_e in the BLR.
