  We present broadband observations and spectral modeling of PKS B0008-421, and
identify it as an extreme gigahertz-peaked spectrum (GPS) source. PKS B0008-421
is characterized by the steepest known spectral slope below the turnover, close
to the theoretical limit of synchrotron self-absorption, and the smallest known
spectral width of any GPS source. Spectral coverage of the source spans from
0.118 to 22 GHz, which includes data from the Murchison Widefield Array and the
wide bandpass receivers on the Australia Telescope Compact Array. We have
implemented a Bayesian inference model fitting routine to fit the data with
various absorption models. We find that without the inclusion of a
high-frequency exponential break the absorption models can not accurately fit
the data, with significant deviations above and below the peak in the radio
spectrum. The addition of a high-frequency break provides acceptable spectral
fits for the inhomogeneous free-free absorption and double-component
synchrotron self-absorption models, with the inhomogeneous free-free absorption
model statistically favored. The requirement of a high-frequency spectral break
implies that the source has ceased injecting fresh particles. Additional
support for the inhomogeneous free-free absorption model as being responsible
for the turnover in the spectrum is given by the consistency between the
physical parameters derived from the model fit and the implications of the
exponential spectral break, such as the necessity of the source being
surrounded by a dense ambient medium to maintain the peak frequency near the
gigahertz region. The discovery of PKS B0008-421 suggests that the next
generation of low radio frequency surveys could reveal a large population of
GPS sources that have ceased activity, and that a portion of the ultra-steep
spectrum source population could be composed of these GPS sources in a relic
phase.
